Utah State University
Department of Mechanical and Aerospace Engineering
Academic year 2009-2010
Design and Testing of a Demonstration Prototype for Lunar or Planetary Surface
Landing Research Vehicle (LPSRV)
Course Handbook
Instructor:
Instructor Phone:
Instructor Email:
Office:
Stephen A. Whitmore
435-797-2951
swhitmore@engineering.usu.edu
ENGR 419F
Table of Contents
Section Name
…………………………………………… Page number
Course Overview
…………………………………………… 3
Assessment Materials
…………………………………………… 6
Section 1
Introduction
…………………………………………… 1-1
USA Space History
Policy, and
Organizations
…………………………………………… 1-9
Section 2
Systems Engineering I
……………………………………………2-1
Systems Engineering II
Design Tools
……………………………………………2-13
Section 3
The Space Environment
……………………………………………3-1
The Lunar and
Martian Environment
………………………………………… 3-10
Section 4
Rockets, Past, Present
And Future
……………………………………………4-1
Rocket Science 101
Basic Concepts and Definitions
………………………………………… 4-16
Section 5
Spacecraft Subsystems Overview
……………………………………………5-1
1
Section 6
Propulsions Systems
Overview
……………………………………………6-1
Propulsion Systems II
Selecting the Right System
………………………………………… 6-18
Section 7
Orbital Mechanics I
Kepler’s Laws
……………………………………………7-1
Obital Mechanics II
Visa Viva Equation
Describing Orbits in
3-Dimensions,
Orbital Maneuvering
………………………………………… 7-9
Section 8
Flight Mechanics I
Launch Dynamics
Energy Analysis, and
Required ΔV
……………………………………………8-1
Flight Mechanics II
Equations of Motion
………………………………………… 8-20
Flight Mechanics III
Motions in 6-degrees
-of-freedom
………………………………………… 8-41
Appendix
Introduction to
Geodesy
………………………………………… 8-55
Section 9
Flight Controls I
Vehicle Stability,
Control Actuators
System Examples
……………………………………………9-1
Flight Controls II
Feedback Control Systems
………………………………………… 9-13
Section 10
Spacecraft Avionics I
Power and Thermal,
Management Systems
……………………………………………10-1
Spacecraft Avionics II
Telemetry and
Communications Systems
………………………………………… 10-16
Section 11
Spacecraft Structures
Structural Dynamics
Resonance
……………………………………………11-1
Mechanisms
………………………………………… 11-13
2
Section 12
Measurements and
Uncertainty Analysis I
Error Classification,
Calibration, and
Data Presentation
……………………………………………12-1
Measurement and
Uncertainty Analysis II
Probabilistic Description
Of Error
………………………………………… 12-16
Appendix
χ-2 Hypothesis Testing
Example
………………………………………… 12-31
Section 13
Technical
Writing
……………………………………………13-1
Course Overview
I) Synopsis: This Course is a two-semester sequence, with MAE 5930 Technical elective
taught fall semester 2009, MAE 4800 Senior Design Class spring semester 2010.
Fall 2009
Spring 2010
Course Title: Launch Systems Design
Course No.: MAE 5930 (3 units)
Class Times, Location: TBD
Office Hours: By Appointment
Prerequisites: MAE Senior with Good
Academic Standing, Concurrent Enrollment
in MAE 5420, Compressible Fluids
Course Title: LLRV Design
Course No.: MAE 4800 (3 units)
Class Times, Location: TBD
Office Hours: By Appointment
Prerequisites: MAE 5930, Launch
Systems Design, MAE 5420
Required texts:
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 5th ed.,
McGraw-Hill, 2005., ISBN 9780073407753
Course Handbook, Class Notes Compendium (Available in Student Book store),
Published as NASA SP(?)
Maximum Class Size: 25
Suggested Teaching Assistants: 1 per Semester
II) Course Description:
This course is developed as partial fulfillment of the requirements of a grant funded
by the NASA Office of Education. The final outcome is a “packaged” senior design
course that can easily be “moved laterally” and incorporated into universities across the
nation. The course materials must adhere to the standards of the Accreditation Board for
3
Engineering and Technology (ABET), and be relevant to one of four areas identified by
NASA’s Exploration Mission Directorate (ESMD):
i)
ii)
iii)
iv)
Spacecraft,
Propulsion,
Lunar and planetary surface systems,
Ground Operations.
This specific design project will target Item iii) -- Lunar and Planetary Surface
Systems – and will develop senior design concepts for a Lunar or Planetary Surface
Landing Research Vehicle (LPSRV). (ESMD# DFRC1-15-SD) Per NASA specifications
concepts must account for reduced lunar gravity, and allow simulated terminal stage of
lunar descent to be flown either by remote pilot or autonomously. The design project will
challenge students to apply systems engineering concepts to define research and training
requirements for a terrestrial-based lunar landing simulator. This Free-flying platform
should allow for both sensor evaluation and pilot training. Selected concept must allow a
small-scale prototype-demonstrator to be constructed within the time and budget
constraints of a university-based senior design project. A prototype of the system concept
will be constructed and flight-tested. Selected concept must be scalable to a full-size
planetary landing research.
III) Significance of the Design Project
One of the many crucial points associated with NASA Constellations systems Lunar
Landing mission is the portion from spacecraft separation in lunar orbit to descent and
touchdown. Flight Training vehicles should be capable of rendering a realistic
environment for both flight crew training and autonomous landing systems verification
and validation. The Lunar Lander Training Vehicle (LLTV) developed for the Apollo
program during the 1960's is considered to be a significant contributor to the success of
the Apollo lunar program. Seven of the nine Apollo Astronauts that trained with the
LLTV believe that such training was an important factor in increasing the probability of a
successful landing and believe that such a vehicle is essential for future lunar missions.1
As NASA’s Constellation program prepares to send astronauts back to the lunar surface,
a similar training vehicle, based on modern technologies, is required to ensure that
astronauts develop skills at same high level of proficiency exhibited by the Apollo
astronauts. Donald K. "Deke" Slayton, NASA's astronaut chief during the Apollo
program, firmly believed there was no other way to simulate a moon landing except by
flying the LLTV.2
Additionally, unlike the Apollo program the Altair lander will require a suite of
sensors that reduce pilot workload and allow for Autonomous Landing and Hazard
Avoidance (ALHAT). The potential role of an Earth demonstrator free flyer platform has
been an ALHAT topic of discussion for quite a while. The general consensus among
NASA researchers is that the most realistic and practical ALHAT approach is to pursue
1
Proceedings, “Go For Lunar Landing, From Terminal Descent to Touchdown, Conference,” Tempe, Arizona, March
4-5, 2008.
2
Bennett, Floyd V., “Apollo Experience Report – Mission Descent and Ascent,” NASA TN D-6846, 1972.
4
field testing on helicopters and airplanes, starting with sensor characterization flights and
evolving towards more integrated testing with onboard processing. The consensus is that
these component-level tests can bring the technology readiness level (TRL) to a level of
approximately 5. However, to bring these components to a TRL that can be deployed on
an operational mission a TRL of 7 or greater is required, and only closed-loop testing on
a free-flying LLT/RV can achieve those results.3
III) Course Objectives and Deliverables:
Fall Semester 2009 will introduce students to design and systems engineering
concepts, and will develop sufficient theoretical background to allow design and
fabrication of a prototype demonstration vehicle. Apollo-era lunar mission designs will
be examined in detail as a point of departure for this design. A minimum of 2 1-hour
lectures will be delivered each week. As necessary design teams will break off into small
development teams. At least 8 one-hour periods will be made available for “break off
team” meetings.
i)
Students will either use or develop simulation code required to fulfill team
objectives as necessary.
ii)
Students will become sufficiently proficient in technical writing to deliver
a professional grade final design report.
iii)
Students will learn the basics of team dynamics and teamwork.
iv)
The final outcome of the fall semester is a conceptual design roadmap
including preliminary design reports, a test and measurements matrix, and
sufficient engineering design drawings to allow construction to begin
during the spring semester.
v)
A conceptual design review (CDR) will be performed during finals week of
fall semester. This review will be made available as requested to NASA
personnel via web cast, and will include faculty members within the
college as peer reviewers.
vi)
As, required technical interchange videoconferences or web casts will be
help with the NASA technical and administrative points of contact.
Spring semester 2010 will emphasize detailed theory for specific sub-system relevant
to the vehicle design, as well as fabrication and testing of the prototype article. Group
lectures will be held at least one hour per week. Internal project design reviews will be
held on a bi-weekly basis. As, required technical interchange videoconferences or web
casts will be help with the NASA technical and administrative points of contact. A final
report will be submitted for the NASA Systems engineering competition. The final
deliverable from this report is a working LLRV prototype. A goal of a successful test
flight before end of Spring Semester 2010 will be targeted.
All materials will be made available for interim review on the MAE 5930/4800 class
web-based bulletin board. These materials include
3
Email correspondence with Chirold Epp, NASA JSC ALHAT Program Manager, June 12, 2008.
5
i)
ii)
iii)
iv)
v)
vi)
Students will either use or develop simulation code required to fulfill team
objectives as necessary.
Assigned Homework and In-class Projects.
All reviews and documentation required by NASA.
Conceptual Design Report, Final Design Report.
Test reports for all critical developmental tests.
As possible, students will be encouraged to submit papers to peer
reviewed conferences and journals.
Assessment Materials
This Course is a two-semester sequence, with MAE 5930 Technical elective taught
fall semester 2009, MAE 4800 Senior Design Class spring semester 2010. The proposed
design course will incorporate of as many of the ABET-recommended4 design issues as
are possible. There is one specific requirement stated by ABET “Students must be
prepared for engineering practice through a curriculum culminating in a major design
experience based on the knowledge and skills acquired in earlier course work and
incorporating appropriate engineering standards and multiple realistic constraints.” In
this design class the students will learn how to integrate their engineering skills to solve a
complex engineering problem, present their engineering designs in an oral presentation,
and document their design in a written report that is the basis of their engineering
portfolio. This design experience is the final course that prepares students to enter the
mechanical engineering profession.
The design course evaluation is a part of the overall USU MAE department plan for
continuous improvement. Assessment measures will consist of student portfolios, student
performance in project work and activity-based learning. Two particularly important
assessments include Success in NASA Systems Engineering Paper competition and
outcomes from the research aspects of this design study. These research outcomes
include student conference presentations and published articles.
Grading: Homework Assignments will cover material presented in class, in the
laboratory, plus material in the text covered by the assigned reading. Laboratory session s
will be held as required to insure that the students are familiar with the testing and
measurement techniques required for achieving the design objectives. Regular laboratory
reports will be turned following laboratory period. Reports may include homework
exercises. Laboratories may include simulation and modeling exercises. Student and
faculty peer reviews and oral presentation evaluations will be an important part of the
grading and assessment process.
MAE 5930 (Fall 2009)
4
Criteria for Accrediting Engineering Programs, 2008-2009, ABET Engineering Accreditation
Commission, http://www.abet.org/Linked%20Documents-UPDATE/
Criteria%20and%20PP/E001%2008
09%20EAC%20Criteria%2012-04-07.pdf, (Retrieved: October 4, 2008).
6
i)
ii)
i)
ii)
iii)
25% of student grades will come from individual homework assignments,
laboratory reports, and class projects.
75% will be a weighted class grade, this grade fraction is scored as
Conceptual Design Report
50%
Conceptual design Presentation
25%
Student Peer Evaluations
25%
MAE 4800 (Spring 2009)
40% will be a weighted class grade, this grade fraction is scored as
Critical Design Report
25%
Critical Design Presentation
25%
Student Peer Evaluations
25%
Systems Engineering Paper Submitted to NASA
40% will be sub-system team grades, this grade fraction is scored as
Subsystems Final Design Report
50%
Interface Control Documentation
25%
Test and Evaluation reports
25%
20% Success of the flight test
Top-Level Objectives
Upon completion of this design class students will be able to synthesize mathematics,
science, engineering fundamentals, and laboratory and work-based experiences to
formulate and solve engineering problems in both thermal and mechanical systems areas.
Students will have proficiency in computer-based engineering, including modern
numerical methods, software design and development, and the use of computational
tools. Students will be prepared to communicate and work effectively on team-based
engineering projects. Students will recognize the importance of, and have the skills for,
continued independent learning.
Desired Outcomes
Program outcomes are statements that describe what units of knowledge or skill
students are expected to acquire during the achievement of this design. These outcomes
are typically demonstrated by the student and measured by the program at the time of
class completion. At the completion of this course each student is expected to have:
i) Ability to apply knowledge of mathematics, science, and engineering,
ii) Ability to design and conduct experiments, and analyze and interpret data,
iii) Ability to design a system, component, or process to meet requirements within
realistic constraints
iv) Ability to function on multi-disciplinary teams,
v) Ability to identify, formulate, and solve engineering problems,
vi) Understanding of professional and ethical responsibility,
vii) Ability to communicate effectively,
viii) a knowledge of contemporary issues,
ix) Ability to use the techniques, skills, and modern engineering practice.
7
Contribution of course to meeting the requirements of ABET Criterion 5:
Math & Basic
Sciences

Professional Component Content
Engineering
General
Topics
Education


Engineering
Design

Relationship of design course to desired USU MAE program outcomes:
Course *
Outcomes

a)
an ability to apply knowledge of mathematics, science, and
engineering,

b)
an ability to design and conduct experiments, as well as to analyze
and interpret data,

c)
an ability to design a system, component, or process to meet desired
needs within realistic constraints such as economic, environmental,
social, political, ethical, health and safety, manufacturability, and
sustainability

d)
an ability to function on multi-disciplinary teams,

e)
an ability to identify, formulate, and solve engineering problems,

f)
an understanding of professional and ethical responsibility

g)
an ability to communicate effectively

h)
the broad education necessary to understand the impact of
engineering solutions in a global, economic, environmental, and
societal context

i)
a recognition of the need for, and an ability to engage in life-long
learning

j)
a knowledge of contemporary issues,

k)
an ability to use the techniques, skills, and modern engineering tools
necessary for engineering practice

l)
an ability to work professionally in both thermal and mechanical
system areas including the design and realization of such systems.
*An  indicates that this course helps the students to achieve the Program Outcomes.
Specific Assessment Metrics
Course Objective
Measurement
Instrument
Design component: Design must be the
major component of the course. Student
teams should explore and evaluate possible
design alternatives. Each member of each
team should play an active role in the design
activities.
Project Reports,
Interface Control
Documents, Student
and NASA Peer
Reviews
Self Assessment
(A-F)
Student
Assessment
(A-F)
8
Ability to deal with realistic project
constraints: These constraints may, for
example, involve cost or performance
considerations in the implementation or
platform size restrictions imposed by the
intended NASA. These issues will be
addressed in the lectures, and students should
be consciously aware of these considerations.
Knowledge of and ability to Apply
Standards: Where appropriate, consideration
of relevant standards should be applied.
These considerations include NASA standard
safety and consistency standards. As
appropriate published NASA systems
engineering documents and standards will be
directly used as instructional materials.
Ability to Consider Ancillary Design
Effects, e.g. Maintainability: The design
should include consideration of how to make
the system maintainable to accommodate
changing requirements or to continue
functioning in a somewhat different
environment, e.g. planetary gravity fields and
atmospheres.
Knowledge of Ethical, social, and
professional issues: Issues relating to
matters such as security, privacy, and
intellectual property are often directly related
to the general area of the capstone courses.
Students should again be consciously made
aware of these issues, perhaps via class
discussions. Other professional issues include
awareness of new methodologies, languages,
tools and systems that may be used in
industry and students' ability to learn about
these on their own and capstone courses often
present opportunities for students to develop
these skills.
Thermodynamics: Students demonstrate
ability understand basic physics and
thermodynamics and equation of state and its
relationship to compressible flow physics
Fluid Mechanics: Students demonstrate the
ability to adapt apply integral form of
conservation, momentum, and energy
equations to one-dimensional flow problems;
solve for isentropic flow properties in ducts,
nozzles and diffusers.
Flight Mechanics and Payload Mass
fraction Analysis: Students demonstrate the
ability to analyze the required
“DV” for a given rocket system payload, and
to calculate the required propellant mass
fractions based on the specific impulse of the
system
Project Reports,
Interface Control
Documents, Student
and NASA Peer
Reviews, Budget
Analysis
Homework
assignment, Project
Reports, Interface
Control Documents,
Student and NASA
Peer Reviews,
Homework
assignment, Project
Reports, Interface
Control Documents,
Student and NASA
Peer Reviews,
Project Reports,
Student Peer reviews
Homework
assignment, flow path
modeling assignment
Homework
assignments, flow path
modeling assignment
Homework
assignments,
Programming
assignments
9
Propulsion System Sizing and Analysis:
Students demonstrate the ability to design
liquid and solid rocket systems, understand
combustion processes, select a particular
system design for a given mission
requirement
Dynamics
and
Control:
Students
demonstrate Ability to model gravity-offset
platform dynamics, and to design a simple
regulator to maintain stability during flight
Test and Evaluation: Students will
demonstrate the ability to plan and execute
the testing required for the development of a
prototype test article. These skill include to
make standard mechanical engineering
measurements and apply calculus-based
statistics in the interpretation of the resulting
data.
Homework
assignments,
programming
assignments
Homework
assignments,
programming
assignments, test and
evaluation
Test readiness
reviews, Test Result
Reports, Systems
Interface Documents,
Final Design Report.
First Flight test.
10
6/14/2009
ESDM Senior
Design Project
National Aeronautics and
Space Administration
Background (1)
Top-Level Course Description:
This course is developed as partial fulfillment of the
requirements of a grant funded by the NASA Office of
Education.
Design and Testing of a Demonstration
Prototype for Lunar or Planetary Surface
Landing Research Vehicle (LPSRV)
Final outcome will be a “packaged” senior design course that can
be “moved laterally” and incorporated into universities across the
nation.
Course materials will adhere to the standards of the Accreditation
Board for Engineering and Technology (ABET).
www.nasa.gov
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
0
Background (2)
1
Background (3)
Target Design:
Top-Level Design Requirements:
NASA is seeking senior design ideas in one of four areas,
identified by, and directly relevant to the Exploration Systems
Mission Directorate (ESMD),
This project will develop concepts for a Lunar or Planetary
Surface Landing Research Vehicle (LPSRV).
Per NASA specifications concepts must account for reduced
lunar gravity, and allow simulated terminal stage of lunar descent
to be flown either by remote pilot or autonomously.
• i) Spacecraft,
• ii) Propulsion,
• iii) Lunar and planetary surface systems,
• iv) Ground Operations.
The design project will challenge students to apply systems
engineering concepts to define research and training
requirements for a terrestrial-based lunar landing simulator.
Project will target Item iii) Lunar and Planetary Surface Systems,
but contains elements essential to all four items in the list.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
2
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
3
1
6/14/2009
Background (4)
ESMD Role within NASA
Top-Level Design Requirements: (cont’d)
One of 5 Mission Directorates within NASA
Aeronautics (ARMD)
Exploration (ESMD)
Science (SMD)
Space Operations (SOMD)
Education (Office of Education)
Free-flying platform will allow for both sensor evaluation and
pilot training.
Concept must allow a small-scale prototype-demonstrator to be
constructed within time and budget constraints of a universitybased senior design project.
Constellations Systems is the execution and planning
wing of ESMD
Prototype of the system concept will be constructed and flighttested.
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
4
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
ESMD Centers
ESMD Project Areas
Spacecraft
Guidance, navigation, and control; Thermal;
Electrical; Avionics; Power systems; Highspeed reentry; Interoperability/Commonality;
Advanced spacecraft materials; Crew/Vehicle
health monitoring; Life-support systems;
Command/Communication software;
Modeling and simulation
Ground Operations
Pre-launch; Launch; Mission
operations; Command, control, and
communications; Landing and
recovery operations
National Aeronautics and Space Administration
5
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Propulsion
Methods that utilize materials found
on the Moon and Mars; On-orbit
propellant storage; Methods for softlanding
Lunar & Planetary
Surface Systems
Precision landing software; In-situ
resource utilization; Navigation systems;
Extended surface operations; Robotics;
Environmental sensors and analysis;
Radiation protection; Life-support
systems; Electrical power and efficient
power management systems
Stephen A. Whitmore, USU MAE Dept.
2
6/14/2009
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Senior Design Projects for ESMD
Course Motivation (1)
Why This Design Class is Important to NASA:
Allow students the practical design
experience of developing
technologies and systems for
space exploration under the
advice, guidance, and mentorship
of university faculty, and NASA
engineers and scientists.
One of the many crucial points associated with NASA Lunar
Landing mission is the portion from spacecraft separation in
lunar orbit to descent and touchdown.
Flight Training vehicles must be capable of rendering a realistic
environment for both flight crew training and autonomous
landing systems verification and validation.
The projects are aligned with a
clear vision for exploration and
serve to stretch one’s imagination
for developing revolutionary
technologies needed to explore
our solar system and beyond.
National Aeronautics and Space Administration
The Lunar Lander Training Vehicle (LLTV) developed for the
Apollo program during the 1960's is considered as a significant
contributor to the success of the Apollo lunar program.
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Course Motivation (3)
Why This Class is Important to NASA: (cont’d)
Why This Class is Important to NASA: (cont’d)
Seven of nine Apollo Astronauts that trained with the LLTV
believe that training was critical to achieving a successful
landing and that such a vehicle is essential for future lunar
missions*.
Additionally, unlike Apollo program the new Altair lander will
require a suite of sensors that reduce pilot workload and allow
for Autonomous Landing and Hazard Avoidance (ALHAT).
General consensus among NASA researchers is that most realistic
and practical ALHAT approach is to pursue field testing on
helicopters and airplanes, starting with sensor characterization,
evolving towards integrated testing with onboard processing.
As NASA prepares to send astronauts back to the lunar surface, a
similar training vehicle, based on modern technologies, is
required to ensure that astronauts develop skills at same high
level of proficiency exhibited by the Apollo astronauts.
The consensus is that these component-level tests can bring the
technology readiness level (TRL) to a level of approximately 5.
*Proceedings, “Go For Lunar Landing, From Terminal Descent to Touchdown, Conference,”
Tempe, Arizona, March 4-5, 2008.
Stephen A. Whitmore, USU MAE Dept.
9
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Course Motivation (2)
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
10
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
11
3
6/14/2009
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Course Motivation (4)
Course Motivation (5)
Why This Class is Important to NASA: (cont’d)
Why This Class is Important to YOU:
However, to bring these components to a TRL that can be
deployed on an operational mission, a TRL of 7 or greater is
required, and only closed-loop testing on a free-flying LLT/RV
can achieve those results.*
It is a requirement for graduation!
It is a serious introduction to design, systems engineering and
integration, and fabrication techniques that will be essential once
you reach the workplace.
The potential role of an Earth demonstrator free flyer platform
has been an ALHAT topic of discussion for quite a while.
It will allow you to understand how one progresses from “taking
tests” and doing assignments, to actualization and realization –
“Hands on” … but not just “hobby” or “garage tinkering” real
scientific design!
Email correspondence with Chirold Epp, NASA JSC ALHAT Program Manager, June 12, 2008.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
12
Lunar Landing Missions (circa 1973)
http://www.lpi.usr
a.edu/lunar/missio
ns
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
13
Past Landing Spots
Mostly Chosen For Benign Landing Terrain
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
4
6/14/2009
Future Lunar Landing Spots
Recent Lunar Mission
Mission
Year
Summary
Lunar Prospector (NASA)
Clementine (USN)
1994
1998
Small spacecraft orbiter that sensed significant
amount of hydrogen (possibly water) in Lunar south
polar craters
Japan Kaguya Orbiter (JNASCA) 2007
First High definition Photographic Images of Lunar
Surface
Lunar Reconnaissance Orbiter
(LRO) (NASA)
2008
Orbiter to map and characterize future landing sites
for In-situ resource utilization (ISRU)
Lunar Crater Observation and
Sensing Satellite (LCROSS)
(NASA)
2008
Launched with LRO to search for water-ice in dark
polar craters, later deploying a spacecraft to impact a
dark crater sensing impact cloud for water-ice
Indian Chandrayaan-1's Moon
Impact Probe
2008
First Lunar Space Mission by “Developing World”,
Hard Impact with Lunar Surface
Orion Crew Exploration Vehicle
(CEV) (NASA)
2020
Human Crewed Program to return the moon (Project
Constellation)
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
Lunar South Pole: Very High payoff … but
Hazardous Terrain!
Hi Resolution Image from
Japan Kaguya Orbiter
National Aeronautics and Space Administration
Future landing Spots (2)
Stephen A. Whitmore, USU MAE Dept.
Course Overview (1)
Synopsis:
Lunar South Pole: Very Hazardous Terrain!
This course is taught a two-semester design-sequence.
Students not already having completed “Design I” register for course as
MAE 3800 for fall semester „09. (3 credits)
Students having completed Design I register as MAE 5930 “Launch
Systems Design” for fall semester „09. (3 credits)
Spring semester ‟10 all students register as MAE 4800 “Design II” (3
credits)
Both semester must be successfully completed for students to
receive senior design credit.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
19
5
6/14/2009
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Course Overview (2)
Course Overview (3)
Course Objectives and Deliverables: (cont’d)
Course Objectives and Deliverables:
Students will use or develop simulation code required to fulfill
team objectives as necessary.
Fall Semester 2009 will introduce students to design and systems
engineering concepts, and develop sufficient theoretical
background to allow design a prototype vehicle.
Students will become sufficiently proficient in technical writing
to deliver a professional grade final design report.
A minimum of 2 1-hour lectures will be delivered each week.
At least 8 one-hour periods will be made available for “break off
team” meetings. … These will de designated as “Design
Friday”
Final outcome of fall semester is a conceptual design roadmap
including preliminary design reports, a test and measurements
matrix, and sufficient engineering design drawings to allow
construction to begin during the spring semester.
As necessary design teams will break off into small development
teams outside of class.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
20
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Course Overview (5)
Course Objectives and Deliverables: (cont’d)
Course Objectives and Deliverables: (cont’d)
A preliminary design review (PDR) will be performed during
finals week of fall semester.
Spring semester 2010 will emphasize detailed theory for specific
sub-system relevant to the vehicle design, as well as fabrication
and testing of the prototype article.
This review will be made available as requested to NASA
personnel via web cast, and will include faculty members within
the college as peer reviewers.
Group lectures will be held at least one hour per week. Internal
project design reviews will be held on a bi-weekly basis.
As, required technical interchange videoconferences or web casts
will be help with the NASA technical and administrative points
of contact.
Stephen A. Whitmore, USU MAE Dept.
21
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Course Overview (4)
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
A Critical Design Review (CDR)with both written and oral
reports will be required. CDR report will be submitted for the NASA
Systems engineering competition. (late March 2010)
22
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Course “Administrivia” (1)
Course Overview (5)
Course Objectives and Deliverables: (cont’d)
Contact Information:
The final deliverable from this report is a working LLRV
prototype.
Course Title:
Course No.:
Class Times:
Office Hours:
Instructor:
Instr. Phone:
Instr. Email:
Office:
TA:
A goal of a successful test flight before end of Spring Semester
2010 will be targeted.
Results from the design and flight experiments will be submitted
to a peer reviewed journal in the class‟ name.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
24
National Aeronautics and Space Administration
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
25
Course “Administrivia” (2)
Grading Policy:
Required Text: Understanding Space: An
Introduction to Astronautics
(Third Edition), Jerry. J.
Sellers, McGraw-Hill, ISBN
978-0077230302, 2005.
Weekly homework and reading assignments will be given.
Up to 25% of student grades will come from individual
homework assignments and/or “pop” quizzes.
40% will be a weighted class grade. Average class grade will be a
combination of
i) Design Reports (PDR, CDR), 50%
ii) Evaluation of Design Presentations, 50%
Supplemental materials … Posted to Course Blackboard site
As required.
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Course “Administrivia” (1)
National Aeronautics and Space Administration
Design I, (Launch Systems Design), Design II
MAE 3800 (MAE 5930), MAE 4800
MWF, 1:30-2:20, ENGR 401
Open Door
Stephen A. Whitmore
435-797-2951
swhitmore@engineering.usu.edu
ENGR-419F
TBD
26
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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6/14/2009
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Course “Administrivia” (3)
Course “Administrivia” (4)
Required Skills:
Grading Policy: (cont’d)
35% of Student’s individual “weighted class grades” will come
from peer evaluations of total performance and a combination of
peer and instructor (my) evaluation of performance in
presentations.
Working knowledge of computer-aided design code like “Solid
Edge” or “Firestar.”
“Attitude,” “Teamwork,” and enthusiasm as essential
components for getting a good grade in this class.
Ability to Program in a high-level , structured language
(FORTRAN, “C”, “C++”, or MATLABTM).
Working knowledge of measurement techniques and skills taught
in MAE 3340 (Instrumentation Systems)
A working knowledge of LAVIEWTM would be very helpful.
Students deemed to be “uncooperative” during fall semester may
not be allowed to continue in MAE 4800 (at least for this design
option) during spring semester.
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Programming assignments in Microsoft ExcelTM will not be accepted.
Students need to establish a “programming environment” comfortable for them.
28
National Aeronautics and Space Administration
Homework
Stephen A. Whitmore, USU MAE Dept.
29
NASA DFRC LLRV, Circa 1965
Download (from Class webpage for section 1),
LLRV Monograph
NASA SP-2004-4535,
“Unconventional, Contrary, and Ugly”
The Lunar Landing Research Vehicle” by Matranga, Ottinger,
and Jarvis
Read Chapters 1,2.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
“Design Friday” Assignment
Class Meets to Select
Finish
….
Project Leader, Chief Engineer, Web Master,
Disciplinary Team Leads:
i) Systems Engineering, Management, and Planning
ii) Mechanical Design, and Fabrication
iii) Structures
iv) Propulsion Systems
v) Pneumatics and Hydraulics
vi) Aerodynamics and Flight Mechanics
vii) Controls and Instrumentation
viii) Operations and Testing
ix) Procurement and Purchasing
x) … any additional disciplinary mixes you deem appropriate
-- Each team should be populated with a minimum of 3 people (Some Students
Questions??
will be members of two disciplinary teams, primary, backup)
-- Prepare a class roster and organizational chart (I am the program manager!)
See Page 20 on LLRV Monograph for chart example
-- Post Both to Design Course Website …. I’ll give you a link to post to
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
ESDM Senior
Design Project
33
National Aeronautics and
Space Administration
USA Space History, Policy, and
Organizations
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
35
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6/14/2009
Dawn of the Space Age?
Dawn of the Space Age
History changed on October 4, 1957, when Soviet Union
successfully launched Sputnik I. The world's first artificial
satellite was about the size of a beach ball weighed only 83.6 kg.
Immediately after the Sputnik I launch in October, the U.S. Defense
Department responded to the political furor by approving funding for another
U.S. satellite project. As a simultaneous alternative to Vanguard, Wernher von
Braun and his Army Redstone Arsenal team began work on the Explorer
project.
That launch ushered in new political, military, technological,
and scientific developments.
Sputnik launch also led directly to the creation of National Aeronautics and
Space Administration (NASA). In July 1958, Congress passed the National
Aeronautics and Space Act (commonly called the "Space Act"), which created
NASA as of October 1, 1958 from the National Advisory Committee for
Aeronautics (NACA) and other government agencies including the Naval
Research Lab (NRL).
While the Sputnik launch was a single event, it marked the start
of the space age and the U.S.-U.S.S.R space race.
Let’s learn a bit about US Space Policy and
Organizations
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
36
National Aeronautics and Space Administration
Space Policy Under … Truman
37
•Sputnik/Vanguard/Explorer
•NASA (1958)
•Missile Gap
•Open Skies
•US & USSR H-Bomb
•U-2
•NASA Formed
•National Aeronautics and Space Act
•NRO (1960)
•ABM/ASAT Systems
•Missile Warning (NORAD)
•Space Surveillance (NAVSPASUR
& USAF)
•R&D of 5000 NM ICBM
•V-2’s from White Sands,
Cape Canaveral & Aircraft
Carrier
•Ballistic Missile Program at
Ft. Bliss, TX (moved to
Huntsville, AL in 1950)
•Cruise Missile (Snark) vice
ICBM until Atlas in 1961
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Eisenhower
Foresaw the dawn of the space age?
National Aeronautics and Space Administration
(2)
38
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
39
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Kennedy
Johnson
•Classified Space Programs
•AF Primary DoD Agency (R&D
and Operations)
•Blue Gemini/MOL
•Orbital H-Bomb Threat
•Starfish Test (High-altitude,
atmospheric H-bomb test)
•Test Ban Treaty
•First Men in Orbit
•Exploration (NASA)
–Manned
–Unmanned
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
•Nuclear ASATS
•Soviet FOBS
•NASA Moon Project
•Outer Space Treaty
40
National Aeronautics and Space Administration
Nixon
Stephen A. Whitmore, USU MAE Dept.
41
Ford
•Soviet Co-orbital ASAT
•ABM Treaty
•SALT
•Liability Convention
•Convention on Registration
•MOL canceled
•Moon Landing
•Skylab
•Apollo/Soyuz Docking
•Space Shuttle
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
•Satellite Vulnerability Assessment
•DoD directed to redress
satellite vulnerability
•DoD directed to develop
operational ASAT & study
options for ASAT Arms
Control
42
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
43
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6/14/2009
Carter
Reagan
•Nat’l Space Policy:
• Right of Self Defense
• Space as possible warfighting
medium
•MHV ASAT
•Directed Energy Weapons
•Space Arms Control
•Environmental Modification
Convention
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
44
•Strategic Defense Initiative
•Reject Soviet Space Weapons
Treaty (Soviet supplement to Outer
Space Treaty)
•Congress limits ASAT $$
•Space Commands:
• USAF ’82
• USN ’83
• US (w/USA) ’85
•Shuttle - Primary launch
National Aeronautics and Space Administration
•National Space Council created:
VP, State, Treas, Def, Comm,
Trans, Energy, OMB, DCI, NASA
•Goals & Objectives
•Strategy to implement
•Monitor implementation
•Resolve specific issues
•Desert Storm - First Space War?
Stephen A. Whitmore, USU MAE Dept.
45
Clinton
Bush I
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
•Nat’l Space Policy 1996
•DoD Space Policy 1999
•Int’l Space Station
•Commercialization
•Cooperation of IC/DoD
46
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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6/14/2009
Bush II
Bush II
•Missile Defense Agency
• NASA Vision for Space Exploration
•ESMD/Constellation
•Shuttle Return to Flight
•Successful Robotic mars Missions
Placeholder… not actual photo
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
48
Obama
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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Review of Treaties
• Limited Test Ban Treaty – 1963
– Ban on Nuke test in Air/Space/Under Water
•????
•Appoints Charlie Bolden
as NASA Administrator
• Outer Space Treaty – 1967
– U.N. Charter Applicable to Space
• ABM Treaty – 1972
– US/USSR
– Ban Dev/Test/Deploy of Space-based ABM system
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
50
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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6/14/2009
Outer Space Treaty
Outer Space Treaty
• All Nations can explore space freely “innocent passage”
• No Nation can appropriate outer space or celestial
bodies
• No weapons of mass destruction in space
• The moon and other celestial bodies are to be used
exclusively for “peaceful” purposes
• States are responsible for governmental and private
space activities
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
• States are liable for damage caused by its space objects
• States retain jurisdiction and control over their space
objects
• States must conduct international consultations before
proceeding with potentially harmful activities
• States must not contaminate outer space or the earth
• Facilities on the Moon are open for inspection
52
National Aeronautics and Space Administration
53
• Liability Convention - 1972
– Launch site absolutely liable
• Registration Convention - 1974
– Register orbital parameters & general function
of all launches
– Routinely evaded via misleading info
• Environmental Modification Convention - 1980
– Prohibits hostile use of environmental
modification techniques
• Between US and USSR
• Prohibits development, testing &
deployment of space based ABM systems
• Allows limited space based sensors
• Prohibits interference with “national
technical means” for verification
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
International Agreements
Antiballistic Missile Treaty
National Aeronautics and Space Administration
(2)
54
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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6/14/2009
Basic Principles of
Space Law
Space Law
• International Law (Treaties, Agreements,
Custom, Principles)
•
•
•
•
– If not specifically prohibited, then permitted
– “Peaceful” = non-aggressive = individual and
collective self defense
– Only binding on signatories during peacetime
– Measurable/Verifiable/Enforcement
• Domestic Law (Legislation, Regulations, Court
Decisions)
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
International law applies to outer space
Space is free for use by all countries
Space will be used for peaceful purposes
Space objects must be registered with the UN
56
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Basic Principles of Space
Law
57
Domestic Law
(2)
• U S Law and Regulations
• A country retains jurisdiction over its space objects
• Nuclear weapons testing is prohibited in outer space
• Development, testing or deployment of space-based ABM
systems is prohibited
• Interference with national technical means of verification is
prohibited
– Communications Act of 1934
• Government can take control of private
communications assets
– Launch Commercialization Act of 1984
• Commercial customers can use DoD facilities
on a cost reimbursable basis
– Budget and appropriations process
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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6/14/2009
International
Telecommunications
Union (ITU)
Legal Issues
• Regulates all uses of frequency spectrum
• Assigns slots in geostationary orbit
• Global Broadcasting Service
(GBS) ~ Landing Rights?
• Targeting
• Future of ABM Treaty?
– First Come First Served
– Use or lose 7 year limit from filing
• General principles and standards relating to
international telecommunications services
• Federal Communications Commission
– Regulates interstate and foreign communications in
the US
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
60
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
61
1996 National Space Policy
• U.S. will pursue greater levels of partnership &
cooperation nationally and internationally to
continue the use of space for peaceful purposes.
Space
Policy
Additional References:
http://ast.faa.gov/licensing/regulations/nsp-pdd8.htm
http://www.fas.org/spp/military/docops/national/index.html
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
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6/14/2009
1996 National Space Policy
1996 National Space Policy
• “Peaceful” allows defense and intelligence
related activities
• U.S. rejects any claim to sovereignty by any
nation over space or celestial bodies
• Space Systems are national property
• U.S. will maintain and coordinate separate
National Security and Civil systems
• Five Goals of US space
– Enhance knowledge of earth and solar system
through human and robotic exploration
– Strengthen and maintain national security
– Enhance economic competitiveness and science &
technology capabilities
– Encourage private sector investment
– Promote international cooperation
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
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National Aeronautics and Space Administration
• Civil
• National Security
• Defense
• Intel
• Commercial
• Intersector
•
•
NASA is lead for civil R&D
Focus on:
•
•
•
•
•
66
Space Science
Earth Observation
Human Space Flight
Space Tech & Applications
To enable this:
•
•
•
•
•
•
Stephen A. Whitmore, USU MAE Dept.
65
Civil Space Sector Guidelines
National Space Policy
Major Guidelines
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
ISS
Work with private sector on next generation RLS
In-situ measure & sample of celestial bodies
Ident planets around other stars
Long-term earth observation program
Robotic presence on Mars by 2000
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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6/14/2009
Vision for Space Exploration
(VSE)
Civil Space Sector Guidelines (2)
•
• Jan 14, 2004 Executive order by President G. W. Bush .. Still “law of the land”
In conduct of this R&D:
•
•
•
•
•
Ensure safety
Reduce $$
Acquire spacecraft from private sector
Use private sector remote sensing
Use competition & peer review to select programs
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
68
National Aeronautics and Space Administration
• Improve support to military ops
• DOD execute 4 mission areas:
• Overseen by SECDEF & DCI
• Defense & Intel closely coordinated;
Architectures integrated as feasible
• Support National Security:
•
•
•
•
Support inherent right of self-defense
Deter, warn & defend against attack
Assure use of space
Counter hostile space systems
Enhance operations of U.S. and allies
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
69
National Security Guidelines
(Defense)
National Security Guidelines
•
•
•
•
•
Stephen A. Whitmore, USU MAE Dept.
Space Support
Force Enhancement
Space Control
Force Application
• DoD as lead agency for ELV’s
• Within treaties - ensure space control
• U.S. will pursue TMD and NMD (deployment
readiness) programs
70
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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6/14/2009
National Security Guidelines
(Intelligence)
Commercial Space Sector Guidelines
• DCI ensure IC space support for Gov’t Policy, Military Ops,
Diplomatic, I&W, Treaty verification
• Continue to develop and apply advanced technology
• Work with DoD to support military operations
• Intel space activities are classified, but plan to release when
appropriate
• UNCLAS:
• IMINT / SIGINT / MASINT from space
• Mapping, charting, geodesy from space
• NRO
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
• Support and enhance US economic competitiveness
• Pursue commercial applications w/o direct federal
subsidies
• Appropriate access to Gov’t space related
infrastructure will be given to stimulate private
sector participation
• Goal of market driven, commercial launch
72
National Aeronautics and Space Administration
• Last major policy revision 1987
• Themes:
• International cooperation
• Cost & Tech sharing
• Enhance relations
• Create new commercial opportunity
• Protect commercial value of intellectual property
Space Transportation – reliable & affordable access
Earth Observation - NPOESS
Non-proliferation, Export controls
Arms Control
Space Nuclear Power – not in Earth orbit
Space Debris
Gov’t Pricing – not seek to recover development $$
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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DOD Space Policy (1999)
Intersector Guidelines
•
•
•
•
•
•
•
Stephen A. Whitmore, USU MAE Dept.
–
–
–
–
–
–
–
–
National Interest
Strategic Enabler to Nat’l Mil Strategy & JV2010
Information Superiority
Deterrence
Defense
Freedom of Space
Integration into Strategy, Doctrine, CONOPS
Defense-Intel Cooperation
Stand by .. This is going to “change”!
74
National Aeronautics and Space Administration
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6/14/2009
Defense Space Mission Areas
Defense Space Control
• Space Support – ops to deploy & maintain;
Launch, command & control
• Force Enhancement – ops to improve
effectiveness; Nav, Meteorology, Warning, C3,
ISR, BDA
• Space Control – ops to ensure freedom of
action & deny adversary; Space Surv, ASAT,
EW, IO
• Force Application – combat ops in, through,
from space to influence outcome of conflict;
BMD, Space Based Weapons
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
•
•
•
•
Assured Access (launch on demand)
Space Surveillance
Protection (threat/attack on board warning)
Prevention (deny adversary access
through non-military means)
• Negation (deny, disrupt, deceive, degrade,
or destroy)
76
National Aeronautics and Space Administration
77
Organizational Implications
Space Control Considerations
•
•
•
•
•
•
•
Stephen A. Whitmore, USU MAE Dept.
•
•
•
•
•
•
Resources
International Coop/Treaty Implications
Dual Use Systems (ABL) and Treaties
Space Based vs Ground Based Weapons
Response to attack on satellite
Space Support to Terrestrial Warfare
Arms race (defense vs offense)
Separate Space Force
Joint Space Component Commander
CINCSPACE (regional vs functional CINC)
Cooperative/Combined/Shared Systems
Military core capabilities?
Commercial augmentation
Stand by .. This is going to “change”!
National Aeronautics and Space Administration
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National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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6/14/2009
NASA BUDGET BY PROGRAMS - FY 1998 Total
Appropriation = $13,638 Million
Aeronautics
$907 6.7%
Sciences
UNCLASSIFIED
Congress
President
NASA
DOI
Civil Service
$1,637 12.0%
DOC
USGS
NRO
DoD
NIMA
NAVY
USSPACECOM
14AF
NAVSPACE
Other Mission Support
$575 4.2%
USASMDC
ASPO
Shuttle
USARSPACE
Any Q uestions?
$2,501 18.3%
Stephen A. Whitmore, USU MAE Dept.
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Defense Space Resources
Military
space
budget
Equals
NASA
BMDO
$.35 B
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
*Based on Station requirements - aproval of transfer authority by Congress
NASA/JSC - Federal Bu dget Process
81
1
US Space Command Components
NAVY
$.43 B
ARMY
$.57 B
Other PE
$6.8 B
$2923 21.4%
Station*
UNCLASSIFIED
National Aeronautics and Space Administration
DISA/ARPA/
DSPO $.02 B
Communications
$590 4.3%
NOAA
ARMY
AFSPACE
Other Human
Space Flight
$256 1.9%
CIA
NSA
JCS
AIR FORCE
$3,685 27.0%
Technology
$564 4.2%
US Space Organization
Relationships
USSPACECOM
C Springs CO
CMOC
C Springs CO
AIR FORCE
$5.3 B
AFSPACE
14th Air Force
Vandenberg CA
NAVSPACE
Naval Space Command
Dahlgren VA
ARSPACE
Army Space Command
(Forward) C Springs CO
$13.5 B for DOD and Intelligence Space Programs
FY98 President’s Budget
83
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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6/14/2009
US Space Command
Army Space Command
http://www.spacecom.af.mil/usspace/index.htm
• CINC is triple hatted
– CINCSPACE
– CINCNORAD
– AFSPC CC
• Forces provided by service
components
• Single POC for military space
operational matters
• Space Ops Center (SPOC)
• Joint Space Support Teams
(JSST)
• CND/CNA Missions
• Army Component to
USSPACE
• DSCS Payload Operations
• Army Space Support
Teams
• Joint Tactical Ground
Stations (JTAGS)
• Missile Defense (operator)
• Ops Center
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
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85
AFSPC
AF Space Command
Peterson AFB CO
Train Org & Equip
21 Space Wing
Peterson AFB CO
Warning/Surveillance
30 Space Wing
Vandenberg AFB CA
Launch
45 Space Wing
Patrick AFB FL
Launch
50 Space Wing
Schriever AFB CO
Satellite C2
SMC
Space & Missile Systems Center
LA AFB CA
System Acquisition
Stephen A. Whitmore, USU MAE Dept.
Air Force Space Units
Air Force Space Organizations
AFSPACE
14 Air Force
Vandenberg AFB CA
Plan/Execute Space Forces
National Aeronautics and Space Administration
Space Warfare Center (SWC)
Schriever AFB CO
AF TENCAP
Phillips Research Site
Air Force Research Lab
Kirtland AFB NM
Space R&D
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Intelligence Community
Air Force Space Units
Missile Warning, Space Surveillance, Satellite C2, Space Weather Sites
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National Reconnaissance Office
http://www.nro.mil/
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DoD & Intelligence Space Related
Organizations
• National Security Agency http://www.nsa.gov/
– Information Systems Security
– Foreign Signals Intelligence
• Central Intelligence Agency
– Office of Development and Engineering
• Defense Information Systems Agency
http://www.disa.mil/disahomejs.html
– Defense Information Systems Network
• Joint Spectrum Center http://www.jsc.mil/
– Spectrum Planning, System Acquisition and Operations support
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NASA Field Centers
NASA http://www.nasa.gov/
•
•
•
•
•
•
•
•
•
•
HQ - Wash DC
Ames Research Center – Astrobiology
Dryden – Flight test, Aeronautics
Goddard - Astronomy, Solar Physics
Jet Propulsion Lab- Planetary Exploration
Johnson Space Center - Human Space Flight
Kennedy - Space Shuttle Launch
Marshall - X-Ray Astronomy, Microgravity Research
Wallops Island - Suborbital Launches
White Sands Test Range/Facility
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NASA Centers, Role within ESMD
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ESMD Role within NASA
One of 5 Mission Directorates within NASA
Aeronautics (ARMD)
Exploration (ESMD)
Science (SMD)
Space Operations (SOMD)
Education (Office of Education)
Constellations Systems is the execution and planning
wing of ESMD
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ESMD Project Areas
Spacecraft
Civil Space
•
•
•
•
Propulsion
Guidance, navigation, and control; Thermal;
Electrical; Avionics; Power systems; Highspeed reentry; Interoperability/Commonality;
Advanced spacecraft materials; Crew/Vehicle
health monitoring; Life-support systems;
Command/Communication software;
Modeling and simulation
Ground Operations
Pre-launch; Launch; Mission
operations; Command, control, and
communications; Landing and
recovery operations
Methods that utilize materials found
on the Moon and Mars; On-orbit
propellant storage; Methods for softlanding
Lunar & Planetary
Surface Systems
Dept of Commerce - NOAA
Dept of Transp - Commercial Launch
Dept of State - Export Controls
Federal Comm Commission - Spectrum
Precision landing software; In-situ
resource utilization; Navigation systems;
Extended surface operations; Robotics;
Environmental sensors and analysis;
Radiation protection; Life-support
systems; Electrical power and efficient
power management systems
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Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Finish
A New Era?
FAA and DOT tasked with monitoring
and regulating “private space flight”
Questions??
"Virgin Galactic, the British company created by entrepreneur Richard Branson
to send tourists into space, and New Mexico announced an agreement Tuesday
for the state to build a $225 million spaceport. Virgin Galactic also revealed that
up to 38,000 people from 126 countries have paid a deposit for a seat on one of
its manned commercial flights, including a core group of 100 "founders" who have
paid the initial $200,000 cost of a flight upfront. Virgin Galactic is planning to begin
flights in late 2008 or early 2009.”
Virgin Galactic has a deal with Rutan to build five spacecraft,
licensing technology from Paul Allen's company,
Mojave Aerospace Ventures.
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National Aeronautics and
Space Administration
ESDM Senior
Design Project
What is Systems Engineering?
A System Is …
Systems Engineering I
Simply stated, a system is an integrated composite of people, products,
and processes that provide a capability to satisfy a stated need or
objective.
Sellers: Chapters 11, 15 + Material
From Auburn University Lunar Excavator
Design Course, Courtesy of David Beale
Systems Engineering Is…
Systems engineering consists of two significant disciplines: the
technical knowledge domain in which the systems engineer operates,
and systems engineering management.
It is an interdisciplinary approach that encompasses the entire technical
effort, and evolves into and verifies an integrated and life cycle
balanced set of system people, products, and process solutions
that satisfy customer needs.
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What is Systems Engineering? (2)
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What is Systems Engineering? (3)
Systems Engineering Management Entails…
Systems engineering management is accomplished by integrating three
major activities:
• Development phasing that controls the design process and provides baselines
that coordinate design efforts,
• A systems engineering process that provides a structure for solving design
problems and tracking requirements flow through the design effort, and
• Life cycle integration that involves customers
in the design process and ensures that the system
developed is viable throughout its life.
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The Systems Engineering Process
The Systems Engineering Process (2)
Significant development at any given level in the system
hierarchy should not occur until the configuration
baselines at the higher levels are considered complete,
stable, and controlled. Reviews and audits are used to
ensure that the baselines are ready for the next level of
development.
• The systems engineering
process is a top-down comprehensive, iterative and recursive problem
solving process, applied sequentially through all stages of development,
that is used to:
• Transform needs and requirements
into a set of system product and process descriptions (adding value
and more detail with each level of development),
• Generate information for decision makers
• Provide input for the next level of development.
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National Aeronautics and Space Administration
The Systems Engineering Process (3)
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The Systems Engineering Process (4)
Primary Function Definitions
• Development includes the activities required to evolve the system from
customer needs to product or process solutions.
• Manufacturing/Production/Construction includes the fabrication of
engineering test models and “brass boards,” low rate initial production,
full-rate production of systems and end items, or the construction of large
or unique systems or subsystems.
• Deployment (Fielding) includes the activities necessary to initially deliver,
transport, receive, process, assemble, install, checkout, train, operate,
house, store, or field the system to achieve full operational capability.
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The NASA “Vee-Chart”
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Pre-Phase A: Concept Studies
Mission-Level Objectives +
multiple R/A/C concepts +
Mission Validation Plan
Domain of Engineering
Design
Domain of Systems Engineering
The Systems Engineering Process (5)
Phase A: Concept Development
Single System-level R/A/C
+ Trade Studies + System
Verification Plan
Phase D(4): SAITL
System Demonstration
and Validation
Phase D(3): SAITL
Integrate Subsystems and
Verify System Performance
Phase B: Preliminary Design
Subsystem-level R/A/C
+ Interfacing + complete technology
+ Subsystems Verification Plan
Phase D(2): SAITL
Integrate Components and
Verify Subsystem Performance
Phase C(1): Final Design and Fabrication
Final Detailed Design
Phase D(1): SAITL
Verify Component Performance
Phase C(2): Final Design and Fabrication
Fabric hardware and software
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The NASA Vee-Chart (2)
The NASA Vee-Chart (3)
• The Design Phases
• Phases of life cycle can be put on a “Vee Chart” --- process starts at top
of left leg with mission objective(s).
• Proceed down left side (the design phases), adding detail to mission
(pre-A), then system (A), and then subsystems (B).
• Pre-Phase A (Concepts Studies) is a short investigation to create a mission
architecture, ConOps and requirements
• Proceed up right side (integration and test phase D).
• Phase A (Concept and Technology Development) delves deeper into the
system to create a system-level architecture and system requirements and
ends with a single concept. Trade studies and reducing risk are important
in Phase A.
• Subsystems are tested, verified, integrated, and then entire system is
assembled, tested, validated.
• Phase B (Preliminary Design and Technology Completion) subsystem
design concepts are developed and all high risk areas are resolved. High
risk elements should br resolved by prototyping or further analysis.
• V chart is divided by a horizontal line that shows responsibility
boundary between systems engineering tasks and tasks performed by
the design & engineering teams directed by subsystems leads.
• Phase C (Final Design and Fabrication) ends with release of all the
detailed drawings for fabrication, and fabrication of all the components.
• Boxes on same horizontal level are at same level in system hierarchy.
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The NASA Vee-Chart (4)
The NASA Vee-Chart (5)
• The Design Phases
• There are 11 Systems Engineering Functions
performed in each phase of the “Vee” (pre-phase
A, phase A, phase B)
•Phase D: System Assembly, Integration and Test
•Phase E/F: Operations and Sustainment, and closeout
• There are 5 functions around triangle
•The phases are best represented on a Vee Chart
–
–
–
–
–
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Mission Objectives and Constraints
Derived Requirements – functional, performance, interface
Architecture/Design – description of elements and layout
Concept of Operation – how the system will operate
Validate and Verify
• Validation -- assuring that the right system is being designed.
• Verification --assuring that the system is built right.
12
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The Documentation and
Review Process (1)
The The NASA Vee-Chart (6)
• … and 6 functions across the triangle
•Interface Control Documentation (ICD). Interfaces are boundaries between areas. interfaces
evolve down the “Vee” as system levels and numbers of sub-systems increase.
•Configuration Management and Documentation is a library and system for documentation control,
access, approval and dissemination.
•Mission Environment – this phase identifies the operating environments …. vibration, shock, loads,
acoustics, thermal, radiation, orbital debris, magnetic, and radio frequency exposure.
•Technical Resource Budgets -- include mass, power, battery, fuel, memory, process usage, data rates
and volume, telemetry, data storage, communication links, contamination, alignment, radiation dose,
Single Event Upsets, charging, meteoroids, propellant, pointing accuracy, etc.
•Risk Management and Failure Mode Analysis -- identifies risks to safety, performance, and
program costs.
•System Milestone Reviews and Reports Mission Concept Review (MCR), Preliminary Design
Review (PDR), Critical Design Review (CDR) and Flight/Test Readiness Review (FRR/TRR)
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Concept Exploration Stage
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The Documentation and
Review Process (2)
Component Development Stage
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The Documentation and
Review Process (3)
System Integration Stage
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The Documentation and
Review Process (4)
System Demonstration Stage
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The Documentation and
Review Process (5)
Production and Deployment Stage
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Systems Engineering Applied to the Space
System Design Process
The Documentation and
Review Process (6)
… “a spacecraft according
to …
• Sometimes individual
subsystem designers get so
focused on their subsystem
designs that they lose sight of
the overall mission objectives
and requirements
• Good systems engineering
coordinates the activities
of disciplinary groups with
disparate design objectives
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National Aeronautics and Space Administration
Systems Engineering Applied to the Space
System Design Process (2)
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Systems Engineering Applied to the Space
System Design Process (3)
• An Alternative Viewpoint,
.. Notice the similarities!
• By following a well-defined process, systems engineers design spacecraft that meet
mission requirements while staying within budget and conforming to constraints
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Systems Engineering Applied to the Space
System Design Process (4)
Systems Engineering Applied to the Space
System Design Process (5)
• Systems Engineering is a
fundamental process that can
be used to design anything
from a backyard grill to a
crewed-space platform.
• Each step utilizes established
design and analysis tools.
• The process is iterative.
• Between process steps there
are “feedback loops” to review
decisions made in previous
steps.
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Notice the Similarities?
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Systems Engineering Applied to the Space
System Design Process (6)
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Systems Engineering Applied to the Space
System Design Process (7)
• First Phase in design process is
to define the mission requirements,
Objectives, and constraints.
• Often documented and detailed in
the mission “Objectives and
Requirements Document.”
(ORD)
Cost, Schedule, Performance
• 3-D trade space that mission must operate within.
• Systems engineers continually trade competing objectives to achieve wellbalanced solution -- “optimal” solution often not-achievable
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Systems Engineering Applied to the Space
System Design Process (8)
Systems Engineering Applied to the Space
System Design Process (9)
Trading Requirements
• Second phase of the design is to define
the required sub-systems, and derive
Their requirements to meet the
programmatic mission requirements
“Derived
Requirements”
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• By trading-off mission requirements versus system-level requirements, an
infeasible mission (too complex or to expensive or both) may become
feasible and affordable
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Requirements Analysis
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Requirements Analysis (2)
Requirements analysis involves defining customer needs and objectives in
the context of planned customer use, environments, and identified system
characteristics to determine requirements for system functions.
Requirements analysis is conducted iteratively with functional analysis to
optimize performance requirements for identified functions, and to
verify that synthesized solutions can satisfy customer requirements.
In general, Requirements Analysis should result in a clear understanding
of:
• Functions: What the system has to do,
• Performance: How well the functions have to be performed,
• Interfaces: Environment in which the system will perform, and
• Other requirements and constraints.
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Systems Engineering Applied to SubSystem Design Process (1)
Requirements Analysis (3)
Subsystems Design
• Subsystem Design Process follows
a distinct order and development
hierarchy
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National Aeronautics and Space Administration
Systems Engineering Applied to SubSystem Design Process (2)
• Hmmmm .. Why is the propulsion
System last on this chart?
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Systems Engineering Applied to SubSystem Design Process (3)
Spacecraft Bus
Spacecraft Subsystems
• Spacecraft bus exists solely to support the payload, with all of the
necessary “bells and whistles” to keep the payload “happy and healthy.”
• Magellan spacecraft subsystems, support payload mission requirements
• Subsystems become part of the spacecraft bus.
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Systems Engineering Applied to the SubSystem Design Process (4)
Systems Engineering Applied to the SubSystem Design Process (5)
• Solar Arrays generate electrical power.
• In considering the payload
requirements for the GPS Satellite,
engineers had to define support
elements for power, temperature
management, and data handling.
• Structural elements hold the spacecraft
together.
•The solid rocket motor and thrusters
make up the propulsion system.
• Magellan spacecraft subsystems,
support payload mission
requirements.
• Star Scanner is a part of the
attitude control subsystem.
• These elements in turn drove the orbits
required for achieving the mission
objectives.
• High gain antenna communicates to
earth-based ground stations and collects
payload data.
• These orbits in turn drives the choice
of launch system and apogee kick motor
• Other bus elements of include data
processing sub-systems, thermal control
system, and miscellaneous avionics
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National Aeronautics and Space Administration
Systems Engineering Applied to the SubSystem Design Process (6)
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Systems Engineering Applied to the SubSystem Design Process (7)
Subsystems Design Revisited
• Subsystem Design chart shows the
Interdependence of all of the
Spacecraft subsystems.
• When the design of one sub-system
is modified, then it typically become
necessary to adjust the designs of
Some or all of the other sub systems.
• In extreme cases, the payload
sometimes needs to be modified as
the result of a mandated sub-system
Change.
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Technology Readiness Levels (TRL)
Technology Readiness Levels (2)
• Designing sub-systems
using high TRL
components is a good
way to reduce or
mitigate programmatic
risk.
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Stephen A. Whitmore, USU MAE Dept.
Design and fabricate when you must
Low TRL’s can “fight” each other and have potential to seriously
impact overall design budget and schedule!
• High TRL systems have “heritage” and offer increased reliability and
(hopefully) enhanced ease of integration.
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Conceptual Technology
Readiness Levels, 1-5
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Integrate when can (high TRL)
Low TRL sub-systems require significant testing and evaluation
before integration
• High TRL systems
have “heritage” and
offer increased
reliability and
(hopefully) enhanced
ease of integration.
National Aeronautics and Space Administration
• Cardinal Sub-system Design Rules:
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Prototype and Deployment Technology
Readiness Levels, 6-9
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Program Management
Program Management (2)
Typical Spacecraft Program Management Structure
(The bottom row is subsystem team leads)
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Subsystem
Organization
Structure
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Systems Engineering
Management Plan (SEMP)
Program Management (3)
CCB keeps track
of design changes
Assures design
Does not grow
“wildly” or worse
Yet – backtracks
Helps to insure
Progressive
changes
in design
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Stephen A. Whitmore, USU MAE Dept.
– Assigns Systems Engineering function responsibility
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
1. Introduction, including Mission Overview, Project schedule with life cycle and reviews.
2. System Engineering Life Cycle, Gates, and Reviews
3. Communication
4. Systems Engineering Functions
4.1 Mission Objectives
4.2 Operations Concept Development
4.3 Mission Architecture and Design Development
4.4 Requirements Identification and Analysis
4.5 Validation and Verification
4.6 Interfaces and ICDs
4.7 Mission Environments
4.8 Resource Budgets and Error Allocation
4.9 Risk Management
4.10 System Engineering Reviews
5. Configuration Management
6. System Engineering Management
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ESDM Senior
Design Project
National Aeronautics and
Space Administration
Systems Engineering II: Design Tools
Sellers: Chapters 11, 15 + Material
From Auburn University Lunar Excavator
Design Course, Courtesy of David Beale
This section provides examples of
systems engineering tools which may be
needed during the design process.
48
www.nasa.gov
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Production Breakdown Structure
Systems Engineering Tools
Allows the systems
engineer to
systematically divide
an entire project into
a set of major
production areas
including, sub-areas,
and sub-sub areas.
Modeling and Simulation
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Production Breakdown Structure (2)
Work Breakdown Structure (WBS)
Program
PBS for the
SOFIA
infrared
telescope
-- WBS allows the systems
engineer to systematically
divide an entire project into a
set of major tasks, sub-tasks,
and sub-sub tasks.
-- In this example, the tasks
for fabrication of the attitude
and orbit control system
(AOCS) are broken into 5
sub-tasks. (Level 1 WBS)
Fundamental Management Tool
-- Each sub-tasks can be
further sub-divided (Level 2
WBS)
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National Aeronautics and Space Administration
Work Breakdown Structure (2)
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Work Breakdown Structure (3)
-- An Alternative Viewpoint
WBS for
SOFIA Project
The first three WBS Levels are organized as:
Level 1 – Overall System
Level 2 – Major Element (Segment)
Level 3 – Subordinate Components (Prime Items)
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Gantt Chart (2)
Gantt Chart
Bar chart that can be used to allot time to tasks, schedule
reviews, and date milestones .. Complements WBS
Microsoft EXCEL Gantt Chart
Microsoft
Project
Chart
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Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Concept of Operations (CONOPS)
CONOPS Example
• As magnetosphere
processes evolve during a
geomagnetic disturbance,
HiDEF E-field
observations provide a
detailed map
Short Verbal or graphic statement, in broad outline, of a
commander's assumptions or intent in regard to an operation or
series of operations.
The concept of operations frequently is embodied in campaign plans
and operation plans; in the latter case, particularly when the plans
cover a series of connected operations to be carried out
simultaneously or in succession.
The concept is designed to give an overall picture of the operation. It
is included primarily for additional clarity of purpose. Also called
commander's concept or CONOPS.
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• HiDEF mission proposed for in-situ
simultaneous E-field measurements
using constellation of pico-satellites
58
National Aeronautics and Space Administration
• Constellation will utilize
natural RAAN precession
to transform cluster from
initially densely packed
“sting of pearls” to a
globally distributed
sensor cluster
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Trade Studies
CONOPS Example (2)
• Trade study is a tool used to help choose the best solution among
alternatives.
Mission Profile
• Numerical values are given based on weight factors and a normalization
scale for the evaluation criteria.
• Evaluation criteria are important factors that are included intrade study.
• Weight factors are used to dictate how important the evaluation criteria
are relative to each other.
• The choice of weight factors and normalization scale are extremely
important to this process.
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• Normalization scale creates a constant interval scale that allows us to set a
numerical for each of the evaluation criteria (e.g. cost, mass, volume,
power consumption legacy, ease of use).
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National Aeronautics and Space Administration
Trade Studies (2)
Trade Studies (3)
Steps to a trade study
1. Define the problem.
2. Define constraints on
the on the solutions.
3. Find 3-5 solutions
4. Define evaluation
criteria.
5. Define weight factors
6. Define normalization
scale
7. Populate trade matrix
8. Rank the solutions
Sample Trade matrix
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Trade Studies (4)
Modeling and Simulation
3)Study Example – Comparison of Controllers for CubeSat
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Allows complex
interactions to be
Discovered prior
to hardware
commitments
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Modeling and Simulation (2)
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Functional Block Diagrams
Schematic Block
Diagram (SBD) depicts
hardware and software
components and their
interrelationships.
Verification,
Validation, and
Accreditation are
integral part of
simulation and
modeling process
Developed at
successively lower levels
as analysis proceeds to
define lower-level
functions within higherlevel requirements.
Useful for developing
Interface Control
Documents (ICD’s)
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Interface Control Document (ICD)
Functional Block Diagram
(example)
Earth Demonstrator Avionics;
GNC Functionality Only is Shown
ALHAT Avionics
HDA S/W
HRN S/W
Lunar-like
Terrain
Velocimeter
Velocimeter
S/W
Altimeter
Altimeter S/W
-- ICD’s define how the block within the SBD schematic are actually
“connected”
AFM
HDA S/W
Flash Lidar
ALHAT
Autonomous
Flight
Manager,
AFM
AFM
HRN S/W
--Interface control documents are a key element of systems engineering as
they define and control interface(s) of a system, and bound its requirements.
ALHAT
Navigation
S/W
Altimeter S/W
Velocimeter
S/W
Accel S/W
GPS
IMU –
(Flash)
Accel S/W
GPS –
(Flash)
National Aeronautics and Space Administration
Star Tracker
Emulator
S/W
Ascent,
Final 30m,
Abort **
Final 30m
S/W
Navigation
S/W
Abort
Guidance
S/W
GPS S/W
Altimeter,
Velocimeter
Gimbal
Pointing
Control S/W
Ascent
Guidance
S/W
GPS S/W
Gyro S/W
-- The purpose of the ICD is to communicate all possible inputs to and all
potential outputs from a system for some potential or actual user of the
system.
ALHAT
Guidance
S/W
Gyro S/W
IMU
-- An ICD should only describe the interface itself, and not the characteristics
of the systems which use it to connect -- The function and logic of those
systems should be described in their own design documents.
*Flash scanning S/W
included in HDA, HRN S/W
Vehicle
Control S/W
Flash Gimbal
Pointing
Control S/W*
**Abort mode requires
navigation input from the
vehicle GPS/IMU only and
does not require the ALHAT
system.
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Interface Control Document (2)
69
Interface Control Document (3)
-- Allows Disparate groups to work integrate sub-systems without complete
working knowledge of what is inside of the “black box
Example ICD
-- In this way, independent teams can develop the connecting systems which use
the interface specified, without regard to how other systems will react to data and
signals which are sent over the interface.
-- An adequately defined ICD will allow one team to test its implementation of the
interface by simulating the opposing side with a simple communications
simulator.
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Interface Control Document (4)
Power and Mass Budget Analysis
Example ICD
Weight and Power
growth are major
enemies of any spacecraft
Power and Mass Budget
Analyses Insure
spacecraft growth is
bounded and eventually
mandates comes in
“under weight” and
“overpowered”
Example
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Power and Mass Budget Analysis (2)
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Power and Mass Budget Analysis (3)
Example
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Failure Modes and Effects Analysis
(FMEA)
Failure Modes and Effects Analysis (2)
-- A failure modes and effects analysis (FMEA) is a procedure for analysis
of potential failure modes within a system for classification by severity or
determination of the effect of failures on the system.
The FMEA discipline was developed by US Military following WWII in 1949
(MIL-P-1629).
Originally used as a reliability evaluation technique to determine the effects of
system and equipment failures .
--FMEA provides an analytical approach, when dealing with potential
failure modes and their associated causes.
FMEA tool is used to evaluate - potential failure modes and their causes.
Failure mode: The manner by which
a failure is observed; it generally
describes the way the failure occurs.“
Prioritizes Potential Failures according to their Risk and drives actions to
eliminate or reduce their likelihood of occurrence.
Failure effect: Immediate
Provides a discipline/methodology for documenting this analysis for future use
and continuous process improvement.
consequences of a failure on operation,
function or functionality, or status of
some item
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By its self, an FMEA is NOT a problem solver. It is used in combination with
other problem solving tools.
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Failure Modes and Effects Analysis (3)
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Failure Modes and Effects Analysis (4)
-- Block diagram of the system gives an overview of the major components or
process steps and how they are related.
Example
FMEA Chart
For
Communications
System
-- FMEA worksheet relates failure modes to causes and severity
-- Recommended mitigating actions are often incorporated
Example FMEA Worksheet
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Failure Modes and Effects Analysis (5)
Eight Rules for Prototyping
1 Recognize That Ideas Are Cheap – Given the connected, Internet-savvy world in
which we live, ideas have become cheap and they will probably become cheaper
with time. The expense lies in testing and verifying what has economic value.
A great prototype is often the best way to start a dialogue with potential customers
and test your idea’s value.
2 Start with a Paper Design – You may be eager to start coding or designing the
electronics too quickly. Fight the urge. Writing code without real consideration for
several design factors leads to heartache and a lot of rework. Start with a simple paper
design. For a user interface or Web software prototype, a paper design is
efficient and effective for quickly working through the functionality.
You can get peers and, hopefully, customers to give feedback on where images,
text, buttons, graphs, menus, or pull-down selections are located. Paper designs
are inexpensive and more valuable than words.
FMEA Template for MS Excel
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National Aeronautics and Space Administration
Eight Rules for Prototyping (2)
5 Design for Reuse in the Final Product – The ideal situation is to design a
prototype you can produce and distribute in high volume. Not many prototyping
tools can deliver on this promise. Typically you give up performance for design
flexibility. Look for prototyping tools that make it possible for you to scale your
prototype from lab to market.
6 Avoid Focusing on Cost Too Early – For hardware designs, a potential time sink
and pitfall is getting caught up in endless cost optimization analysis during the
early stages of your prototype design. Cost is always important, but your goal with
a prototype is to be within striking distance of a profitable design. Initially, focus
on proving the value of your innovation, and design with modularity in mind.
While frustrating, your design may follow many paths that do not ultimately lead
to value. Focus on securing your first set of customers and then work on cost
optimization.
4 Anticipate for Multiple Options – Design your prototype with modularity in
mind. Great prototypes are often modular, which means you can quickly adapt
them to meet customers’ unforeseen needs. Customers ultimately decide how to
use your product, not you. Design in options for expansion, performance,
packaging, and lower cost.
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Eight Rules for Prototyping (3)
3 Put in Just Enough Work – Know your objectives and stick to them. There
are two good reasons to prototype: the first is to test the feasibility of a
hardware or software architecture, and the second is to create a demonstration
and gain customer feedback so you can price and put a value on your
innovation. Keep these objectives in mind and be careful not to fall in love with
the process. Prototyping is fun and innovators love to tinker, but you want to
invest just enough time and work to meet the objectives.
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Eight Rules for Prototyping (4)
Keys to Holding a Successful Meeting
7 Fight “Reversion to the Mean” – When prototyping, the tendency is to
develop something easy rather than develop something that has a “wow”
factor. Stay true to your vision and make sure your prototype captures the
original thought of your innovation.
• Meetings are essential to any team effort, be it designing a rocket System,
or launching a new cosmetic product
• Done properly, meetings can quickly disseminate information, solve
problems, create consensus, and get everyone “on the same page”
8 Ensure You Can Demonstrate Your Prototype – Your prototype should be
easy to demonstrate. With customers, venture capitalists (VCs), and potential
employees, you want to start strong and show the most amazing capabilities
first. Do not build up to a crescendo. Most people’s attention spans are limited
to less than 60 seconds. In presentations, whether they are for a new employee
or a VC, get to the demonstration as fast as possible. If the demonstration is
amazing, all else falls into place.
• Done improperly, meetings can bog down, cause dissention, delay, and
sometimes cripple a project.
• Every meeting must a specific purpose – before arranging a meeting one
need to think precisely about what it is that needs to be accomplished.
http://zone.ni.com/devzone/cda/pub/p/id/579?metc=mtnxdy
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Keys to Holding a Successful Meeting (2)
There may be a mixture of objectives and desired outcomes for a particular
meeting,; however, primary objectives should kept clearly in mind and
those should prioritiszed above others.
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Keys to Holding a Successful Meeting (3)
• Typical Meeting Purposes”
Brainstorming new ideas
Developing an idea or plan
Having a progress update
Technical interchange
Considering options and making a collective decision
Selling something to a potential buyer
Building a relationship with somebody
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1.
Invite the right people. Make sure these people attend.
2.
Start with a clear objective for the meeting. Particularly with routine
meetings, it's tempting to hold the meeting because it's “checking a
box”, but what are you really trying to accomplish? People don't
actually bond very much in unproductive meetings that lack clear
objectives.
3.
Set up a written agenda in advance. As you build the agenda, get real
about how long it will take to address each topic. As a guideline,
assume that if the goal is to make a decision, it will take four times
longer than if the goal is to simply provide a status report.
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Keys to Holding a Successful Meeting (4)
4.
5.
Keys to Holding a Successful Meeting (5)
Formally track problem-solving and decision-making discussions. If
everyone is in same room, use a flipchart or whiteboard, otherwise use
electronic recording media. Appoint someone to take notes at the
beginning of the meeting. Formally archive meeting notes in a data base
with access to participating team members.
Formal Tracking Tools:
a. Action Items – Requests for Action (RFA)
Who is assigned action?
When is action due?
Who are action’s “customers”
b. Information Items – Requests for Information (RFI)
Who provided the information and verification?
When is action due?
Who needs the information
Stephen A. Whitmore, USU MAE Dept.
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6.
Log and Track RFA,’s RFI’s .. Don’t let people “off the hook” require
that action forms be formally CLOSED.
7.
End each meeting with a “consensus” check. Is everyone clear on
assigned actions, and due dates. FORMALLY set a tentative time and
date for a follow-up meeting, and who needs to be in attendance at this
meeting. Log that follow up meeting time.
88
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Sample RFA Form
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Sample RFA Form (2)
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Review Item Disposition (RID) Process
Sample RFI Form
• Formally tracks and dispositions requested actions, insures items
do not “slip through the cracks”, no one is “let off of the hook” --Responsibility of program management to set up RID Process.
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Review Item Disposition (RID) Process (2)
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Example RID Form
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“Design Friday” Assignment
Example RID Form (2)
A) Down Load Langley LLRF trainer reports, Read TN D3828, TM X-57213, AIAA 68-254
B) Read Section II (Chapters 5-7) in LLRV Monograph
C) Identify essential subsystems of both LLRV and LLRF
D) Apply systems engineering tools here to describe why
design features were applied, contrast systems pro’s, con’s
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E) Prepare 20 slide-briefing detailing design features of
each platform … You! Decide What is relevant, which
teams will present
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“Design Friday” Assignment (2)
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“Design Friday” Assignment (3)
Langley: LLRF
Set up RID Process, Appoint Review Board Officers,
Design Appropriate RFA, RFI, RID Forms
Prepare Briefing to Team Detailing Process, Rules,
Responsibilities, and Procedures
DFRC: LLRV
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ESDM Senior
Design Project
National Aeronautics and
Space Administration
Space In Our Daily Lives
• Satellites are Used For:
Space … the Final Frontier!
–
–
–
–
–
–
–
–
–
Sellers: Chapters
1, 3.
FS-2006-08-022-JSC
Weather Forecasting
Relay of Television Broadcasting
Radio Traffic Reporting
Urban Planning
Research on the Internet
Credit Card Verification
Gas Station Point of Sale Terminals
Pagers, Phone Calls, Long Distance
Direct to Home Television
…. And it’s a lot more than “just a vacuum”
0
www.nasa.gov
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1
Interest of Entities
Emerging Applications
Military Space Activities
Civil Space Activities
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Communications
Missile Warning
Launch Operations
Meteorology & Geodesy
Navigation
Imaging & Signal Intelligence
Satellite Tracking
Anti-Satellite Weapons
Wide Area/Ocean Surveillance
Science
Launch Operations
Disaster Relief/Monitoring
Astrophysics
Human Space Flight
Meteorology
Microgravity Research
Environmental Modeling
• Remote Sensing of the
Environment
• Geographic Information
Systems
• Global Positioning System
(Real-time Tracking of
Vehicles and Equipment)
• Microgravity (R&D for
Biomedical,
Semiconductors, etc.)
Commercial Space Activities
•
•
•
•
Design, Development, and Operation of Launch Vehicles/Facilities,
Satellites/Spacecraft, Ground Stations, and Sensors
Telecomm. (including Personal Communications, Television/Cable, Radio, etc.)
Support Services (including standards/allocations, insurance, consulting, etc.)
Emerging Applications & Technologies (including remote sensing, geodesy,
navigation, microgravity, broadband, etc.)
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Remote Sensing Image Use
Oil and Gas
Disaster Management
Forestry
Government (All Levels)
Environ. Monitor
Civil Planning
Agriculture
Tax Mapping
Mining
Zoning
Transportation
Defense
Utilities
Near-Term GPS Markets
Aircraft Tracking and Control
Direction Assistance
Automobile Theft Prevention
Emergency Assistance
Electronic Maps
Other Emerging Applications
Space Power Stations
Waste Disposal
Tourism and Human Activities
Stephen A. Whitmore, USU MAE Dept.
XM Radio (Satellite
Radio Broadcasting)
3
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Eyes in Space
What is Space? (1)
• Various Definitions
1) Top of the atmosphere - 99.9% of air is below 50 km
2) Navigable air space - limit of dynamic lift - 40 km
3) Shuttle reentry over-flight (Canada) at 80 km without
permission
4) USAF Astronaut Wings awarded above 90 km
5) Soviet Delegates to UN called for 110 km
6) The lowest short term stable satellite orbit (130 - 160 km)
WHY DO WE CARE? Is the definition arbitrary?
Sept. 15, 2001: World Trace Center &
Pentagon Damage (spaceimage.com)
CA Dust Storms from
Mongolia & China
Cloud/Fog Evaluation in
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Afghanistan
Suspected Oil Spill
Determined to be Algae
Weather Determines
GPS or Laser Weapons
Global Comm
Stephen A. Whitmore, USU MAE Dept.
- IRIDIUM
5
4
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What is Space? (3)
What is Space? (2)
Did these guys go into space??
1)Aspects of the Space Environment
Gravity
Orbital Velocity
Atmosphere/Vacuum
Space Debris and Micro-meteoroids
Radiation
Charged Particles
Effect of Multiple Bodies
• Built by Burt Rutan (Scaled Composites®) with Paul Allen’s (Apple co founder)
Money in Mojave CA SS1 wrote history, when the first private suborbital
spaceflight was conducted on June 21, 2004 (with pilot Mike Melvill).
• SS1 won the X-Prize with flights on 29.09.2004 (Melville)
and a follow up flight on 04.10.2004. (Brian Binneie)
• Powered by a 16700 lbf thrust Hybrid Motor (SpaceDev)
6
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What is Space? (4)
100 km Flight apogee (62 miles)
Gravity
What is the difference? A Lot of DV!
What keeps a Satellite in Orbit? … Gravity!
m
FM m = G M
ir
2
r
Orbital
Sub-Orbital
m
y
F
M
ir
8
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r
x
“inverse square law”
Isaac Newton, (1642-1727)
Gravity (2)
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Orbital Velocity (1)
Gravitational Physics
Isaac Newton explains how to launch a Satellite
(cont'd)
You’ve seen this
before!
• Constant G appearing in Newton's
law of gravitation, known as the
universal gravitational constant .
• Numerical value of G
Nt-m2 = 3.325 0x-111lbf-ft2
G = 6.6720x-111
kg2
lbm2
10
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Orbital Velocity (2)
Orbital Velocity (3)
• Still ―in orbit‖
Around earth center
• But this time Orbit
Intersects surface
of the earth
Sub Orbital Launch
• Insufficient Orbital
Velocity
13
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Orbital Velocity (4)
Stephen A. Whitmore, USU MAE Dept.
Zero-Gravity vs Micro-gravity
Objects in Orbit are not at zero gravity
They are in freefall, moving just fast enough to
―miss‖ the earth as they fall towards it
Since the whole satellite is falling at the same rate,
objects on board do not exert force on each other
Hence the term: Micro-gravity
3.9860044
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Atmospheric Influence on Space (1)
Zero-Gravity vs Micro-gravity (2)
Compare Accelerations of Gravity
3.9860044 10
14
45o Lat @ Sea Level : g 
ISS Orbit : g 
Fgrav

m

r2
Fgrav
m


r
2

 6375 10 
3
m3
 9.8067 m /sec2
sec2
2
m
3.9860044 1014 m3

sec2
  6375  400  10 
3
2
 8.6866m /sec2
• Drag forces on satellites up to at least 600 km
– Height of atmosphere dependent on solar cycle
– Non-linear decrease in density
– Narrow beam tracking/pointing can ―lose‖ satellite
– Re-boost low orbits; circularize elliptical orbit
•
m
ISS orbit gravity ~ 89% of sea level
High in atmosphere, Oxygen does not re-associate into
molecules. The individual atoms are much more corrosive
than molecular oxygen, and can damage structures,
coatings and sensors
16
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Atmospheric Influence on Space? (3)
Atmospheric Influence on Space (2)
Atmospheric Density
What is a Stable orbit?
• Orbiting Object with altitude less than 600 km experiences
effects of Earths' outer atmosphere
• Resulting Drag is a non-conservative force, and removes
energy from the orbit
Drag Force
• Energy Loss causes orbit decay
600
Distribution of the Atmosphere?
400
h,
kilometers
200
0
10-15
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10-10
10-5

1
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Atmospheric Influence on Space? (4)
Atmospheric Influence on Space? (5)
• Vacuum environment will not support life, need for
Environmental life-support systems
• Out-gassing - under a vacuum, any gasses trapped in a
material will be expelled, and can contaminate adjacent
components with either corrosive effects or conductive paths.
• Cold Welding - perfectly smooth surfaces usually are
lubricated by a layer of air that keeps them separated.
In a vacuum, there is no separation, and the surfaces stick together.
• Heat Transfer - In a vacuum the only heat transfer
mechanisms are conduction and radiation - no convection.
Apollo A7LB “Moon Suit”
Shuttle/ISS
Extravehicular
Mobility Unit
(EMU)
Shuttle Launch-Entry
(partial Pressure) Suit
Shuttle Advanced Crew
Escape Suit (ACES)
(Full Pressure)
20
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Charged Particles
Radiation
• Come from three general sources
• The sun produces radiation in the visible, IR, X-ray, and
gamma ray spectrums
99% in Visible/IR/Near UV
• Thermal and Power Implications
• UV can degrade solar cells and coatings
• ªSolar pressure - small (1 lb/sq km) but impacts satellite
design
– The Sun
• Steady state - solar wind (1 Billion Kg/sec)
• Bursts - solar flares/CME (intensity fluctuations due
to Mag Field distortion from differential rotation
• electrons, protons, and some heavier ions
– Galactic Cosmic Rays - Similar to solar sourced
particles, but with more heavy ions.
– The Van Allen radiation belts - a collection of
particles trapped in the earth’s magnetic field
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6/13/2009
Van Allen Radiation Belts
The Van Allen Belts (cont’d)
• Two belts (sometimes considered as a single belt of
varying intensity) of radiation outside the earth's
atmosphere
• Particles trapped in the Earth’s Magnetic Fields
• Discovered by first U.S. earth satellite, Explorer 1
• Named for James A. Van Allen, American astrophysicist
who first predicted the belts and then interpreted the
findings of Explorer 1 satellite
• Phenomenon of the magnetosphere as opposed to the
atmosphere
• Protects Earth’s Surface and LEO from
Cosmic
radiation/Solar Flares
• Electrons and Protons, in two regions
Responsible for Aurora
in Polar Regions
•
•
•
•
•
•
Particles originate in periodic solar flares and are Carried
to earth by the solar wind
Inner Belt: ~ 2000 - 10,000 km
– High energy protons
Outer Belt: ~ 10,000 - 30,000 km
– Lower energy protons and electrons
Present Significant hazard for orbiting spacecraft
Implications: Higher LEO pushing into Inner Belt
Growing interest in MEO constellations (Iridium, GPS)
24
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South Atlantic Anomaly
(Off-set of Dipole Field)
Van Allen Belts (cont’d)
A part of a Van Allen belt dips into the upper
region of the atmosphere over the southern Atlantic
Ocean to form the South Atlantic Anomaly
Electron belt
Proton belt
Must mean something … "H" in front of the "Allen" and to
remove one "l" to make "Van Halen,"
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ISS Regularly Crosses Through South Atlantic Anomaly
And Requires Radiation Shielding
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Space Environment Induced Anomalies (2)
Space Environment Induced Anomalies
(cont’d)
• Single Event Upset --Single high energy particle causes
• Spacecraft Charging
―bit-flip‖ in computer memory altering logic or data…
Potentially very hazardous
– Potential arcing/discharge - both on surface and deep
within electronics
• Sputtering
– ―Sandblasted‖ coatings and sensors
• Single Event Phenomenon
– Upset, Latch-up, Burnout
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Solar Phenomena (sunspots and flares)
Stephen A. Whitmore, USU MAE Dept.
Solar Cycle (sunspots)
•11 Year repeating cycle -- 4 year rise, 7 year fall
•Solar Minimum - Sunspots form @ 40 deg latitude
•Solar Maximum - Sunspots form @ Equator
•Solar Magnetic Poles reverse each cycle
Potentially deadly
To spacecraft and
astronauts outside of
Van Allen belts
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Solar Phenomena (2)
Solar Phenomena (4)
• Exotic environment of space beyond Earth’s protective atmospheric is
highly variable and far from benign.
An astronaut caught outside when the storm hit would've
gotten sick … symptoms of radiation sickness would appear:
vomiting, fatigue, low blood counts.
• A host of inter-connected physical processes, strongly influenced by solar
variability, affect health and safety of all space assets including human
travelers
• As example consider violent solar eruptions of late October 2003. 59% of
reporting spacecraft and 18% of onboard instrument groups were affected by
these storms.
These symptoms might persist for days, a potentially dangerous
Scenario that far from home!
• Electronic upsets, science data noise, solar array degradation, changes to
orbit parameters, high levels of accumulated radiation, ozone depletion, and
proton-induced heating were observed.
Apollo 16 Returned to earth back in 1972 just in time to escape the
Legendary August 1972 Solar storm that could have been fatal to
the crew!
• When the storms arrived at Mars the MARIE instrument on board the
Mars Odyssey failed completely.
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Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Finish
Questions??
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National
NationalAeronautics
Aeronautics and
and Space
SpaceAdministration
Administration
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ESDM Senior
Design Project
National Aeronautics and
Space Administration
Geophysical Comparisons
The Lunar and Martian Environments!
NASA Images
NASA Images
Sellers:
Appendix B, C +
Material
From Auburn University
Lunar Excavator
Design Course, Courtesy
of David Beale.
Mean Volumetric
Radius: 6371 km
Mass: 5.9736 x 1024 kg
Surface Atmospheric
Pressure: 101325 pa
Stephen A. Whitmore, USU MAE Dept.
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Surface Gravity Comparisons
kg 2
g
Fgrav
m

sec2
sec 2
GM

 2
r2
r
3.9860044  105 km3
sec 2
63712 km2
4.28327  10
Earth :
Mars :  g mean 
Moon :
sec 2
4.902794  10
 1.0014 g ' s
 3.72824

m
sec 2
1
g 's
2.630
3
m3
sec 2
National Aeronautics and Space Administration
m
sec 2
km3
3389.52 km2
1737.12 km2
 9.8203
4
 1.624478
m
sec 2

Thus the need
for gravityoffset in our
landing
simulator
1
g 's
6.036
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(Hard Vacuum)
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Earth Mean Orbital Elements (Heliocentric, JD2000)
6.6727005  1011 Nt  m2  0.07349  1014 kg  4.902794  103 m3
kg 2
Mean Volumetric
Radius: 1737.1 km
Mass: 0.07349 x 1024 kg
Surface Atmospheric
Pressure: 3 x 10-10 pa
Ephemeris Comparisons
6.6727005  1011 Nt  m2 NASA
5.9735
 10 24 kg  3.9860044  105 km3
Images
Earth :
kg 2
sec 2
11
Mars :    6.6727005  10 Nt  m2  0.64185  1024 kg  4.28327  104 km3
Moon :
(39 km earth altitude)
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National Aeronautics and Space Administration
Mean Volumetric
Radius: 3389.5 km
Mass: 0.64185 x 1024 kg
Surface Atmospheric
Pressure: 636 pa
Semi-major axis (AU)
1.00000011
Orbital eccentricity
0.01671022
Orbital inclination (deg)
0.00005
Longitude of ascending node (deg)
-11.26064
Longitude of perihelion (deg)
102.94719
Mean Longitude (deg)
100.46435
Solar Day
23 hrs, 56 min, 4.1 seconds
Mars Mean Orbital Elements (Heliocentric, JD2000)
Semi-major axis (AU)
1.52366231
Orbital eccentricity
0.09341233
Orbital inclination (deg)
1.85061
Longitude of ascending node (deg)
49.57854
Longitude of perihelion (deg)
336.04084
Mean Longitude (deg)
355.45332
Solar Day
24 hrs, 41 min, 58.8 seconds
Moon Mean Orbital Elements (Geocentric, JD2000)
Semi-major axis (106km)
0.3844
Orbital eccentricity
0.05489
Equatorial Orbital inclination (deg)
18.28-28.58
Mean Orbit Obliquity to Ecliptic (deg.)
5.9
Solar Day
29 days, 6 hrs, 21 min
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The Lunar Environment
The Lunar Environment (2)
• Lunar Gravity Field
• Hostile Environment, “Very Long Way” from Home
-- Major characteristic of the Moon's gravitational field is the presence of mascons,
which are large positive gravitational anomalies associated with some of the giant
impact basins.
• Environmental challenges include:
– No liquid water (possible water-ice at the lunar poles)
– Lethal radiation that degrades materials and limits human activities outside
protected shelters, potential for large solar flares
– Fine, invasive and abrasive lunar dust
-- These anomalies greatly influence the orbit of spacecraft about the Moon, and an
accurate gravitational model is necessary in the planning of both manned and
unmanned missions.
• Gravitation acceleration on moon’s surface is 1.622 m/sec2, or 1/6 ―g‖.
• Hard Vacuum (< 10-12 mBars).
– Without an atmosphere the sun’s radiation is more intense than on earth, and
particularly harmful types or radiation reach the surface.
– Convective heat transfer is not possible
– Micrometeoroids reach the surface, often, and with high kinetic energy
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The Lunar Environment (3)
Stephen A. Whitmore, USU MAE Dept.
The Lunar Environment (4)
• Lunar Magnetic Field
• Equatorial Lunar day is 29.5 Civil Earth days
-- Moon has an external magnetic field of the order of one to a hundred nanotesla—less than one hundredth that of the Earth.
• At Poles, Day/Night cycle is ~ 6 months
-- Weak magnetosphere does little to protect against external radiation phenomena
on lunar surface
• Moon’s Rotation is
“gravitational-locked” to
the earth.
• Opposite side of the moon
(misnomer “darkside”) is
never visible from the earth
-- Moon does not have a dipolar magnetic field (compass will not reliably work)
and the varying magnetization that is present is almost entirely crustal in origin.
Earth Magnetosphere
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Lunar Magnetic Field
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The Lunar Environment (6)
The Lunar Environment (5)
Both Sun and Earth have
Effects on Lunar Orbit
Ambient Lunar Surface Temperatures
Solar Perturbations cause
Lunar orbit to vary from 18.28
To 28.58 deg. Inclination with
respect to Earth’s equator
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Solar Phenomena and
the Lunar Surface (2)
Solar Phenomena and
the Lunar Surface
An astronaut caught outside when the storm hit would've
gotten sick … symptoms of radiation sickness would appear:
vomiting, fatigue, low blood counts.
January 27, 2005 -- The biggest solar proton storm in
15 years erupts…. what it might have done to someone on the Moon.
Moon is totally exposed to solar flares
Space Flight Center.
These symptoms might persist for days, a potentially dangerous
Scenario that far from home!
It has no atmosphere or magnetic field to
deflect radiation.
Apollo 16 Returned to earth back in 1972 just in time to escape the
Legendary August 1972 Solar storm that could have been fatal to
the crew!
Protons rushing at the Moon simply hit the
ground--or whoever might be walking
around outside.
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Other Lunar Radiation Causes
Radiation Effects and Mitigation
•
Solar flares are relatively infrequent, only occurring several times a year, but the high energy
particles that are emitted, can linger for several days. They have the potential to damage the
habitat’s surface and electronic components. Again, care must be taken when choosing
structural materials and consideration given to component placement within the habitat.
•
Galactic cosmic rays are even more infrequent than solar flares, but have extremely high
energies. Important electrical devices would need to be shielded to prevent system failure.
•
The effect of the radiation on humans is an important issue when considering the safety of the
colonists. The best cure for radiation is prevention.
•
Radiation can kill in four ways:
The thin lunar atmosphere also creates radiation and micrometeorite
impact concerns for equipment deployed on the surface.
Three radiation sources affect the Moon:
i) galactic cosmic rays, ii) solar flare particles, and
iii) solar wind particles
–
–
–
–
Direct brain hemorrhage and brain cell destruction
Diarrhoea-induced dehydration
Damage to the immune system
Long term cancer
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The Lunar Surface
Radiation Effects and Mitigation (2)
•
Most Effected: Astronauts (even in protective suits), solar cells (photovoltaic
semiconductors), organic materials, polymers, integrated circuits and electronics.
•
Mitigation Methods:
–
–
–
–
Shielding (the thickness needed depends on the radiation event and the shielding materials)
Software routine can reroute electrical flowpaths around the damaged circuit elements.
Coverslides have been used for solar cells to absorb and protect against radiation.
Humans and equipment are effectively shielded by at least 2m of regolith
•
Design of shielding for equipment should involve a trade study and risk analysis, comparing
all the alternative shielding methods, their cost and the risks involved.
•
The radiation dose is the amount of radiation deposited, measured in Rad. The damage
threshold depends on the material. Indium arsenide solar cells are more resistant than gallium
arsenide solar cells, which are more resistant that silicon solar cells.
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• Surface Regolith – Fine Abrasive Surface Dust, gets
“onto and into everything”
Neil Armstrong:
―the surface is fine and powdery. I can pick it up loosely with my toes. It does
adhere in fine layers like powdered charcoal to the sole and sides of my boots.
I only go in a small fraction of an inch. Maybe an eighth of an inch, but I can see
the footprints on my boots and the treads in the sandy particles‖
Alan Bean:
―After lunar liftoff . . . a great quantity of dust floated free within the cabin.
This dust made breathing without the helmet difficult, and enough particles were
present in the cabin atmosphere to affect our vision. The use of a whisk broom
prior to ingress would probably not be satisfactory in solving the dust problem,
because the dust tends to rub deeper into the garment rather than to brush off‖
Nasty Stuff!
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The Lunar Surface (2)
The Lunar Surface (3)
• Surface Regolith – Fine Abrasive Surface Dust, gets
• Definitions
“onto and into everything”
Neil Armstrong:
―the surface is fine and powdery. I can pick it up loosely with my toes. It does
adhere in fine layers like powdered charcoal to the sole and sides of my boots.
I only go in a small fraction of an inch. Maybe an eighth of an inch, but I can see
the footprints on my boots and the treads in the sandy particles‖
Alan Bean:
―After lunar liftoff . . . a great quantity of dust floated free within the cabin.
This dust made breathing without the helmet difficult, and enough particles were
present in the cabin atmosphere to affect our vision. The use of a whisk broom
prior to ingress would probably not be satisfactory in solving the dust problem,
because the dust tends to rub deeper into the garment rather than to brush off‖
Nasty Stuff!
– Lunar regolith … fragmented surface rock material.
– Lunar soil … regolith excluding rocks larger than 1 cm in size.
– Lunar dust … defined as having particle sizes less the 20 μm with a bulk density of 1.5
g/cm3.
• Lunar soils are far more abrasive than earth soils.
• Surface made up significant amount of sharp and angular particles..
• Four types of particles:
– mineral fragments (minerals possess a characteristic chemical composition, a
highly ordered atomic structure and specific physical properties),
– glasses (without distinct grains and without a highly ordered atomic structure,
that are often sharp and are the major cause the abrasiveness),
– lithic fragments (pieces of broken lunar rock which also contains minerals) and
– agglutinates (which are small (<1 mm) lunar regolith particles bonded together
with glass).
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The Lunar Surface (5)
The Lunar Surface (4)
Some of Lunar Soil’s Bad habits!
Surface Soil Properties
•
Chemical Composition: 45% oxygen, 21% silicon, 13% aluminum, 10% calcium,
5.5% magnesium, 6% iron with less than 1% titanium, sodium and sulfur.
•
Other volatile elements called solar-wind-implanted element - hydrogen,, helium,
with some carbon and nitrogen. The concentrations are believed to be quite low
(less than 100 micrograms/gram)
•
The dark craters at the poles do have significantly higher concentration of
hydrogen, possibly as water-ice.
•
Roughly once every Lunar orbit, the Moon passes through Earth's magnetotail for
approximately 6 days, starting 3 days before lunar noon (full moon) and ending 3
days after.
•
This phenomenon leads to surface soil static charging
• Electrostatically Charged - sticks to anything not grounded
(space-suits, tools, equipment, polished reflectors, solar cells
and telescope lenses) Easily disturbed by machinery or
vehicles. Erodes bearings, gears, and other mechanical
mechanisms not properly sealed, reduces radiator efficiency,
damages sensitive equipment.
• Free Radicals?? Regolith can contain many free radicals,
which are atoms or molecules with unpaired electrons which
make them highly reactive – very bad for long term human
exposure.
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Lunar Surface Soil Simulants
Lunar Surface Soil Simulants (2)
• Less than 300 kilograms of lunar soil was brought to the earth,
so it is not generally available ―generic‖ use.
• Simulants were synthesized to test components like surface
excavators, airlocks, structures, and space suits,
• The first simulant for general use was JSC-1.
• http://ares.jsc.nasa.gov/HumanExplore/Exploration/EXLibrary/
DOCS/EIC050.HTML
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Properties of JSC-1
Properties of JSC-1 (2)
What Does JSC-1 Simulate?
What Does JSC-1 Not Simulate?
• Chemistry similar to some Apollo soils
• Spectral properties
• Lunar regolith <1mm particles (mineral crystals,
• Elemental iron and magnetic properties
lithic fragments, and glass)
• Solar wind loading and trace elements
• Grain size distribution within envelope of
• Morphology and shapes of agglutinates
measured lunar soils
• Other specialized lunar regolith properties
• Best fit to a submature lunar mare soil
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Lunar Environment: General References
Environmental Challenges
• General references with detailed information
• Environmental challenges for astronauts and equipment
include:
–
–
–
–
No free water (except for the possibility of water-ice at the lunar poles)
No atmosphere and pressures of a hard vacuum (<10-6 torr)
Severe temperature fluctuations from day to night
Lethal radiation that degrades materials and limits human activities
outside protected shelters
– Fine, invasive and abrasive lunar dust
– Micrometeoroid activity
– There is some seismic activity due to moonquakes (the largest ever
recorded was an earth equivalent magnitude of 4)
– The Lunar Sourcebook (Heiken, Vaniman, & French, 1991) is the best
source for a detailed presentation of the lunar environment.
– Lunar and Planetary Institute (LPI, 2008), which has Apollo Mission
summaries, information on lunar samples and Apollo documents
describing the Apollo mission equipment, including Lunar Roving
Vehicles (LRVs) and landing modules. There are many photographs,
maps, reports and information about lunar samples.
– The Moon (Schrunk, 2008) and The Lunar Base Handbook (Eckart,
1999)
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The Martian Environment
Stephen A. Whitmore, USU MAE Dept.
The Martian Environment (2)
The “red planet” is so named because of its surface color , which is
strikingly red. -- Simply put, Mars has rusted—iron oxides are
responsible for its orange hue.
NASA Images
Mars has seasons because the tilt of its axis relative to the solar
ecliptic plane. (25.19o for Mars, compared with 23.45o for Earth.)
Mars rotates on its axis once every 24 hours and 40 minutes, so a
Martian day (Sol) is just a little longer than one of ours, and its year is
687 (Earth) days long.
NASA Images
Martian atmosphere is less than 1% as dense as Earth's, and is made
mostly of carbon dioxide, with trace amounts of nitrogen and argon.
Atmospheric CO2is the major source of Mars's polar ice caps.
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At the Martian surface the atmospheric pressure is equivalent to 38-40
km altitude on earth (the edge of space)
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The Martian Environment (3)
The Martian Environment (4)
Elsewhere are long, eroded channels telling us that at some time in the
past water flowed freely on the Martian surface.
Mars's thin atmosphere holds very little heat—a blazing summer day on
Mars might get up to the freezing point of water 32°F (0°C), but at night
Temperatures plummet well back below 0°F (-18°C).
There is abundant evidence of river systems draining the southern highlands,
and the drainage is mainly toward the northern plains (or lowlands) across the
global escarpment.
At the poles, temperatures drop well below -100°F (-73°C), sufficiently
cold for the carbon dioxide in the atmosphere to freeze.
Although no life has been found on Mars (to date), the planet's surface does
have very Earth-like features.
NASA Images
Olympus Mons
Valles Marinaris
There are enormous volcanoes, the
largest of which, Olympus Mons, is
almost the size of the entire state of
Arizona.
USGS Photos
NASA Images
http://science.jrank.org/pages/4143/Mars-Physical-properties-Mars.html">Mars - Physical Properties Of Mars
National Aeronautics and Space Administration
Valles Marinaris, cuts across this escarpment, showing where water drained
from south to north during a period in Mars history when abundant water was
present.
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The Martian Environment (5)
Mars Weather
Solar energy and winds, collisions with asteroids and comets, and changing
magnetic fields have all altered the environment of Mars, a planet that may
have been able to support life during its history
The atmosphere of Mars is coldest at high altitudes,
from about 40 to 78 miles (65 to 125 kilometers)
above the surface.
At those altitudes, typical temperatures are below 200 degrees F (-130 degrees C).
Unlike the Moon, Mars has an incredibly complex surface environment
with widely variable weather conditions, chiefly dust storms that will
challenge every piece of gear, and disrupt solar collection so badly that
Power collection becomes a significant issue.
The temperature increases toward the surface,
where daytime temperatures of -20 to -40 degrees F
(-30 to -40 degrees C) are typical. In the lowest few
miles or kilometers of the atmosphere, the
temperature varies widely during the day.
The near vacuum environment will require that human explorers would
use full pressure suits similar to the Space Shuttle ACES suit.
Unlike Earth's core, which is partially molten, the core of Mars probably is solid, and
Mars does not have a significant magnetic field. … see earlier radiation discussion
A sunset on Mars creates a glow due to the presence of tiny
dust particles in the atmosphere. Mars Pathfinder, Image
credit: NASA/JPL
Atmospheric temperatures can be warmer than
normal when the atmosphere contains much dust.
The dust absorbs sunlight and then transfers much
of the resulting heat to the atmospheric gases.
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Mars Weather (2)
Mars Weather (3)
MARS GLOBAL REFERENCE ATMOSPHERIC MODEL
(Mars-GRAM 2005), 1976 US Standard Atmosphere
http://www.nasa.gov/worldbook/mars_worldbook.html
In Martian atmosphere, clouds made up of particles of
frozen CO2 and particles of water ice can form at high
altitudes.
The Martian atmosphere, like Earth, has a general
circulation, a wind pattern that occurs over the entire
planet.
Global-scale winds occur on Mars as a result of
atmospheric advection.
The sun heats the atmosphere more at low latitudes than at
high latitudes. At low latitudes, the warm air rises, and
cooler air flows in along the surface to take its place.
Dust Storm in Valles Marinaris , Image credit: NASA/JPL
The warm air then travels toward the cooler regions at
higher latitudes. At the higher latitudes, the cooler air
sinks, then travels toward the equator.
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Mars Geology
Mars Weather (4)
http://www.nasa.gov/worldbook/mars_worldbook.html
Surface winds on Mars are mostly gentle, with typical
speeds of about 10 km/hr.
• Mars morphology probably has three main layers, as Earth has: (1) a crust of rock, (2) a mantle of
denser rock beneath the crust, and (3) a core made mostly of iron.
Wind gusts as high as 90 km/hr have been observed.
Because of low surface density, dynamic pressures exerted
by these winds are significantly lower than on earth.
Large dust storms begin as wind lifts dust into atmosphere
and dust absorbs sunlight, warming the air around it.
As warmed air rises, more winds occur, lifting still more
dust. As a result, storm becomes stronger.
At larger scales, dust storms can blanket areas from more
than 2000 kilometers across even the entire planet surface
(1971, 2001)
Comparison of Mars and Earth Dust Storms
NASA Images
Storms present a significant hazard to landing spacecraft.
• The average thickness of the Martian crust is about 50 kilometers and is mostly composed of a
volcanic basalt. Basalt is also common in the crusts of Earth and the moon
• Some Martian crustal rocks, particularly in the northern hemisphere, may be a form of andesite.
Andesite is also a volcanic rock found on Earth, but it contains more silica than basalt does.
• Researchers commonly have four main sources of information on the interior of Mars:
(1) calculations involving the planet's mass, density, gravity, and rotational properties;
(2) knowledge of other planets;
(3) analysis of Martian meteorites that fall to Earth; and
(4) data gathered by space probes.
Lunar and Planetary Science XXVIII, 1797.pdf, JSC MARS-1: MARTIAN REGOLITH SIMULANT, Carlton C. Allen, Richard V. Morris,
David J. Lindstrom, Marilyn M. Lindstrom, and John P. Lockwood, Lockheed Martin Engineering & Sciences, Houston, TX 77058 NASA Johnson
Space Center, Houston, T X 77058 3, Hawaiian Volcano Observatory, Hawaii Volcanoes NP, HI 96718
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Mars Soil Simulant
Mars Soil Simulant (2)
JSC Mars-1 Compared to Martian Soil / Rock
•“JSC Mars-1”is the < 1 mm size fraction of altered
volcanic ash from a Hawaiian cinder cone.
JSC Mars-1 Soil Simulant
• Material was collected from Pu'u Nene cinder cone,
located in the saddle between Mauna Loa and Mauna
Kea volcanoes on the Island of Hawaii.
(2)
• Palagonitic tephra from this cone has been
repeatedly cited as a close spectral analog to the
bright regions of Mars.
• The simulant closely matches the reflectance spectrum
and approximates the mineralogy, chemical
composition, grain size, density, porosity and magnetic
properties of Martian soil.
NASA Images
Lunar and Planetary Science XXVIII, 1797.pdf, JSC MARS-1: MARTIAN REGOLITH SIMULANT, Carlton C. Allen, Richard V. Morris,
David J. Lindstrom, Marilyn M. Lindstrom, and John P. Lockwood, Lockheed Martin Engineering & Sciences, Houston, TX 77058 NASA Johnson
Space Center, Houston, T X 77058 3, Hawaiian Volcano Observatory, Hawaii Volcanoes NP, HI 96718
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Lunar and Planetary Science XXVIII, 1797.pdf, JSC MARS-1: MARTIAN REGOLITH SIMULANT, Carlton C. Allen, Richard V. Morris,
David J. Lindstrom, Marilyn M. Lindstrom, and John P. Lockwood, Lockheed Martin Engineering & Sciences, Houston, TX 77058 NASA Johnson
Volcano Observatory, Hawaii Volcanoes NP, HI 96718
Stephen A. Whitmore, USU MAE Dept.
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Space
Center, Houston,
T X 77058 3, Hawaiian
National
Aeronautics
and Space Administration
“Design Friday” ….
Homework (2)
• Read Pages 1, 27, 71-101 in Sellers …. Answer
Sellers, Section 3.2 Homework Questions, Page
99,100
i) MATLABTM Tutorial
Demonstration
• Calculate and compare the orbital velocities for
a 200km orbital altitude for Earth, Mars, and the
Moon
ii) LLRV/LLTV Student
Presentation (from previous
week’s assignment)
• What will the orbital period of each be?
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Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Finish
Questions??
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National
NationalAeronautics
Aeronautics and
and Space
SpaceAdministration
Administration
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National Aeronautics and Space Administration
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ESDM
Senior title style
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National Aeronautics and
Space Administration
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Rockets:
Design Project
This IS! Rocket Science
Sellers: Chapter 2
Robert Goddard
With his Original
Rocket system
Delta II Rocket Launch Platform
for NASA MARS Phoenix Lander
Delta IV … biggest commercial Rocket
system currently in US arsenal
Material from Rockets into Space by Frank H. Winter, ISBN 0-674-77660-7
www.nasa.gov
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1
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to edit
Master
title style
Earliest
Rockets
as Weapons
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
2
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to edit Master
titleFlight
style
First Principle
of Rocket
• “For every action there is an equal and opposite
reaction.” Isaac Newton, 1687, following
Archytas of Tarentum, 360 BC, and Hero of
Alexandria, circa 50 AD.
• Chinese development, Sung dynasty (A.D. 9601279)
– Primarily psychological
• William Congreve, England, 1804
– thus “the rockets red glare” during the war of
1812.
– 1.5 mile range, very poor accuracy.
• V2 in WWII
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National Aeronautics and Space Administration
• “Rockets move because the flame pushes against
the surrounding air.” Edme Mariotte, 1717
• Which one is correct?
3
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1
The
Reaction-Propelled
Spaceship
Click
to edit Master title
style of
Hermann Ganswindt (1890)
toAmigos
edit Master
title styleTheory
TheClick
Three
of Spaceflight
• The fuel for his spaceship consisted of heavy steel
cartridges with dynamite charges. They were to
be fed machine gun style into a reaction chamber
where they would fire and be dropped away.
•
•
•
•
• “Shock absorbers protected the travelers”
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
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Three Amigos
6
1857 - 1935
• Deaf Russian School Teacher - fascinated with space
flight, started by writing Science Fiction Novels
• Discovered that practical space flight depended on liquid
fuel rockets in the 1890’s, and developed the fundamental
Rocket equation in 1897.
• Calculated escape velocity, minimum orbital velocity,
benefit of equatorial launch, and benefit of multi-stage
rockets
• Excellent theory, Not well published, not as important as
he could have been.
• Famous for development of “Rocket Equation”
•Oberth
•Tsiolkovsky
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
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Konstantin
Tsiolkovsky
•Goddard
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Konstantin Tsiolkovsky
Hermann Oberth
Robert Goddard
Independent and parallel development of Rocket
theory
7
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2
Click Robert
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Goddard
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Master
title style
Goddard
his Rocket
1882 - 1945
• Also a loner, developed rocket theory in 1909-1910,
• Forte was as an experimenter, actually building and testing
liquid fuel rockets (first flight in 1926.)
• In a report to his sponsors (Smithsonian Institute) in 1920,
he described a rocket trip to the moon. This subjected him
to ridicule since the common belief was still that a rocket
needed air to push against.
• Goddard ended with 214 patents covering details of rocket
design
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Hermann
Oberth
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Master Moon
title style
Valier-Oberth
Gun
1894 - 2006
• His 1923 book: Die Rakete zu den Planetenraumen (The
Rocket into Planetary Space) covered the entire spectrum
of manned and unmanned rocket flight.
In the 1920's members of the German VfR
(Society for Space Travel)
amused themselves by redesigning
Verne's moon gun. In 1926
rocket pioneers Max Valier and
Hermann Oberth designed a
gun that would rectify Verne's technical
mistakes and be actually
capable of firing a projectile to the moon.
• Because it was published and widely read, he had more
influence on the growth of rocket concepts then either of
the others. His book spawned several rocket societies in
Germany, significantly the German Rocket society, out of
which the German army recruited Werner Von Braun in
1932 and started the project which produced the V2.
“Claimed Extra-terrestrials Gave him the secrets of rocketry”
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3
• Click
V-2 Rocket
Operational
to editFirst
Master
title styleSystem
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The V2
• Challenge was to deliver a one ton warhead, 180 nm range.
• Final design: 2300 lb warhead, 190 nm range. 47 ft long,
5.4 ft diameter, 28,229 lb takeoff weight. 59,500 lb thrust
for 68 seconds.
• 6400 weapon launches
• The Americans got Von Braun and 117 other scientists,
and about 100 rockets. The Soviets got the facilities and
about the same number of rockets.
• 60 plus V2’s and V2 mods were launched in the late 40’s
in US. All were sub-orbital, highest altitude was 244 miles
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Sounding
Rockets
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National Aeronautics and Space Administration
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First
Launchers
Russia (Soviet Union)
• Sputnik - SS-6/R7
• Both the Soviets and the US built sub-orbital
rockets in the late 1940’s, 50’s and 60’s
– WAC-Corporal - 1500 lbs thrust
– Aerobee - 2600 lbs thrust and up
• Viking -developed by NRL to replace the V-2’s 20,600 lbs thrust
• Redstone Missile … suborbital
•217,000 lbs thrust •2900 lbs to LEO
nuke weapons delivery system
R7 Semiorka Rocket
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4
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First to
Satellite
Launchers
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First to
Satellite
Launchers
(cont’d)
(cont’d)
USA
• Explorer I - Jupiter C - 75000 lbs thrust - 20 lbs to
LEO
Comparison of R-7 and Jupiter C
• Russians started out with a
BIG lead
• Sergi Korolev
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Stephen A. Whitmore, USU MAE Dept.
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Manned
Space
flight
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Master
title(cont’d)
style
Manned
Flight
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• Yuri Gagarin, April 12, 1961 …
• Alan Shepard, Mercury 3 … May 5, 1961
• Modified R-7 Launcher
Redstone missile sub-orbital …
• Liftoff Thrust: 80,000 lbf
• Payload to LEO : 0
• Liftoff Thrust: 870,000 lbf
• USA is still Way behind
• Payload to LEO: 10,000 lbm
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5
Manned
Space
flight
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style
Manned
Space
flight
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Master
title(cont’d)
style
• John Glenn, Mercury 6 … Feb. 20, 1962
• Gemini 3 - Titan II
Launch vehicle, Atlas-D
• Liftoff Thrust: 360,000 lbf
• Liftoff Thrust: 430,000 lbf
• Payload to LEO : 3100 lbm
• Payload to LEO : 7000 lbm
• USA starting to catch up
• Still behind R-7
• First Flight March 23 1965
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Manned
Space
flight (cont’d)
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to edit
Master
title style
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Manned
Space
flight
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to edit
Master
title(cont’d)
style
• Apollo Saturn 1-B
• Apollo Saturn V
• Liftoff Thrust: 1.64 M lbf
• Liftoff Thrust: 7.7 M lbf
• Payload to LEO : 41,000 lbm
• Payload to LEO : 260,000 lbm
• Third Most Powerful
Rocket ever flown
• Lunar payload capable
• Most Powerful
Rocket ever flown
• First Flight October 11, 1968
• First Flight December 21, 1968
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National Aeronautics and Space Administration
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6
Modern Operational USA Launch
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title style
Systems
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Shuttle
• First Flight April 12, 1981
U.S. LAUNCH
• Liftoff Thrust: 6.7 M lbf
• Payload to LEO : 54,000 lbm
Systems
• Only man rated US Launch System
• Aged fleet of orbiters due for
retirement by 2010
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Orbital
Pegasus
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to editSciences
Master title
style
Stephen A. Whitmore, USU MAE Dept.
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Orbital Sciences Taurus
• 3-Stage Winged, SRM Booster for Small
Payload Class
• First Commercial Air-Launched System
• Ground-Launched Taurus Is Comprised of a
Standard Pegasus (w/o wings) With a Castor
120 SRM First Stage
• Developed to Launch from Austere Launch
Sites
 Started Service in 1990
 Lifts 975 lbs. To LEO, 730 lbs. to Polar
• Air-Launched From L-1011
Permits Launches from Different Facilities
 Set Up in Ten Days; Mobile Launch
Control/Support
• Small Vehicle Payload Class
 Launch Sites - VAFB, CCAFS, Wallops,
Kwajalein, Grando AFB (Canary Is.)
 Started Service in 1994
 Lifts 2,360 lbs. to Polar
 Launch Site - VAFB
• 31 Launches to Date, 12 Commercial
• All Stage/Payload Integration at VAFB
• 3 Commercial Launches to Date
 Irrespective of Launch Site
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 ROCSAT-2 Planned for 2003
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7
Minotaur IV-V (1)
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Minotaur IV-V (2)
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Heavy Lift OSC Launch Vehicle Configuration
Uses legacy Government Furnished Equipment (GFE) for
Stages 1-3
• First Flight
Scheduled for
Minotaur IV in
late 2009
Peacekeeper 1st stage (Motor TU-903)
Peacekeeper 2nd stage (Motor SR-119)
Peacekeeper 3nd stage (Motor SR-120)
4th Stage – Star 48B long
5th Stage – Star 37FM (spin stabilized)
• USAF payload
-- Space Based
Surveillance
(SSBS) mission.
or Star 37 FMV (3 axis)
• Star 37 FM motor designed for GEO Final Orbit kick
• ATK Star 48V Replaces (Minotaur IV)
Orion -38 4th Stage for Hi-Energy
Trajectory
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Lockheed
Martin title
Athena
Vehicle
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to edit Master
style
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Delta II/III
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title style
• Athena I Uses One Castor 120; Athena II
Uses Two Castor 120’s. Uses Orbus 21 As a
2nd or 3rd Stage and a Liquid Propelled Orbit
Assist Module
• Renamed From Lockheed Launch Vehicle to
Athena in 1997 (After Merger of Lockheed
and Martin Marietta)
• Small Launch Vehicle Payload Class
• Based on Thor Vehicle Technology
Developed in the 1950’s
 Com’l Launch - 1989
• LOX-Kerosene First Stage, Nitrogen
Tetroxide-Aerozine Second Stage, and
Optional SRM Strap-ons
• Delta II - Medium Class
Delta
III - Intermediate Class
Lifts 11,300 lbs. to LEO, 8,590 lbs.
to Polar; III – 18,280 lbs. to LEO
Launch Sites – II – VAFB, CCAFS
III – CCAFS
• Will Be Replaced by Delta IV
 Started Service in 1993
 Total of 7 Com’l Launches - 4 From VAFB, 2
From CCAFS, 1 From Kodiak
 Lifts 1,750 Lbs. To LEO, 1,200 Lbs. To
Polar; II – 4,350 Lbs. To LEO; 3,470 Lbs. To
Polar
• Launch Sites - VAFB, CCAFS, & Kodiak
• 1 Vehicle in Inventory, Launch Date: TBD
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National Aeronautics and Space Administration
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8
Atlas
II/III
ClickLockheed/Martin
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style
Click EELV
to editDevelopment
Master title style
• National Space Transportation Policy, Signed by President
Clinton on August 5, 1994
– NASA Responsible for Reusable Launch Vehicle (RLV)
Development
– DoD Responsible for Expendable Launch Vehicle (ELV)
Development and Improving Launch Infrastructure
• Partnership With Industry to Develop National Launch
Capability
– AF Provided $500M for Technology Development
• Lockheed Martin and Boeing Awarded Production Contracts for
Eastern and Western Range
• Competes with Ariane Class Vehicles on World Market
• Stage and a Half Design Based on 1950’s
Atlas ICBM Technology; Com’l Launch
1990
 Atlas IIAS Has Four SRM Strap-Ons
• Atlas III is Transition Between Atlas II and
Atlas V (EELV); Launched 2000
 RD-180 Main Engine Developed by Russia
Under Russian-American Partnership
 Flight Tested 85% of Atlas V Hardware
• Atlas IIAS/III – Intermediate Class
 Lifts 19,000 lbs. to LEO, 15,900 lbs. to
Polar; III – 23,600 lbs. to LEO
 Launch Sites – II – VAFB, CCAFS
III CCAFS
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Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
33
EELV Baseline
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34
Boeing Delta IV
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Develop a Family of Launch Vehicles to
Support Government and Commercial Needs
• Oxygen/Hydrogen Common Booster Core
•
•
 First New Liquid Rocket Engine Developed in U.S.
Since Space Shuttle
Two – Four SRMs, Two Types of Upper Stages and
Three Payload Fairings
 Five Versions Depending on Payload
Horizontal Processing Away From Pad
 Launch Pad Time Reduced from 24 Days (DII) to 7
Days
• Medium to Heavy Class
 First Launch – 2002
Lockheed Martin
 Lifts 8,120 – 23,040 lbs. to LEO
 Lifts 9,285 – 28,950 lbs. to GTO
 Heavy Lifts up to 56889 lbs to LEO
Boeing
Commercial Services Replacing Military Heritage Systems –
Titan, Atlas, and Delta. Reduce Launch Costs by 25%
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Stephen A. Whitmore, USU MAE Dept.
 Launch Sites - VAFB, CCAFS
35
National Aeronautics and Space Administration
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9
Lockheed/Martin Atlas V
Sea Launch
Company,
Click
to edit Master
titleLLC
style
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• Common Core Booster First Stage
•
•
• Multinational Joint Venture
 Eliminates Pressure-Stabilized Fuel Tanks; Load
Payload Without Rocket Being Fueled
 RD-180 Main Engine Developed by Russia For
Atlas III; Pratt & Whitney Build for Gov.
Launches
Vertical Processing Away From Pad
 Transported to Pad on Mobile Launcher
400 and 500 Series has Variety of SRMS and Three
Payload Fairings
 Boeing (USA), RSC-Energia
(Russia), Kvaerner A.S. (Norway)
and NPO-Yuzhnoye (Ukraine)
• Sea-Going Launch Platform
 Ukrainian/Russian Zenit 3SL
 Liquid Oxygen and Kerosene
 Transport to International Waters,
Avoids Safety Restrictions
• Assembly and Command Ship; 1012 Day Sail To Location
• Heavy Class
• Medium Class (No Heavy Lift)
 First Launch – 2002
 400 Lifts 10,910 – 16,843 lbs. to GTO
 500 Lifts 8,750 – 19,110 lbs. to GTO
 500 Lifts up to 45202.5 lbs to LEO
 First Launch – 1999
 Lifts 12,566 lbs. to GTO
 Launch Site – Pacific Equator
 Launch Site - CCAFS
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Falcontitle
1 (2)style
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to edit Master
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title1 style
Falcon
• Privately Funded Endeavor … Started by Pay Pal Founder
Elon Musk
• Falcon 1 is a two stage, liquid oxygen and rocket grade
kerosene (RP-1) powered launch vehicle.
• Designed in-house from the ground up by SpaceX for
cost efficient and reliable transport of satellites to low Earth
orbit.
• Liftoff of the SpaceX Falcon 1 Flight 4, from Omelek Island in
the Kwajalein Atoll, at 4:15 p.m. (PDT) / 23:15 (UTC).
• Acheived elliptical orbit of 621x643 km, 9.3 degrees inclination, and carried
a payload mass simulator of approximately 165 kg (364 lbs).
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10
Space-X
Falcon
9 (2)style
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title
ClickSpace-X
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title9style
Falcon
• Medium/Heavy Lift Option from Space-X
• Falcon 9 is a two stage, liquid oxygen and rocket grade
kerosene (RP-1) powered launch vehicle.
• Uses the same engines, structural architecture (with a
wider diameter), avionics and launch system.
• First Launch Scheduled for Early 2010.
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41
Space-X
Falcon
9 (3)style
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to edit Master
title
• European
• Indian
•Japanese
• Russian
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to edit
MasterSystems
title style
Foreign
Launch
• Falcon 9 Heavy
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National Aeronautics and Space Administration
The list grows!
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11
Russian and Ukrainian Vehicle
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European,
Indian,
Japanese
Click toChinese,
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titleand
style
( 2001)
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
Performance(2001)
45
National Aeronautics and Space Administration
Click to edit Master title style
Russian’s Soyuz
•
Chart Depicts the Nation's Family of
Long March Rockets (Chinese National
Space Administration)
• The Russian Soyuz Rocket Is One of the
Oldest and Most Reliable in the World
•
China Has Developed Its Own
Spaceship, the Shenzhou, or "Sacred
Vessel,'' Whose Round Body and Winglike Solar Panels Resemble Russia's
Venerable Soyuz Space Capsule
•
Yet to Fly Chinese Booster, Long
March 2EA, Will Lift 12-14 Metric
Tons into Low Earth Orbit
– Will Be Used to Launch Shenzhou
to Future Space Stations
• The Soyuz U Was Adopted for Military Use
Some 25 Years Ago in May 1976. Rockets in
the Series Have Been Launched About 400
Times From Both the Baikonur and Plesetsk
Cosmodromes
Stephen A. Whitmore, USU MAE Dept.
46
Click to Long
edit Master
title
style
China’s
March
Rockets
• The Vehicle Is Used to Launch Commercial
and Government Satellites. It Also Launches
Humans to Orbiting Space Stations
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12
A New Vision for Space Exploration…
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Shenzhou
•
The Shenzhou Flights Started With Its Maiden
Voyage in November 1999. Shenzhou 2 Followed
in January 2001
•
Each Mission Has Expanded the Capabilities of
the Spacecraft, Furthering China's Goal of
Launching a Piloted Vehicle by 2003
•
Shenzhou 5 launched on October 15, 2003 first
manned flight
•
Shenzhou 6 launched on October 12, 2005 second
manned flight
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Master
title style
The
Future?
– Destination for Future Manned Flights May Be a
Chinese Space Station
•
Lunar Orbiter Mission Planned for 2006
National Aeronautics and Space Administration
The First Unmanned Shenzhou Space Capsule
Lies on the Inner Mongolian Desert After Its
Successful Re-entry
in November 1999
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Click to edit Master title
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
364ft
Space
Shuttle
Mercury
Mercury
Gemini
Apollo
Apollo
Ares I,
style
Atlas
Titan
Saturn
Saturn
1-B
V
Redstone
Ares V
50
358 ft
321 ft
Click to edit Master title style
NASA’s Exploration Launch Architecture
305 ft
184 ft
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13
Ares V Heavy Lift System
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Future
Launch
Systems (2)
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to editNASA
Master
title style
Heavy
Lift
Vehicle
For Lunar
Mission
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Stephen A. Whitmore, USU MAE Dept.
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Comparison of Orion and
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Master title style
Orion
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MasterModules
title style
Command
Orion Crew Module
(NASA Concept)
16.404 feet
Apollo Command Module
12.795 feet
NASA DLN Network
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14
Comparison of Altair and
Click to Altair
edit Master
Landertitle style
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Master
title style
Apollo
Lunar
Landers
Altair Lunar Surface Access Module
(NASA Concept)
Lunar Excursion Module
(Apollo)
32.152
feet
Approximate upper
stage dimensions
National Aeronautics and Space Administration
20.013
feet
Design still very much in flux
Altair is a Very Large Vehicle
Currently no “mass closure”
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ClickLunar
to edit
MasterProfile
title style
Mission
NASA DLN Network
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title style
Space-X
Dragon
• Fully Automates ISS re-supply
Spacecraft
• Funded under NASA COTS
Contract
• Potential Manned ISS Option?
Using Falcon 9 as launcher
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15
EELV
Options
fortitle
ISS?style
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to edit
Master
Summary
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Master title style
• Commercial Space Launch Industry is of Great Importance and
National interest to the U.S.
May be used on Interim basis for
Orion Certification while Area I
is in development and Testing
• Federal Government is Actively Working to Facilitate,
Encourage, and Support the Commercial Space Launch
Industry
… or as alternate/complementary
access to ISS … stand by!
things are about to change!
• In spite of current problems with NASA and Commercial
Launch industry …. Rockets and space flight have a long and
bright future
Questions?
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Stephen A. Whitmore, USU MAE Dept.
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National Aeronautics and
Space Administration
ESDM
Click to
edit Senior
Master title style
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Design Project
Rocket Science 101:
Basic Concepts and Definitions
Sellers: Chapter 14
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www.nasa.gov
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16
Rocket Science 101:
Basic Concepts and Definitions
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Click to edit Master title style
Newton's Laws
as
Applied to
"Rocket Science"
... its not just a job ... its an
adventure
• How Does a Rocket Work?
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Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
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66
ClickMomentum
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title style
equation
 exit
Procket  mV
•
•
•
•
•
•
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67
P is the time rate of change of momentum of the rocket (N)
m is the mass flow rate of the exhaust products (kg/s)
Vexit is the exit velocity of the exhaust products (m/s)
This is also called the momentum thrust of the rocket.
W is the weight of propellant being burned per second
go is the standard gravity (9.8067 m/sec2)
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ClickConservation
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of Momentum
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We shrink time
As small as possible
Engine massflow
F=
Reaction Force on Rocket
Engine thrust equation
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18
Rocket Thrust Equation
Click toPressure
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title style
Thrust
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Fthrust  m Vexit  Aexit ( Pexit  Patmosphere )
• Total thrust must be greater than the weight, or the rocket
will not fly.
• Vexit and Pexit are related (inversely)
• Ideal thrust is achieved when Pexit = Patmosphere
• Pressure is identical from all directions except for the Area
of the exit nozzle. This pressure difference produces a
thrust (which may be negative.)
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Rocket Thrust Equation (2)
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Effective Exhaust Velocity
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• Thrust + Oxidizer enters combustion
Chamber at ~0 velocity, combustion
Adds energy … High Chamber pressure
Accelerates flow through Nozzle
Resultant pressure forces produce thrust
Ce  Vexit 
Aexit
( Pexit  Patmosphere )
m
• An easy way to capture the impact of the pressure thrust,
so the Thrust equation remains:
 e
Fthrust  mC
The thrust must be greater than the weight of the rocket, or…..
•
F  m e Ve  pe Ae  p Ae 
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19
Click
to edit
Master
title style
Rocket
Thrust
Equation
(3)
Click to edit Master title style
Specific Impulse
• Specific Impulse is a scalable characterization of a rocket’s
Ability to deliver a certain (specific) impulse for a given weight
of propellant
t
What Causes Thrust?
I sp 
Impulse
g0 M propellant
F
thrust

dt
0
t
•
g0  m propellant dt
0
m
 g0  9.806 2 (mks)
sec
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Impulsetitle style
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Mean specific impulse
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Impulsetitle style
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(cont’d)
(cont’d)
• At a constant altitude, with
Constant mass flow through engine
t
I sp 
Impulse
g0 M propellant
F
thrust

dt
0
t
•
g0  m propellant dt

Fthrust
•
g0 m propellant
0
• Instantaneous specific impulse
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Impulsetitle style
ClickSpecific
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Specific Impulse (cont’d)
(cont’d)
1
I sp 
g0
I sp 
1
g0
Fthrust
•
m
• Example
•
•
 m e  m propellant 
propellant

pA p A  C
Ve  e e •  e   e

 g0
me
“Units ~ seconds”
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Specific Impulse (cont’d)
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Specific Impulse (cont’d)
• Look at instantaneous impulse for a rocket
• Look at total impulse for a rocket
t
• Mean Isp
I sp 
Impulse
g0 M propellant
F
thrust

dt
•
Instantaneous
0
t
m
propellant
•
g0  m propellant dt
• Not necessarily the same
0
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National Aeronautics and Space Administration
I sp 
1
g0
Fthrust
•
m
propellant
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21
Example 2
Click to edit Master title style
Click
toRocket
edit
Master
title style
Equation
How
Much
Fuel?
"The Rocket Equation"
• A man is sitting in a rowboat throwing bricks over the stern. Each
brick weighs 5 lbs, he is throwing six bricks per minute, at a velocity
of 32 fps. What is his thrust and Isp?
F
•
m
propellant
Ce 
6 bricks
ft
1min
 5 lbm  32


1min
sec 60 sec
brick
6  5  32 lbm  ft
...ooops...need....gc
60
sec 2
6  5  32 lbm  ft
1
F


lbm  ft
60
sec 2
32.1742
lbf  sec 2
I sp 
F
•
m
propellant

g0
0.497lbf  32.1742
ft
sec 2
6bricks
1min
lbm  ft
 5 lbm 
 32.1742
1min
60sec
lbf  sec 2
brick
 0.994 sec
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Re-visit
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(cont’d)
(cont’d)
•
•
•
dV
dM
 m propellant Ce  g0 I sp m propellant  m propellant  
dt
dt
M -> rocket mass
dM

dV
dM
 g0 I sp dt  dV  g0 I sp
dt
M
M
M
• Assuming constant Isp and burn rate …. integrating over a burn time tburn
 M0 
Vfinal  V0  g0 I sp ln  M final   g0 I sp ln M 0  g0 I sp ln 

 M final 
•
 m propellant Ce
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
 M0 
Vfinal  V0  g0 I sp ln 

 M final 
87
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(cont’d)
• Consider a rocket burn of duration tburn
(cont’d)
• Or rewriting
Initial Mass
 M0 
V final  V0  g0 I sp ln 

 M final 
Initial Velocity

V  g0 I sp ln 1 


Final Mass
National Aeronautics and Space Administration
m
M final  M 0  m propellant  t burn
Stephen A. Whitmore, USU MAE Dept.
m
propellant
M final

  g I ln 1  P 
0 sp
mf 



Pmf  "propellant mass fraction"
•
Final Velocity
M 0  M final  m propellant
V  V final  V0
• Sometimes
89
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propellant
M final  m propellant
National Aeronautics and Space Administration
Is also called
propellant mass
Fraction or “load mass fraction”
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Propellant
Propellant mass fraction
Load mass fraction
"Propellant Mass
Fraction"
National Aeronautics and Space Administration
Relating Delta V delivered by a rocket
burn to propellant Mass fraction
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23
Click to edit Master title style
Click to edit Master title style
Ramifications of "the
Rocket Equation"
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Rockets
• In general, the benefit of discarding the empty tanks and
structures outweighs the additional cost and complexity.
• For a single stage rocket:
V  go I sp ln(
mi
mf
)  go I sp ln(
wi
wf
)
• For a multiple stage rocket:
Vt  V1  V2  V3  ...
Specific Impulse
(revisited)
• The improvement is because the final weight of stage 1
does not equal the initial weight of stage 2.
450 sec is “best you can get” with chemical rockets
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Velocity
1 vs 2 stage
Click
toprofiles,
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style
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Trades
• Advantages:
–
–
–
–
Reduces total vehicle weight for the same payload and DV
Conversely, increases payload from the same vehicle
Increases the max velocity for a given vehicle
Decreases required Isp
• Disadvantages:
– Increased Complexity
– Decreased Reliability
– Increased Cost
SS 3850
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Master4 title style
Example
wi
wf
• Two stage rocket, payload 1000 lbs., stage 1 weighs 10000
lbs. and has 90,000 lbs. propellant, stage 2 weighs 2000
lbs. and has 18000 lbs. propellant. ISP is 300 sec for both.
)
V  32.2 * 300 ln(121000
V  21,500 ft
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4 (cont’d)
• Single stage Rocket, wi=121000 lbs, 1000 lb. Payload,
12000 lb structure, Isp=300 sec.
V  go I sp ln(
Stephen A. Whitmore, USU MAE Dept.
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wi  1,000  10,000  90,000  2,000  18,000  121,000
13000
w f 1  1,000  10,000  2,000  18,000  31,000
)
V1  32.2 * 300 ln(121000
sec
31000
)
V1  13,155 ft / sec
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Example 4
(cont’d)
wi 2  1,000  2,000  18,000  21,000
• Read Sellers, Chapters 2, 14 …., Appendix C, Pages 731, 732
w f 2  1,000  2,000  3,000
Work problem detailed on the following pages
V2  32.2 * 300 ln( 21000
3000
)  18,797 ft / sec
VT  V1  V2  18797  13155  31,952 ft / sec
Compare to 21,500 for the single stage rocket, same initial
weight, structure weight, propellant weight and payload.
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Homework
3 (cont’d)
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Homework
3 title style
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(cont’d)
• Space Shuttle has the following mass fraction characteristics
• The SRB’s each burn for approximately 123 seconds and
produce 2,650,000 lbf thrust
• The three SSME engines each burn ~509.5 seconds and
each produces 454,000 lbf thrust
• Each SSME consumes 1040 lbm/sec of propellant
• Calculate the propellant mass fraction
• Assume that the Shuttle
needs 7.608 km/sec of V
• Assume Constant Thrust, Massflow
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Homework
3 title style
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Homework
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(cont’d)
(cont’d)
4) Now repeat the process ... except break the launch into "stages"
•1) Calculate the launch Isp for the COMBINED shuttle launch system ...
• “two-stage” system
1) SRB’s+SSME’s
2) SSME’s alone
that is the mean Isp of the SRB boosters and the SSME's
boosters ... assuming no altitude effects and constant thrust (the shuttle
actually throttles back during flight to lower dynamic
pressure loads) ... this Isp will act for the first 123 seconds of flight ..
until the SRB's burn out
... ASSUME THAT DURING STAGE 1 ... ALL OF THE SRB PROPELLANT
IS CONSUMED ... AFTER 123 SECONDS
.. THE SHUTTLE STACK JETTISONS THE SRB CASINGS ...
2) Based on this Mean ISP ... calculate the propellant mass fraction needed
to achieve orbit ... that is a .. delta V 0f 7.608 km/sec
3) Based on the listed weights ... GTOW is the gassed up on the pad weight
... compute the ACTUAL propellant mass fraction of the shuttle
... CALCULATE THE ACHIEVED DELTA DURING "STAGE 1"
... How does it compare to the required mass fraction based on the
mean launch ISP?
... NOW START THE PROCESS OVER ... WITH THE REMAINING MASS,
ISP, AND MASS FRACTIONS
... 3A ... WHY DO WE EVEN NEED THE SOLID BOOSTERS? ...
…3B … How does the shuttle manage to reach orbit
5) ... WHAT IS THE NEW ACHIEVED DELTA V FOR STAGE 2
6) FINALLY WHAT IS THE ACHIEVED TOTAL DELTA V?
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Friday”title
…. style
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• Tethered Lander Concept Introduction
Questions?
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“Design Friday” ….
Friday”title
…. style
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Background
• The maneuvering capability of the Lunar landing vehicle is
derived by pitching the thrust vector using the attitude control
system to give a resultant a horizontal component of thrust in
the desired direction.
• One of the many crucial points associated with NASA
Constellations systems Lunar Landing mission is the portion
from spacecraft separation in lunar orbit to descent and
touchdown.
• Flight Training vehicles should be capable of rendering a realistic
environment for both flight crew training and autonomous
landing systems verification and validation
• A key element of the trainer is the accurate representation of the
low lunar gravitational acceleration, approximately 1/6th earth’s.
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“Design Friday” ….
• For a Lander maneuvering near the Earth’s surface under 1-g
gravity the required pitch or roll angle is small to achieve the
required horizontal acceleration.
• However, when operating near the lunar surface in 1/6th onesixth gravity, the required angular offset is approximately 6
times greater, resulting in entirely different visual motion
queues to the pilot or landing algorithm.
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“Design Friday” …
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• Thus a key component of the landing flight trainer is the
decoupling of the thrust required to offset ONE-G gravity
from the thrust required for executing the landing or hazard
avoidance maneuvers.
• Accounting for aerodynamics effects is a secondary
consideration due to the low flying airspeeds, although
crosswinds can be an issue
• Using Rocket Systems with onboard propellant storage for
the gravity offset in hover is infeasible due to large
required propellant mass fractions
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“Design Friday” ….
“Design Friday” …
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• DFRC LLRV overcame this problem using an air breathing jet engine
which had a very high effective I sp > 2000 sec.
•Langley LLTF overcome this problem by using suspension
and support cables. “Not a realistic simulation”
• For a given total vehicle mass, earth-gravitational offset thrust is 5
times larger than the maneuvering thrust required for a lunar landing
•Astronauts did not believe the simulation was at all a realistic
simulation of the hover visual and motion cures.
• The Apollo-Era Lunar Landing trainer vehicle (LLTV) accomplished
this graving offset by using a jet engine that was gimbal mounted and
was designed to support 5/6ths of the vehicle weight, while two
throtteable rocket systems were used to control the rate of descent,
hover, and translation during the landing phase.
•"Deke" Slayton, then NASA's astronaut chief, firmly believed
there was no other way to simulate a moon landing except by
flying the LLTV (an follow-on to the LLRV).
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LLTV
Details
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Master
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National Aeronautics and Space Administration
• Jet engine also attempted to counter the effects
Of aerodynamic forces on Vehicle
• Two mono-prop (H2O2) lift rockets with thrust
that could be throttled from 100 to 500 lb controlled
LLRV's rate of descent and horizontal movement.
• LLRV used General Electric CF-700-2V turbofan
engine mounted vertically in a gimbal, with 4200
lb of thrust.
• Sixteen smaller hydrogen peroxide rockets,
mounted in pairs, gave the pilot control in pitch,
yaw, and roll.
• The engine would deliver the LLRV to test altitude
and was then throttled back to approximate the
reduced (1/6th) gravity of the moon.
• As safety backups on the LLRV, six 500-lb
rockets could take over the lift function and
stabilize the craft for a moment if the main
jet engine failed.
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Detailstitle
(2)
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style
• Built of aluminum alloy trusses and shaped like a
giant four-legged bedstead, the vehicle
approximately simulated a lunar landing profile
during the final
approach phase
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Detailstitle
(3)
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style
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“Tethered Lander”
• What is proposed here is a “compromise” free flying vehicle.
• The pilot had a zero-zero ejection seat that
would then lift him away to safety.
• Offload gravity offset propellant from vehicle and use pneumatic “tether” to
supply compressed air to “cold jet” offset thrusters. Offloaded propellant
“tank farm” has almost unlimited capacity
• Vehicle was severely cross-wind limited
• Pilot Comments (Pete Conrad) indicate that the
simulation was most useful from 200 ft to ground
during terminal descent
• Simple design “bulletproof” and has required minimal developmental time
• This system was extremely complex and resulted
in a vehicle that was more difficult to fly that the
actual lunar module.
• In fact 3 of the 5 training vehicles were lost during
the build up to the Apollo lunar landing missions.
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• Infinitely scalable, infinitely throttleable, run time limited only by size of
ground-based “tank farm”
• Maneuvering and control provided by onboard scaled-size thruster that
accurately models actual landing thruster.
• Tethered lander will have limited horizontal mobility, but can approximate
vertical descent and ground proximity maneuvering quite well
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Tethered
Click
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Master Concept
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“Tethered Lander” (2)
• Offload gravity offset propellant from vehicle and use pneumatic
“tether” to supply compressed air to “cold jet” offset thrusters.
• Offloaded propellant “tank farm” has almost unlimited capacity
• Simple design “bulletproof” and has required minimal developmental
time
• Infinitely scalable, infinitely throttleable, run time limited only by size
of ground-based “tank farm”
“Free Flyer”
• Maneuvering and control provided by onboard scaled-size thruster that
accurately models actual landing thruster.
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“Tank Farm”
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Click
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Tethered
(2)
Click
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Master Concept
title style(3)
Tethered
Pneumatic Feed
Lines
Gimbaled Platform
RCS
Thrusters
Test Pod with
Sensors, lidar
Camera, etc
Spring Loaded
Inertial-reel
Support cables
High Pressure
Pneumatic Flex-hose
(~200-250 psi)
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Existing
Concepts
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Tethered
(4)
• Naval Postgraduate School 3-DOF Floating
Motion Simulator
• Maneuvering
Thruster
• Cold-Jet
Gravity Offset
Thruster
Landing Pads
Attached to
Gimbaled
platform
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• USC “Leapfrog” Lander
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31
NPS 3-DOF Floating
Motion Simulator
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USC
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Reaction
Wheels
Onboard
CPU
Floating
Platform
Ballast
Weights
Weight ~ 22 kg
Air Bearing
USC Information Sciences Institute
Kerosene powered JetCat
P200 jet engine, 24 oz/min
fuel consumption, 200 Nt
thrust, effective Isp ~1800 sec
Photo Courtesy Brij Agwral, NPS
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“Leapfrog”
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Design
Issues
Proof of Concept, Hover and Landing
Simulator/Trainer
• Cold-Jet exhaust is very cold ~ 100 K, Potential problems with icing using
compressed air, dry nitrogen my be required
• For large scale lift system May need feedback system on 4-posted gas nozzles to
regulate flow to keep platform horizontal if Reaction wheels can not provide
sufficient torque
• Tethered line pressure losses can potentially be very large, feed line diameter very
important
• Cross-wind limits need to be assessed or look at indoor operations
-- Kerosene powered JetCat P200 jet engine for hover and descent flight.
-- Lateral and rotational control provided through cold-gas thrusters.
-- Inner Platform PID Control system/avionics well developed
-- Inertial reel safety tether prevents los of vehicle / “runaway”
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• Can cold jet system account for aerodynamic effects on vehicle and remove these
in realistic manner? (less of an issue indoors)
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Systems
Tools
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Master title
style
Click Design
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Master title style
• Develop a functional block diagram for the
tethered lander system
• Identify all required support subsystems, assume
we will built a scaled model including truss
support and min tank farm … scale system based
on available 50% Jet-cat thrust levels
Modeling and Simulation
• Propose Level 2 PBS, WBS to achieve desired
design
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33
6/13/2009
National Aeronautics and
Space Administration
ESDM Senior
Design Project
Elements of a Space Mission
Space Craft Subsystems Overview
Sellers: Chapters 12, 13
National Aeronautics
and Space Administration
www.nasa.gov
0
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Stephen A. Whitmore, USU MAE Dept.
Satellite Design
Principle Requirements and Constraints
•
•
•
•
•
•
Mission
Payload
Orbit
Environment
Launch
Ground-System Interface
Mission
•
•
•
•
•
P
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Operations Concept
Spacecraft Life and Reliability
Communications Architecture
Security
P
Programmatic Constraints
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Spacecraft Design According to:
Trajectory
Designers
The Design Process
point mass
Controls
Designers
Rocket
Designers
Payload
Designers
payload
Structural
Designers
Power Syste m
Designers
Communication
System Designers
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Stephen A. Whitmore, USU MAE Dept.
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Systems Engineering Tools
5
Spacecraft Building Blocks
Structure
• Payload
• Launch and Propulsion System
• Attitude Determination & Control
System (ADCS)
• Reaction Control System (RCS)
• Electrical Power System (EPS)
• Thermal Control System (TCS)
• Structure
• Telemetry, Tracking & Command
System (TT&C)
Modeling and Simulation
6
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Bus
Propellant
Payload
15%
25%
30%
30%
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Orbit & Environment
Payload
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Single most significant driver
Physical Parameters
Operations
Pointing
Slewing
Payload
Environment
Designers
• This Part is the PI’s Responsibility
(defined by the mission)
Defining Parameters
Eclipses
Lighting Conditions
Maneuvers
Radiation Exposure
Particles and Meteoroids
Space Debris
Hostile Environment
point mass
Detailed Discussion Deferred to Section 7
National Aeronautics and Space Administration
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National Aeronautics and Space Administration
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Attitude Determination & Control System
(ADCS)
• It is necessary to establish and maintain satellite stability
– Mission requirements: payload pointing and slewing
– Solar array pointing and tracking
– Directional antennas
– Orientation of satellite for thrust maneuvers
– Thermal Maneuvers
– Station keeping
• Roll, Pitch and Yaw Control
Launch Strategy
Boosted Weight
Propellant Mass Budget
Envelope
Environments
Rocket
Designers
Interfaces
Launch Sites
Detailed Discussion Deferred to Sections 6, 8
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
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Stephen A. Whitmore, USU MAE Dept.
Launch and Propulsion
•
•
•
•
•
•
•
Trajectory
Designers
Detailed Discussion Deferred to Section 9
11
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Spacecraft Attitude
ADCS (cont.)
x
p
f
y
r yaw
Y y
q
x
z
q
• Principle stabilization techniques
– Gravity Gradient, Spin, Rate Damping, 3-Axis
Reaction Control System
• Sensors
– Star, Sun, Earth, Gyros, Magnetometers, GPS
• Actuation Devices
– Reaction Wheels. Reaction Control Thrusters, Gyros,
Magnetic Torquers,
• Control Systems
z
National Aeronautics and Space Administration
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
Reaction Control Systems - Propulsion
(RCS)
RCS Example: Cold Jet Thruster
• The spacecraft propulsion system provides
controlled impulse for:
Gas Storage Tank
– Orbit insertion and transfers
– Orbit maintenance (station keeping)
– Attitude Control
Gas Exhaust Nozzle
Pressure
Regulator
• Propulsion Types
Actuator Valve
for Gas Flow
– Cold gas, monopropellant, bipropellants, ion
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Stephen A. Whitmore, USU MAE Dept.
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Stephen A. Whitmore, USU MAE Dept.
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• No Combustion
• Thrust provided by
expansion of gas
through Nozzle
• Low Isp
• Simple Mechanism
National Aeronautics and Space Administration
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4
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Solar Cells
Electrical Power System
(EPS)
Pout = Pin  cos q
• Solar Cells/Batteries, Radioactive Thermal
Generators (RTG)
• Solar Cells
–
–
–
–
–
Silicon (14% Efficiency) - 190 W/m2
Gallium Arsenide (18%) - 244 W/m2
Degradation (3-4%/yr LEO)
Temperature (.5% decrease per degree)
Sun Incidence angle
q
P
in
Effect of
Temperature
On 

Solar Cells
( ~ 0.15)
P
out
Power Syste m
Designers
Surface Temperature, K
National Aeronautics and Space Administration
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National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Solar Cells
18
Solar Cell Efficiency
Pout = Pin  cos q
Vmax
'I/V" Curve
Design Point
(Max Power Output)
P
in
P
out
Solar Cells
( ~ 0.15)

Effect of
Temperature
On 
Voltage, V
q
P=IV
Surface Temperature, K
National Aeronautics and Space Administration
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
19
Current, I (amps)
Stephen A. Whitmore, USU MAE Dept.
20
5
6/13/2009
Effect of Eclipses
Cyclic Power Production
• Most Spacecraft
Pass into Earth’s
Shadow Once
Each Orbit

Torbit
Tec lipse
Power
Output
W/m2
Time
• Cyclic Power Production Requires Significant Power
Conditioning and Storage capacity
• Effect Causes
Cyclic Power
Production
National Aeronautics and Space Administration
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
21
Power Distribution and Storage System
22
Batteries and Storage Systems
Solar
Panel
Regulation
Spacecraft
Power Bus
Bus Voltage
Regulation
Battery
System
Charge/Discharge
Max
Battery
System
National Aeronautics and Space Administration
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
23
Stephen A. Whitmore, USU MAE Dept.
24
6
6/13/2009
Power Distribution and Storage System
Batteries and Storage Systems
(example)
• Batteries
– Nickel Cadmium, Nickel Hydrogen
– Cycles
• LEO - every orbit (5000/yr)
• GEO - two 45 day periods
• Issues
–Depth of Discharge (Deep-Cycle Tolerance)
–Charge/Discharge Time
–Weight
–Power Regulation and Distribution
National Aeronautics and Space Administration
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DC/DC
Converter
100 W (3.6 amps
@28 Vdc)
DC/DC
Converter
12 W (2.4 amps
@5 Vdc)
DC/DC
Converter
15 W (1.5 amps
@10 Vdc)
DC/DC
Converter
5 W (0.5 amps
@10 Vdc)
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Thermal Control System
26
Thermal Control Systems (2)
• Spacecraft Heat Sources
•Internal, Direct Solar, Albedo, Earth, Space
• Manages Heat Flow Through Spacecraft to
Keep Systems within Operating Temperature
Ranges
-- Typical operating ranges (C):
– 0 to 40 for Electronics
– 5 to 20 for Batteries
– 7 to 35 for Hydrazine
Propellant
– -100 to +100 for
Solar Arrays
– -200 to -80 for IR
payload sensors
payload
•
q
•
q
in
out
subsystems
National Aeronautics and Space Administration
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
27
Stephen A. Whitmore, USU MAE Dept.
28
7
6/13/2009
Heat Pipes
Structures
• Provides stable support and maintains its integrity
during all mission phases
• Provide a compatible interface with the launch vehicle
• Must meet the functional requirements of all
subsystems
• Low Boiling Point Liquid
• Liquid Absorbs Heat at “Hot-end”
• Vaporized Liquid Condenses at Cold end
…. Releases heat
• Capillarity Action Carries Liquid back to Hot End of Tube
National Aeronautics and Space Administration
Structural
Designers
Detailed Discussion Deferred to Section 10
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
31
Stephen A. Whitmore, USU MAE Dept.
30
Mechanisms
Example: Launch Loads
• Electro-mechanical devices employed to carry
out key functions:
– Separation systems
– Antenna deployment and pointing
– Attitude control
– Experiment orientation and control
• One-shot or Continuous
National Aeronautics and Space Administration
National Aeronautics and Space Administration
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33
35
Stephen A. Whitmore, USU MAE Dept.
8
6/13/2009
Telemetry, Tracking and Command
(TT&C)
Telemetry, Tracking and Command (TT&C)
• Telemetry
– Gathers data from other subsystems
– Processes and formats data
– Transmits data to the ground station
• Tracking
– Determines satellite position
Communication
System Designers
• Command
– Satellite control is established and maintained
Detailed Discussion Deferred to Section 11
National Aeronautics and Space Administration
38
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
39
Ground System Interface
•
•
•
•
Data
Mgmt
Degree of Autonomy
Ground Stations
Space Links
Guidance & Navigation
(Orbit Determination)
Questions?
Uplink
Facility
Output
Communication
System Designers
National Aeronautics and Space Administration
40
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
43
Stephen A. Whitmore, USU MAE Dept.
9
6/13/2009
Homework
“Design Friday” Assignment
• Continue with Lander functional block diagram,
PBS, WBS development
• Read Through Armstrong/Conrad Notes with
Highlights (web page and handbook)
• Present interim report on progress
• Pay special attention to comments regarding
landing simulators
•
NASA MSC Minutes of Meeting Flight Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas,
January 12, 1970
National Aeronautics and Space Administration
44
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
45
Stephen A. Whitmore, USU MAE Dept.
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C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
I-I
Capt. Conrad's comments:
"I guess I don't have a formal presentation, but I guess the question is, one, that after
we made some lunar landings, is the vehicle a requirement for training for
subsequent crews? And I have to preface my remarks by saying were. I to go back to
the moon again on another flight, I personally would want to fly the LLTV again as
close to flight time as practical.
Now, for the following reasons, I look at the vehicle myself in terms of our
Gemini docking trainer and simulator devices like that and felt, I think as many
people did, that we would have made some landings before we determine whether
we really needed this kind of training or not, and as you know, I think that our
simulators do an adequate job on formation flying around other vehicles that we
don't need the dynamic docking simulators.
I do feel that we need the LLTV and for the following reasons. I think the LMS [Lunar
Mission Simulator, a fixed-base simulator with no dynamic motion simulation] does an
outstanding job for sight recognition and basic flying of the vehicle down to an altitude
of 200 feet. At that time, and in the transition time, the visual and the LMS simulators
do not come into the real world that well.
The LMS is certainly an adequate vehicle to do your instrument training
necessary to land, to go all the way down and land. I'm not sure that everybody
is aware of the fact that the probes on the L&A normally shuts you off visually
at an altitude of about 100 feet and so you don't get the last part of it, nor do you
get the transition part of flying. It doesn't do the job of flying safe velocities of
80 feet per/sec on down into this area of going into a hover.
The Langley vehicle No. 1, flying it at night, the night lighting does not even come
close to what the moon looks like from my opinion. So it doesn't make any
difference whether you are flying the Langley A-frame simulator at nighttime or in
the daytime. The other thing that the Langley simulator cannot do is restrain
laterally to plus or minus 25 feet, and the maximum horizontal velocity that I have
ever been able to achieve in the Langley simulator are 10 feet per/sec and that's
nothing. The problem, I feel, is in this flying regime from 500 feet down until the
time to get in a hover, and you decide either that you are going to land visually, or
you are going to land on the gauges.
The problem of determining proper pitch attitude is one that I feel I got most
benefit out of the LLTV, and if you will look at the films very closely of my
landing, you will see some pretty healthy pitch attitude excursions or changes right
down in the area of the heavy dust and this was strictly when I was going from
outside the cockpit to inside the cockpit.
1
C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
If you will look at my LLTV landing summary, you will find I went into
backup autopilot on several lunar sim landings for the plain and simple
reasons, I stayed out of the cockpit and landed on the rear skids.
I-II
Now, one of the things that I learned that really helped me on the moon, was to build
the confidence in the actual flight vehicle; to put my head back in the cockpit again.
One of the recommendations that I would make on the LLTV, if we continue to fly, is
that we really put the LM instrumentation as it is properly arranged in the LM, in the
LLTV as much as possible. Because, the more you fly lunar landings in the LLTV, the
more you will fly them in the cockpit and the better landings you will make because
you cannot determine pitch, either in the LLTV or in the LM. Pitch is too easy to
determine, I think, in the A-frame at Langley, that's another draw back of Langley.
Gilruth:
"You mean you can't determine by looking out the window?"
Conrad:
"You can't determine by looking out the window. You've got to
have this confidence, you don't care what you are doing in the LMS. The last 100 feet
you can sit there and fly it all the way down looking in the cockpit and land. In the LMS
you don't have enough visual simulation to determine pitch anyhow, so you do it all on
gauges in the LMS and that's not real world.
I guess the next thing that I feel, as we continue on the program, is that we are asking
pilots to go into tougher and tougher sites. There will be smaller areas to land in and I
feel that to get the most benefit out of learning how to translate with the little fuel that
you have, both laterally and horizontally, the LLTV does the job. Now that sounds a
little strange and I'm going to have to qualify that. As we are constrained to fly the
LLTV down the runway, and you normally don't, make large lateral translations with
the LLTV; however, with the wind situation you normally don't get into the lunar sim
mode going down the runway properly and you wind up having to make these
translational corrections laterally to stay on the runway and you got the --. I think that
all of us formerly have wound up out over the grass somewhere and had to fly it back
into the runway.
One of the comfortable things of my landings was to make that lateral translation,
and I put all the confidence, and if you will listen to the tapes, even A1 Bean
remarked that about how we were doodling around in the sky, because he had not
flown in a real vehicle. He is not used to those kind of physiological feelings and
sensations that you get by flying the LLTV, and it's probably one of the more
uncomfortable vehicles to be rolled about 10 or 15 degrees and pitched up about
20 degrees and you don't get that in a Langley simulator either, because you are at
low horizontal velocities and you make a very quick transition to a hover and come
down.
2
C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
The fact that we are going to get to more difficult sites and the fact we are taking
people continually that have not been there before, and you look at the number of
touch and go landings that anybody treats in any kind of airplane that they are
checking out, we are banking our whole program on a fellow not making a mistake
on his first landing. To build that confidence, I feel:, we should continue to fly the
LLTV.
As I said earlier, I would want to fly it myself if I were to go again. The more difficult the
landing site the more confidence a man has to have in being able to drive this vehicle. I
can't assign a number to a confidence factor, but the reason I took over initially was that I
thought I was going to overfly the target, and I maintained a pretty healthy pitch attitude
coming into our landing site and made a rather steep descent. I guess it's in the order of
40 degrees, which looked straight down, and these all looked perfectly normal to me and
caused me no concern up there, and I base all that on my LLTV experience, and I can't
base it on anything else.
That is just about all I can say and that pretty well pointed out the draw backs of other
simulators, and I don't feel that we can drop it in the same manner that we dropped the
docking simulator. I think that it is a dynamic vehicle, and there is no replacement for
that type of training."
I-III
Enclosure 2 II-I
After Capt. Conrad's conversation, the following discussion took place between Dr.
Gilruth and Capt. Conrad:
Gilruth: Pete, one of the things you said I think is pretty significant. That is, that
with a vehicle like the LM or the LLTV it's very difficult to determine pitch
attitude, because you don't have anything up in front of you to line up with the
horizon or anything. In raw, I guess you might get use to having some horizontal
lines you could line up.
Conrad: In the upper part of the window and camera horizon the roll is relatively easy to
keep points level.
Gilruth: So I guess that I would like to ask you if there is anything that could be done in
providing a reference to make it easier to fly? Is there something that you have thought
about?
3
C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
Conrad: I don't think adding a piece of structure to the vehicle would do that for the other
reason and I didn't discuss the dust. I guess when everybody went back and engineered
out our tapes and all concluded that the dust really wasn't that bad until we were in the
neighborhood of 30 feet. I was calling this in the area of 50 feet, and all of my altitude
callouts were based on what the LMP called in my ear, and we were reading some 19
feet on the lunar surface on our inertial platform, and so I was off quite a considerable
factor at the end, percentage-wise, on saying where the dust was. .
The following boxed paragraphs were left out of the monograph.
But the other problem with the dust is the fact that it is a dynamic moving field that is of
varying intensity, and every time you look out of the window to do something you
cannot help but physically be -- your eyes are physical1y attracted to a darker cloud that
just went off that way, from one that went off that way. And I think that the two factors
on pitch: one, that you don't have it, but if you put a boom or you put a device out there
that would put some structure out there to give the normal physical clues of pitch, that
the dust would still be distracting whether it obscures the ground or whether it doesn't
obscure the ground, and I felt much more comfortable with my head in the cockpit. And
as I stated, the only reason that I continued to put pry head out of the cockpit was
because I, in retrospect, it was a mistake, and we should have added it to the checklist, to
verify that our horizontal and lateral velocity indicator was in fact working, and it was.
It's just that up --high enough. I killed off all of, the lateral and horizontal velocities, to
the point where it was not registering on the gauges. I probably really wanted that gauge
in what Al called out in my ear in the neighborhood of 50 to 60 feet. When I first looked
at it, and I think the data shows that we were pretty well in a hover at 50 feet, actual
attitude. And had I felt that gauge was working, I probably would never have looked out
that window again and I was perfectly satisfied that we were in a clear enough spot that I
didn't need to look out anymore. And the only reason I did, and the other thing I did, had
not gone back to look at my data, and I don't understand why I made 10 degrees attitude
excursions right at the end, but they were plus or minus, but I don't remember. which way
it was exactly, but the first time that I came back in the cockpit, I was pitched up 10; and
I leveled it and I looked back out the window and it was very plain on the film, and I
looked back out the window and I was pitched down 10° when I brought my head back in
the cockpit and brought the vehicle back level when it was just about that time --that we
got lunar contact.
Now I don't know whether I made control inputs or whether some slosh actually
disturbed the vehicle's yaw and attitude hold mode. I suspect that I physically put some
control inputs in, and I suspect that I may have done it instinctively when I was looking
out the window thinking I was keeping things level. As I say, you have to look at the
film three or four times, but the pitch experience is very plain in the film right at the end.
The pitch was down the first time. That's because I went back into the cockpit, and I
4
C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
looked out the window again, and when the pitch was back up, I put my head back in the
cockpit and leveled away.
It is very difficult to say, and I know that it was a very difficult thing to do in the LLTV,
but I think Joe or Bud will remember. I think I made my first three landings that went in
backup auto pilot in the LLTV on my training runs just before the flight because of this
pitch attitude, and the only way I can tell in the LLTV is to put my head in the cockpit.
You can't guess it sitting in there and looking out. As slow as you want to come down,
you'll screw it up every time unless you cross check that attitude ball. You can't convince
yourself to do this properly in the LMS. You just don't have enough visual, and you
pretty nearly fly the last part of the approach in the LMS on the gauges only, to stay
within the constraints so you don't bomb out the simulator.
As I said in our debriefing, I see no need to change anything in our procedures. I was
extremely well satisfied with our training in all vehicles as far as landing on the moon
went, and I had all the confidence in the world in the inertial guidance system, which
made it very easy to put my head in the cockpit when I thought I had to do it. And I
would have kept it there the whole time at the end had I thought that one gauge was
working. That is the only recommended change I can see to our procedures.
I felt that -- that I combined … I could leave the Langley simulator out of it
completely. If I were going to go again tomorrow, and I would fly the LLTV as
close to flight as practical and I would stretch it out a. little bit too. I think it's
good to come back and fly the vehicle for a certain number of flights in a row.
You are thinking about landing on the moon and this is a complex vehicle. The
LLTV should be as up to speed on its system as possible and not to interfere with
proper training on the LM. It's not that difficult a vehicle that you can't do it. But
I began to run out of gas on that Sunday, I'd flown nine flights in a row, four of
them one day, three the next day, and two the next day, and we were going to fly
again but the wind was up and I was tired, and I just felt that I was beating myself
to death, with two vehicles and a little less sweat. I would like to have been able
to come home a couple of weekends later and maybe flown two or three more
flights.
II-III
I personally -- I don't know what Neil's feelings are. I think that we are pretty much in
agreement on this though. I understand the problem of flying close to flight, but you only
get one chance. It will be a long time before we send somebody up there again that's
already been there once and each time you bring a new guy along, you are putting him in
a more difficult landing site and I don't think there is anything unsafe with our training. I
got the decided impression we might abort out of a possible landing situation that could
be avoided by a man having a little bit more confidence than you would get out of
Langley and the LMS but not having had the LLTV.
5
C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
This concluded Capt. Conrad's conversation
II-II
III-1
The following are Mr. Armstrong's comments:
"Actually, Pete's covered most of the factors and I agree with everything all the points
that Pete's made. I'm probably a little more reluctant to accept an instrument landing
than Pete was. One, because we never did it before and never saw how the instruments
operated, and the second reason, is that I've flown a Doppler radar in a Ryan's helicopter
which had the following interesting characteristics. (Mr. Armstrong illustrated his point
by drawing an altitude versus velocity bias diagram on the blackboard.) Plot altitude
versus velocity bias, horizontal velocity. So say you came straight down vertically -- this
is zero. At 25 feet you were 0-0, horizontal velocity and as you came below, your
indicators suddenly said that you had one feet per/sec., two feet per/sec., three feet
per/sec., finally six feet per sec., at zero altitude. And then, if you were flying 0-0 on the
cross pointers; saying if you were flying zero at instrument landing, you would actually
be touching down at six feet per/sec., horizontal velocity.
McDivitt: Now, Neil, is that a function of altitude, purely, or altitude rate?
Armstrong: I'm not really sure, Jim. But the important thing is that it is probably an
effect of rotor interference by the helicopter rotor/engine. Interference into the reflection
of the Doppler waves somehow puts this bias in there. But it probably would not exist in
the LM. I wouldn't be concerned about it, but when you are first doing something, you
think there might be something like flight data problems somewhere. But I've been
exposed to it one time and I knew that it would be a terrible thing, like in Pete's case. If
he ended up flying 0-0-0 and pulling it right on the moon, and you ended up with seven
feet per/sec., or something like that going sideways.
McDivitt: I: think if he had those velocities, dust or not, he would see it.
Armstrong: Yes, but I was just verifying his point, that one thing is really important in
setting yourself up for a possible instrument landing, is that you really have to assure
yourself that the instruments you are operating on are correct, without any significant
bias, and that they don't do something like this to you at the last minute. I believe Pete
had a worse case than I did --. I had a little less dust, I think -- a significant amount --a
little less problem than Pete had. I felt that by looking at a few rocks and protrusions and
craters through the moving sheet, I could.
Gilruth: You are looking out the window during the last hundred feet of descent?
Armstrong: Yes, I cross-checked back and forth, but I was pretty well convinced
that my instruments seemed to be correct, but I was still
6
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+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
III-2
looking for maybe something like this to go wrong.
Gilruth: When you are looking out the window, how do you keep . . . what do you use
for a reference?
Armstrong: I agree with Pete. The roll is really fairly easy. Pitch is always
somewhat more difficult. This is something I think that we all found early in the
simulation game. That this was, in fact, true. It's true in the LLRF. Even though it's
to a less extent because intuitively you would have a lot more with an A-frame
around you, and all that stuff, and a little more information coming into you whether
you want it or not.
Conrad: Yes, and in the LLRF you also get that big boom sticking out in front.
Armstrong: Yes, that's right. With trim rockets on it, but still in all, I did pick up an
unwanted horizontal velocity to the left during, final phase and got a lot closer to that
little double crater
than I wanted to and I really can't account for that. Although, I will admit, in my case, I
was a little spastic in final approach and you see a lot more attitude changes and throttle
changes than you would like to see. Still all-in-all, I felt very comfortable -- I felt at
home. I felt like I was flying something I was used to and it was doing the things that it
ought to be doing.
Gilruth: You must be controlling the attitude by keeping your drift low, rather than
by the . .
Armstrong: Yes, you infer it, particularly if you are flying at a constant pitch angle.
You can tell your horizontal velocity and vertical velocity are related if you are flying
along . . . They are proportionate to each other as you are flying along at a constant
pitch angle so you infer in a close loop fashion vertical velocities from horizontal
velocities that you see over the ground and later on your horizontal velocity becomes
your vertical velocity as you know you had. It's a closed loop thing, it's probably more
a specific way to gather some of this information but I don't really have a hold on it. I
don't really think it's worthwhile having that additional information - it's not necessary.
However, it may be useful, but I don't think it would help as much as having the
confidence as in your own knowledge that you can fly the job in. Our own problem
was getting into a small area. I felt that we would never find a spot that was good
enough to land in. That's a kind of problem that's impossible to duplicate in the LMS,
or in the LLRF. It's even that difficult to do in the LLTV unless you sort of play the
game to yourself, as you fly into a touchdown area and you say no, I don't want to land
7
C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
there -- I want to land over there. As you get a little closer you say no, I really want to
land over there, and make yourself do that. So you have to force yourself to do that
problem.
In general, I guess what we all have to ask ourselves is, do we want to keep buying
this insurance policy? We've paid a lot of money to buy this
III-3
insurance policy to improve our ability to do the landing job, and in a couple of times,
we've had to pay excess premiums. Premiums that we felt that we were really
unwilling to pay or at least to continue paying. And now, we are at the point where we
say maybe, at this point in time, we don't need to buy the policy at all. Discontinue the
premiums on it and avoid the possibility of these excess premiums that might burden us
in the future with another crash or something like that. My own conclusion is that we
still can't afford not to insure against this particular catastrophe. A catastrophe of one
sort or another, on final approach at the moon, and I think, we should continue to buy
the policy.
Gilruth: I guess, I agree with you. I've been trying to understand, from a point of view,
trying to understand, the mechanics of flight in this kind of vehicle and why the flying of
an LLTV gives… . I can see why it gives you the feeling of confidence because you
know that you have flown something that is as close to a landing, a lunar landing vehicle,
as anybody can devise and so from that point of view alone, it would give a real feeling
of confidence.
Armstrong: It is the only device we've had. The only simulation at all where you can
allow the process to take place, of a closed loop process where you infer the velocities
from attitude, velocities over the ground, and the actual vertical velocities coming into
the picture at the appropriate velocity. I'm talking of 50 feet per/sec. over the ground
which is the transition phase. That phase from breaking where you are essentially, just
watching out the window and pre-designating and doing those things, to come into a
hover. That's the 150 feet per/sec. to 10 feet per/sec. region --that's where you really
have a lot of flying.
Conrad: In my case, a couple of times, I had to fly off the short runway. And there
were a couple of times, at the end there, I nearly landed on the axis but, I had to get it
stopped and I only had 60 seconds to do it, and it's not a question of saying reset the
simulator. I blew that one. If I landed that LLTV on the grass, I'm in deep yogurt,
and there is no way you can get that confidence, and you do get yourself in situations
in the LLTV that you can't get in any place else except at the moon.
Gilruth: Yes.
8
C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
Armstrong: The forcing function of a limited time is in many respects quite radical.
Still it didn't really worry me, because I knew just what 10 seconds or 20 seconds
were in terms of a flight situation.
Gilruth: Any of the group here have any questions or further discussions? Jim?
McDivitt: Yes, I have a couple of questions. What is your opinion of the number of
flights needed?
Conrad: I think Charlie's charts pretty well show that. If you want to, scan some of Neil's
flights, and my flights, that show how long it takes us to lunar sim mode. To really start
flying the vehicle smoothly from when you first go into lunar sim and go in the thing we
.… and these
III-4
have a very definite tendency to begin to level out after about five or six flights in lunar
sim mode. Now, one problem here is, Neil and I have been in and out of, Neil more than
I have, but Neil and I have been in and out of the LLRV program, and so when we came
into the LLTV we went through a five flight job or two, and I suspected the schedules
that which they have laid out now, which was what? Thirteen flights do you have for
guys that have never flown before?
Haines:
Eleven.
Conrad:
What?
Haines:
Eleven.
Conrad: Eleven flights and then he goes into . . . You have them all the way up to 40
before you add that last fully lunar sim mode. At that point in time, the guy starts
training in the lunar sim mode. This is a problem in the vehicle. There is no doubt
about it. You've got two different vehicles here, flying gimbal lock versus lunar sim.
And you've got a guy that's never flown before. He needs those 10 flights. I agree
with that, and I agree with the wind restrictions and everything else. Once you get the
lunar sim mode, you get that proficiency. I feel that a guy should fly about -- if he's
never flown the vehicle before, I feel that he should fly at least eight lunar sim flights
at some reasonable time period -like a week, two a day; or two, one day, and one the
next or something, because you've got to get the hang of that vehicle in lunar sim.
And I don't mean the aerodynamic hang of it either; I mean getting that baby back and
landing it in front of the spot. I don't think that I have the capability of parking in
lunar sim mode from 300 feet, where we started, right exactly where I wanted to put
it. I'd put it within 50 feet or 100 feet, but I don't really know about our future landing
9
C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
sites, but I'm sure that we are getting into more and more difficult places to get into,
maybe not dust-wise, but the guys are going to have smaller and smaller spots that
they are not going to be able to over-fly 1,000 feet or 2,000 feet -- just go and land it.
Armstrong: Yes, you are always going to have to have the capability of landing within a
specified area.
Conrad: That's pretty hard to do with the LLTV until you fly it quite a bit, I
think.
Armstrong: I think both Joe and Bud have watched a lot of guys fly up there .….
point out that everyone's experience is probably about the same as Pete's and
myself. That is to say you have to fly about half dozen lunar sims before you
have really seen everything that's happening. You are flying through it, but it's
flying you for awhile, unless you fly three flights, or beginning to fly it; by the
time you fly half dozen flights, you're flying the vehicle, going where you want
to go and with the instruments.
III-5
Gilruth: How much is that because of a very complicated bunch of machinery to learn to
do it? How much of that goes into actually learning the control of that kind of a vehicle?
Armstrong: About half and half, in my view. Although, it's really a simple vehicle,
it's nontrivial. You feel the pressure of trying to keep track of as many things as you
can. And the other half is the fact that it is such a cotton picking unusual
environment--so different from anything you've ever been in before --that you are
continually amazed at how machines can fly like that.
Conrad: That's what prompted Al's remark. He'd never been in a vehicle like that, and
he didn't look out the window. He probably looked at the eight ball when I started the
left translation, and I venture to say, I don't think we had more than 10° at the most, roll
in there. But we were
sitting in the neighborhood of 20° or 25° pitch. I didn't want to go by the crater, and it
upset him, you know. He made the remark that you really leaned on it, and I told him
that it's O.K. I felt fine. But that's the weirdest feeling in the whole world flying down
that runway in that vehicle with it all pitched up and rolled over a little bit trying to get
it back off the grass. You can't get that in a Langley simulator. You're not transitioning
out of those kind of velocities. You're not coming from that kind of altitude. You can't
even get a good lateral velocity going in the Langley simulator -- you will be into the
stops.
10
C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
McDivitt: Dr. Gilruth, you asked a question about how much of that time is cut just
because you are looking at that kind of machinery. I can't speak for the LLTV, because I
have not flown it. But if you will, look at airplanes. The Air Force and the Navy have
standardized their airplanes on the inside very much. The Air Force flies almost
universally VH and stick grips and they have the same kind of air speed indicators, and
things like that. Most airplanes have dials and handles and things like that, that are very
familiar to pilots when they check out in new airplanes. It may be a little farther away,
but everytime you check out a new airplane it's a very unfamiliar thing. Not because the
gauges and handles look different, but because it flies different. I wouldn't be a bit
surprised if that wasn't what you find here.
Conrad: First, let me . . . if I go out here and fly a Cessna 310 which I have never
flown before, now, I'm an experienced pilot and I'm behind that airplane or least equal
to it. The first couple of times you go to do that and here stick a guy up there at the
moon and expect him to come down there. I was extremely surprised at the fact that I
stayed as far in front of the LM as I did on the way down. I fully expected to be
further behind on what was going on. And I contribute that to the total training
program, to the LMS, to the LLTV, and I included in there Langley, because I was
auto mode and I came in about the right time and we do have a good simulation. They
can't beat that L&A for LTV and getting use to starting over where you want to go,
but that L&A falls apart about 200 feet. There is no doubt about it. But it does an
outstanding job.
Gilruth:
O.K. Chris?
III-6
Kraft: I guess the only problem I have is, I think: some kind of automotive mode, in that
period, might make you think a little differently about it. But, even at that, you've still
got to be prepared.
Conrad: May I comment on that? I went over the simulator in the program and
granted it is not the optimized way in going back into this auto . . . and I think Gene
Cernan and some of the rest of the boys have spent a lot more time on this little fix
right now. You know they had two different authorities. And I think their conclusion
is that the auto mode kills the horizontal and lateral velocities very good. But their
vehicle gets pretty spastic since you have large ones in there. And they all agree, at the
end, whether you are on the gauges or at the
window, you had better have things in relatively good shape before you go back to the
auto mode.
Kraft: But I still think even, you know, if when you have this auto mode, I think it's
going to make you feel a lot more comfortable about landing sites.
11
C:\Documents and Settings\MechEng\My Documents\My Notes\ESMD Senior Design\Web page
+notes\Section5_Subsystems\Armstrong_Conrad_with_higlt.doc, NASA MSC Minutes of Meeting Flight
Readiness Review Board Lunar Landing Training Vehicles, Houston, Texas, January 12, 1970
Conrad: Well, I agree with what you're saying, but I would go back tomorrow
with what I had.
Kraft: Oh, sure you would. But, I think once you are given that mode that you are
going to do precisely what you just described. You are going to kill off all those
velocities and get it going where you want to go, and you will put that thing into
auto and then monitor it down. I just think that – would change your feeling about
the LLTV but even at that you have got to be prepared . . .
McDivitt: Chris, that auto mode is not doing us much good. These guys just got
through discussing those auto modes and the complications in flying straight
down with it.
Kraft: It's not going to do that at a higher altitude as a result of having the auto
mode.
McDivitt: Yes, I know there are a number of phases to this thing. Auto mode only
takes care of the lunar phase and hardly takes care of the landing part at all.
Lee: That probably works fine in a simulator, but if this bias you were talking
about happened to get in there --it could cut the auto. So you would have to
(cannot decipher from the tape).
Kraft:
I don't deny that, but I don't buy that bias bit.
Conrad: I think our photographs show that we really have it as about as close to zero
in any direction you can get or at least I didn't see any indications of skidding in any
direction. And I understand that the inertial system was showing a 1.7 feet per/sec.
forward. And I don't believe that we had that. I believe that, that bias was really the
inertial system.
III-7
Kraft: Yes, it is and you can expect that. It's going to be around two or three feet
per/sec. Did that come in?
Conrad: I don't remember any numbers over two feet per/sec. I looked at a paper, just
before we went, that went through all the phases that were manual, that were a fallout of
P65 and what you can expect. You could expect to stay within the landing envelope, and
all of them showed you could, and I didn't remember any number over two feet per/sec.
I also did understand that we did, right at the end, get some false radar data. But that is
going to be taken care of --I understand. The radar goes off at 50 feet, is that right? And
that will probably improve it.
12
6/13/2009
ESDM Senior
Design Project
National Aeronautics and
Space Administration
What does a rocket “do”?
Rockets take
spacecraft to
orbit
Propulsion Systems Overview I
Sellers: Chapter 14
Move them
around in space,
and
Additional Material from
J. D. Anderson, Modern Compressible Flow with
Historical Perspective, 3rd ed.
1
www.nasa.gov
National
NationalAeronautics
Aeronautics and
and Space
SpaceAdministration
Administration
Stephen A. Whitmore, USU MAE Dept.
2
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Basics
Slow them down
for atmospheric
reentry
Basics (2)
Rocket’s basic
function is to
take mass, add
energy, and
convert that to
thrust.
Combustion is an exothermic chemical reaction. Often an external heat
source is required (igniter) to supply the necessary energy to a threshold
level where combustion is self sustaining
3
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
Propellants that combust spontaneously are referred to as Hypergolic4
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
1
6/13/2009
Basics (2)
What is a NOZZLE? (1)
• Combustion Produces High temperature gaseous By-products
• FUNCTION of rocket nozzle is to convert thermal energy
in propellants into kinetic energy as efficiently as possible
• Gases Escape Through Nozzle Throat
• Nozzle Throat Chokes (maximum mass flow)
• Nozzle is substantial part of the total engine mass.
• Since Gases cannot escape as fast as they are produced
… Pressure builds up
• Many of the historical data suggest that 50% of solid rocket failures
stemmed from nozzle problems.
• As Pressure Builds .. Choking mass flow grows
The design of the nozzle must trade off:
1. Nozzle size (needed to get better performance) against nozzle weight
penalty.
• Eventually Steady State Condition is reached
5
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Mach Number: Revisited (cont’d)
• Based on thermodynamics and conservation equations
we derived TWO relationships Whose ramifications are
fundamental to this class



dp
1 V 2

dA
M2 1 A

 dV 
 dp 
M 1 
0  0
 dA 
 dA 
 dV 
 dp 
M 1 
0  0
 dA 
 dA 
dp
1 V 2

dA
M2 1 A

1
V
 dV 

 dA 
M2 1 A

1
V
 dV 

 
2
dA
M 1 A
National Aeronautics and Space Administration
6
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Mach Number: Revisited

2. Complexity of the shape for shock-free performance vs. cost of
fabrication

7
Stephen A. Whitmore, USU MAE Dept.
8
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
2
6/13/2009
Fundamental Properties of Supersonic
and Supersonic Flow
Why does a rocket nozzle look like this?
M 1
M 1
 dA 
   0
A
 dV 

 0
V 
National Aeronautics and Space Administration
 dV 

 0
V 
 dA 
   0 .... M  ?
A
10
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
… Hence the shape of the rocket Nozzle
Equation of State for a Perfect Gas
• Relationship Between pressure, temperature, and density
derived empirically in Modern form by John Dalton
• Theoretically derived by Ludwig Boltzmann using statistical
Thermodynamics
• In perfect gas … intermolecular (van der Waals) forces are neglected
p V = n Ru T
•p•V•n• Ru •T-
John Dalton
11
National
NationalAeronautics
Aeronautics and
and Space
SpaceAdministration
Administration
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
p
v
T
pressure acting on gas
n
volume of gas in system
Number of moles of gas in system
Universal gas constant
Temperature of gas
1-mole --> 6.02 x 1023
Avagadro's number
12
Stephen A. Whitmore, USU MAE Dept.
3
6/13/2009
Thermodynamics Summary
Equation of State for a Perfect Gas (cont’d)
• Re organizing the equation of state
p
•p•V•n• Ru •T• Mw• Rg •M-
• Equation of State:
M n
R
R
R T   u T   u T   RgT
V M u
M /n
Mw
pressure acting on gas
volume of gas in system
Number of moles of gas in system
Universal gas constant
Temperature of gas
Molecular weight of gas
Gas Specific Constant
Mass of gas contained in volume
M
1
v
V

M
R
 M w  Rg  u
n
Mw
• Useful working form for Gas Dynamics
p   RgT
13
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
p   RgT  > Rg 

-
Ru
= 8314.4126
Rg (air) = 287.056
Ru
Mw
J/K-(kg-mole)
J/K-(kg-mole)
• Relationship of Rg to specific heats, 
g = cp/cv
cp  cv  Rg
~ 1.4 for air
• Internal Energy and Enthalpy
de
h = e + Pv
cv   
 dT  v
cp  
dh 
 dT  p
14
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Thermodynamics Summary (2)
Gas Constant and Molecular Weights
• Speed of Sound for calorically Perfect gas
• Mach Number M 
V
g RgT
c  g RgT
• Second Law of Thermodynamics, reversible process
T 
p 


• Molecular Weight
of various gases
s2  s1  cp ln2  2   Rg ln  2 
T
p
1

1
• Gas Specific constant is
Universal constant divided
by the average molecular
weight of the gas

• Second Law of Thermodynamics, isentropic process
(adiabatic, reversible)
------> s2 - s1 = 0
National Aeronautics and Space Administration
p2
p1
g
 T  g 1
 2
 T1 
• Numerical Values for Universal Gas Constant
Ru = 1545.40 ft-lbf/R-(lbm-mole)
Ru = 49722.01 ft-lbf/R-(slug-mole)
Ru = 8314.4126
J/K-(kg-mole)
(steam)
15
Stephen A. Whitmore, USU MAE Dept.
16
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
4
6/13/2009
Gas Constant and Molecular
Weights(concluded)
Specific Heats
cp  cv  Rg
• Molecular weight of Air
Average molecular weight of the gases in the atmosphere.
Air on earth at sea level is a mixture of approximately 78% nitrogen,
21%oxygen, with the remaining one percent a mix of argon,
carbon dioxide, neon, helium and other rare gases,
~ 28.96443 kg/kg-mole
• Numerical Values for Air Specific Gas Constant
Rg = 53.355 ft-lbf/R-(lbm)
Rg = 1716.658 ft-lbf/R-(slug)
Rg = 287.056 J/K-(kg)
17
18
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Momentum Equation for
Quasi 1-D Control Volume
Continuity Equation for
Quasi 1-D Control Volume
• Similar Analysis for Momentum Equation Yields
dS
   
   V  ds   0
V1
C .S.
p1
• Upper and Lower Surfaces …
no flow across boundary

dS
dS
V2
Control Volume
T1
p2
A1

T




1
1
1
1
1




2

2
1

V2 •  ds  2 V2 cos(0 o )  ds  2 V2 A2
2
2
p1
dS
dS
p2
A1
T
2
A2
C.S.


1V1A1  2V2 A2
• Because of duct symmetry the “Z-axis”
Component of pressure integrated to zero
dS

ix
“Unit vector” x-direction
19
National Aeronautics and Space Administration
V2
Control Volume
T1
1
1 1
• Inlet (properties constant across Cross section) -->
   V  ds  
Control Surface
V1
p1 A1V1  1V12 A1   p ds • ix  p2 A2V2  2V2 2 A2
o
1

    
   V  ds V     p dS 
2
dS
   V  ds   V •  ds   V cos(180 )  ds    V A
1
• Newton’s Second law-Time rate of change of momentum
Equals integral of external forces
C.S.
• Inlet (properties constant across Cross section) -->

2
A2
V  ds  0

dS
Control Surface
Stephen A. Whitmore, USU MAE Dept.
20
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
5
6/13/2009
Engine Thrust Model (revisited)
Engine Thrust Model (cont’d)
• Steady, Inviscid, One-Dimensional Flow Through Ramjet
• Adding
pe Ae  p Ae 
to Both Sides, and collecting terms
•
•
P
dAwall  p Ai  pe Ae  pe Ae  p Ae   m e Ve  m i Vi  pe Ae  p Ae 
P
dAwall  p Ai  Ae   m e Ve  m i Vi  pe Ae  p Ae 
wall
wall
wall
•
•
wall

   p dS 
C.S.




 
   V  ds V
C.S.
•
Integrated Pressure
Forces Acting on
External + Internal
Surface of Engine
Wall = Thrust
•
Pwall dAwall  p Ai  pe Ae  eVe Ae  iVi Ai  m e Ve  m i Vi
2
2
wall
•
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
•
Thrust  m e Ve  mi Vi  pe Ae  p Ae 
21
22
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Energy Equation for
Quasi 1-D Control Volume
Rocket Thrust Equation, revisited
•
•
mi  0
Thrust  m e Ve  pe Ae  p Ae 
• Thrust + Oxidizer enters combustion
Chamber at ~0 velocity, combustion
Adds energy … High Chamber pressure
Accelerates flow through Nozzle
Resultant pressure forces produce thrust
•
Q



 ( pd S ) • V     e 
C.S.
C.S.
V 2   
V•d S 
2 
V1
p1
T1
dS
Control Surface
dS
dS
Control Volume
A1
q h1 
V12
V2
 h2  2
2
2
Stephen A. Whitmore, USU MAE Dept.
p2
T
2
A2
dS
23
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V2
24
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6
6/13/2009
Stagnation Temperature for the
Adiabatic Flow of a Calorically Perfect
Gas
• From Earlier Analysis
• Consider an adiabatic flow field with a local gas
Temperature T(x), pressure p(x), and a velocity V(x)
• Since the
Flow is adiabatic
V2
2  g g  1 M 2 
cvT
2
T(x)
x
V2

2g cv
p(x)
V(x)
h(x) 
V (x)2
V (x)2
 c pT (x) 
 Const
2
2
V(x)2
V(x)2
c pT (x) 
 c pT0  To  T (x) 
2
2c p
• Therefore
V2
V2
g  1 M 2

T
cp
2c p
2
2 cv
cv
To  T (x)  T (x)
g  1 M (x)2
2
Holds anywhere
Within an adiabatic
Flow field
25
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Stagnation Temperature for the
Adiabatic Flow of a Calorically Perfect
Gas (cont’d)
26
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Stagnation Temperature for the
Adiabatic Flow of a Calorically Perfect Gas
Stagnation Temperature for the
Adiabatic Flow of a Calorically Perfect Gas
(cont’d)
(cont’d)
• In general for an adiabatic Flow Field the
Stagnation Temperature is defined by the relationship
T0
g  1 M 2
 1
T
2
• Stagnation temperature is a measure of the Kinetic
Energy of the flow Field.
• Largely responsible for the high Level of heating
that occurs on high speed aircraft or reentering space
Vehicles …
• Stagnation Temperature is Constant Throughout
An adiabatic Flow Field
• T0 is also sometimes referred to at Total Temperature
T0
g  1 M 2
 1
T
2
• T is sometimes referred to as Static Temperature
27
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28
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7
6/13/2009
Stagnation Properties (concluded)
Stagnation Pressure for the
Isentropic Flow of a Calorically Perfect Gas
• Now Consider an Isentropic flow field with a local gas
Temperature T(x), pressure p(x), and a velocity V(x)
• In Isentropic Nozzle, T0, P0 are constant
T (x) 
T(x)
x
p(x)
V(x)
g
g
P(x) 
P0
g
 g 1
 g 1
M (x)2 
 1 

2
• Mass flow tuned with T0, P0 to give sonic velocity
At Throat …
• Since the Flow is isentropic, from Section 1
p0  T0  g 1  g  1 2  g 1

 1 
M 
p  T 
2


T0
g 1
1
M (x)2
2
“stagnation”
(total) pressure:
Constant throughout
Isentropic flow field
29
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
30
Temperature/Entropy
Diagram for a Typical Nozzle
•
q  h1 
V12
V2
 h2  2
2
2
Tds   q  dsirrev
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Chamber pressure
• Why can we assume that the Rocket Chamber pressure is
Approximately stagnation pressure in an isentropic Nozzle?
cp  
dh 
 dT  p
• Less than 0.6% error
In Assumption
•
q
cp
• Combustion Velocity is initially in all directions .. .Little net
axial velocity ~ Mchamber ~0.1 … Pchamber
1
Isentropic
Nozzle
P0 chamber
31
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National Aeronautics and Space Administration

1.2
 0.994 
 1.2  1 2 1.21
1
0.1 
2


32
Stephen A. Whitmore, USU MAE Dept.
8
6/13/2009
Nozzle Mass Flow per Unit Area
Chamber temperature
• Combustion Flame temperature Temperature of
Endothermic reaction of propellants
• Solve for the Mass Flow per Unit area in a 1-D, steady,
isentropic
flow field as function of T0, P0, M (hint start with continuity )
•
• Less than 0.01% error
In Assumption
m
p
p
 V 
V
gV 
Ac
RgT
g RgT
p
g RgT
g
• Combustion Velocity is initially in all directions .. .Little net
axial velocity ~ Mchamber ~0.1 …
T flame
T0 chamber

1
 0.9990 
 1.2  1 2 
1

0.1 
2


g
Rg
33
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
•
Rg
V
g
p
M
T
1

g RgT
Rg
T0 p p0
M
T p0 T0
g  1 M 2
2
g
 g  1 2  g 1
1  2 M 


p0
M
T0
g
Rg
p0
T0
M
g 1
 g  1 2  2 g 1
1  2 M 


34
Stephen A. Whitmore, USU MAE Dept.
Nozzle Mass Flow per Unit Area (cont’d)
as a function of mach number
 m• T
0

 Ac p0
•
m T0
Ac p0
• At what mach number does
gp
M
g RgT
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Nozzle Mass Flow per Unit Area (cont’d)
• Plot m T0
Ac p0
Rg
g

Rg   0.68473

max
• maximum
Massflow/area
Occurs when
When M=1
Rg
have the greatest value
• Assume g=1.4, Rg= 287.056 j/kg-K
•
m T0
Ac p0
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Rg 
gM
g 1
 g  1 2  2 g 1
1  2 M 


Stephen A. Whitmore, USU MAE Dept.
35
36
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9
6/13/2009
Isentropic Nozzle Flow: Area Mach
Relationship
Nozzle Mass Flow per Unit Area (concluded)
• maximum
Massflow/area
Occurs when
When M=1
• Effect known
as Choking in a
Duct or Nozzle
• i.e. nozzle will
Have a mach 1
throat
 m• T
0

 Ac p0

 m• T
0
Rg    *

 A p0
max
g 1
 g  1 2 g 1
1  2 


m

A*
• Then comparing the massflow
/unit area at throat to some
Downstream station
g 1
g
•
• Consider a “choked-flow”
Nozzle … (I.e. M=1 at Throat)

Rg  

g  2 
Rg  g  1
 2  g 1
 g

 g  1
g 1
•
m T0
A* p0
g 1
g 1

•
m T0
A p0
p0
T0
Rg
A

A*
National Aeronautics and Space Administration
Isentropic Nozzle Flow: Area Mach
Relationship
 2  g 1
 g  1 
1
g 1

g 1
 g  1 2  2 g 1
1  2 M 


37
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Rg
1  2  
g  1 M 2   2g 1
1

 
M  g  1  
2

38
Stephen A. Whitmore, USU MAE Dept.
Example: SSME Rocket Engine
(cont’d)
• A/A* Directly related to Mach number
g 1
• The Space Shuttle Main Engines
Burn LOX/LH2 for Propellants with
A ratio of LOX:LH2 =6:1
A
1  2   g  1 2   2 g 1

1
M 

A* M  g  1 
2

• “Two-Branch solution: Subsonic, Supersonic
• Nonlinear Equation requires
Numerical Solution
• The Combustor Pressure, p0
Is 18.94 Mpa, combustor
temperature, T0 is 3615K,
throat diameter is 26.0 cm
• “Newton’s Method”
• What propellant mass flow rate
is required for choked flow in the
Nozzle?
^
^
^
M ( j 1)  M ( j ) 
F(M ( j ) )
 F 
 M 
|( j )
• Assume no heat transfer Thru Nozzle
no frictional losses, g=1.196
39
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National Aeronautics and Space Administration
40
Stephen A. Whitmore, USU MAE Dept.
10
6/13/2009
Example: SSME Rocket Engine (cont’d)
Example: SSME Rocket Engine (cont’d)
-- By product ~ Burns rich, byproduct
is water vapor + GH2
Massflow rate
• Compute Throat Area
2
 26   =0.05297 m2


100 4
MW ~ 13.6 kg/kg-mole
-- Rg = 8314.4126 /13.6 = 611.35 J/K-kg
g 1
•
m

A*

2
 1.196 




 611.35 1.196 + 1
g  2  g 1 p0
Rg  g  1
T0
 1.196 + 1   0.5
1.196  1 


18.94  106
=437.1 kg/sec
 3615 0.5
= 8252.59 kg/sec-m2
National Aeronautics and Space Administration
• Mass flow =
 m• 
 *   A* 8252.59
8252.59  0.05297
0.04714  389.03kg /sec
 A 
=
41
Stephen A. Whitmore, USU MAE Dept.
42
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Example: SSME Rocket Engine (concluded)
Example: SSME Rocket Engine (cont’d)
• The nozzle expansion ratio is
77.5 -- what is the exit mach number
g 1
A
1  2   g  1 2   2 g 1
 77.5 
1
M 

A*
M  g  1 
2

Compute Exit Mach Number
A
1  2   g  1 2  

1
M 

A* M  g  1 
2

• Non -linear function of mach number
• Solution methods
=
 1 + 1.196  1  4.677084 2    2  1.196
 

1.196 + 1
2
4.677084
2
 1
= 77.49998 ----> Mexit = 4.677084
i) Plot A/A* versus mach
ii) Numerical Solution
Newton Solver comes in handy here!44
43
Stephen A. Whitmore, USU MAE Dept.
Expansion ratio = 77.5
1.196 + 1


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g 1
2 g 1
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11
6/13/2009
Example: SSME Rocket Engine (cont’d)
Example: SSME Rocket Engine (cont’d)
Compute Exit Temperature
Mexit = 4.677084
Compute Exit Velocity
T0
g  1 M 2
 1
T
2
Texit 
3615 1 +
Mexit = 4.677084
Vexit  M exit g RgTexit 
4.677084  1.196 611.35 1149.9 0.5
T0

g  1

1
M exit 2
2
= 4288.61 m/sec
1
1.196  1
2
 4.677084   =1149.90 K
2
45
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Example: SSME Rocket Engine (cont’d)
Compute Exit
Pressure
Mexit = 4.677084
46
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Example: SSME Rocket Engine (cont’d)
Compute Effective Exhaust Velocity (Vacuum)
Pexit 
P0
g
g 1

g  1
2
 1  2 M exit 

Ce 
Thrust
•
m
 Vexit 
4288.61 +
Aexit * ( pexit  p )
A

•
A*
m
77.5 0.0529708  17.455 1000
437.14
6
18.94 10
 1 + 1.196  1  4.6770842  


2
 1.196=17.45511



1.196  1
kPa
= 4452.53 m/sec
47
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48
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12
6/13/2009
Example: SSME Rocket Engine (cont’d)
Example: SSME Rocket Engine (cont’d)
Compute Thrust (Vacuum)
Compute True Isp (Vacuum) (ignore nozzle Losses)
•
Thrust  m Ce 
437.14 4452.53
106
I sp 
= 1.9464 mNt
Ce

g0
4803.891
= 454.06 sec
9.806
49
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Example: SSME Rocket Engine (cont’d)
Example: SSME Rocket Engine (cont’d)
Compute Effective Exhaust Velocity (Sea level)
Ce 
Thrust
•
m
4288.61 +
 Vexit 
50
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Compute Thrust (Seal level) (ignore nozzle Losses)
Aexit * ( pexit  p )
A

•
A*
m
•
Thrust  m Ce 
77.5 0.0529708  17.455 1000  101325
437.14
437.14 3500.976
106
= 1.540 mNt
= 3500.98 m/sec
P sea Level =101.325 kPa
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Stephen A. Whitmore, USU MAE Dept.
52
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Stephen A. Whitmore, USU MAE Dept.
13
6/13/2009
Example: SSME Rocket Engine (cont’d)
Example: SSME Rocket Engine (cont’d)
Compute True Isp (Seal level) (ignore nozzle Losses)
C
I sp  e 
g0
Ideal
Calc.
Calc.
Actual
Actual
Vac.
S.L.
Vac.
S.L
________________________________________________________________
Isp
529.69
454.06 357.03
452.5
363
(sec):
Thrust: 2.271
1946.37 1530.42
2.10
1.67
(mNt)
3500.976
= 357.024 sec
9.806
53
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Stephen A. Whitmore, USU MAE Dept.
• Obviously Out estimate of throat area is a bit small ….
… but you get the point …
54
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Exit Pressure has a dramatic
effect on Nozzle performance
Example: SSME Rocket Engine (cont’d)
• When we automate the process …
Conical Nozzle
Bell Nozzle
… It appears
that A* ~ 0.05785
… or a
Throat diameter
Of ~ 27.2 cm!
Vacuum (Space)
Lift off
Large area ratio nozzles
at sea level cause flow
separation, performance
losses, high nozzle
structural loads
Under expanded
Bell constrains flow
limiting performance
Over expanded
55
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National
NationalAeronautics
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and Space
SpaceAdministration
Administration
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14
6/13/2009
Example: Atlas V 401
First Stage
The
"Opti
mum
Nozz
le”
National
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and Space
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• Thrustvac
= 4152 kn
• Thrustsl
= 3827 kn
• Ispvac
= 337.8 sec
• Ae/A*
= 36.87
• P0
= 24.25 Mpa
• Lox/RP-1
Propellants
• Mixture ratio
= 2.172:1
• Chamber pressure= 25.74 MPa
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
Atlas V, Revisited
Look at Thrust as function of Altitude (p)
• ATLAS V
First stage is
Optimized for
Maximum
performance
At~ 3k altitude
7000 ft.
• Thrust increases
With the
logarithmic of
altitude
“Best nozzle”
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6/13/2009
Summary (1)
Summary (2)
-Gas Law:
p   RgT
- Exit Pressure, Temperature, Velocity….
g 1
•
g  2  g 1 p0
Rg  g  1 
T0
m

-Choking Massflow: A*
Pexit 
-P0, T0 ~ Constant for Lossless Nozzle
Iterative Solution ….
-Exit Mach Number ….
Function of Expansion
Ratio only
g 1
A
1  2   g  1 2   2 g 1
 77.5 
1
M 

A*
M  g  1 
2

Texit 
P0
g

g  1 M 2  g 1
1
exit 
2


T0

g  1

1
M exit 2
2

Vexit  M exit g RgTexit 
61
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National Aeronautics and Space Administration
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Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Summary (3)
Summary (4)
Finally, Thrust, Effective Exit Velocity, and Specific Impulse
•
Thrust  m e Ve  pe Ae  p Ae 
Ce 
Thrust
•
m
 Vexit 
I sp 
National Aeronautics and Space Administration
Aexit * ( pexit  p )
A

•
A*
m
Ce
g0
Credit: Aerospace web
Plume Expansion
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Nozzle Divergence Correction Coefficient
Nozzle Divergence Correction Coefficient (2)
• Quasi-1-D analysis assumes
exit flow leaves parallel
to longitudinal axis of the nozzle
• In reality … this rarely happens

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nozzle
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Actual
Momentum
Thrust
Momentum
Thrust of
idealized
Nozzle
Application of
Correction
Factor
Faxial
•
m Vexit

1
1  cos[ ]  
2
•
Thrust   m Vexit  Aexit Pexit  P 
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Nozzle Divergence Correction Coefficient (3)
Questions?
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ESDM Senior
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Propulsion Systems II: Selecting the Right
System
Sellers: Chapter 14
Additional Material from
C. D. Brown, Spacecraft Propulsion,
Sutton and Biblarz, Rocket Propulsion Elements,
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Types of Propulsion Systems:
A Quick Overview
• Delta II 7720 Launch Vehicle
www.nasa.gov
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What does a rocket “do”?
Rockets take
spacecraft to
orbit
• Aerojet MR-103G 1-Newton Thruster
Move them
around in space,
and
“Rocket”
“thruster”
Rockets if they are big,
Thrusters if they are small.
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Slow them down
for atmospheric
reentry
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Specific Impulse (Revisited)
A Very simple rocket system
Rocket’s basic
function is to
take mass, add
energy, and
convert that to
thrust.
73
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Specific Impulse (Revisited)
Stephen A. Whitmore, USU MAE Dept.
5 Types of Chemical Thrusters
•
•
•
•
•
Cold Gas
Monopropellant
Bipropellant
Solid
Hybrid
Specific Impulse
(revisited)
450 sec is “best you can get” with chemical rockets
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Cold Gas Thrusters
Cold Gas Thrusters
• No Combustion
• The balloon model: A big tank of gas, a
valve, and a nozzle.
• Used on early satellites for simplicity
• Isp of 50 seconds
• thrust less than a pound
Gas Storage Tank
Gas Exhaust Nozzle
• Thrust provided by
expansion of gas
through Nozzle
• Low Isp
Pressure
Regulator
• Simple Mechanism
Actuator Valve
for Gas Flow
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Monopropellant systems
• Often used for
spacecraft RCS
system
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Monopropellant Thrusters
• An unstable chemical that will decompose
exothermically in the presence of a catalyst.
• The chemical needs to be unstable, but not
too unstable.
• V2 used hydrogen peroxide, but it
decomposes in storage, leading to
overpressures and water.
• Current systems use Hydrazine, which
decomposes into Hydrogen, nitrogen, and
ammonia in the presence of iridium. Isp is on
the order of 230, and total thrust can reach 80
hundreds of lbs.
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Typical Solid and Liquid Rockets
Bi-propellant System
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Bi-Prop plumbing
Bi-propellant Rockets
• Turbine Fed Bi-Prop
System
• Bi-prop offers the most performance (Isp
as high as 450 sec) and the most
versatility. They also offer the most
failure modes and the highest price
tags.
• Almost all first stage liquid rockets are
Bi-prop.
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Bi-Prop plumbing (cont’d)
Rocket Nozzle Cooling
• Pressure Fed Bi-Prop
System
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Solid Rocket Motors
Pump Fed Engine
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Solid Rocket Motors
Solid Propellants
• The oxidizer and fuel are stored in the
combustion chamber as a mechanical
mixture in solid form
• Two conditions for use:
• Black Powder
• Composite Propellant: organic binders,
aluminum powder, and an oxidizer
(usually ammonium perchlorate NH4CIO4.) The binders are rubberlike
polymers that are both fuel and binder.
– The total Impulse is known accurately in advance
– Restart is not required
• Elements include: Case, Igniter, Grain,
Nozzle, liner/insulation
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Burning Patterns
Thrust Profiles
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Space Shuttle Reusable Solid Rocket
Motor (RSRM)
Hybrid Motors
• Relatively Low Isp, Capable of High Thrust
• Throttleable, Restartable, Limited
explosion potential
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Space Dev® Hybrid Powered
“Spaceship 1” (cont’d)
Electric Propulsion
P
 ,u
m
• Built by Burt Rutan (Scaled Composites®) with Paul Allen’s (Apple co founder)
Money in Mojave CA SS1 wrote history, when the first private suborbital
spaceflight was conducted on June 21, 2004 (with pilot Mike Melvill).
• SS1 won the X-Prize with flights on 29.09.2004 (Melville)
and a follow up flight on 04.10.2004. (Brian Binneie)
• Powered by a 16700 lbf thrust Hybrid Motor (SpaceDev)
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Basic Concept
Benefits of Electric Propulsion
(Specific Impulse)
P
 ,u
m
0.7
BIPROP
Chemical
400
Solar Thermal
800
Nuclear Thermal
800+
Electric
ANY
(s)
Propellant Fraction
0.6
Isp
SOLAR
THERMAL
HALL
ION ENGINE
0.5
0.4
m g0
0.3
V = 1000 m/s
0.2
• Use electric power to accelerate the propellant to
produce thrust.
• Because the effective velocity of the exhaust, Ce, is
limited only by the speed of light, the Isp can be very
high.
– As Isp increases, the required propellant mass
decreases.
pA p A
F
C
Ce  Ve  e e •  e
 e
– I sp  •
g0
m ex
0.1
0
100
400
700
1000
1300
1600
1900
2200
2500
Specific Impulse (s)
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2800
• However, unless we have megawatts of electricity
available, the total thrust will be small. Accelerations
in the range of 0.001g
Power Required
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Power Required (2)
• Mechanical Power of a Rocket Exhaust
 Pex 
mblob
1
F  Ce
2
• Define Power Plant Efficiency

Pout
 Pex    Pin
Pin
• The electrical power needed is a function of the thrust
required, and the Isp.
Ce
Pin 
F
1
Ce  •  g0 I sp  Pex  F  go  I sp
2
m
F  I sp  g0
2
(High Isp means
low Thrust Unless
you have a BIG!
Power source.)
•  is an efficiency factor that depends on the specific
electric thruster, and varies from 0.3 to 0.95
99
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Power Required (cont’d)
Classes of EP Thrusters
• Electro-Thermal - The propellant gas is
electrically heated and expanded through a
nozzle.
P
 ,u
m
– resistojets and arcjets.
• Electro-Static - The propellant is ionized and
the resulting ions are accelerated through an
electric potential.
• Specific Mass (Kg/KW)
How much systems weighs per unit of
power delivered
– Hall effect and Kaufmann type thrusters.
• Electro-Magnetic - Both electric and
magnetic body forces are used to accelerate
ions.
• EP systems tend to have larger
specific
Masses than chemical rockets due to
Higher complexity of systems
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– Magnetoplasmadynamic thruster, or MPD
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Choice of System:
Which Rocket is Best?
Three Classes of Electro-propulsion
• It all depends on your requirements
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Steps in the Selection Process
• Mission Needs and Objectives
– dictate performance, trajectory, launch site
• Dedicated or shared launch
• Mission requirements
– orbit altitude, inclination, right ascension
– satellite weight and size
– date
• Select candidate Launch systems (more than
1!)
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Costs, US systems
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Selection Drivers
•
•
•
•
•
•
Cost
What Velocity (V)?
How Much Weight?
Reliability
Availability
Secondary Issues
– payload envelope
– environments
– interfaces
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Costs, Foreign Systems
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Launch Cost Model
Launch Cost Model
• Groundbreaking paper presented by Dr. James S. Wertz (SMAD) at the International
Aerospace Federation Congress in October 2000 addressed this misconception.
-- This paper presented an analytical launch cost model that considered a wide
range of cost elements and allowed an objective assessment of launch costs to be
performed.
 Key factors
o 1) cost of development,
o 2) cost of recovery,
o 3) cost of refurbishment,
o 4) cost of insurance.
-- For a reusable launch vehicle these factors are significantly larger than for an
expendable launch stack.
The only cost not incurred by the RLV is the cost of the ELV hardware and
assembly.
For a minimal number of flights, the RLV costs far exceed the costs of the ELV hardware
and assembly.
Stephen A. Whitmore, USU MAE Dept.
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Comparison of Expendable vs.
Reusable Launch Cost Factors
ELV
RLV
FACTOR
X
X
Amortization of Non-recurring
development production cost
X
X
ELV Recurring production cost
RLV Amortization of production
cost
RLV’s are starting to look more
And more impractical … hence
End-of-life for Space shuttle
Higher for RLV due to larger
nonrecurring cost
ELV uses learning curve: RLV is more
complex and expensive to produce
Amortization rather than recurring
production is the major RLV cost savings
X
Recovery cost
$0 for ELV
Refurbishment cost
May be substantial for RLV; $0 for ELV
X
X
Flight Operations
RLV has more complex systems; more
expensive check-out and recovery
X
X
Vehicle insurance
Depends on both replacement cost and
reliability; ELV or RLV could be cheaper
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Comparison of Expendable vs.
Reusable Launch Cost Factors
DISCUSSION
X
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Is there a break even point?
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Multi-Stage Trades
Multi-stage Rockets
•
•
In general, the benefit of discarding the empty tanks and structures
outweighs the additional cost and complexity.
For a single stage rocket:
V  go I sp ln(
mi
mf
)  go I sp ln(
wi
wf
)
•
For a multiple stage rocket:
•
The improvement is because the final weight of stage 1 does not equal
the initial weight of stage 2.
Vt  V1  V2  V3  ...
• Current state-of-the art-solution
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System Weight Comparison
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• Advantages:
– Reduces total vehicle weight for the same payload and delta
V
– …or, increases payload from the same vehicle
– Increases the max velocity for a given vehicle
– Decreases required Isp
• Disadvantages:
– Increased Complexity
– Decreased Reliability
– Increased Cost
• Although additional stages improve
performance – to a point – the greatest single
improvement is with the second stage
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Propellant Comparisons
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Issues in Launch System
Propellant Comparisons
Type
Propellant
Cold Gas
Solid Motor
Mono prop
Bi-Prop
Bi-Prop
Bi-Prop
Bi-Prop
Bi-Prop
Bi-Prop
N2, NH3, Freon, He
Various
H2O2, N2H4
O2 and RP-1
O2 and H2
N2O4 and MMH
F2 and N2H4
OF2 and B2H6
CIF5 and N2H4
National Aeronautics and Space Administration
Vacuum
Isp
50-75
280-300
150-225
350
450
300-340
425
430
350
Thrust Range
(lbf)
0.01-50
10 - 106
0.01-0.1
1 - 106
1 - 106
1 - 106
1 - 106
1 - 106
1 - 106
Avg Density
(gm/cm3)
0.28-0.96
1.8
1.44, 1.0
1.14 and 0.80
1.14 and 0.07
1.43 and 0.86
1.5 and 1.0
1.5 and 0.44
1.9 and 1.0
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• Performance Capability - weight capacity to selected
orbit.
• Vehicle availability - Is there a rocket available when
you want to launch? How about a matching facility?
Ground Stations (launch phase?)
• Spacecraft-to-launcher compatibility - Will your
spacecraft survive the launch environments?
• Cost - can you afford it?
• Fairing Size - Will your satellite fit in the nose of the
rocket?
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Maximum Available Thrust
Mass Fractions
• What percentage of each vehicle is
devoted to each of the functions … e.g.
– propellant mass fraction: 0.85
– Structure mass fraction: 0.14
– payload mass fraction: 0.01
• spacecraft bus
• upper stages
• payload
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Availability
Margins
• Budget resources!
• Power, Weight, Propellant, Dollars, computer
memory space,…...
• Develop an allocation for each component or
subsystem, and keep a reserve.
• Weight is the resource that most affects
launch systems.
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• Reliability - How likely is it that this one will blow up?
• Production capacity - How many are there, and how
fast can the supplier deliver another?
• Operations support - Range issues - How many
compatible launch facilities are there, and what is
their turnaround time?
• Stand-down after failure.


 L 1 - R T

d
A =1- 
1 


 1 -  
S 

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Payload Integration
• Match the environments and interfaces of your satellite to
several launch vehicles. - design for the worst case.
– Fairing size and shape
– Maximum Accelerations
– Vibration Frequencies and magnitudes
– Acoustic frequencies and magnitudes
– Temperature extremes
– air Cleanliness
– Orbital Insertion Accuracy
– Interfaces to launch site and vehicle
A=availability
L=launch rate
R=reliability
Td=stand down
S=surge capacity
Packaging Issues
• Size
• Margins
(clearances)
• Protection from
aerodynamic loads
– Heat
– Buffeting
• Protection from
contamination
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Structural and Electrical Interface
• Bolt patterns and adapter Rings - part of the
payload weight budget.
• Electrical I/F - matching plugs, voltage sense.
• Optical and R/F I/F - depending on the
payload, it may need to be tested, examined,
or stimulated before launch, but after mating
to the launch vehicle.
• Separation devices and separation control
circuits
• Communications architecture for the launch
and insertion phase.
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Payload Environments
• Contamination - conditioned and filtered air
post-mate and pre-launch.
• Thermal environment - keep the satellite
within the design range (or design the range
to match what the vehicle can support.)
• Pressure - flight environment can increase
pressure. Satellite and fairing must vent
excess pressure as the vehicle approaches
vacuum
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Vibration and Acceleration Loads
• Static (steady state) and Dynamic (vibration)
loads on the vehicle.
• Design for the worst case sum, with margin.
• Causes
–
–
–
–
–
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vehicle acceleration
variable engine thrust
aerodynamic drag
acoustic pressure from the engine
response of the vehicle (frequency response)
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Example Acceleration Table
Example Vibration Environments
Human-Crew G-Loads
7.0 G’s De-Conditioned
Crew Load Limit Reclined
(eyeballs-in)
(ref. NASA-STD-3000 &
JSC-28351)
4.0 g’s De-conditioned
Crew Load Limit Sitting
Upright (eyeballs-down)
or Sick/Injured Crew
Load Limit Reclined
(eyeballs-in)
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Example Fundamental Frequencies
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Example Shock Environments
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Homework 4
Sellers: 14.1
Questions?
Probs. 28, 29, 34, Page 602
133
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Notional Gravity Offset System Design
Design Friday ….
i)
LabviewTM Tutorial Demonstration
ii)
Isentropic Rocket Nozzle Simulation Overview
iii)
Design cold-gas system for gravity 5/6th’s offset for a candidate 100
kg LLRV demo model (must support 5/th of vehicle weight)
A) Assume Dry Nitrogen Working Fluid
B) Optimize for USU Campus Altitude (4750 ft elevation)
C) Show Trade Plots of Chamber pressure versus thrust, massflow
D) Size the System to give a 5 minute run time (including tank
volume)
E) Develop Preliminary plumbing layout
F) Prepare 20-page Slide Summary for Next “Design Friday”
• Maneuvering
Thruster
• Cold-Jet
Gravity Offset
Thruster
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Landing Pads
Attached to
Gimbaled
platform
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Example N2 Tank Farm
Notional Gravity Offset System Design (2)
•
Off-loading gravity offset propellant provided significant
payload savings and allows for almost infinite run time,
scalable to ANY size and weight
USAF Plant 42, Site 1 - Palmdale
Nitrogen System
LN2 Tank (PV-301)
 26,000 Gallon capacity
 43 PSIG MAWP
•
Allows for reasonable onboard propellant mass fraction for
maneuvering engine, especially for higher specific impulse
designs
GN2 Receiver Tank (PV-302)
 650 Cubic Feet
 5500 PSIG MAWP … (7854 kg capacity)
Cold jet run time … @ 0.19 kg/sec … 11.6 hours!
•
Cold-gas system can be throttled almost infinitely, can be
scaled to support any load as long as “tank farm” is sufficiently
large
Refurbished and repainted, Recertified (10 years) in
summer 2007
US Government (NASA) owned
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National Aeronautics and
Space Administration
ESDM Senior
Design Project
Background
Orbital Mechanics I
Kepler’s Laws
Sellers, Chapter 4
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www.nasa.gov
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Background (2)
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Background (3)
Gravitational Attraction on a
10,000 kg Spacecraft
Attractive Force, Newtons
100
Geo
Attraction of Earth
10
1
Attraction of Sun
0.1
0.01
0.001
Attraction of Moon
10000
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20000
30000
Orbital Altitude, kilometers
40000
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Background (4)
Background (5)
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4
Kepler’s Laws
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5
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7
Kepler’s Laws (2)
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Kepler’s Laws (3)
Kepler’s Laws (3)
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Closed-Conic Section Orbits
9
Closed-Conic Section Orbits (2)
Elliptical Orbits:
Radius, angular
velocity no longer
constant
Angular velocity
within circular orbit
is constant
• Adding " V" turns a circular
orbit into an elliptical orbit
 VT
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Parameters of the Elliptical Orbit
Fundamental Definitions
“Line of Apsides”
apogee
Rp
Ra
perige e
2b
2a
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a -- Semi-major axis
b -- Semi-minor axis
e -- Orbital eccentricity
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Fundamental Definitions (3)
Fundamental Definitions (2)

apogee
Rp
Ra
perige e
2a
Orbit Apogee and Perigee (closest and farthest approaches)
… semi major axis and eccentricity related to apogee and perigee radius
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2b
Angular Location within an Orbit: “true anomaly” 
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Open-Conic Section Orbits
Vcirc 
Open-Conic Section Orbits (2)

Vcirc 
r

r
p=“perigee radius”
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Open-Conic Section Orbits (3)
17
Open-Conic Section Orbits (4)
Hyperbolic Trajectories:
"Excess Hyperbolic Velocity" approach/departure" V  > 0
Parabolic approach/departure" V  = 0
• If "V " > 0 , then probe will approach and
depart along a hyperbolic trajectory
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Kepler’s First Law
(Summary)
Kepler's Second Law
Kepler’s First
Law Describes the
Shapes of Orbits
Closed-Orbits
Kepler’s Second Law
Describes the Travel
Within the Orbit
Open-Orbits
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21
Alternate Statement of Kepler's
Second Law:
Kepler's Second Law (2)
Mathematical Representation of Kepler's Second Law
T  Orbit Period
Aellipse  a 2   1  e2
At2 t1  swept area from point 1 to point 2
t2  t1  " time  of  flight " from point 1 to point 2
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Kepler's Third Law
Time of Flight Graphs
Area Swept from Perapsis
t1
0
1
t0
0
“same  ?”
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Time of Flight Graphs (2)
25
Time of Flight Graphs (4)
“swept area” from Perapsis
2
2

1
1  a 1  e  
A   r  2 d   
 d
2
2  1  e  cos   
0
0

“Very Difficult Integral”
“time-of-flight” from Perapsis
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Final position
0
Time of
Flight
Postscript I: What is  ?
Time of flight
1
0
1
Propogation of Orbital Position
Kelper's Second Law, Normalized Time vs. true anomaly, elliptical orbit
1.0
Better form of the "Area Plots"
0.8
“same  !”
0.6 time from perapsis
Torbit
e = 0.0
e = 0.1
e = 0.2
e = 0.4
e = 0.6
e = 0.8
e = 0.9
e = 0.95
e = 0.99
e = 0.99
0.4
0.2
t0
T
t1 - t0
T
200
50
250
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Space Administration
1 150
0
true, anomaly, , deg.
300
350
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Postscript II: Escape Velocity
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Postscript II: Escape Velocity (2)
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Postscript II: Escape Velocity (3)
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Orbital Mechanics II
Vis-Viva Equation, and Hohmann
Transfer, Describing Orbits in
Three Dimensions, Out of Plane
Orbital Maneuvering
Sellers, Chapters 4, 5, 6, Appendix C
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Kinematics versus Dynamics
• Up to now we have mostly dealt with orbital motions
from a kinematics point of view … iI.e. Kepler’s laws
Were used simply as descriptors of orbital motion
• Kepler's laws are a reasonable approximation of
the motions of a small body orbiting around a
much larger body in a 2-body universe
… but there are no Physics (I.e. Isaac Newton)
Involved
• Kepler derived his laws of planetary motion by
Empirical observation only.
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Newton …
Isaac Newton
• Sir Isaac Newton used his new calculus and
laws of motion and gravitation to show that
Kepler was right.
•Halley then pressed Newton to publish his findings, but he
realized that he'd forgotten the proof.
• One day in 1682 he came up to his friend,
Edmund Halley, and casually mentioned to him
that he'd proved that, with a 1/r2 force law like
gravity, planets orbit the sun in the shapes
of conic sections.
• After struggling to remember how he had proved the theorem,
he published his work and it later appeared in full
form in his classic work: Philosophiae Naturalis Principia
Mathematica -- commonly known as the Principia -published in 1687.
• This undoubtedly took Halley aback, as Newton
had just revealed to him the nature of the Universe
(at least the Universe as it was known then).
• OK … let walk down Newton’s path to enlightenment!
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Conservation of Energy
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Gravity, Revisited
As described in section 3
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Gravitational Potential Energy
Kinetic Energy
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Total Mechanical Energy
of the Spacecraft
41
Total Mechanical Energy
of the Spacecraft (2)
Specific Energy
• Specific Energy ~ energy divided
by the mass
ET   = 1 m V2 - G M m = constant
T m
m
r
2

2 
  G M  planetary
T = V - r
2
gravitational parameter
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Total Mechanical Energy
of the Spacecraft (3)
The “Vis-Viva” Equation
See Sellers: Appendix C,
Pages 720, 721
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Vis-Viva Equation for All the ConicSections
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45
Application of the Vis-Viva Equation:
The Hohmann Transfer
Rc
2
Rc
1
Not-Feasible
Trans fer Orbit
How do we transfer from
Orbit to Another?
Feasible
Trans fer
Orbit
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6/13/2009
Optimal-Energy Transfer Orbit
(Hohmann Transfer)
Excess-Energy Transfer Orbit
“Wasted”
V
Two curves
Are tangential
In space
Target
Orbit
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The Hohmann Transfer (2)
The Hohmann transfer
•Most fuel efficient method
–All velocity changes are tangential
–(change velocity magnitude but not direction)
•Between circular or (aligned elliptical orbits)
•Takes longer than other less efficient transfers
•Tangential elliptical transfer orbit
•(example: Geosynchronous Transfer Orbit GTO)
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The Hohmann Transfer (3)
The Hohmann Transfer (4)
Hohmann Transfer Steps
• 0 : Calculate transfer orbit semi-major axis & eccentricity
1:
2:
3:
4:
5:
6:
7:
Calculate circular velocity of parking orbit
Calculate perigee velocity of transfer orbit
Determine perigee delta V
Calculate apogee velocity of transfer orbit
Calculate circular velocity of final orbit
Determine apogee delta V
Determine total delta V
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Hohmann Transfer Problem … Solved!
53
Hohmann Transfer Problem … Solved!
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Example: V required for Hohmann
Transfer from LEO to GEO
Example: V required for Hohmann
Transfer from LEO to GEO (2)
• Compute Orbit ratio
• Compute Normalized V
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Example: V required for Hohmann
Transfer from LEO to GEO (3)
57
Example: V required for Hohmann
Transfer from LEO to GEO (4)
• Compute Initial Orbit Velocity
• Compute Required V
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Orbital Elements (2)
Orbital Elements
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Orbital Elements (4)
Orbital Elements (3)
• i, Inclination , Defines the orientation
of the orbit with respect to the Earth's
equatorial plane
Inclination
Angle
Equatorial Orbit
Ascending Node
Inclined Orbit
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0<i<90 prograde
90<i<180 retrograde
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Orbital Elements (6)
Orbital Elements (5)

• , Argument of perigee, Defines
periapsis (low point) of the orbit relative
to a fixed line in inertial space
Inclined Orbit
Equatorial Plane
Ascending Node
Perigee
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Line-of-Nodes
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Orbital Elements (8)
Orbital Elements (7)
“RAAN”
Inclined Orbit
“Celestial Longitude”
225
315
0
Ascending Node
45
180
135
Line of Nodes
0 degrees = First Point of Aries or Vernal Equinox
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Orbital Elements: collected
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View From Orbital Plane
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Inertial Reference Axis
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“Line of Equinoxes”
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“Line of Equinoxes” (2)
Orbital Plane Changes
• Once Launch Systems burns out … ..
And payload is placed in orbit … …
your orbit inclination is fixed unless…
you add energy to the orbit
• You can only change planes
When the planes at your
orbits cross
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Simple Plane Change
Simple Plane Change (2)
Why?
 i 
V  2  V sin  
 2
 i 
V  2  V sin  
 2
Vfinal
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I
Vplane change
Vinitial
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Combined Plane Change
What if we need to change planes and inclination simultaneously?
Combined Plane Change (2)
We could do ….
z
V1
i
RGEO
Hohmann Transfer
from LEO
RGEO
V2
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Combined Plane Change (3)
5
Vcombined  V2 2  V12  2  V2V1 cos  i 
 i 
Vcombined  2  V1 sin    V2  V1 
 2
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Homework
Homework
Parabolic and Hyperbolic Trajectories (cont'd)
Parabolic and Hyperbolic Trajectories (cont'd)
• After dropping photo-torpedos, Captain Checkov
wants to get out the sphere of influence (SOI) ofAltair 5
as fast as possible without being spotted
• United Federation of Planetsstarship Excelsior
approaches Klingon outpost Altair 5 on a
covert retaliatory bombing mission
• The Excelsior has enough impulse power left for one
big burn before, having to recharge the dilithium crystals
• A cloaking device uses enormous energy & Warp
drive is non-operational with the cloak engaged
• The best way to "get out of town fast" is to fire
impulse engines at closest approach to Altair 5 -- taking
advantage of the gravity assist to give the highest
approach speed without using impulse power and
then use impulse power to depart
on a hyperbolic trajectory at angle of 45 degrees
• All maneuvering must be done on impulse power
alone
• The Excelsior uses a gravity assisted parabolic
approach trajectory to Altair 5 in order to save
on waning impulse power and insure a stealthy
approach
• What is the "Delta-V" required to depart on a
Hyperbolic trajectory with an asymptotic
departure angle of 45 degrees
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Homework:
Homework:
Parabolic and Hyperbolic Trajectories (concluded)
Parabolic and Hyperbolic Trajectories (cont'd)
• Hint 3: For a Parabolic to Hyperbolic
trajectory transfer
• Hint 1: For a Parabolic trajectory
"V" =Vh -Vp =Vp
r is measured from the parabolic focus to
the location of the Excelsior
Vh
-1
Vp
• Hint 2: For a Hyperbolic trajectory
• Hint 4: At closest apprach, the distance
from the parabolic focus to the Excelsior
must equal the distance from the Hyperbolic
right focus to the Excelsior
r is measured from the right (perifocus) focus to
• Your answer should be expressed in terms
 and rmin (closest approach distance)
the location of the Excelsior
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Design Friday ….
i)
ii)
Design Friday …. (2)
Go Through cold-gas presentations from previous week
Investigate the mass fractions and propellant Usage for a “jet cat”
Maneuvering thruster , platform integration designs
• Assume ~ 1 g operation for hover
- Cold-jet accounts for 5/6 weight
- Maneuvering thruster JetCat P200 accounts for additional 1/6 weight
- Kerosene Propellant for JetCat P200 , Isp ~ 1800
- Only maneuvering propellant stored on board vehicle
- Estimate Lift capacity
http://www.jetcatusa.com/hp5.html
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ESDM Senior
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The “Optimal” Launch Trajectory
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•Without Atmosphere or topology
variations, optimum launch
trajectory is the Hohmann transfer
from the Earth surface to the
destination orbit.
Flight Mechanics I
Orbital Launch Dynamics, Energy
Analysis, Required DV
Thrust vector normal to the
(instantaneous) radius vector.
Sellers, Chapters 9, 14, Appendix E
• Not Practical in real world!
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What Happens at Launch?
1
What Happens at Launch? (2)
A launch vehicle must get to
the required altitude and have
sufficient inertial velocity to
maintain desired orbit
Launch is a compromise of
Lift and acceleration
while minimizing drag
Launch Phases: Vertical Ascent, pitch over,
gravity turn, and vacuum flight
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What Happens at Launch? (3)
What Happens at Launch? (4)
• Velocity and Position at Burnout Determine Orbit
Final Stage Burnout
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What Happens at Launch? (5)
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What Happens at Launch? (6)
6
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What Happens at Launch? (7)
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What Happens at Launch? (8)
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What Happens at Launch? (concluded)
9
Launch Azimuth
See Sellers
Appendix E for
derivation
90o    degrees 

   radians 
 2

  

cos  i   cos    sin   
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Achievable Direct Launch
Inclination Angles
Launch Azimuth (2)

Launch Azimuth –  -- is the angle from true north
(at launch site) clockwise to the launch direction
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Achievable Direct Launch
Inclination Angles (2)
13
Launch Inclination Bottom Line
• Launch Opportunities
Chances to launch occur when the launch site latitude
equals the orbital inclination (1 per day),
or if the launch site latitude is less than the orbital inclination
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(2 per day)
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Launch Inclination Bottom Line (2)
Launch Inclination Bottom Line (3)
Inclination versus latitude:
An orbital plane extends thru
the earth’s center
Plane extends north and south to
latitude lines equal to the orbit’s
Inclination angle.
Orbit at inclination lower than
launch latitude never
intersects launch site!
See Sellers Appendix E
for derivation
To Launch directly, must wait until
Launch site intersects orbital plane
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17
What is the Earth’s angular velocity with
respect to inertial space?
Terms Affecting Launch Delta V
• Sidereal (Inertial) Day Versus Solar Day Solar day is slightly longer
because earth must rotate slightly more than one revolution to bring the
same point to the same solar angle.
• Need to accelerate from “standing still” on the ground
to orbital velocity, while lifting to orbital altitude, and
overcoming drag losses and insert into proper orbit inclination
Sidereal Day  23hrs  3600 sec  56 min  60 min  4.1sec 
• But are we really “standing still”
on ground? No! The earth is rotating
with respect to inertial space
hr
hr
86164.1sec
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6/13/2009
What is the Earth’s angular velocity with
respect to inertial space? (2)
2 rad
 
day
86164.1 sec
What is the tangential
velocity of the earth at Equator?
Req  6378km
V  Req    
 7.2921151105 rad  0.002089deg/ sec 
 0.4651km
sec
day
Equatorial
radius
sec
This is the equatorial inertial velocity
See Appendix 8 on Class Web page for introduction to Earth
Geodetic Calculations
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Example Delta V Calculation
Velocity at other latitudes
KSC Latitude ~ 28.5degEastward launch to 200 km orbit altitude
Velocity  Ve  cos(lat )
Latitude
cos(lat)
0
10
20
30
40
50
60
70
80
90
1
0.98481
0.93969
0.86603
0.76604
0.64279
0.50000
0.34202
0.17365
0.00000
velocity
(km/sec)
0.4638
0.45675
0.43583
0.40166
0.35529
0.29812
0.23190
0.15863
0.08054
0.00000
21
velocity (ft/sec)
Vearth =
1521
1497.89259
1429.27248
1317.22464
1165.15360
977.67995
760.50000
520.21264
264.11888
0.00000
Vorbit 

r
= 0.4084 km/sec

3.9860044 105 km3 sec2
6373  200
Rearth KSC  6373km

= 7.7873 km/sec
DVorbit =
7.7873 - 0.4084 = 7.3789 km/sec
Tangential velocity of a point on earth’s surface is function of latitude.
Higher latitudes (north or south) have gradually reduced inertial velocity
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6/13/2009
Example Delta V Calculation (2)
Example Delta V Calculation (3)
KSC Latitude ~ 28.5Eastward launch to 800 km orbit altitude
200 km orbit altitude: DV= 7.3789 km/sec
Vearth =
= 0.4084 km/sec
800 km orbit altitude: DV= 7.0461 km/sec
Vorbit 

r

3.9860044 105 km3 sec2
6373  800
R KSC  6373km

= 7.4545 km/sec
Hmmmm … higher orbit, less required DV
… does this make sense?
DVorbit =
7.7873 - 0.4084 = 7.0461 km/sec
.. Well no!
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24
25
Potential Energy Revisited (2)
Potential Energy Revisited
•


 P.E.ground   R 
e

  DP.E.  P.E.h  P.E.ground
 

P
.
E
.


h


R

h
e


  

 DP.E.   R
  
Re  h  Re 
But in High School
Physics you learned
That gravitational
Potential energy
(per unit mass) was
Just …… g•h
… how do these models
reconcile?
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  Re  h  Re  
 Re  h  Re
P.E.h  

Re  h
h
P.E.ground  

Re
Re

 
 h
  Re  h  Re 

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Stephen A. Whitmore, USU MAE Dept.
27
7
6/13/2009
Gravity Losses
Potential Energy Revisited (3)
Fgrav 
_ Re h
g
Re

1
h
Re  h

Re
Fgrav
mMG _

ir 
 g(r)  2
r2
m
r
1 
dr   
r
h r

 R e  h  R e  
h R e  h R e
Re h
2
Re
Use “Gravity Loss” to
account for the energy
Needed to lift from
Launch altitude to
orbital altitude

  
1 
   h R  h   R   


e
 e



 R e  h R e 

_



 DP.E.  
h  gh

 R e  h R e 
QED! .. Let’s take
advantage of this
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28
Total “Conserved” DV
Gravity Losses (2)
From
earlier


 DVgravity 



loss


 DP.E.  
 h 
2
 Re  h Re 
 DVgravity
loss
2
And we can define a general “DV” vector as
 
DV  Vorbit
2  h

Re  h Re
or...more...generally  DVgravity 
loss
29
@ burnout


 DVgravity  Vearth
loss

launch  site

 
 
 

 
0
Vorbit
 Vorbit   0
 

 
north
north
 

  
    

DV   Vorbit    0
   Vorbit  Vearth

   Vearth
east
launch

site
east
launch

site

 
 

 


V
  DV
 V
 
0
 DVgravity 
gravity
orbit
 orbit





loss
vertical 
loss

 
  vertical
2     Rburnout  Rlaunch 
Rburnout  Rlaunch
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6/13/2009
Total “Conserved” DV (2)
Total “Conserved” DV (2)
Writing in terms of the launch azimuth and flight path angle
For a circular orbit,



Vorbit cos  cos 









DV   Vorbit cos  sin   Vearth

launch  site 





 Vorbit sin   DVgravity

loss



vertical

DVcircular
orbit
  launch azimuth
  flight path angle
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


 
V
orbit

 
north

  

 Vorbit  Vearth
   Vorbit
 east launch  site  
 DV
 
gravity

 
loss






sin   Vearth

launch  site 


DVgravity

loss

Stephen A. Whitmore, USU MAE Dept.
32
Total “Conserved” DV (3)



 
V
orbit

 
north

  

 Vorbit  Vearth
   Vorbit
east
launch

site

 

 DV
 
gravity

 
loss

33
Total “Conserved” DV (4)
And the total magnitude of DV needed is:
For a circular orbit,
orbit

Vorbit cos 
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.

DVcircular

Vorbit  0,   0

DV 

Vorbit cos 





sin   Vearth

launch  site 


DVgravity

loss

 2
 2

DVnorth  DVeast  DVvertical
2
Circular orbit with due east launch …


DV  02  Vorbit  Vearth
2
launch  site

 DVgravity
2

loss

  2 h 
DVtotal   Vorbital  Vearth   

boost 

 re  re  h  
2
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6/13/2009
Drag Losses
Drag Losses
… and
This decay
Also applies
To launch
trajectory
(2)
Energy losses due to drag
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36
Drag Losses (2)
Drag Losses


2at

DVdrag 2
2

2a0
t


t

DragV
m
0
t
DVdrag  2 
0
DragV
m
0
dt 
dt  equivalent kinetic energy loss
DragV
m
(3)
dt
V ---> Airspeed not inertial velocity
… ground speed with no wind
1 2
C V 3
V  DVdrag  Aref  D
dt
2
m
0
t
Drag  C D Aref
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Stephen A. Whitmore, USU MAE Dept.
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6/13/2009
Drag Losses
Drag  CD Aref
1
V
2
DVdrag  Aref

2

CD V 3
dt
m
0
t
Total DV Required (3)
(4)
• Drag Losses <10% for well
designed trajectory for Clean
Rocket .. Factor of two higher
(20%)for Booster with strap-ons
Drag Losses are integrated along flight path Of Vehicle during
endo-atmospheric phase of launch… as well as trajectory
dependent … Other launch losses include maneuvering
thrust, wind shears, etc. … Often lumped with drag loss

DV 

DV north
2

 DVeast
2

 DV
vertical
2
CD V 3
0 m dt
t
 Aref
• Why does shuttle
Launch Straight up?
41
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Drag Coefficient Examples
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Example Calculation
42
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11
6/13/2009
Nomenclature
Reference material
International Reference Guide
to Space Launch Systems, 4th
ed., Stephen J. Isakowitz,
Joseph P. Hopkins, Jr., and
Joshua B. Hopkins, American
Institute of Aeronautics and
Astronautics, Reston, VA, 2003.
ISBN: 1-56347-591-X
44
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Stephen A. Whitmore, USU MAE Dept.
Stage 1 Properties
45
Gem 40 Augmentation Rocket Properties (ATK)
• 3 Boosters Total – Ground Lit
• Boeing Delta II Rocket…Stage 1
- Sea Level Thrust: 890kN
- Vacuum Thrust: 1085.8 kN
- Nozzle Expansion Ratio: 14.25:1
- Conical Nozzle, 30.434 deg exit angle
- Sea Level Thrust: 499.20kN
- Vacuum Thrust: 442.95 kN
- Nozzle Expansion Ratio: 10.65:1
- Conical Nozzle, 20 deg exit angle
• Combustion Properties: (Gem 40)
• Combustion Properties:
(R2-27A Rocketdyne Engine)
- Lox/Kerosene, Mixture Ratio: 2.24:1
- Chamber Pressure (P0): 4840 kPa
- Combustion temperature (T0 ): 3465 K
- g = 1.2220
- MW = 21.137 kg/kg-mol
- Propellant Mass: 96.1 Metric Tons
- Stage 1 Launch Mass: 101.8 Metric Tons
- Ap/Aluminum/HTPB
- Chamber Pressure (P0): 5630 kPa
- Combustion temperature (T0 ): 3554 K
-  = 1.2000
- MW = 28.15 kg/kg-mol
- Propellant Mass (Each): 11,765 kg
- Launch Mass: 13,080 kg
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6/13/2009
Stage II Properties
Stage III Properties
• Payload Inside of 3 meter shroud
• Boeing Delta II Rocket…Stage 2
AJ10-118K Aerojet Engine
- Vacuum Isp: 319 seconds
- Vacuum Thrust: 43.657 kN
- Chamber Pressure: 5700 kPa
- Mixture Ratio: 1.8:1
- Nozzle Expansion Ratio: 65:1
- Propellant Mass: 6004 kg
- Stage 2 Launch Mass: 6954 kg
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48
Launch Profile
49
Problem Objectives (1)
• Estimate Total Payload mass that can be delivered to a 200
km Leo orbit at inclination 28.5 … KSC Launch Due East
• Assume 10% DV losses due to drag (interference from
GEM 40 Boosters)
• Assume 1040 kg (3 meter) shroud+adapter weight
(not budgeted as part of payload)
… first use conventional conical Nozzle for Main Stage 1 (slide 2)
… Then repeat using aerospike nozzle for stage 1
… assume GEM-40’s use standard conical nozzle
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13
6/13/2009
DV to 200 km orbit
… due east launch from KSC
Compute Gravity Loss, Required Total DV
DVgravity  2
• Orbital velocity
V

Re  h
5  0.5
 3.986004 10


 6371 + 200 
• Earth “Boost” velocity …
= 7.7885 km/sec
 2 3.9860044 105 200  0.5
h

 
R e R e  h   6371  6371 + 200 
=1.9515 km/sec
• Compute DV required for mission
DVtotal 
(Solar Day: 86164.1 sec)
V
orbit
 Vboost  DVdrag
  DV 
2
2
=
gravity
Vboost  earth R earth cos(Lat) 
2

6371 cos 
28.5 = 0.40828 km/sec
 23 3600 + 56 60 + 4.1
180
[ (7.7885 – 0.40229) 1.10) 2 + 1.95162 ]1/2= 8.3559 km/sec
10% drag loss
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Calculate Available Delta V (1)
• Stage “1a” Mass Fraction (3 Gem 40’s + Stage 1)
• Stage “1b” Mass Fraction (Stage 1 Only)
Pmf "1b " 
.
.
3  M p gem 40  m stage1  Tburn Gem 40



 M gross TO   3  M p gem 40


stage1
burn Gem 40
53
Calculate Available Delta V (2)
Pmf "1a " 
 
.
  m T
Stephen A. Whitmore, USU MAE Dept.
52
M

   M gross 2  M shroud  M payload

• Stage “1a” DV

m stage1  TMECO  Tburn Gem 40
inert stage1
M
gross 2

 M shroud  M payload
• Stage “1b” DV
DV"1a"  I sp"1a " g0 ln 1  Pmf "1a " 
DV"1b"  I sp"1b " g0 ln 1  Pmf "1b" 
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55
14
6/13/2009
Calculate Available Delta V (4)
Calculate Available Delta V (3)
DV required for mission = 8.3559 km/sec
DVtotal  DV"1a "  DV"1b"  DV2 
• Stage 2 Mass Fraction (stage 2 Only)
Pmf 2 
M


.


3  M p gem 40  m stage1  Tburn Gem 40

I sp g0 ln 1 
.
"1 a "
 



  M gross TO   3  M p gem 40  m stage1  Tburn Gem 40    M gross 2  M shroud  M payload 

 

M p2
gross 2


 M p 2  M shroud  M payload
• Stage 2 DV







M p2

I sp2 g0 ln 1 
 M gross 2  M p 2  M shroud  M payload 

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Stephen A. Whitmore, USU MAE Dept.

.


m stage1  TMECO  Tburn Gem 40

I sp g0 ln 1 


"1 a "
 M inert stage1  M gross 2  M shroud  M payload 


M p2

DV2  I sp2 g 0 ln 1 
M gross 2  M p 2  M shroud  M payload 





Stephen A. Whitmore, USU MAE Dept.
56
57
Stage “1a” (2)
Stage “1a”
* 3 x Gem 40 + Stage 1 (RS-27A)
-- Gem 40 Burnout Altitude ~ 8.8 n. mi. (16.31 km)
Hint(s):
Use FSL, Fvac, expansion ratio  to find A*, Aexit
Choking Massflow (per rocket)
-- Calculate:
i) Total Lift off Thrust
ii) Burn Time for Gem-40(s)
iii) Plot total Thrust profile during Burn “1a” vs Altitude
iv) Mean specific Impulse (3 x Gem 40 + RS-27A)
over operating altitude range (SL to 16.31 km)
v) Total propellant consumed during “stage 1a” burn
vi) Compare “actual” length of RS-27A nozzle to
minimum length nozzle with same expansion ratio
and A*
Stephen A. Whitmore, USU MAE Dept.
 1 

.
   2   1  P0
m  A*  

 
 Rg    1   T0


Thrust of Conical Nozzle

nozzle
•
Thrust   m Vexit  Aexit Pexit  P 
1
  1  cos[nozzle ]
2
Stephen A. Whitmore, USU MAE Dept.
15
6/13/2009
Stage “1a” Thrust Profile
Stage “1a” mass flows, burn times
RS-27A = 366.99 kg/sec
 1

m A
Gem 40 = 186.75 kg/sec
Tburn
GEM 40
 M prop
  2   1 P0


Rg    1 
T0
 M prop 
11,765kg
  

 63.33sec


185.76
kg /sec
 m GEM 40

RS 27 A
*
 m Tburn
GEM 40
Total  M prop   M prop
 366.99kg /sec  63.33sec  23,243.1kg
RS 27 A
 3   M prop 
GEM 40
 58538.1kg
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Stage “1a” (3)
Hint(s): Mean Isp for “Stage 1a”
I
sp mean

 3  F
gem 40
stage "1a "

61
Stage “1a” Mean Specific Impulse
16.32 km
 FRS 27 A  dt
Tburn gem 40
.
 .

g 0   3  m gem 40  m RS 27 A   Tburn gem 40



16.32 km
_
 _

 3  F gem 40  F RS  27 A 

 SL
.
 .

g 0   3  m gem 40  m RS  27 A 


Stephen A. Whitmore, USU MAE Dept.
_
 _

3

F

F
gem
40
RS  27 A 


 SL
I sp mean


.
.
stage "1a "


g 0   3  m gem 40  m RS  27 A 


3
2433.15 10 Nt
 268.44sec
9.8067 m /sec2   3 185.76  366.99 


Stephen A. Whitmore, USU MAE Dept.
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6/13/2009
Stage “1b”
Stage “1b” Propellant Consumed, Burn Time
During Stage “1a” Burn
Stage 1 (RS-27A) burning from Gem 40 Burnout
Altitude ~ 8.8 n. mi. (16.31 km) to MECO altitude,
56.4 nm (105.52 km)
 M prop

RS 27 A
 m Tburn
GEM 40
 366.99kg /sec  63.33sec  23,243.1kg
During Stage “1b” Burn
 M prop
-- Calculate:
stage "1b "

 M prop stage   M prop
1
RS 27 A


stage "1a "
96100kg  23,243.1kg  72,856.9kg
vii) Burn Time from Gem-40(s) burnout to MECO
viii) Plot thrust profile during “1b” burn vs altitude
ix) Mean Isp Over Altitude Range (16.31 km to 105.52 km)
x) Compare final Gross Takeoff weight to Available thrust
at liftoff and estimate Liftoff acceleration level
Tburn

stage "1b "
72,856.9kg
366.99kg /sec
 198.53sec
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Stephen A. Whitmore, USU MAE Dept.
Stage “1b” Thrust Profile, Mean Isp
Delta II 7320 Stage Summary
RS-27A
103 Nt 198.53sec
 301.295sec
 I sp stage"1b"  1084.34
9.8067 m/sec2  72,856.9 kg
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66
Stage
1”a” -- 3 GEM 40+
RS-27A
1”b” RS-27A
2 AJ10-118K
Mean Thrust
(0-16.31 km
altitude)
2433.15 kNt
1084.34 kNt
43.657 kNt
Mean Isp
268.44 sec
301.295 sec
319.2 sec
Minitial
141,040 kg
78,556.9 kg
6954 kg
M final
82,501.9 kg
5700 kg
950 kg
T burn
63.33 sec
198.53 sec
430.5 sec
Stephen A. Whitmore, USU MAE Dept.
17
6/13/2009
Delta V/Payload Analysis
Sanity Check
Bit on the High side
International Reference Guide to
Space Launch Systems, 4th ed.,
Stephen J. Isakowitz, Joseph P.
Hopkins, Jr., and Joshua B. Hopkins,
American Institute of Aeronautics
and Astronautics, Reston, VA, 2003.
ISBN: 1-56347-591-X
PAGE 100
DV required for mission = 8355.9 m/sec
68
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DV required for mission = 8355.9 m/sec
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Delta V/Payload Analysis
Try Larger Interference Drag Penalty
DVgravity  2
 2 3.9860044 105 200  0.5

 
R e R e  h   6371  6371 + 200 
h
=1.9515 km/sec
• Compute DV required for mission
16% drag penalty
DVtotal 
V
orbit
 Vboost  DVdrag
  DV 
2
2
=
gravity
[ (7.7885 – 0.40229) 1.16) 2 + 1.95162 ]1/2= 8787.4 km/sec
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16% drag loss
DV required for mission = 8787.4 m/sec
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6/13/2009
Lift Off Thrust-to-Weight Comparison
Sanity Check
M gross 

Probably More Realistic
TO

3  M gross gem 40  M gross
stage1
ThrustTO  2218.84kNt 
International Reference Guide to
Space Launch Systems, 4th ed.,
Stephen J. Isakowitz, Joseph P.
Hopkins, Jr., and Joshua B. Hopkins,
American Institute of Aeronautics
and Astronautics, Reston, VA, 2003.
ISBN: 1-56347-591-X
 M gross
stage 2
 M shroud  M payload  151,891kg
2218.85 103kg  m /sec2
Thrust

 1.490 g ' s
Weight 9.8067 m /sec2 151,891kg
DV required for mission = 8787.4 m/sec
PAGE 100
DV required for mission = 8787.4 m/sec
72
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Homework
Sanity Check
Read AIAA 2008-1131
Launch and Deployment Analysis for a Small, MEO,
Technology Demonstration Satellite
Stephen A. Whitmore and Tyson K. Smith
Utah State University, Logan, UT, 84322-4130
Probably More Realistic
International Reference Guide to
Space Launch Systems, 4th ed.,
Stephen J. Isakowitz, Joseph P.
Hopkins, Jr., and Joshua B. Hopkins,
American Institute of Aeronautics
and Astronautics, Reston, VA, 2003.
ISBN: 1-56347-591-X
(Section 8, Class web page) …. Prepare 2 page summary
of design trades and final recommendations
PAGE 100
DV required for mission = 8787.4 m/sec
74
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ESDM Senior
Design Project
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Space Administration
Flight Mechanics II
Planar Equations of Motion
Sellers, Chapters 9, 14, Appendix E
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www.nasa.gov
Real World Launch Analysis
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Real World Launch Analysis (2)
Trajectory Verification
Trajectory Design & Optimization
After POST has been used to determine the
optimum launch trajectory, a Pegasus-specific
six degree of Freedom simulation program is used
to verify Trajectory acceptability with realistic attitude
dynamics, including separation analysis on all stages
Orbital Sciences Corporation (OSC) designs a
unique mission trajectory for each Pegasus
flight to maximize payload performance, while still
complying with payload and launch vehicle constraints.
• 6-DOF simulations Costs A
LOT! To run And are typically
Not used for Trajectory
design!
Using 3-Degree of Freedom Program for Optimization of Simulation
Trajectories(POST), a desired orbit is specified and a set of optimization parameters and
constraints are designated.
Appropriate data for mass properties, aerodynamics, and motor ballistics are input.
• We are going to develop A
simple 2+-D code That works
well For mission profile
development
POST selects values for optimization parameters that target desired orbit with specified
constraints on key parameters such as angle of attack, dynamic loading, payload
thermal, and ground track..
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Orbital Energy Revisited
Kepler’s Laws
o
N
er
ng
Lo
ly
pp
A
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Perifocal Coordinate System
Orbital Dynamics
• Must resort to Newton’s laws to describe these orbits
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Perifocal Coordinate System
Sub-orbital Image
Velocity Vector
Vr
V

Stephen A. Whitmore, USU MAE Dept.
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85
Acceleration Vector (cont’d)
Acceleration Vector
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Newton’s Second Law
Stephen A. Whitmore, USU MAE Dept.
Newton’s Second Law
88
Gravitational (Conservative)
Forces


r2
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Vehicle Mass
_
ir
Initial mass of vehicle
• Assume spherical earth .. Always acts in ir direction
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Non-Conservative Forces

Aerodynamic Forces
 
 Fr   Flift cos( )  Fdrag sin( )  Fthrust sin( )
m 
m
 
 F   Flift sin( )  Fdrag cos( )  Fthrust cos( )
 m   

m

Aref … reference
Area … planform
Or diameter based





“Dynamic Pressure”
_
Flift  C L Aref q   C L Aref
   
_
V 
  tan  r 
 V 
1
2
Fdrag  C D Aref q   C D Aref
1
V 2
1
2
V 2
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Aerodynamic Forces
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92
Aerodynamic Forces
(2)
93
(3)
See appendix 1 at end of slides
Airspeed
_
1
_
_
_
_
_
q   V 2  V  V inertial  V atmosphere  V inertial   earth  R
2
Inertial Velocity
Air “sticks” to
Earth boundary
_
• Good Approximation:
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_
_
V  V inertial  V earth  V wind
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Aerodynamic Forces
Aerodynamic Forces
(4)
(5)
• Look at STS 114-aero example
STS-114 Example
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Aerodynamic Forces
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97
Drag (revisited)
(6)
• Look at STS 114-aero example
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• Several Types of Drag Act
on Flight Vehicles
– Simplest case
• Pressure drag (form
drag)
– Fore-body
– Base
– Wave drag
– Induced or
Compressive
drag due to lift
• Viscous drag
– Fore-body
• Total drag
Drag
PA
 wA
Forebody
Pressure
Drag
Total Drag
Fore-body
Viscous
Drag
Base
Pressure
Drag
Drag due to lift
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Base Drag (2)
Base Drag: What is it?
Boundary
Layer
U
u(y)
Separation
Low Pressure
Separated Region
Wake
• Boundary Layer on Vehicle Base Area
Separates
• Low Pressure Separated Region Forms
• Low Pressure Causes a Large net Pressure
Difference
• Especially significant during endoatmospheric phase of Launch after
rocket burnout
Linear Aerospike Rocket Engine
Drag
High
Pressure
Low
Pressure
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100
101
Vector Form of 2-D State
Equations
Collected Planar Equations
•
X  f X, Fthrust , 
Flift cos( )  Fdrag sin( )  Fthrust sin( )
V

V•    
 2
m
r 
 r  r
1  Vr 
•
    V V Flift sin( )  Fdrag cos( )  Fthrust cos( )     tan  
 V 
V      r  

m
    r

  

 

Vr
 •  

r  

V

 •  

  
r

•
 •  

F
X  f  X, Fthrust ,
m 
 thrust
 
g
I
0
sp


2

 V 2 Flift cos( )  Fdrag sin( )  Fthrust sin( )  
V• 
 2
 r 
m
r 
 r

• 
  VrV Flift sin( )  Fdrag cos( )  Fthrust cos( )  
V

 
  r 

m
 

 
V 
 
•


  tan 1  r 


X
 f X, Fthrust ,  

 V 
Vr
 • 


   
r 


V
 • 


 
r


 • 


Fthrust
m



 
g
I
0
sp



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6/13/2009
Integrated Equations of Motion
Numerical Approximation of
the Integral
t
•
X  f X, Fthrust ,  X(t)  X(t 0 )   f X, Fthrust , dt
t0
 approximate over fixed interval DT 
t 0  Dt
X(t 0  Dt)  X(t 0 ) 
 f X, F
thrust
, dt
t0
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Numerical Approximation of
the Integral
Numerical Approximation of
the Integral
(2)
X(t 0  Dt)  X(t 0 ) 
(3)
“Trapezoidal rule”
t 0  Dt
 f X, F
thrust
, dt
fk  f  X k , Fthrust k , k 
fk 1  f  X k 1 , Fthrust k1 , k 1 
t0
 ~^

f k 1  f  X k 1 , Fthrust k1 , k 1 


~
^
“Trapezoidal rule”
x(t)
105
x(t+ Dt)
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6/13/2009
Predictor/Corrector Algorithm
Numerical Approximation of
the Integral
(4)
 Dt, X^ , F

k
thrust k , k 


“trapezoidal rule”
~
^
^
^
 X k  X k  Dt f  X k , Fthrust k , k 


^
^
 X k 1  X k 
“trapezoidal rule”
Dt
2


f


 ~^


 X^ , F



 k thrust k , k   f  X k 1 , Fthrust k1 , k 1  



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Higher Order Integrators
109
4th Order Runge-Kutta Method
•Simple Second Order predictor/corrector works well for
Small-to-moderate step sizes … but at larger step sizes can
be come unstable
Lets add two more points
To the curve before summing
• Good to have a higher order integration
scheme in our bag of tools
• 4th Order Runge-Kutta method is one most commonly used
• Lots of arcane derivations and Mystery with regard to
This method … lets clear this up!!!
x(t)
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x(t+ Dt)
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4th Order Runge-Kutta Method
4th Order Runge-Kutta Method
(2)
(3)
• Now correct this derivative estimate with what we have learned
• The basic Differential equation is:
• Approximate the first derivative by finite difference
• This is almost equivalent to what we have already done
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113
4th Order Runge-Kutta Method
4th Order Runge-Kutta Method
(5)
(4)
• Repeat this process twice more to give us 4 points on the curve
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• Finally take a weighted average of the results
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Initial Conditions:
Ground Launch, Rotating Earth
4th Order Runge-Kutta Method
Summary
Initial Velocity Vector :
Vr  V0 sin( ground )  V0  Initial Groundspeed



2
2
V  V cos( 
 
 
launch ) cos   ground    V0 sin( launch ) cos   ground   Vearth cos  Lat   
 
 0

Vnorth
Initial "Orbit "
Veast
15 m/sec
• See Sellers, Appendix C for eccentricity derivation



a  


2


 Vr 2  V 2  



 R e ( Lat )  h



2




R

h

2 
e ( Lat )

2
e

V


V
V
 
  r  


R

h
e ( Lat )




Launch Azimuth
• Slide Indices and repeat
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Initial Conditions:
Ground Launch, Rotating Earth
85
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117
Velocity Off of the Rail
(2)
Vrail
15 m/sec
Initial Position
15 m/sec
Fdrag
Fthrust
 r  R e ( Lat )  h



a


2 Vr a
2






atan2
1

e
,
1

e

1
 
V r 
 


r


Ffric
•
V rail  
•
85

m
• Initial Mass, m0
• See Sellers A5ppendix C, Chapter
 rail
m 

 c  C A 
D ref

  careful ! with units

  c  " Ballistic Coefficient "

g 
2
 Re  h  

Vrail 2
F

sin( rail )  C f  cos( rail )   thrust

2 c  Re  h 2 
m
Fthrust
g 0 I sp
{rail, Vrail}-->ground relative
85
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{V0=0, m0=Mtotal}
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Ballistic versus Non -Ballistic Trajectories
Ballistic Launch (2)
• In practice ballistic Trajectories give
“lofted orbits” with Very high apogee
Altitudes … compared to the total orbital
Energy
• Most often used for sub-orbital launches
(sounding rockets)
• Non-ballistic trajectories sustain
significantly non -zero angles of attack
… lift is a factor in resulting trajectory
… so is induced drag
• Orbital trajectories need to
“turn the corner” at some non-zero
angle- of-attack to get proper
Apogee/velocity phasing
• Ballistic trajectories trim rocket at ~ zero degrees angle of attack (  )
… lift is a negligible factor in resulting trajectory
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Non Ballistic Launch Trajectory, revisited
 V 2 F cos( )  Fdrag sin( )  Fthrust sin( )  
V•     lift
 2
m
r 
 r  r
 •    V V Flift sin( )  Fdrag cos( )  Fthrust cos( )  
r 
V

   


m
    r

  

 

Vr
 •  

r  

V

 •  

  
r

 •  

Fthrust
m 


 
g
I
0 sp


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120
121
Example of Ballistic Trajectory
Pitch angle actively
controlled
~ Symmetric
trajectory
   
• Ballistic Trajectories
Offer minimum
drag profiles
( ~ 0-->No induced drag)
“pitch profile”
Key to accurate
Orbit insertion
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123
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6/13/2009
Shuttle Launch is VERY Non-Ballistic
Example of Non-Ballistic Trajectory
Space
shuttle
mission
profile
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124
More “Gravity Turn” … non-Ballistic
125
Ballistic Launch, Revisited
Space Shuttle
Launch (STS 115
– Atlantis) as
seen
from ISS
To visualize a ballistic trajectory, slice the earth open like
And apple .. This action reveals the launch site latitude,
0, target latitude, T , and the angular range, L.
“definitely
Not ballistic”
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Ballistic Launch, Revisited (2)
Ballistic Launch, Revisited (3)
Ballistic Range Graphs, Closed form
Solution ignoring drag
 TOF

 P  non-dimensional time of flight 


L  angular range


   flight path angle (same as  ) 


2


V

Q   burnout 




 Vcircular 


R 3burnout


P  2





Flight path Angle and Trajectory .. Maximum range is achieved
with a burnout flight path angle of 45 degrees.
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129
Ballistic Coefficient, c
Ballistic Launch, Revisited (4)
• When effects of lift are negligible aerodynamic effects can be
incorporated into a single parameter …. Ballistic Coefficient (c )
• b is a measure of a projectile's ability to coast. … c = M/CdAref
… M is the projectile's mass and … CdA is the drag form factor.
• At any given velocity and air density, the deceleration of a
rocket from drag is inversely proportional to c
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6/13/2009
Collected Equations,
Ballistic Trajectory
Ballistic Trajectory .. Bottom Line
V 
V 2   Fthrust V 2 

  tan 1  r 
 2 

•  
 sin( ) 
 V 
V
r
r
r
m
2

c


  

•  

2


V     VrV   Fthrust  V  cos( ) 
m
  

r
2 c 
c =
 m
C D Aref
  

 

 •  

Vr
 r  
 Pitch profile passively
V
 •  
 results from Natural
  
 trim at zero angle
r
 •  

Fthrust
m 
 of attack

  

g
I
0
sp

  0
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Example I: Minotaur V Launch to Medium
Earth Transfer Orbit (MTO)
• In practice ballistic Trajectories give
“lofted orbits” with Very high apogee
Altitudes … compared to the total orbital
Energy
• Most often used for sub-orbital launches
(sounding rockets)
• Orbital trajectories need to
“turn the corner” at some non-zero
angle- of-attack to get proper
Apogee/velocity phasing
• “Pitch profile” Key to accurate
Orbit insertion
• Negative lift used to “turn
the corner” during
• Induced Drag Penalty
Accepted to achieve
correct orbit parameters
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Mission CONOPS/Timeline
Star 27
1st Stage – TU-903
2nd Stage – SR-119
3rd Stage – SR-120
4th Stage – Star 48B long
5th Stage – Star 27 with 25-30% propellant offload
(depending on final payload mass)
• Required Orbit 13,000 by 19,000 km altitude
• Proposed configuration allows 400+ kg payload delivery
to 19,000 km altitude MEO orbit without 6th stage
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6/13/2009
Launch Mission Plan
Launch Mission Plan
geocentricX/Z plane plot
geocentric Y/Z plane plot
35000.0
35000.0
Transfer orbit
30000.0
Stage IV Burnout
20000.0
10000.0
10000.0
0.0
0.0
20000.000000
18000.000000
30000.0
20000.0
geocentric X/Y plane plot
-10000.0
16000.000000
-10000.0
35000.0
14000.000000
12000.000000
10000.000000
8000.000000
-20000.0
30000.0
-20000.0
-30000.0
20000.0
-30000.0
-35000.0
-35000.0 -20000.0
6000.000000
4000.000000
0.0
20000.0 35000.0
-35000.0
-35000.0 -20000.0
10000.0
2000.000000
0.000000
-2000.000000
-4000.000000
Final orbit
-6000.000000
-8000.000000
-10000.0
-20000.0
-10000.000000
-12000.000000
-30000.0
-14000.000000
-35000.0
-35000.0 -20000.0
-16000.000000
• Direct insertion into MTO orbit
-18000.000000
-20000.000000
-28000.0000000
-10000.0000000
0.0000000
Stephen A. Whitmore, USU MAE Dept.
12000.0000000
0.0
20000.0 35000.0
3D MTO
Orbit Profile
(ref. First Point
of Ares)
0.0
0.0
20000.0 35000.0
8 August 2010
launch
Stephen A. Whitmore, USU MAE Dept.
136
137
Pitch Profile Optimization
Ballistic Launch Profile
Ballistic trajectory
Optimized Pitch Profile
• 3-Degree of freedom Launch simulation used to optimize pitch profile for
maximum stage IV mass to MTO
• Negative lift used to “turn the corner” during stage 2 burn.
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6/13/2009
Example II : Comparison of Constant
Thrust Maneuver
Versus Impulsive Maneuver
Optimized (Non-Ballistic)
Launch Profile
• Hohmann
transfer
… elliptical
trajectory
… Kepler’s laws
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Comparison of Constant Thrust Maneuver
Versus Impulsive Maneuver
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Comparison of Constant Thrust Maneuver
Versus Impulsive Maneuver
(cont’d)
(2)
• Continuous
Thrust transfer
• Continuous
Thrust transfer
Higher
Thrust
Transfer
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Worked EP Example
Initial Conditions
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Worked Example
Initial Conditions (2)
145
(2)
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6/13/2009
Worked Example
(2)
Worked Example (cont'd)
• Continuous Thrust GTO
Thrus t
Termination
a(1+e)
GEO
Orbit
Final DV
Required to
Circularize Orbit
Final
(continuous-thrust)
Orbit
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Worked Example
148
Worked Example
(4)
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149
(5)
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Worked Example
Worked Example
(6)
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Worked Example
152
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Worked Example
(8)
154
(7)
153
(9)
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6/13/2009
Compare to Hohmann transfer
using Conventional Propulsion
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Design Friday: Lunar Descent Simulation
157
Lunar Descent Simulation (2)
Apollo LM powered descent trajectory design established… as a 3-phase maneuver…
Braking phase .. designed primarily for the efficient propellant usage while
reducing orbit velocity and guiding to “high gate” conditions for initiation of the
second phase, (essentially Hohmann transfer)
Approach phase … term “high gate” is derived from aircraft pilot terminology for
beginning the approach to an airport. The approach phase is designed for pilot
visual (out the window) monitoring of the approach to the lunar surface. (constant
thrust descent)
Landing phase … begins at “low gate” conditions designed to provide continual
visual assessment of the landing site and allow for the pilot takeover from automatic
control for the final touchdown on the surface. (maneuvering descent)
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6/13/2009
Lunar Descent Simulation (3)
Lunar Descent Simulation (4)
Over Next Three Weeks we are going to build this simulation
… then we are going to fly it with a Joystick
… Build functional block diagram of the simulation
… Identify key variables, computational block, and “pilot”
displays
Show example ISS Launch Simulation
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ESDM Senior
Design Project
161
National Aeronautics and
Space Administration
Flight Mechanics III
Motions in 6-Degrees of Freedom
Sellers, Chapters 9, 14, Appendix E
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National
Aeronautics and Space Administration
www.nasa.gov
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Degrees of Freedom
Degrees of Freedom (2)
Trajectory Design & Optimization
Linear Degrees of Freedom
Typically performed with point-mass assumption with 3-Degrees of Freedom (3-DOF)
Trajectory
Designers
Degrees of freedom only
Consider linear motions
point mass
 Ax  Vx   x 
 A   V    y 
 y  y  
 Ax  Vx   z 
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Degrees of Freedom (4)
Euler Angles
Collected  Linear + Rotational Dynamics = 6 DOF
body
+
Trajectory
Designers
165
Body Axis – fixed
To Vehicle … { i’, j’, k’} unit vectors
point mass
Inertial Axis – fixed
in space { i, j, k} unit vectors
Euler Angles– describe orientation
between body and inertial axes
Body axis moves with the vehicle
In space, inertial axis does not change
Free-flying vehicles also have Rotational degrees of freedom,
governed by rotational dynamics, and described by Euler Angles –
the orientation between the inertial and body reference frames
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6/13/2009
Euler Angles (2)
Euler Angles (3)
body
body
body
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Single -Axis Rotation in 3-D (2)
Single -Axis Rotation in 3-D
(Section 8.2)
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6/13/2009
Single -Axis Rotation in 3-D (3)
Single -Axis Rotation in 3-D (4)
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Single -Axis Rotation in 3-D (5)
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Rotation about Z-axis (yaw-rotation)
1-rotation “do this first”
y
y
y
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6/13/2009
Rotation about Y-axis (pitch-rotation)
Rotation about Z-axis (yaw-rotation)
2-rotation “do this second”
Axis you rotate
From goes first ….
R = MTy R’
Believe it or not
Newton Didn’t
know how to do
This transformation
Y-rotation looks “backward”
y
cos(y) -sin(y)
cos(y)
sin(y)
y
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Rotation about Y-axis (pitch-rotation) (2)
Rotation about X-axis (roll-rotation)
3-rotation “do this last”
That! is why
Newton Didn’t
know how to do
This transformation
Axis you rotate
From goes first ….
Y-rotation looks “backward”
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6/13/2009
Rotation about X-axis (roll-rotation) (2)
Arbitrary Orientation in Space
1-2-3
Rotations
y
y M
Order of
rotations is
Critical for
Proper
orientation
y
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Stephen A. Whitmore, USU MAE Dept.
Arbitrary Orientation in Space (2)
1-2-3 Rotations in Space Three Successive Right Handed Rotations


R 'body   M 3 ( ) M 2 ( ) M 1 (y )   Rinertial
0  cos  0  sin   cosy sin y 0   x 
 x '
1 0
 y '   0 cos  sin   0 1 0   sin y cosy 0   y 
 



 



0 1   z inertial
 z '  body  0  sin  cos   sin  0 cos   0
Inertial
Axis
 to 
Body
Axis
Stephen A. Whitmore, USU MAE Dept.
Arbitrary Orientation in Space (3)
Performing the matrix multiplications
 cos 
 0

 sin 

0
1
0
 sin   cosy
  sin y

cos  
 0
0
 cos  cosy
 
sin y
0
cosy
0    siny

1   sin  cosy
0
cos  siny
cosy
sin  siny
0
0   cos  cosy cos  siny  sin  
1

 0 cos  sin     siny
cosy
0 


 0  sin  cos    sin  cosy sin  sin y cos  



cos  cosy
cos  siny


 sin  sin  cosy  cos  sin y sin  sin  sin y  cos  cosy
 cos  sin  cosy  sin  sin y cos  sin  sin y  s in  cosy

 sin  

0 
cos  
 sin  

sin  cos  
cos  cos  
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6/13/2009
Arbitrary Orientation in Space (4)
Three Successive Right Handed Rotations
Three Successive Left Handed Rotations for the Inverse Transformation
 x '
Inertial
Body
 to 
.........  y ' 
Axis
Axis
 z '  body
cos  cosy


sin

sin

cosy  cos  siny

 cos  sin  cosy  sin  siny

Arbitrary Orientation in Space (5)
Body
Axis
cos  siny
sin  sin  siny  cos  cosy
cos  sin  siny  sin  cosy
 sin    x 

sin  cos    y 
cos  cos    z  inertial
“Direction Cosine Matrix
 to 
Inertial
Axis


T
.........Rinertial   M 3 ( ) M 2 ( ) M 1 (y )   R 'body
 x '


Rinertial   M 1 (y )T M 2 ( )T M 3 ( )T   R 'body   y '

 z '  inertial
cos  cosy


 sin  sin  cosy  cos  siny

 cos  sin  cosy  sin  siny
 cos  cosy

  cos  siny
  sin 

cos  siny
sin  sin  siny  cos  cosy
cos  sin  siny  sin  cosy
sin  sin  cosy  cos  siny
sin  sin  siny  cos  cosy
Stephen A. Whitmore, USU MAE Dept.
sin  cos 
 sin  

sin  cos  
cos  cos  
T
 x
 y
 
 z  body
cos  sin  cosy  sin  siny   x 

cos  sin  siny  sin  cosy   y 

cos  cos 
  z  body
Stephen A. Whitmore, USU MAE Dept.
Arbitrary Orientation in Space (6)
Inertial Coordinate Systems
cos  cosy
cos  siny
 sin    x 
 x '

 y '   sin  sin  cosy  cos  siny sin  sin  sin y  cos  cosy sin  cos    y 

 
 
 z '  body  cos  sin  cosy  sin  siny cos  sin  sin y  sin  cosy cos  cos    z inertial
 cos  cosy sin  sin  cosy  cos  siny cos  sin  cosy  sin  sin y   x 



Rinertial   cos  siny sin  sin  siny  cos  cosy cos  sin  sin y  sin  cosy   y 
  sin 
z
sin  cos 
cos  cos 

   body
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6/13/2009
“Line-of-Equinoxes”
“Line of Equinoxes” (2)
First Day of Spring
First Day of Summer
sun
First Day of Winter
“First-Point-of-Aires”
First Day of Fall

Figure 7: Direction of Vernal Equinox,
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Inertial Coordinate Systems (2)
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Inertial Coordinate Systems (3)
Local Vertical, Local Horizontal (LVLH) (sometimes called
Topocentric Coordinate System (SEU) )
“South (x), East (y), Up (z)”
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6/13/2009
Inertial Coordinate Systems (4)
Body Axis Coordinate System
Translates and rotates with vehicle
Local Vertical, Local Horizontal (LVLH) (sometimes called
TopoCentric Coordinate System (NED) )
v
Xbody – longitudinal axis
Ybody – lateral axis
Zbody – normal axis
u
“North (x), East (y), Down (z)”
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w
192
Wind Relative Coordinate System
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Wind Relative Coordinate System (2)
   angle  of  attack 
   angle  of  sideslip 


   pitch  angle





flight

path

angle


Points Into the Wind

V
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6/13/2009
Rotational Kinematics
Wind Relative Coordinate System (3)
 p, q, r 
x
rotational rates
about body axes
r yaw
Y y
p

   angle  of  attack 
   angle  of  sideslip 


   pitch  angle





flight

path

angle


y

x
q
z
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Rotational Kinematics (2)

 p
   q  
z
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Rotational Kinematics (3)
rotational rates
about body axes
 r 
u 
  
velocity components
V  v 
along body axes
 w
cos  cos  


V  V  sin  
 sin  cos  
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
body
.
 
 p
.



  q   inertial   
.
 r 
y 
 
Using a similar rotation
process as earlier
. 
.


    1 sin  tan  cos  tan    p 
0
 sin    
 p  1
 
. 

 . 


cos 
 sin    q    q    0 cos  sin  cos    
    0
. 
 r   0  sin  cos  cos    . 
sin 
cos    r 

y   0
y 
cos 
cos  
  
 
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Rotational Dynamics
Body Axis Equations of Motion
Newton’s Laws of linear motion can be extended to
describe angular motion

Ainertial
Direct rotational Analogs for velocity, acceleration,
force (torque) , and momentum
.
u   i j
 Ax 
V    .  


  Ay  
  V   v    p q
t
 .  u v
 Az 
 w 
 
.
u
k     q  w  r v 
. 

r    v    r  u  p  w
w  .   p  v  q  u 
 w
 
.
u   r v  q  w 
 Fx 
. 
  1 F 
v

p

w

r

u
  

 y
 .  q u  p v  m F 


 z
 w
 
Can also re-write linear equations of motion in
vehicle body axis
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Body Axis Equations of Motion (2)
 Ax 
 Fx   Aerodynamic Forces 
1  1  
Ay 
Fy 
Thrust Forces 
m  m  
 Fz   Gravity Forces 
 Az 
 _

C y aero

T 
 q Aref  C
x aero  2 sin  
 m
r
m

 Fx   _

1    q Aref

F


C

sin

cos



y
y
2
aero
m   m
r

 Fz 
_


 q Aref


C

cos

cos

x aero
z
2
aero
 m

r


C
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200
201
Body Axis Equations of Motion (3)
From Section 8.2 .. We can
write aerodynamics forces
in terms of lift and drag coefficient
 Cx aero    cos 

 
C y aero    0

   sin 
 Cz aero  
CD aero    cos 

 
 C y aero    0

  sin 
 CL aero  
C z aero
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202
0 sin   CD aero 

 
1
0    C y aero 
0  cos    CL 
 aero 
 sin    Cx aero 


0  C y aero 


0  cos    Cz 
 aero 
0
1
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203
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Angular Momentum, Velocity, and
Acceleration
Angular Momentum, Velocity, and
Acceleration (2)
• Analogous to
• The Angular Acceleration Equation is:
 d 

d
d  . 
M
L   J     J  
dt
dt
dt 

 
• The Angular Acceleration Equation is:
In terms of Body Axis Components
 d 

d
d  . 
M
L   J     J  
dt
dt
dt 

 


 L 
  J   

M
 L 
    J  
t
t
J = Inertia Tensor
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

 = angular velocity
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What is the Inertial Tensor?
Angular Acceleration Equation


 L 
  J   

M
 L 
    J  
t
t
• Resistance to Rotation in Three Axes
Using a process similar to the Linear body-axis equations
 Ix

  I xy
  I xz

 I xy
Iy
 I yz
205
J=
.
p
 I xz   
 .
 I yz    q  
I z   . 
r 
 
 q  r  I y  I z    q 2  r 2  I yz  p  q  I xz   r  p  I xy  

 M x 
 r  p  I z  I x    r 2  p 2  I xz  q  r  I xy   p  q  I yz     M y 

  
 p  q  I x  I y    p 2  q 2  I xy  r  p  I yz   q  r  I xz    M z 


ix
ixy
ixz
iyx
iy
iyz
izx
izy
iz
Diagonal Components of the Inertia Tensor
are commonly referred to as the “Moments of Inertia”
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207
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6/13/2009
Inertial Tensor (2)
J=
ix
ixy
ixz
iyx
iy
iyz
izx
izy
iz
Moment of Inertia
Off-Diagonal Components of the Inertia Tensor referred to as the “CrossProducts(or cross-moments) of Inertia”
• Typically, Diagonal Components >> Off-Diagonal Components
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I xy  I yx , I yz  I zy , I xz  I zx
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Calculating the Moment of Inertia
209
Calculating the Moment of Inertia (2)
• Multiplying by  (density) and t
(thickness of the element)
Gives the Mass-moment of Inertia
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211
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6/13/2009
Cross-Products of Inertial
Calculating the Moment of Inertia (3)
iyx = ixy = t xy dA
A
iyz = izy =  t yz dA
A
izx = ixz =  t
xz dA
A
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212
213
How Does Torque Change Attitude
What is a Moment?
Often referred to as
a “Torque”
t
=
d
dt
“damping
term”
i.e. friction
  
M  R F
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J  dt 
J + b  
t0
t
- b 
Jt  (t) = J0 o +
dt
t0
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215
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6/13/2009
6-DOF Body Axis Equations
of Motion, Summary
What if We Don’t Control Attitude
t
Linear
- b 
Jt  (t) = J0 o +
.
u   r v  q  w 
 Fx 
. 
1  

 v    p  w  r  u   m  Fy 
 .  q u  p v 
 Fz 

 w 
 
Rotational
dt
t0
• Assume No Damping, Constant Inertia, and Constant Torque
Vector
d
J0 dt  = J0 o +  t-t0
• Our Initial Attitude Degrades in a Hurry (Spacecraft Tumble)
t = 0 + o t-t0 + J0 -1 
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t-t0 2
2
Stephen A. Whitmore, USU MAE Dept.
 Ix

  I xy
  I xz

 I xy
Iy
 I yz
.
2
2
p 

 I xz     q  r  I y  I z    q  r  I yz  p  q  I xz   r  p  I xy    M x 
 . 
2
 I yz    q   r  p  I z  I x    r  p 2  I xz  q  r  I xy   p  q  I yz     M y 


I z   .   p  q I  I  p 2  q 2 I  r  p I  q  r I   M z 
 xz  
 x y 
 yz 
 xy
r  
 
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ESDM Senior
Design Project
217
National Aeronautics and
Space Administration
Appendix to Section 8
Introduction to Geodesy
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National Aeronautics and Space Administration
www.nasa.gov
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6/13/2009
Appendix to Section 8: A brief overview of
Geodetics
Geodesy
• Navigation Geeks do
Calculations in
Geocentric (spherical)
Coordinates
• Map Makers Give
Surface Data in Terms
of Geodetic (elliptical)
Coordinates
earth
• Need to have
some idea how to
relate one to another
-- science of geodesy
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How Does the Earth Radius
Vary with Latitude?
k
z
REarth =
x?+ y2
+ z2
=

Ellipse:
2
r 2+
z
=1
Req Req 1 -e2Earth
r 2+
z
R eq
Req 1 - e2Earth
R
r
"a"
How Does the Earth Radius
vary with Latitude?
r? + z2
y
j

j
y
Rearth
x

i
"b"
r

Pr im e Meridian
x
Stephen A. Whitmore, USU MAE Dept.
2
=1

2
2
2
1 - eEarth
r2 + z2 = Req
1 - eEarth

z2
2
2
z
r
2
2
Req = r +
= r 1+
1 - e 2Earth
1 - e2Earth
r
z
r2 = R2earthcos2 
z 2= tan2 
r
Stephen A. Whitmore, USU MAE Dept.
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6/13/2009
How Does the Earth Radius
vary with Latitude?
R2eq
= cos2 
R2earth
tan2 
1+
1 - e2Earth
1 - e2Earth cos2  + sin2 
2
1 - eEarth
=
=
Earth Radius vs
Geocentric Latitude
Rearth
=
Req
1 - e2Earth
1 - e2Earth cos2 
Polar Radius: 6356.75170 km
Equatorial Radius: 6378.13649 km
Inverting ....
cos2  + sin2  - e2Earth cos2 
1 - e2Earth cos2 
=
1 - e2Earth
1 - e2Earth
Rearth
=
Req
eEarth
=
2
1- b
a =
a2 - b2 =
a2
2
6378.136492 - 6378.13649
= 0.08181939
6378.13649
1 -e2Earth
1 -e2Earthcos2 
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Earth Radius … alternate formula
Earth Radius vs
Geocentric Latitude
• Earth radius as Function of Latitude
(concluded)
6380.
6375.
6370.
Radius,
Km
6365.
6360.
6355.
-100
-50
0
50
100
Geocentric Latitude, deg.
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227
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6/13/2009
What is the mean radius of the earth?
dA =  [
RE

2
cos ( 
]
RE = Req
RE
• IAU Convention:
Based on
Earth's Volume
2
1 - eEarth
2
1 - eEarth
cos2 


(continued)
• Earth's (ellipsoid) Volume
cos(
RE
Sphere Volume:
What is the Earth's Mean Radius?

2


VE =
R E d cos (
-
2


2
4  RE3 = VE
mean
3
R3eq

-
2
dV =  [
RE
2
cos(
] x RE d cos (
1 - e 2Earth
1 - e2Earth cos 2 
4
3

 RE cos  3 d =
1- e 2
earth
3/2
cos 3  d =
R3eq
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Earth Radius vs
Geocentric Latitude
(concluded)
6380.
“Gaussian Surface”
6375.
6370.
Radius,
Km
6365.
6360.
6355.
-100
Stephen A. Whitmore, USU MAE Dept.
-50
0
Geocentric Latitude, deg.
50
100
Stephen A. Whitmore, USU MAE Dept.
231
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6/13/2009
Geocentric vs Geodetic
Coordinates
Geocentric vs GeodeticMean
Cooordinates
North (Celestial)
Pole
• Map makers
define a new
latitude which is
the angle that
normal to the
Earth's surface
makes with the
respect to the
equatorial plane
2
Req 1 - e(earth)
Mean
Greenwich
Meridian
• Geodetic latitude
RE


Geocenter
Req
'

Req
Geocentric vs Geodetic
Coordinates
(contined)
•Since the Earth is
Elliptical only along the
z-axis ... geodetic
and geocentric
longitude are
identical
Mean
• Altitude is an
extension of the
line of latitude
geodetic)
Mean
North (Celestial)
Pole
Req 1 - e2(earth)
Greenwich
Meridian
h
RE


Geocenter
'
Req

Req
Equator
Equator
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Geocentric vs Geodetic
Coordinates
(contined)
•Complex nonlinear
equations describe
relationship between
geocentric and
geodetic latitude
• Derivation requires
Extensive
Knowledge of
Spherical
Trigonometry
Mean
North (Celestial)
Pole
Req 1 - e2(earth)
Mean
Greenwich
Meridian
h
RE


Geocenter
'
Req

Req
Equator
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6/13/2009
Geocentric vs Geodetic
Coordinates
Geocentric vs Geodetic
Coordinates
(contined)
Geocentric Polar Coordinates
Rtarget =
x target 2
+
y target 2
+
ztarget 2
rtarget
h
z
y
target = tan -1 xtarget
target
xtarget2 + ytarget2
- R''
cos '
y
ztarget
xtarget 2 + y target 2
R''
'
r
rtarget
Req
"Radius of Curvature"
Pulling it all together
i) Compute geocedtric cartesian coordinates
Range, runway threshholds, radar antennae, beacon ....
xtarget= R'' +h cos ' cos
ytarget= R'' +h cos ' sin
ztarget= R'' 1 - e2
earth
+h sin '
Req
1 - e2
earth
'target=tan-1
ztarget
xtarget2 +ytarget2
1

1 -e2earth
R'
'
Stephen A. Whitmore, USU MAE Dept.
• Given geodetic coordinates -compute geocentric
R'' =
h=
target = tan-1 xtarget
target
'

target = tan -1
(concluded)
Inverse Relationships, non-linear no direct solution
Stephen A. Whitmore, USU MAE Dept.
Pulling it all together
Stephen A. Whitmore, USU MAE Dept.
(continued)
• Given geodetic coordinates -- compute geocentric
ii) Compute Geocentric polar coordinates next
Rtarget =
x target 2
+
y target 2
+
ztarget 2
y
target = tan -1 xtarget
target
target = tan -1
sin2 '
R'
'
+htarget
ztarget
xtarget 2 + y target 2
Stephen A. Whitmore, USU MAE Dept.
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6/13/2009
Pulling it all together
(concluded)
• Given geocentric (usually x,y,z) coordinates -compute geodetic
R eq
R'
'
=
1 - e2
earth
GPS, INS, TLE's ....
No explicit solution:
requires
1) series expansion solution,
2) numerical iteration,
3) or a special solution
called "Ferrari's method"**
' target = tan
-1
h=
sin
• Edwards Air Force Base, Radar Site #34
target = tan
ztarget
xtarget2 + ytarget2
2
+
-1
1 - e2earth
- R''
y target
x target
1

R'
'
Numerical example
'
2
xtarget ytarget
cos '
2
Numerical Example
R'
' =
34.96081°
 = –117.91150°
h = 2563.200 ft
'
+ htarget
**NASA Technical Paper 3430, Whitmore and Haering,
FORTRAN Program forAnalyzing Ground-Based
Tracking Data: Usage and Derivations, Version 6.2,
1995
• Find corresponding geocentric cartesian
and polar coordinates
Stephen A. Whitmore, USU MAE Dept.
Numerical Example (cont'd)
Stephen A. Whitmore, USU MAE Dept.
Numerical Example (cont'd)
• Compute X and Y (geocentric)
• Compute Local Radius of Curvature
R'' =
1
Req
2
-e sin2 '
earth
6392.1871 +2536.2 3. 048 10-4
=
 =
cos 34.96081 180
5239.3131 km
6378.13649 km =
  2
1 - 0.08181939
sin34.96081
180
6392.187109 km
rtarget = R'' +h cos ' =
xtarget=rtargetcos =
ytarget= rtargetsin =
5239.3131 km
 cos -117.91150
  =
180
5216.0074 km
 sin -117.91150
  =
180
-2452.5602 km
Stephen A. Whitmore, USU MAE Dept.
-4629.83218 km
Stephen A. Whitmore, USU MAE Dept.
61
6/13/2009
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Numerical Example (concluded)
• Comparison
Geodetic
' =
Geocentric
34.96081°

=
 = –117.91150°

= –117.91150°
h = 2563.200 ft
Dgeoid = 48228.25 ft
34.7803°
• Earth Oblateness is NOT trivial, and in the REAL
World -- it must be accounted for
Stephen A. Whitmore, USU MAE Dept.
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62
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Spacecraft Design According to:
National Aeronautics and
Space Administration
ESDM Senior
Design Project
Trajectory
Designers
point mass
Flight Controls I
Controls
Designers
Equations of Motion in 6-Degrees of
Freedom, Control Actuators,
Control System Examples
Rocket
Designers
Payload
Designers
Sellers, Chapter 12
Structural
Designers
Power Syste m
Designers
0
www.nasa.gov
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Stephen A. Whitmore, USU MAE Dept.
Linear
.
u   r v  q  w 
 Fx 
. 
1  

 v    p  w  r  u   m  Fy 
 .  q u  p v 
 Fz 

 w 
 
Rotational
+
point mass
 Ix

  I xy
  I xz

Free-flying vehicles also have Rotational degrees of freedom,
governed by rotational dynamics, and described by Euler Angles –
the orientation between the inertial and body reference frames
Stephen A. Whitmore, USU MAE Dept.
1
6-DOF Body Axis Equations
of Motion, Summary
Collected  Linear + Rotational Dynamics = 6 DOF
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National Aeronautics and Space Administration
Degrees of Freedom (revisited)
Trajectory
Designers
Communication
System Designers
2
 I xy
Iy
 I yz
.
2
2
p 

 I xz     q  r  I y  I z    q  r  I yz  p  q  I xz   r  p  I xy    M x 
 . 
2
 I yz    q   r  p  I z  I x    r  p 2  I xz  q  r  I xy   p  q  I yz     M y 


I z   .   p  q I  I  p 2  q 2 I  r  p I  q  r I   M z 
 xz  
 x y 
 yz 
 xy
r  
 
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3
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6/13/2009
Guidance and Navigation
Control System
Trajectory
Designers
Guidance and Navigation
Control System (2)
point mass
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4
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Attitude Determination &
Control System (ADCS)
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5
Attitude Determination &
Control System (2)
• It is necessary to establish and maintain vehicle stability
– Mission requirements: payload pointing and slewing
– Solar array pointing and tracking
– Directional antennas
– Orientation of satellite for thrust maneuvers
– Thermal Maneuvers
– Station keeping
• Roll, Pitch and Yaw Control
6
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2
6/13/2009
Why Does the Spacecraft
Attitude Change?
Why Does the Spacecraft
Attitude Change? (2)
Remember
…
• Disturbing Torques:
–
–
–
–
–
–
Right?
Atmospheric drag
Solar wind
Radiation pressure
Magnetic fields
Non-uniform Gravitational fields
Micrometeorite impact
 d 

d
d  . 
M
L   J     J  
dt
dt
dt 

 
• Well … not exactly !….
9
Stephen A. Whitmore, USU MAE Dept.
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8
How Does Torque Change Attitude
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
What if We Don’t Control Attitude
t
- b 
Jt  (t) = J0 o +
dt
t0
• Assume No Damping, Constant Inertia, and Constant Torque
Vector
d
J0 dt  = J0 o +  t-t0
t
=
d
dt
J  dt 
J + b  
“damping
term”
i.e. friction
• Our Initial Attitude Degrades in a Hurry (Spacecraft Tumble)
t0
t
- b 
Jt  (t) = J0 o +
t = 0 + o t-t0 + J0 -1 
dt
t0
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t-t0 2
2
Stephen A. Whitmore, USU MAE Dept.
11
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6/13/2009
Vehicle Stability
Example: Rocket Flight Stability
During rocket flight small wind gusts or thrust offsets can cause the rocket to
"wobble", or change its attitude in flight.
Rocket rotates about its center of gravity (cg)
Lift and drag both act through the center of pressure (cp) of the rocket
When cp is behind cg, aerodynamic forces provide a “restoring force” …
rocket is said to be “statically stable”
When cp ahead of cg, aerodynamic forces provide a “destabilizing force” …
rocket is said to be “unstable”
Condition for a statically for a stable rocket is that center of pressure
must be located bhind the center of gravity.
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12
Example: Rocket Flight Stability (2)
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13
Example: Rocket Flight Stability (3)
If center of gravity (CG) is forward of the (Cp) , vehicle responds to a
disturbance by producing aerodynamic moment that returns Angle of attack
of vehicle towards angle that existed prior to the disturbance.
If CG is behind the center of pressure, vehicle will respond to a disturbance
by producing an aerodynamic moment that continues to drive angle of attack
further away from starting position.
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14
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4
6/13/2009
Example: Rocket Flight Stability (5)
Example: Rocket Flight Stability (4)
Weather Vane Analogy
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National Aeronautics and Space Administration
17
Static Margin and Pitching Moment (2)
Static Margin and Pitching Moment
Static margin is a concept used to characterize the static stability and controllability
of aircraft and missiles.
For a Rocket Static margin
is the distance between the CG
and the CP; divided by
body tube diameter.
In aircraft analysis, static margin is defined as the non-dimensional distance between
center of gravity and aerodynamic center of the aircraft.
In missile analysis, static margin is defined as non-dimensional distance between
center of gravity and the center of pressure.
Stability requires that the pitching moment about the rotation point, C m, become
negative as we increase CL:
c
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5
6/13/2009
Static Versus Dynamic Stability
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Stephen A. Whitmore, USU MAE Dept.
Static Versus Dynamic Stability (2)
20
Static Versus Dynamic Stability (3)
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21
Static Versus Dynamic Stability (4)
22
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23
6
6/13/2009
Launch Controls
ADCS Techniques
• Principle stabilization techniques
– Gravity Gradient, Spin, Rate Damping, 3-Axis
Reaction Control System, Aerodynamic Controls
• Sensors
– Star, Sun, Earth, Gyros, Magnetometers, GPS
• Actuation Devices
– Reaction Wheels, Gyros, Thrusters, Magnetic Torquers,
Moveable Aerodynamic Controls Surfaces, Thruster
Gimbal
• Control Systems
24
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National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
25
Gravity Gradient Stablization
Launch Controls (2)
“Pico-sat”
gravity =
3
I - I sin 2 
2 r3 z y

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26
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Stephen A. Whitmore, USU MAE Dept.
27
7
6/13/2009
Spin Stabilization
Spin Stabilization (2)
• Spinning mass
has angular momentum
that is naturally conserved.
• Spacecraft Tends Towards Same Inertial Orientation in Space
L
• This angular momentum
resists the disturbance
of perturbing torques
L
L
L
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28
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Why Does Spin Stabilization Work?
29
Three-Axis Stabilization
J0 ddt  = J0 o +  t-t0
L wheel 1
Spin Acts as a Virtual Torque
Spin keeps this small• If we spin counter to the direction of the
expected perturbing torques … then
we can counter much of its effects … at
least in initially
• Reaction Wheels
Allow More Precise 3Axis Control
L wheel 2
L wheel 3
• Rapid response
• Subject to Saturation
• Eventually, the perturbing torques eat
Away at the initial spin and the spacecraft
Spins down … and must periodically
be “Spun-Up” (Reaction Control System)
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30
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31
8
6/13/2009
Three-Axis Stabilization (2)
Magnetic Torquers
• External Torque Applied
• Slow Response Time
• Will not Saturate
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National Aeronautics and Space Administration
32
"De-spun" Inner Section
L
L
Spinning
Inner Section
L
L
L
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33
Dual-Spun Spacecraft (2)
Dual-Spun Spacecraft
• Single-Spin Spacecraft not
very useful for earth pointing
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
• Spinning Outer section
Provides Stability
• Inner Section can
be Pointed in
Desired Direction
De-Spun Section Rotated to
Always Look Towards Earth
L
Stephen A. Whitmore, USU MAE Dept.
34
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
35
9
6/13/2009
Can We Use Damping to Keep
Angular Rates Small?
Can We Use Damping? (2)
t
- b 
Jt  (t) = J0 o +
Primary axis
of rotation
Cavity Filled with
Vis cous Fluid
dt
• Perturbing torques cause
a local angular velocity
differential
Iz inner
t0
• If rate-damping if used to counter perturbing torques
… we can keep the angular rates from growing beyond
our RCS-System’s ability to control the rates
Stephen A. Whitmore, USU MAE Dept.
• Frictional Damping of
Fluid limits max angular
velocities
t
Bearings
- b 
Iz outer
• As rates build up … so do the effective torques of our
rate-damping system
National Aeronautics and Space Administration
• Inner and Outer Hulls have
Differing inertias …
Outer Hull
36
Reaction Control Systems - Propulsion
(RCS)
National Aeronautics and Space Administration
dt
t0
Stephen A. Whitmore, USU MAE Dept.
37
Reaction Control Systems (RCS)
• The spacecraft propulsion system provides
controlled impulse for:
Thrusters
– Orbit insertion and transfers
– Orbit maintenance (station keeping)
– Attitude Control
• Propulsion Types
– Cold gas, monopropellant, bipropellants, ion
Thruster rockets apply force at some distance
away from center of mass, causing a torque that
rotates the spacecraft
38
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39
10
6/13/2009
RCS Control Maneuvers
RCS Example: Cold Jet Thruster
• Rate Nulling
rate-gyro
sensors
• No Combustion
p
Gas Storage Tank
• Thrust provided by
expansion of gas
through Nozzle
Gas Exhaust Nozzle
Pressure
Regulator
q
r
• Simple Mechanism
Actuator Valve
for Gas Flow
x
p
= q
r
• Low Isp
q
p
z
r
Y
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
RCS Control Maneuvers (2)
t
0
Example: Yaw Damping
rate-gyro
sensors
p
dt
q
r
t0
t
42
0
- b 
Jt  (t) = J0 o +
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
41
x
t
i
p
 dt =
•
thrusters
t0
F  R cg
dt = -
z
J0 o
r
q
t0
Y
RCS Torque Impulse Counters rates
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Stephen A. Whitmore, USU MAE Dept.
43
j
J =
National Aeronautics and Space Administration
ix
ixy
ixz
iyx
iy
iyz
izx
izy
iz
0
0
0  iz r k
r
k
Stephen A. Whitmore, USU MAE Dept.
44
11
6/13/2009
Example: Yaw Damping (2)
t
• Thrusters Tend to
Fire Impulsively
t
•
thrusters
rate-gyro
sensors
RCS Thrust Profile
4 Fy xt hrust ersdt
F  R cg = k
t0
Total
Impulse
xthrusters
p
q
t
r
pulse
Burn Time
Time
x
t
p
z
q
Y
Stephen A. Whitmore, USU MAE Dept.
45
Tells Flight Control Computer
How Long to Fire Thrusters
tburn
i r
Fy dt = 4 xz
4 Fy dt = iz r 
4 xt hrust ers
r
National Aeronautics and Space Administration
Calibration
Tota l Impulse
Thru st
t0
t0
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t hrust ers
0
Stephen A. Whitmore, USU MAE Dept.
46
Attitude Control:
and Even More Complex Feed-back
Control Problem
Propellant Budget for the “Burn”
tburn
Isp = F
g0 m
i r
Fy dt = 4 xz
0
tburn
tburn
m dt 
Mpropellant =
0
Sensor
t hrust ers
4
g0 Isp
Magnetometer
Fy dt
Attitude Determination Loop
0
From Calibration
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Attitude Determination and Control System (ADCS)
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48
12
6/13/2009
Attitude Control:
Feed-back Control Problem (2)
thrusters
J d t2 
+ b dt = 
Feed-back Control and Actuation Loop
d2
d
50
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
ESDM Senior
Design Project
49
Spacecraft Design According to:
National Aeronautics and
Space Administration
Trajectory
Designers
point mass
Flight Controls II
Controls
Designers
Feedback Control Systems
Rocket
Designers
Payload
Designers
Sellers, Chapter 12
Structural
Designers
Power Syste m
Designers
www.nasa.gov
National Aeronautics and Space Administration
Communication
System Designers
51
Stephen A. Whitmore, USU MAE Dept.
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52
13
6/13/2009
Degrees of Freedom (revisited)
Static Versus Dynamic Stability
Collected  Linear + Rotational Dynamics = 6 DOF
+
Trajectory
Designers
point mass
Free-flying vehicles also have Rotational degrees of freedom,
governed by rotational dynamics, and described by Euler Angles –
the orientation between the inertial and body reference frames
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Stephen A. Whitmore, USU MAE Dept.
53
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Control System Basics:
54
Control System Basics (2):
Single Input, Single Output System
reference
error
controller
command
Plant
(the system
being controlled)
response
response
feedback
sensor
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56
14
6/13/2009
Control System Basics (3):
Control System Basics (4):
Y  s   P  s  U  s   U  s   C  s  E  s   E  s   R  s   F  s  Y (s )
P sC s
 " closed loop transfer function "
1 F  s P sC s
solving for Y ( s) 
Y ( s) 
P sC s
R s
1 F  s P  sC  s
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
P  s  C  s   " loop gain "
“Closed-Loop”
System Response
57
PID Controller
58
PID Controller (2)
The proportional, Integral, Derivative (PID) controller is probably
the most-used feedback control design. "PID" refers to 3 terms
operating on the error signal to produce a control signal.
The control signal is constructed as
t
u (t )  K p e(t )  K I  e( )d  K D
r (t )  " desired " reference or tracking signal
0
proportional 
u (t )  control signal sento to the system
y (t )  system response
yˆ(t )  measured system response
Kp 
Stephen A. Whitmore, USU MAE Dept.
integral 
de(t )
dt
derivative
proportional gain
K I  integral gain
K D  derivative gain
e(t )  r (t )  yˆ (t )
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59
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60
15
6/13/2009
PID Controller (3)
PID Controller (4)
Applying Laplace transform to control signal (very similar to
Fourier transform)
Plugging into the closed-loop response function for the system
K


K  I  K D  s   E (s)
U  s   p s

U s  C s E s  C s 

E s
E s
K
u ( s)  K p E ( s)  I E ( s)  K D  s  E ( s) 
s
K


I
 K D  s   E (s)
 Kp 
s


K


P  s   K p  I  KD  s 
s


Y (s) 
R s 
K


1 F  s P  s  K p  I  KD  s 
s




P  s   K D  s 2  sK p  K I 
Y ( s ) 
R  s 
2
s  F  s  P  s   K D  s  sK p  K I 


Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
61
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Example Pitch Feedback Control
62
Example Pitch Feedback Control (2)
Neglect Cross Products of Inertia
 Ix

  I xy
  I xz

Assume “wings level” .. That is f ~ 0
. 
 f   1 sin f tan 
. 
    0
. 
sin f
   0
cos 
  
National Aeronautics and Space Administration
.

cos f tan    p 
.

 sin f   q     q
cos f   r 

cos  
Stephen A. Whitmore, USU MAE Dept.
.
2
2
p 

 I xz     q  r  I y  I z    q  r  I yz  p  q  I xz   r  p  I xy    M x 
 .
 I yz    q    r  p  I z  I x    r 2  p 2  I xz  q  r  I xy   p  q  I yz     M y 


I z   .   p  q I  I  p 2  q 2 I  r  p I  q  r I   M z 
 xz  
 x y 
 yz 
 xy
r  
 
 I xy
Iy
 I yz
..
 q  
My
Iy
r p
 Iz  Ix 
Control moment
63
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Iy
Disturbance torque
Stephen A. Whitmore, USU MAE Dept.
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Example Pitch Feedback Control (4)
Example Pitch Feedback Control (3)
 assume perfect feed back data  F  s   1
 (s) 
..

My
Iy
 s 2 ( s ) 
M y (s)
Iy
  (s) 
1  u (s) 
1

  P(s)  2
s 2  I y 
s Iy
1
 K D  s 2  sK p  K I 
s2 I y
 ( s) reference 
1
s  2  K D  s 2  sK p  K I 
s Iy
Closed Loop Response
 (s) 
K
D
 s 2  sK p  K I 
s 3 I y   K D  s 2  sK p  K I 
 ( s) reference
Commanded Pitch Torque
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K


M y ( s )   K p  I  K D  s    ( s ) reference   ( s ) 
s


65
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Multivariable Control
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66
Multivariable Control (2)
A common method for feedback is to multiply
the output by a matrix K and setting this as
the input to the system:
The closed-loop system becomes:
Eigen-modes of system can be
Controlled by “tweaking” K
Through eigen-decomposition
Of
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Solving for y(t) and substituting into state
equation
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Optimal Control
Optimal Control (2)
Multi-variable control technique that seeks to “limit” control
activity to only that which is necessary, i.e. minimize
Optimal Solution (via calculus of variations) is
u (t )   R 1BT P  x(t )
1
1

J    xT Qx  uT Qu   dt
2
2


t
Subject to solution of the matrix Riccati Equation for … P
Subject to
PA  AT P  Q  PBR 1BT P  0
(typically D(t) = 0 )
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“Design Friday”
Optimal Control (3)
Read “Leapfrog” paper AIAA 2007-2764
Closed Loop Control Law is:
LEAPFROG: Lunar Entry and Approach Platform For
Research On Ground
.
.
x(t )  A  x(t )  B  u (t )  u (t )   R 1BT P  x(t )
y (t )  C  x(t )
y (t )  C  x(t )
closed  loop  response : x (t )   A  R 1B T P   x (t )
.
Using Information Presented in sections 8.3, 9.1, and 9.2
Derive form for Linear Quadratic Regulator Control that
Nulls and trims the gravity assist platform at zero pitch
and roll angle, and nulls yaw rate
.. Assume contoller commands {Mx, My, Mz,} directly
… write block diagram for the controller
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ESDM Senior
Design Project
Spacecraft Building Blocks
National Aeronautics and
Space Administration
Trajectory
Designers
Spacecraft Avionics I: Power and
and Thermal Management
Systems
point mass
Rocket
Designers
Controls
Designers
Sellers Chapter 11, pp 382-388,
Chapter 15, pp. 617-629.
Payload
Designers
Power Syste m
Designers
Structural
Designers
Communication
System Designers
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Spacecraft Building Blocks
1
Spacecraft Bus
Structure
• Payload
• Launch and Propulsion System
• Attitude Determination & Control
System (ADCS)
• Reaction Control System (RCS)
• Electrical Power System (EPS)
• Thermal Control System (TCS)
• Structure
• Telemetry, Tracking & Command
System (TT&C)
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Bus
Propellant
Payload
15%
25%
30%
• Spacecraft bus exists solely to support the payload, with all of the
necessary “bells and whistles” to keep the payload “happy and healthy.”
30%
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2
• Subsystems become part of the spacecraft bus.
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3
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6/14/2009
Electrical Power System
(EPS)
Spacecraft Bus (2)
• Solar Arrays generate electrical power.
• Structural elements hold the spacecraft
together.
•The solid rocket motor and thrusters
make up the propulsion system.
• Magellan spacecraft subsystems,
support payload mission
requirements.
• Star Scanner is a part of the
attitude control subsystem.
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• High gain antenna communicates to
earth-based ground stations and collects
payload data.
• Other bus elements of include data
processing sub-systems, thermal control
system, and miscellaneous avionics
Stephen A. Whitmore, USU MAE Dept.
• Solar Cells/Batteries, Radioactive Thermal
Generators (RTG)
• Solar Cells
–
–
–
–
–
Silicon (14% Efficiency) - 190 W/m2
Gallium Arsenide (18%) - 244 W/m2
Degradation (3-4%/yr LEO)
Temperature (.5% decrease per degree)
Sun Incidence angle
Power Syste m
Designers
4
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Power System Components – Solar Arrays
Solar Cells
Pout = Pin  cos 
The most widely used and cost efficient form of energy conversion is the photovoltaic solar array.
• Types –
–
Single-Crystal Silicon Cells
•
•
–
Advantage: Widely available and have been used as the “workhorse” of the space industry
Disadvantage: Expensive manufacturing process for space qualified cells
Advantage: High conversion efficiency in comparison Single-crystal Silicon cells
Disadvantage: Extremely expensive to manufacture
P
in
Semi-Crystalline & Poly-Crystalline Cells
•
•
Advantage: Low cost of manufacture which gives a net reduction in the cost per watt
Disadvantage: Low energy conversion efficiency
–
Thin Film Cells
–
Amorphous Cells – Not enough data to be selected as a serious candidate for space applications (new
technology).
Multi-Junction Cells – High efficiency and good manufacturability.
•
•
–

Gallium Arsenide Cells
•
•
–
6

Advantage: Less expensive to manufacture
Disadvantage: Has not been used widely in space applications (lack of data).
P
out
Solar arrays can provide power requirements from tens of watts to several kilowatts with a life
span of a few months to fifteen years.
The life of a solar array degrades due to the space environmental effects on the photovoltaic cells.
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Effect of
Temperature
On 
Solar Cells
( ~ 0.15)
Surface Temperature, K
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6/14/2009
Solar Cells
Solar Cell Efficiency
'I/V" Curve
Pout = Pin  cos 
Vmax
P
in
Effect of
Temperature
On 

P=IV
Voltage, V

Design Point
(Max Power Output)
Solar Cells
( ~ 0.15)
P
out
Surface Temperature, K
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Current, I (amps)
9
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Max Power Point (2)
Where is Maximum Power Point
 2 2
2
P Ž
 V =
d
V max
Vmax
- V2V V
V ŽVV
ŽP
=
I = V2max - V2 
ŽV
P = I V = V2max - V2 V
V2max - V2
Ž
Condition for max power: ŽPVP =0 0
V

V2
=0
V2max - V2
V2max - V2 = V2  Voptimum = 2 Vmax
2
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6/14/2009
Effect of Aging
'I/V" Curve
Vmax
Voltage, V
Design Point
(Max Power Output)
Effect of Eclipses
Beginning-of-Life
Power Must be
Large Enough to
Accommodate
End-of-Life Power
• Most Spacecraft
Pass into Earth’s
Shadow Once
Each Orbit
• Effect Causes
Cyclic Power
Production

3-4 % per year
Current, I (amps)
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Cyclic Power Production
Torbit
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How Long Will the Eclipse Last
• Ignore Effect of Elevation Angle (worst case scenario)
Tec lipse
Power
Output
W/m2
Time
• Cyclic Power Production Requires Significant Power
Conditioning and Storage capacity
 = sin-1
Teclipse = 2  =
orbit
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Rearth
horbit + Rearth
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2 =2 T
orbit
 / R3 2 
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6/14/2009
Power Distribution and Storage System
Batteries and Storage Systems
Solar
Panel
Regulation
Spacecraft
Power Bus
Max
Bus Voltage
Regulation
Battery
System
Charge/Discharge
Battery
System
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Power System Components - Batteries
17
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18
Power System Components – Batteries (2)
• Rechargeable Energy Storage Systems
– Silver Zinc Batteries
– Nickel Cadmium (NiCd)
– Nickel Hydrogen (NiH2) – Currently used in place
of Nickel Cadmium for space applications
– Nickel Metal Hydride (NiMH)
– Lithium-Ion (Li-Ion)
• Perform a trade study to choose the best for the
application and conditions
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6/14/2009
Power Distribution and Storage System
Batteries and Storage Systems
(example)
• Batteries
– Nickel Cadmium, Nickel Hydrogen
– Cycles
• LEO - every orbit (5000/yr)
• GEO - two 45 day periods
• Issues
–Depth of Discharge (Deep-Cycle Tolerance)
–Charge/Discharge Time
–Weight
–Power Regulation and Distribution
21
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Thermal Control System (TCS)
DC/DC
Converter
100 W (3.6 amps
@28 Vdc)
DC/DC
Converter
12 W (2.4 amps
@5 Vdc)
DC/DC
Converter
15 W (1.5 amps
@10 Vdc)
DC/DC
Converter
5 W (0.5 amps
@10 Vdc)
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22
Thermal Control System (2)
• Manages Heat Flow Through Spacecraft to
Keep Systems within Operating Temperature
Ranges
-- Typical operating ranges (C):
– 0 to 40 for Electronics
– 5 to 20 for Batteries
– 7 to 35 for Hydrazine
Propellant
– -100 to +100 for
Solar Arrays
– -200 to -80 for IR
payload sensors
National Aeronautics and Space Administration
payload
•
q
•
q
in
out
subsystems
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6
6/14/2009
Thermal Control Systems (3)
Temperature Versus Heat
• Spacecraft Heat Sources
•Internal, Direct Solar, Albedo, Earth, Space
• Often the concepts of heat and temperature are thought
to be the same, but they are not.
• Temperature is a number that is related to the average
kinetic energy of the molecules of a substance. If temperature
is measured in Kelvin degrees, then this number is directly
proportional to the average kinetic energy of the molecules.
• Heat is a measurement of the total energy in a substance.
That total energy is made up of not only of the kinetic
energies of the molecules of the substance, but total energy
is also made up of the potential energies of the molecules.
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Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Temperature Versus Heat (2)
26
Temperature Versus Heat (3)
• Relationship between temperature and heat transfer
• When heat, (i. e., energy), goes into a substance one of two things
can happen:
1.
…. Heat flows from “cold to hot”
The substance can experience a raise in temperature. That is, the heat can be
used to speed up the molecules of the substance.
m  cp
2. The substance can change state. For example, if the substance is ice, it can
melt into water. This change does not cause a raise in temperature. The
moment before melting the average kinetic energy of the ice molecules is
the same as the average kinetic energy of the water molecules a moment
after melting. Although heat is absorbed by this change of state, the
absorbed energy is not used to speed up the molecules. The energy is used
to change the bonding between the molecules.
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
27
T q


dt
dt
m  cp
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m  mass of object ~ kg
c p  specific heat of object
~
J
kgoK
T  temperature of object ~o K
q
 rate of heat transfer J
~
...watts
dt
sec
“heat capacity” ~ J/oK
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28
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6/14/2009
Heat Transfer: How Does Heat flow?
How does Heat flow (2)
• Conduction – the transfer of
• Forms of Heat transfer
heat energy by making direct
contact with the atoms/molecules
of the hotter object
• Convection – the transfer of
heat due to a bulk movement of
matter from hotter to colder areas
• Radiation – energy transferred
by electromagnetic waves
-- Convection … fluid molecules impacting surface
transfer energy
-- Conduction … molecules with a structure transfer
energy
-- Radiation … photons transfer energy
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30
Convection
Heat Transfer from Radiation
• All matter that has thermal energy will emit electromagnetic
radiation.
• Humans sense this radiation as visible light or infrared
radiation (heat).
Buoyancy forces
cause bulk
movement of the
water.
www.physics.arizona.ed
http://www.newt.com
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6/14/2009
Conduction
Heat Flux
Heat energy is transmitted
by collisions from neighboring
atoms/molecules.
http://www.ucar.edu/
• Heat Flux is the heat transfer per unit surface area
m  cp

dT dQ
1 dQ

q
dt
dt
A dt
m   Vol    A  dx    c p  dx

dT 1 dQ

q
dt A dt
dT 

 q     c p  dx  dt 
33
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34
Radiative Heat Transfer
Heat Flux (2)
• look at thin monolithic slab
•
q in
•
q out
1  dQ   dQ   m  c p dT
 
 

Asurf  dt in  dt out  Asurf dt
•
•
 q in  q out    c p  wall
•
 q ~ " heat flux "
“heat flux”
“ wall”
~
J
m2 sec
dT
dt
  wall  dx
• If heat flux “in” is greater than heat flux “out” wall heats up
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6/14/2009
Radiative Heat Transfer (2)
Radiation
• Radiation -- heat transmission through space

Incoming
Radiation
abs orbe d radiation
Reflected
Radiation
• Incoming Radiant Energy
 -- transmissivity (% energy that gets through) < 1
 -- reflectivity (% energy that gets reflected) < 1
 -- absorptivity (% energy that gets absorbed) < 1`



 + + = 1
Transmitted
Radiation
Emitted
Radiation
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Radiation (2)
38
Radiation (3)
• Emitted Radiant Energy
-- as object heats up, it radiates energy
back into space
Radiation law:
4
q
= T
Asurf
Asurf
 -- emissitivity < 1
 -- Stefan-Bolzman constant
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National Aeronautics and Space Administration
5.67 x 10-8 W/m2K4
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6/14/2009
Example: How Fast Does an Insulated
Plate Heat Up
Example (2)

Incoming
Radiation
q
=  cos  1358 W/ m2
Asurf
4
q
Emitted heat flux:
=  T
Asurf
Asurf
Absorbed heat flux:
Reflected
Radiation
q
Asurf

Transmitted
Radiation

Emitted
Radiation
Assume Sun angle is 
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41
Internal  U = M
ass
Energy
plate
Mass
Cp Tplate
U
=
total
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Asurf
Mass
=
C
plate p
Asurf
q
Asurf
Tplate
Stephen A. Whitmore, USU MAE Dept.
plate
Asurf
Cp "specific heat"
Ž
Žt
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42
Radiation Heating Example (2)
Change in Internal Energy of the Plate
q
Asurf
Total heat Flux to Plate (W/m2):
4
=  cos  1358 W/m2 -   T
A
surf
total
=
plate th Asurf
Asurf
= plate th Cp Tplate =
total
4
 cos  1358 W/ m2 -   T
Asurf
43
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6/14/2009
Radiation Heating Example (3)
Tplate =
 cos  1358
plate th Cp
W/m2
-
How Do TCS Work
  T4
plate th Cp Asurf
• Radiation, Conduction (limited Convection -- no air)
• Conduction -- heat transmission through a solid
Fourier law:
q
= - k ŽT
Žx
Across
•
q
x
k -- thermal conductivity
W/  k m
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46
Heat Pipes
Monolithic Slab Conduction
•
q
in
Tsurface
• Low Boiling Point Liquid
• Liquid Absorbs Heat at “Hot-end”
• Vaporized Liquid Condenses at Cold end
…. Releases heat
• Capillarity Action Carries Liquid back to Hot End of Tube
Tinterior
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6/14/2009
Convection Ovens
Forced Convection
• Forced Convection is not from to the natural
forces of buoyancy induced by heating.
A fan circulates the air so hot
air is not trapped at the top of
the oven. More cookies can
be baked at one time and all
will cook at the same rate.
• Instead, there is a external force that causes the
fluid to convect, such as a fan or a pump.
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51
Ablation Example
Ceiling Fans
Ceiling fans resemble Joule’s
famous paddle wheel
experiment where work done
on the fluid increases the
temperature. In both hot and
cold weather, ceiling fans are
useful for circulating air to force
convection.
-Heat shield consisting of phenolic resin in a metal “honeycomb” At high heat flux, resin
-Material decomposes via pyrolysis absorbing heat (phase change)
-Products form a barrier between hot gasses and spacecraft structure
-Surface temperature remains low
Rooms with high ceilings are a
problem during the winter as
the hot air rises and moves
away from the floor area.
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Stephen A. Whitmore, USU MAE Dept.
Laub, B. Thermal Protection Technology and
Facility Needs for Demanding
Future Planetary Missions, NASA Ames
Research Center, October 2003
52
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6/14/2009
Space Shuttle
Thermal Protection Systems
What Happens as Space Shuttle
Tile is Heated?
• 

 q in 
 convective
• Space Shuttle
Thermal
Protection
System (TPS)
“soaks up” heat
and stores it
internally due
to TPS low
internal
thermal
conductivity
 T 
4
radiation
back from
surface
 T 
k

 x  conduction
into tile (soak)
S is the Stefan-Bolztmann Constant,  the emissivity of the surface
 ~ 0.8-0.9 for
Shuttle tile
Stephen A. Whitmore, USU MAE Dept.
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54
What Happens as Shuttle Tile is heated? (2)
Because thermal conductivity of shuttle tile is so low … heat is radiated
back from the surface faster than it is absorbed into the body
--- Assume 1260 C surface temperature
--- 80 C interior wall temperature
Always work in absolute
--- 10 cm thick tile
temperature units
 T 

4
Stephen A. Whitmore, USU MAE Dept.
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55
Thermal Soak
• Space Shuttle Thermal Protection System “soaks up” heat
and stores it internally due to its very high heat capacity and low
thermal conductivity
= 26.62 W/cm2
radiation
back from
surface
Tile radiates back 180 times more heat than it
Conducts into the structure! (Surface cools rapidly)
 T 
k

 x  conduction
into tile (soak)
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
= 0.149 W/cm2
“heat transfer rate per unit area”
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
56
Stephen A. Whitmore, USU MAE Dept.
57
14
6/14/2009
Thermal Soak (2)
Thermal Soak (3)
HSRI Shuttle Tile (High
Temperature
Reusable Surface Insulation)
Silica (SiO2)
Density
144.2 kg/m3 (9 lb/ft3 LI-900)
352.5 kg/m3 (22 lb/ft3 LI-2200)
Specific heat
0.628 KJ/kg-K (0.15 BTU/lb-oF)
Thermal
conductivity
0.0485 W/m-K (0.028 BTU/ft-hr-oF) at 21 oC)
0.126 W/m-k (0.073 BTU/ft-hr-oF at 1093 oC)
One of the best “heat
soaks” in the world
Maximum reuse
temperature
Mostly made up of empty
space
Maximum single
1538 oC
use temperature
Reusability at
2300 oF
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
58
Compare Shuttle Tile Thermal
Conductivity to Conventional Materials
Material
Shuttle Tile (LI-900)
Air
Rubber
Thermal grease
Thermal epoxy
Glass
Concrete, stone
Sandstone
Stainless steel
Lead
Aluminium
Gold
Copper
Silver
Diamond
Thermal
conductivity
W/(m·K)
0.048-0.126
0.025
0.16
0.7 - 3
1-7
1.1
1.7
2.4
12.11 ~ 45.0
35.3
220 (pure)
120--180 (alloys)
318
380
429
900 - 2320
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>1260 oC
National Aeronautics and Space Administration
>100 missions
Stephen A. Whitmore, USU MAE Dept.
59
Thermal Analysis Techniques
More or Less … Only Air is a better insulator
(except for exotic materials like aero gels)
… a copper penny conducts heat almost 7000
Times faster than a shuttle tile
Stephen A. Whitmore, USU MAE Dept.
60
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
61
15
6/14/2009
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Thermal Analysis Techniques (2)
Finish
Questions??
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Stephen A. Whitmore, USU MAE Dept.
62
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
ESDM Senior
Design Project
63
National Aeronautics and
Space Administration
Spacecraft Avionics II: Telemetry
and Communications Systems
Sellers Chapter 11, pp 382-388,
Chapter 15, pp. 617-629.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
16
6/14/2009
Spacecraft Building Blocks
Spacecraft Building Blocks
Structure
Trajectory
Designers
• Payload
• Launch and Propulsion System
• Attitude Determination & Control
System (ADCS)
• Reaction Control System (RCS)
• Electrical Power System (EPS)
• Thermal Control System (TCS)
• Structure
• Telemetry, Tracking & Command
System (TT&C)
point mass
Rocket
Designers
Controls
Designers
Payload
Designers
Power Syste m
Designers
Structural
Designers
Communication
System Designers
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
66
Bus
Propellant
Payload
15%
25%
30%
30%
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Spacecraft Bus (2)
Spacecraft Bus
• Solar Arrays generate electrical power.
• Structural elements hold the spacecraft
together.
•The solid rocket motor and thrusters
make up the propulsion system.
• Magellan spacecraft subsystems,
support payload mission
requirements.
• Spacecraft bus exists solely to support the payload, with all of the
necessary “bells and whistles” to keep the payload “happy and healthy.”
• Subsystems become part of the spacecraft bus.
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Stephen A. Whitmore, USU MAE Dept.
68
• Star Scanner is a part of the
attitude control subsystem.
National Aeronautics and Space Administration
• High gain antenna communicates to
earth-based ground stations and collects
payload data.
• Other bus elements of include data
processing sub-systems, thermal control
system, and miscellaneous avionics
Stephen A. Whitmore, USU MAE Dept.
69
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Telemetry Tracking and
Control System (TT&C)
Mission Satellite
Relay Satellite
Ground Station
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Communication System Architecture
Control Center
Stephen A. Whitmore, USU MAE Dept.
71
National Aeronautics and Space Administration
• Electromagnetic Radiation!
• EM radiation -- transverse waves produced by moving charges.
A charge can radiate electromagnetic radiation only if it is
undergoing accelerated motion.
• Electromagnetic radiation also can be described as
discrete packets known as photons.
• As objects are
heated up, electrons
are stripped from
Lattice and
randomly accelerated
• Thus hot objects
glow (emit EM
radiation)
Light is a general term referring to electromagnetic radiation in
the visible part of the spectrum.
• Naturally occurring
EM
Stephen A. Whitmore, USU MAE Dept.
72
What Produces Electromagnetic
Waves?
How do These Remotely Located Systems
Communicate?
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Stephen A. Whitmore, USU MAE Dept.
73
National Aeronautics and Space Administration
When an object reaches a certain
temperature, it begins to re-emit
radiation, and glows hot.
Stephen A. Whitmore, USU MAE Dept.
74
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6/14/2009
How are EM Waves “Manufactured”
Example: Remote Sensing Mission
Dipole Antenna
• Naturally
occurring
EM
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
75
• Accelerating Charge Induces an Electrical
Field
• Process
Described
By Maxwell’s
equations
• Electric Field Induces a Magnetic Field
• If charge is accelerated back and forth
along the
Antenna at a prescribed Frequency ….
Maxwell’s Equations
Any
Questions?
…. Electromagnetic radiation at that
Prescribed Frequency is produced
Stephen A. Whitmore, USU MAE Dept.
76
Antenna Theory (3)
Antenna Theory (2)
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77
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Stephen A. Whitmore, USU MAE Dept.
78
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6/14/2009
Electromagnetic Waves
c
Antenna Theory (4)
=

 -- w avelength (m)
• Maxwell showed that these equation implicitly required the
existence of electromagnetic wave traveling at the speed of
light.
c -- speed of light in vacuum (3 x081 m/sec )
f -- w ave frequency (Hz)
• He also proposed a physical ether theory. He abandoned
attempts to formulate a specific mechanical model, instead
using formalism of Lagrangian dynamics.


• His theory of electromagnetic fields led directly
to discovery of theexistence of electromagnetic
waves.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
E field
S
Direction of Propogation
B field
S=E
79
B
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Stephen A. Whitmore, USU MAE Dept.
80
Electromagnetic Spectrum
Electromagnetic Wave Energy
Ew = h f 
f
Ew -- wave energy (joules)
h -- Plank's Constant (6.626 x 1 0-34 J sec)
f -- wave frequency (Hz)
• High Frequency waves are more energetic
than low frequency waves
High energy end of spectrum
Low energy end of spectrum
• Radio Frequency (RF) band
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Stephen A. Whitmore, USU MAE Dept.
81
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
82
20
6/14/2009
Radio Waves
• Why do we use RF Spectrum for communications?
(revisited)
Atmospheric transmissivity
Atmospheric is nearly transparent to long-wave radiation
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
83
Encoding and Modulation
84
(2)
• Modulation, in communications, is a process in which some
characteristic of a wave (the carrier wave) is made to vary
in accordance with an information-bearing signal wave (the
modulating wave);
• Demodulation is the process by which the original signal is
Recovered from the wave produced by modulation. The original,
Un-modulated wave may be of any kind, such as sound or, most
often, electromagnetic radiation, including optical waves.
• The carrier wave can be a direct current, an alternating current,
or a pulse chain. In modulation, it is processed in such a way
that its amplitude, frequency, or some other property varies.
Morse Code
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Encoding and Modulation
• Artificially produced EM waves are used to transmit
Information over long distances by using encoding and
modulation
• Encoding embeds a
message into a
mathematical code
100
1111 10 1
• Morse code, example
Of pulse-width-encoding
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85
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
86
21
6/14/2009
Beat Frequency and Heterodyning (2)
Beat Frequency and Heterodyning
• In telecommunications and radio astronomy, heterodyning is the generation
of new frequencies by mixing two or more signals in a nonlinear device such as
a vacuum tube, transistor, diode mixer, Josephson junction, or bolometer. The
mixing of each two frequencies results in the creation of two new frequencies,
one at the sum of the two frequencies mixed, and the other at their difference.
A low frequency produced in this manner is sometimes referred to as a beat
frequency.
A beat frequency, or "beating," can be heard when multiple engines
of an aircraft are running at close but not identical speeds, or two musical
instruments are playing slightly out of tune. For example, a frequency of 3,000
hertz and another of 3,100 hertz would beat together, producing an audible beat
frequency of 100 hertz. A heterodyne radio or infrared receiver is one which uses
such a frequency shifting process.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
87
Beat Frequency and Heterodyning (3)
• Consider two waveforms of same amplitude
AND TWO NEARLY EQUAL FREQUENCIES
y(t)  Asin  0 t  Asin  1t 
Let ….
1   0  
-->  ~ small
• Then
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
88
Beat Frequency and Heterodyning (4)
• Collected waveform
    0    1   0  
y(t)  Asin  0t  Asin 1t  2Acos  1
 t  sin 
 t
 2    2  
Slowly beating amplitude High Frequency wave
• An electromagnetic carrier wave which is carrying a signal by means
of amplitude modulation or frequency modulation can transfer that signal
to a carrier of different frequency by means of a process called heterodyning.
This transfer is accomplished by mixing the original modulated carrier
with a sine wave of another frequency.
This process produces a beat frequency
equal to the difference between the
frequencies, and this difference frequency
constitutes a third carrier which will be
modulated by the original signal.
• Heterodyning is extremely important in radio
transmission -- in fact, the development of
heterodyning
schemes was one of the major
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/audio/radio.html
developments which led to mass
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
89
National Aeronautics and Space Administration
communication
by radio.
Stephen A. Whitmore, USU MAE Dept.
90
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6/14/2009
Encoding and Modulation
Amplitude Modulation
(3)
• Modulation embeds this code onto an
electromagnetic carrier wave
• Amplitude modulation (AM) is the modulation method
used in the AM radio broadcast band.
• AM modulation varies the STRENGTH of the radio
signal according according to the information encoded
into the carrier wave.
• This form of modulation is not a very efficient way
to send information; the power required is relatively large
because the carrier, which contains no information, is sent
along with the information
• Amplitude Modulation
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Encoding and Modulation
• Frequency Modulation
91
National Aeronautics and Space Administration
(2)
Stephen A. Whitmore, USU MAE Dept.
92
Frequency Modulation
Carrier wave
• In Frequency modulation the instantaneous frequency
of a sinusoidal carrier wave is caused to depart from the center
frequency by an amount proportional to the instantaneous value
of the modulating signal.
1.00
0.50
• The baseband signal is the original information bearing signal
by a transducer, such as a microphone, telegraph key, or other
signal-initiating device, prior to initial modulation.
0.00
-0.50
Modulation
Wave (Baseband)
-1.00
28 0
30 0
National Aeronautics and Space Administration
32 0
34 0
36 0
38 0
40 0
Stephen A. Whitmore, USU MAE Dept.
93
• Baseband frequencies are usually characterized by being
much lower in frequency than the frequencies that result
when the baseband signal is used to modulate a the carrier
wave.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
94
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6/14/2009
Frequency Modulation
(2)
Frequency Modulation
(3)
• Example: Modulating a Test Tone onto a Carrier Wave
Proportional to the amount of information you can encode
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
95
Modulation /De-Modulation
Systems
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
96
Communication Link Budgets
• How big should we make the antennas?
• How powerful do the transmitters need to be?
• Baseband Spacecraft data encoded onto carrier signal
by Modulator
• Signal is amplified for broadcast
• Antenna Broadcasts data to ground (telemetry)
• Ground receiver amplifies weak spacecraft signal
• Demodulator re-creates and decodes the baseband signal.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
97
• How sensitive must the receivers be?
• How accurately do the antennas need to track?
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
98
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6/14/2009
Transmitter Power
(Isotropic Power Flux Density)
F
Antenna Gain
•
•
•
Power
P

Surface Area of Sphere 4R 2
Transmitted
power
DiPole Antenna
Isotropic (dipole) antenna radiates equally in all directions.
Dish Antennas focus the radiation in a desired direction.
Dependent on the size of the antenna and the wavelength of the signal
Gt  
4 A
2
2
 D  4 Ae

 2
  

 Antenna Efficiency (.5 - .9)
c f
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
99
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Antenna Gain Analogy:
100
Antennae

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Stephen A. Whitmore, USU MAE Dept.
101
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Stephen A. Whitmore, USU MAE Dept.
102
25
6/14/2009
Effective Isotropic Radiated Power
(EIRP)
More Antennae
Antennae
(cont’d)
• Three factors (transmitter power, line loss,
and antenna gain) are often combined into
one number, the Effective Isotropic
Radiated Power, or EIRP
Transmitter power output
EIRP  Pt  Gt
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
103
EIRP
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Antenna Gain
Stephen A. Whitmore, USU MAE Dept.
104
Received Signal Strength
• EIRP Maps
into
Received Signal Power
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Stephen A. Whitmore, USU MAE Dept.
105
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Transmitted Signal Power
Stephen A. Whitmore, USU MAE Dept.
106
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6/14/2009
Received Signal Strength (2)
Srcv r 
 Pt Gt 
A
 4R 2  ercv r
Aercvr 
2
National Aeronautics and Space Administration
2Gr
4
• The intensity of a signal is inversely proportional to the
square of the distance from the transmitter
Receiver Antenna
Effective Area
Effective power spread of
Sphere of radius R
Free Space loss term
  
Srcv r  Pt Gt
G
 4 R  rcv r
Free Space Loss
• As the beam travels out into space it spreads out so the
power is spread over a wider area.
Receiver
gain
  Drcv r
Grcv r  
  
Stephen A. Whitmore, USU MAE Dept.
• Not a true “attenuation” just an Inverse-square loss
  
L fs 
 4 R 
2
107
2
R is distance from
transmitter
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Atmospheric Attenuation
108
Other Factors (losses)
• Line losses in transmitter and receiver hardware
• Antenna pointing losses--the gain of an antenna is not constant across
its beamwidth. In a well designed antenna it peaks at the boresight.
•Atmospheric attenuation losses
depend heavily on the signal frequency
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
109
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
110
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6/14/2009
Putting it all Together
Noise?
•Hot objects radiate in all frequencies, and the hotter they are, the more they radiate.
• The Received Signal is equal to the power
transmitted multiplied by all of the gain/loss
factors
•Major Source of Noise in Communication Systems
S  Pt  Gt  L fs  Gr  (other loss es) =
2
  
Srcv r  Pt Gt
G  (other loss es)
 4 R  rcv r
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
When an object reaches a certain
temperature, it begins to re-emit
radiation, and glows hot.
111
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
112
Wien’s Displacement Law (radiant frequency)
Black Body Radiation Curve
Solar Radiation
max = 2898 
T
The hotter the object, the more EM
Radiation it emits at shorter waveLengths.
Huh? … let’s
re-visit this later
max  Wavelength of maximum energy output, (
T
m)
 Object temperature, deg Kelvin
 m
max = 2898
6000 K
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Stephen A. Whitmore, USU MAE Dept.
113
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sun
= 0.483 m
Stephen A. Whitmore, USU MAE Dept.
114
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6/14/2009
Emitted Radiation
Noise (revisited)
• Emitted Radiant Energy (magnitude)
-- as object heats up, it radiates energy
back into space
• Because Thermal radiation is the dominant source for noise in
Communication Systems, the system Noise is modeled as a function of
temperature.
• The usual noise equation is N = k T Bw, where
E=
A
emitted energy
– k is Boltzmann’s constant, 1.38*10-23 Joules/K
=   T4
per unit area
(all wavelengths)
– T is the system temperature (noise) rating in degrees Kelvin
– Bw is the bandwidth of the receiver - the range of frequencies it is
designed to receive.
 -- emissitivity < 1
 -- Stefan-Bolzman constant
5.67 x 10-8 W/m2K4
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
115
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
116
Signal to Noise Ratio
To Improve Signal-to-Noise Ratio
S
2
 PtGt      Grcv r
N   kBw    4 R    T 
• Increase Signal Strength
• Reduce the Signal bandwidth
What Effects Signal-to-noise ratio?
•
•
•
•
•
• Reduce the receiver temperature rating
Changes in transmitter distance
Changes in receiver or transmitter antenna size
Changes in carrier frequency
Changes in Signal Bandwidth
Changes in Receiver Temperature rating (Noise)
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
• All things being equal Higher frequency generally
gives a better signal-to-noise ratio (huh?)
S
117
2
 PtGt      Grcv r
N   kB    4 R    T 
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
118
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6/14/2009
Improve Signal-to-Noise Ratio ? (2)
Improve Signal-to-Noise Ratio ?
S
S  P  t rcv r  Drcv rDt 
t
N
 kBT  4  R 
2
 PtGt      Grcv r
N   kB    4 R    T 
Gt  t
 Dt 
  
2
 D rcv r 
G rcv r   rcv r
  
2
National Aeronautics and Space Administration
• Increase Transmitted Signal Strength
2
2
S   Pt  t Dt       rcv r  Drcv r
N  kBT      4 R 
  
Stephen A. Whitmore, USU MAE Dept.
2
• Increase the Sizes of the Antennae
• Reduce the Signal bandwidth
2
• Reduce the receiver temperature rating
• Higher frequency carrier generally gives a
better signal-to-noise ratio
119
Improved Signal to Noise Ratio (3)
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Stephen A. Whitmore, USU MAE Dept.
120
Improved Signal to Noise Ratio (4)
• OK …. How about Visible light?
• Sometimes we do!
• OK …. So Why don’t we use Gamma rays
for Communication?
Atmospheric transmissivity
Atmospheric transmissivity
• Because High energy EM waves are almost
completely attenuated by the atmosphere
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Stephen A. Whitmore, USU MAE Dept.
• Fiber Optic Communications
121
National Aeronautics and Space Administration
• Remote Sensing/
Reconnaissance
Stephen A. Whitmore, USU MAE Dept.
122
30
6/14/2009
Hubble Space Telescope
Telescopes: One Way Communication
Devices
2.5 mm
2.4
• All remote sensors are basically one of two variations on a
Telescope
• Reflecting telescope (Hale (Mt. Palomar), Radar,
Radio telescopes, DSS)
Primary
Mirror
Eyepiece
• Refracting telescope (very cumbersome and expensive)
Objective lens
Catadioptric
Design
Eyepiece
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
123
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Disadvantages of Using Visible Spectrum
for Remote Communications
Solar Radiation
Gain (re-visited)
• The gain of an element is the ratio of the
power out to the power in.
The Sun Emits most of its energy
in the visible spectrum
Pin
Tremendous
Noise Source
Amplifier
Gain 
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Stephen A. Whitmore, USU MAE Dept.
124
125
National Aeronautics and Space Administration
Pout
Pout
Pin
Stephen A. Whitmore, USU MAE Dept.
126
31
6/14/2009
Decibels
A Series of Elements
• Engineers hate to multiply when they can add or subtract
instead, particularly very large or small numbers
• The Gain of the series is the product of the
gains of the individual elements
Pin
• Defined to be 10 times the log of the power or a ratio of
powers
Pout
Element 1
Element 2
Element 3
Element 4
PdBW   10 log10 PW 
GT  G1  G2  G3  G4
P
power ratio  10 log10  1  dB
 P2 
Pout  Pin  G1  G2  G3  G4
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
127
Example
Pout
Pin
Gain 
0.82
 0.82
1
Gain  10  log 0.82   0.86 dB
Pin  10  log 1  0 dBW!!!
Pout  10  0.086  0.82 watts
Pout  Pin  Gain  0.86 dBW
National Aeronautics and Space Administration
128
Points to note
• Your car phone is advertised to have a 1 watt transmitter.
Actual measurement at the antenna input connector is 0.82
watts. What is the gain of the antenna cable?
Gain 
Stephen A. Whitmore, USU MAE Dept.
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Stephen A. Whitmore, USU MAE Dept.
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• Gains are always positive, but if they are less
than one, they are actually losses
• When expressed in dB, Gains are added and
losses are subtracted.
• Power is always positive, so a negative dBW is
just a very small power.
• You also may see dBm, which is decibelmilliwatts. The conversion is 103. 30dBm is 1
dBW
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Example EIRP
Questions
• How many dB’s are represented by gains of
0.25, 0.5, 0.66, 1, 2, 5, 10, 100?
• What is the gain of -3db, -10db, -20db, 3
db, 6 db, 10
db, 30
 db?
PdBW
10 log10 PW 
PW   10
• Your ground station design has a 50 watt transmitter, the
allocated frequency is 2 GHz (2*109 ) and you intend to use
a 1 meter dish antenna. Assuming a  of 0.7 and only
1 dB of line losses, what EIRP can you expect?
Pt  50 watts
Pt  10 log 50   17 dBW
P dbW 
10

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c 3 10 8

 0.15 m
f 2 10 9
131
• For our 2 GHz transmitter example, what will be the free space
loss if we are trying to communicate with satellites at an
altitude of 1,000 km? Assume that the slant range from the
effective horizon will be approximately 1,400 km
• What is the gain of the 1 meter antenna:
2
 D 
Gt  

  
0.15
   

Ls  
 
6 
 4R   4    1.4  10 
2
 3.14  1 
Gt  0.7
  307.05  24.87dB
 0.15 
2
EIRP  17  1  24.87  40.87dBW
2
Ls  0.0000000000 000000727  161 .38 dB
EIRP  50 .7943 307.05  12,195W
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Space Loss Example
Example EIRP (2)
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Example (cont)
Example (cont)
• For simplification (and because they are usually small factors)
we will ignore pointing errors and atmospheric attenuation, but
we need to model the receiving antenna. Assume a half meter
dish, but an efficiency of only 0.55. We will also assume a
1db line loss.
 D 
Gr   

  
2
   0.5 
Gr  0.55

 0.15 
Transmitter Power
Transmitter Line Loss
Transmitter antenna gain
Free Space Loss
Receive antenna gain
Receive line loss
Received Power
Received Power (watts)
2
Gr  60 .314  17 .8dB
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Overall Link Margin
Noise Example
• The signal to noise margin is:
• In our continuing example, let us assume a noise
temperature of 1000 degrees Kelvin, (this is hotter that it
will actually be, but gives us some design margin, and a
very poor receiver) and a bandwidth of 100 Khz.
S
4  10 11

 2.9  10 4
N 1.38  10 15
S
 10 log 2.9  10 log 104  4.62  40  44.62dB
N
S
 10 log 4  10 log 1011  10 log 1.38  10 log 1015
N
S
 6.02  110  1.39  150  44.62dB
N
N  kTB
N  1.38 1023 103 105  1.38 1015 watts
N  10 log 1.38  10 log 10 23  10 log 10 3  10 log 10 5
N  1.39  230  30  50  148.6dBW
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17 dBW/50 W
-1 dB/.79
24.9 dB/307
-161.4 dB/7.3x10-17
17.8 dB/60.3
-1 dB/.79
-103.7 dBW
4x10-11 Watts
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Desired Signal-to-Noise Ratio?
Desired Signal-to-Noise Ratio?
The Link budget
•How much received signal power is enough?
•The answer depends on the “Signal-to-Noise” ratio.
•Depends on modulation technique and acceptable
bit error rates
•Rule of thumb is a received signal power at about
10 dB more than the noise.
Curves available for
S/N required to
support desired
Bit Error Rates
(BER) for various
modulations.
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What is the Signal-to-Noise
Magnitude Ratio of 10 db?
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Example: Iridium Global Star
141
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Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Homework
Finish
Satellite Communication Systems and
Link Budgets Homework
Questions??
Work Trough Example 15-2, Sellers Page 628, 629. … Show all work
Do Sellers, pages 648-649, Problem 13, Problem 14
Note: Use an antenna efficiency of ~.55
Will this be an effective link for a Geo-stationary satellite?
(Rgeo ~ 42,165 km)
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Homework (3)
144
Homework (2)
A key factors that drive the design of a satellite based personal
communication system is size and allowable power of handset
transmitter.
Satellite Antenna
If handset is limited to a one watt transmitter, and has a dipole
antenna with gain of only 2 dB, what is the maximum range
over which the uplink can be closed with an acceptable signalto-noise margin (10 dB)
Given:
1-Watt, 2-Db Gain
a) satellite antenna diameter of 1 meter (.55 efficiency)
b) transmitter frequency 250 MHz
c) bandwidth 100 KHz
d) receiver noise temperature rating, 500K.
What effect will doubling the carrier frequency have on the S/N ratio?
Calculate time delay for a signal to travel from a ground-based antenna at
nadir (directly below satellite), up to a geo-stationary satellite and back.
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ESDM Senior
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Spacecraft Design According to:
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Trajectory
Designers
Structures, Structural
Dynamics, and Resonance
point mass
Controls
Designers
Rocket
Designers
Sellers: Chapters 12, 13
Payload
Designers
Structural
Designers
Power Syste m
Designers
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0
Communication
System Designers
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Systems Engineering and
Structural Design
Structures
• Provides stable support and maintains its integrity
during all mission phases
• Provide a compatible interface with the launch vehicle
• Must meet the functional requirements of all
subsystems
Structural
Designers
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Structural Stress Analysis
Structural Stress Analysis (2)
Structural loads are specified at the maximum
expected level and referred to as the design or
limit loads. Usually, two or more of these loads act
simultaneously and their combined effect
needs to be considered. Note that the loads
environment applied to the structure during the
verification testing may be more significant than
the loads experienced during flight. Many
structural failures have occurred during testing in
the past. Therefore, these loads must be
considered very carefully in the strength and
fatigue calculations.
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Structural Stress Analysis (3)
Structural Analysis Methods
Essential for the analysis to be conservative, i.e., the failure load predicted should
be less than actual load structure can withstand. Necessary in view of uncertainties
in analysis assumptions and variations applied loads and material properties.
Concept of an overall safety factor (SF) is introduced to account for various
uncertainties and the limit loads are increased in proportion to the SF
(Ultimate Load = SF x Limit Load).
Static Analysis-Used to determine displacements, stresses, etc. under static loading
conditions. Both linear and nonlinear static analyses.
Typical Ultimate Load “Factors of Safety”
Type of material
By Proof Test
Metallic,
Monocoque
1.25 Limit Load
2.25 Limit Load
Composite
1.5 Limit Load
2.75 Limit Load
Transient Dynamic Analysis-Used to determine the response of a structure to
arbitrarily time-varying loads. All nonlinearities mentioned under Static Analysis
above are allowed.
Modal Analysis-Used to calculate the natural frequencies and mode shapes of a
structure. Different mode extraction methods are available.
By Analysis
B
7
Harmonic Analysis-Used to determine the response of a structure to harmonically
time-varying loads.
Spectrum Analysis-An extension of the modal analysis, used to calculate stresses
and strains due to a response spectrum or a PSD input (random vibrations).
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Summary of Spacecraft Loads
Example: Launch Loads
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Types of Loads
• Axial
Compression
Tension
• Lateral
11
Types of Loads (2)
• Torsional
• Shear
• Bending
•T
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Stress/Strain Basic Definitions (1)
Stress/Strain Basic Definitions
• Strain … deformation due to load
a 
Break!
Yield Deformation Range
Point
E = “Young’s
Modulus”
F
LL

L
L
x 
Engineering calculations are often based on stress. If we want to do experiments to
confirm our theory, we need to measure the result of stress rather than stress directly.
Stress results in the deformation of material, which is called strain. For most
engineering materials, there is a rather simple relationship between stress and strain.
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Fx
Ac x
 a  Ea
“applies over
linear range”
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dL L2  L1 L


L
L1
L1
14
Stress/Strain Profiles

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Stress/Strain Profiles (2)
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Lateral Strain, Poisson’s Ratio (1)
Stress/Strain Profiles (3)
If we stress a rod by pulling on it, and is stretches
axially as a result, it will also get thinner. This
behavior is quantified by Poisson’s ratio:
Stress/Strain
Profile Terminology

lateral strain

 L
axial strain
a

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Lateral Strain, Poisson’s Ratio (2)
19
Lateral Strain, Poisson’s Ratio (3)
Works the
opposite
direction for
compression
Compression
Tension
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6/14/2009
E, , G are properties of material
General Stress States, 2-D
Relate the 2-D stress field to the 2-D strain field.
y
y 
x 
E
x
x 
y 
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G = Shearing Modulus
E


x
• two equations,
two unknowns
E
y
E
E x  y 
1  2
E y   x 
1  2
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23

Stress versus Strain in 3-D
General Stress States, 3-D
• Stress (force per unit
area tensor)
ij =
Fx
Ax
Fx
Ay
Fx
Az
Fy
Ax
Fy
Ay
Fy
Az
Fz
Ax
Fz
Ay
Fz
Az


 x 
1
  1
  y   E 1
  z 
1


 x 
1
 

 y   E 1
  z 
1
1
 x    y   z 

E
1
 y   y    x   z 
E
1
 z   z    x   y 
E
Fz
Fz
x 
Fx
Fx






   x 
 
   y  
    z 
 
 
 
1
 x 
 
 y 
  z 
• We measure strain in one or more directions and infer the stress state
from that. In general, in order to know the 3-D stress state, we would need
3 components of strain. In some cases (like pure axial stress) we may be
able to reduce the number of required components.
Fy
• 3-equations, 3 unknowns … typically a numerical solution
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6/14/2009
Strain Measurements
Strain Measurements (2)
IM  0
• Now consider a Strain Gauge of a material with a known Resistivity ….
And the design is far more sensitive to strain in the vertical direction than in
the horizontal direction.
M
• Now stretch the device ….
L
• In terms of Strain properties
Vex
 R Rg 
VBD  Vex 
  R Rg  GF 
 4  2R Rg 
Vex
• Cross section does not change
Much … but length changes
significantly
L+L
As strain sensor …
“quarter bridge”
R  
L
A
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“One arm” bridge
 L  L 
R  R    
 A  A 
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 GF  
Vout  Vex 
 4  2GF  
• Not Quite linear to Strain
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27
“Laundry List” of Strain Measurement
Methods (1)
Strain Measurements (3)
 GF  
Vout  Vex 
 4  2GF  
Rg
• More Sensitive Response
• Completely Linear
• Reversed Polarity
Rg
1

Vout  Vex  GF  
2

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“Laundry List” of Strain Measurement
Methods (2)
“Laundry List” of Strain Measurement
Methods (3)
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“Laundry List” of Strain Measurement
Methods (4)
31
“Laundry List” of Strain Measurement
Methods (5)
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6/14/2009
“Laundry List” of Strain Measurement
Methods (6)
Structural Dynamics Basics
• Spring Mass Damper
• Look at Displacement
2
b
x
M
F cos  0t
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d
b dx k
F
x

x
cos  0t
dt 2
M dt M
M

k   natural frequency
 n 

M 
 let 
b 

 
  damping ratio
2 kM 

d2
dx
1
x  2 n
  n 2 x   n 2 F cos  0t
dt 2
dt
k
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Structural Dynamics Basics
35
Structural Dynamics Basics (2)
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Structural Dynamics Basics (3)
Structural Dynamics Basics (4)
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Structural Dynamics Basics (6)


39
Resonance
Structural Resonance Occurs as Forcing frequency
Vibration Frequency Approaches Natural Frequency
Effect of Damping
Ratio on Second Order
Frequency Response


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Resonance (2)
Predicting Dynamics Response
Consequences of Resonance
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43
Controlling Vibration and Resonance
Predicting Dynamics Responses (2)
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Controlling Vibration and Resonance (2)
Controlling Vibration and Resonance (3)
NASA’s Stratospheric Observatory
for Infrared Astronomy (SOFIA)
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SOFIA Telescope
Vibration Dampers
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Controlling Vibration and Resonance (4)
47
Homework
Work Through Examples 13-4, 13-5 in
Sellers (pp. 523, 524), prepare 5 page
summary report
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Questions?
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ESDM Senior
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ESDM Senior
Design Project
Mechanisms
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Mechanisms
Sellers: Chapters 12, 13
Sellers: Chapters 12, 13
+ Material
From Auburn University Lunar Excavator
Design Course, Courtesy of David Beale.
+ Material
From Auburn University Lunar Excavator
Design Course, Courtesy of David Beale.
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Spacecraft Design According to:
Trajectory
Designers
Caveat
point mass
• Objective is a working LLRV prototype, and it is not
necessary to procure specialized components or
manufacture using materials that would be expected to
be in a lunar mission-ready lander.
Controls
Designers
Rocket
Designers
• However team should be able to justify that their
prototype, if tested successfully, could be a basis for
further development beyond prototyping.
Payload
Designers
Structural
Designers
Power Syste m
Designers
Communication
System Designers
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• This justificationrequires an awareness of components’
design and selection choices for a lunar mission.
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Mechanisms
Mechanisms (2)
• Here the focus is on components that would be a
concern of a mechanical designer.
• This includes mechanical components (bearings,
fasteners, lubricants), motors, materials and an
overview of power systems.
• This topic is too broad to consider in great detail
here, so references are often cited instead.
• Often the selection of a component is not clear, and
many choices are possible. In these situations a trade
study may be appropriate.
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• Electro-mechanical devices employed to carry
out key functions:
– Separation systems
– Antenna deployment and pointing
– Attitude control
– Experiment orientation and control
• One-shot or Continuous
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Component Legacy
Foldable frame constructed from Aluminum 2219 welded tube
• Component design and selection is driven by the application
and the environment
• Legacy “refers to the original manufacturer’s level of quality
and reliability that is built into the parts which have been
proven by (1) time and service, (2) number of units in
service, (3) mean time between failure performance, and (4)
number of use cycles.”
• If a candidate component has a successful legacy, then a
designer should strongly consider using it.
• If you can buy it .. Don’t build it!
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Traction Drive
Standards and References
• Four ¼ horsepower electric motors located at each wheel
• Speeds up to 17 km/h.
• The motors were speed reduced 80:1 with a harmonic drive gearing
(http://www.gearproductnews.com/issues/0406/gpn.pdf), which are known
for large gear ratios, light weight, compact size and no gear backlash when
compared to a planetary gear system.
• The motors and harmonic drive were hermetically sealed and pressurized to
7.5 psia to protect from lunar dust and for improved brush lubrication.
• Braking was both electodynamic by the motors and from brake shoes
forced against a drum through a linkage and cable.
•
•
•
•
•
•
•
•
•
•
•
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Stephen A. Whitmore, USU MAE Dept.
AIAA S-114-2005, “Moving Mechanical Assemblies for Space and Launch Vehicles”
The Proceedings of the Aerospace Mechanism Symposium are published annually and papers
are concerned with actuators, lubricants, latches, connectors, and other mechanisms.
NASA/TP-1999-2069888 NASA Space Mechanisms Handbook. The Handbook (including
CD/DVD) is available only to US citizens who need the material. It is restricted under ITAR
(International Traffic in Arms Regulations).
MIL-HDBK-5 Metallic Materials and Elements for Aerospace Structures, contains
standardized mechanical property design values and other related design information for
metallic materials, fasteners and joints.
Other Standards:
DOD-HDBK-343 Design, Construction, and Testing Reqmts for One of a Kind Space
Equipment
MIL-STD-100 Engineering Drawing Practices
MIL-STD-1539 Direct Current Electrical Power Space Vehicle Design Requirements
DOD-E-8983 General Specification for Extended Space Environment Aerospace Electronic
Equipment
MIL-S-83576 General Specification for Design and Testing of Space Vehicle Solar Cell
Arrays
DOD-STD-1578 Nickel-Cadmium Battery Usage Practice for Space Vehicles
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Stephen A. Whitmore, USU MAE Dept.
15
6/14/2009
Flight Qualified
Fasteners
• Space Fasteners design choices, with attention given
to aerospace applications, materials and temperature
ranges, are presented in the Fastener Design Manual
(Barrett, 1990),
http://gltrs.grc.nasa.gov/reports/1990/RP-1228.pdf.
• Any hardware or materials used for lunar
missions will need to be of a special variety
know as "Flight Qualified".
• Flight qualified materials and parts are always
flight proven hardware with program heritage.
•
• The process to get any new material or part
flight qualified is an arduous and long task.
National Aeronautics and Space Administration
• MIL-HDBK-5 also contains allowable strengths for
many fasteners. Fasteners for MS (military standard)
and NAS (national aerospace standard) can be found
at http://www.standardaeroparts.com/.
63
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64
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Bearings
Lubricants
• The three types of lubricants are liquids (lubricating oils,
lubricant greases) and solid films.
• Lubricant inadequacies have been implicated as a cause of a
number of space mechanism failures.
• An ideal lubricant would retain the desired viscosity over a
wide temperature range and be nonvolatile.
• The ability of a lubricant to resist becoming a gas is related to
its molecular weight. Low molecular weight lubricants are
more volatile in vacuum and heat than higher molecular
weight lubricants.
• Solid films, such as soft metal films, polymers and low-shear
strength materials, find use in bearings, bushings, contacts and
gears. See (Conley, 1998) and (Fusaro, 1994) for details.
• Rolling-element bearings for lunar applications must capably withstand the
challenges of the lunar environment (temperature extremes, penetrating
regolith and the vacuum environment) and be highly reliable to minimize
repairs.
• For space flights the AISI 440C (a high hardness, corrosion resistant steel)
and AISI 52100 (not as hard or corrosion-resistant, but better wear
resistance) are the most common bearing materials.
• Shields and seals cover the rolling element so they are not exposed and
protected to a certain degree from outside contaminates like regolith.
Shields and seals are attached on a bearing’s outer race, and move with the
outer race. A shield will not touch the inner race because of a small
clearance gap. Seals do rub against the inner race but will be less likely to
allow regolith particles inside.
• Thermal control is a concern in a lunar environment where convection is
not an available heat transfer mechanism. Thermal conductivity through a
bearing is increased by the presence of a lubricant.
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Stephen A. Whitmore, USU MAE Dept.
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Stephen A. Whitmore, USU MAE Dept.
16
6/14/2009
What is Choked Flow?
Pneumatics
In a compressible flow, it can be shown that mass flow per
unit area is:
•
Unlike Hydraulic Systems, Pneumatic Systems are dramatically
influenced by compressible flow effects
m

A

Rg
p0
T0
Density is not constant for these systems and choking has a severe
limitation on the available maximum mass flow
M
 1
   1 2  2  1
1  2 M 


• maximum
Massflow/area
Occurs when
When M=1
Pneumatic Feed
Lines
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Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
What is Choked Flow? (2)
What is Choked Flow? (3)
Collect terms
Thus for a given upstream pressure and temperature, and
a give cross section Area, the maximum mass flow is at
Mach 1, and it is given by (the “*” indicates choked flow)
 1
 1
 1
Pin
.
mmax
A*
Pout
 1
.
 P 
Pin  2   1
  2   1
*
m max   in  Ain* 

  Ain   Pin

 
 T 
R


1
R


g
g T0    1 
0


.
 P 
  2   1
m max   in  Ain* 


 T 
Rg    1 
 0
.
 2   1
 m max  Ain*   Pin in 

  1
Allow for Non-isentropic pressure losses (friction)
When flow is choked, mass flow depends only on upstream pressure,
downstream pressure does not feed back (pressure waves cannot go
backwards across a sonic boundary with violating second law of
thermodynamics)
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 1
69
Stephen A. Whitmore, USU MAE Dept.
.
 2   1
mmax  Cd Ain*   Pin  in 

  1 
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Stephen A. Whitmore, USU MAE Dept.
17
6/14/2009
What is the “Choking” pressure ratio (2)
What is the “Choking” pressure ratio
4500 psig
Choking ... pressure...ratio :
Pout

Pin
1

   1 2   1
1
M 
2


 chokes @ M  1
0 psig
 Pout 
1

 diatomic...gas    1.4



 Pin critical    1   1
1  2 
= 0.5283
Pout

Pin
= 0.00326 < 0.5283
Flow is choked!
 Pout 



 Pin critical
What happens when valve is initially opened?
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72
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
What about UnChoked Flow?*
•
m

A

Rg
Pout

Pin
p0
T0
M
   1 2 
1  2 M 


1

   1 2   1
1  2 M 
 1
2  1
M 
What about UnChoked Flow? (2)
General
Massflow
Equation
 1


2  Pin  
 1



  1  Pout 


.
m A
General
Pressure Ratio
Equation
.
Substitute lower equation into above equation
 APin


2  Pin 


RgT0   1  Pout 

 1

 Pin 


 Pout 

 1

 P 
  in 
 Pout 

 1





2
 1
2
 1




 P  P  
 P   P  
Pin 2
2
Pin  in    out    A
in Pin  out    out  
 Pin   Pin  
RgT0   1  Pout 
Pin  
 1





*Assumes flow velocity at inlet condition is small
*Assumes flow velocity at inlet condition is small
73
Stephen A. Whitmore, USU MAE Dept.
 Pin 


 Pout 
 1
2
Simplify
m A
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 Pin

Rg T0
 1


2  Pin  


  1


  1  Pout 

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74
Stephen A. Whitmore, USU MAE Dept.
18
6/14/2009
1-D “Lossy” Mass Flow
Equations, Collected
What about UnChoked Flow? (3)
Simplify
.
m A
Unchoked Flow
2
 1
2
 1




 P  P  
 P   P  
Pin 2
2
Pin  in    out    A
in Pin  out    out  
 Pin   Pin  
RgT0   1  Pout 
Pin  
 1





.
m  Cd A
2
 1


 P   P  
2
in Pin  out    out  

 1
 Pin   Pin  


Allow for Non-isentropic pressure losses (friction)
 1
.
 2   1
m  Cd Ain*   Pin  in 

  1 
*Assumes flow velocity at inlet condition is small
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 Pout

 Pin
Choked Flow:
2
 1


 P   P  
2
m  Cd A
in Pin  out    out  

 1
 Pin   Pin  


.
75
 Pout 
1



 Pin     1  1
1  2 

1


    1  1
1  2 
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Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Flow Coefficient Definitions
Incompressible Flow Equation
 Pout 
1



 Pin     1  1
1  2 
For Incompressible flow it can be shown in a similar manner that
Start with.
m  Cd A 2   Pin  Pout 
.
m  Cd A 2   Pin  Pout 
Divide by density at STP (15.6 C, 1 atms)
.
Q STP 
Assumption here is that density is constant. The Volumetric flow for
incompressible Orifice is:
Q
Cd A
 STP
2   Pin  Pout  
P P 
 Cd A 2  in out 




m
77
Stephen A. Whitmore, USU MAE Dept.
 STP
2
Pin
 Pin  Pout 
Rg T0
2116.2 lbf
 STP 
ft 2
53.355 lbf  ft   459.7  60  o R
o
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Cd A
C A 2 
 Pin  Pout 
 d
 P

  STP Rg  in  T0



.
.
UnChoked Flow
 0.07632 lbm
ft 3
R lbm
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Stephen A. Whitmore, USU MAE Dept.
19
6/14/2009
Flow Coefficient Definitions (3)
Flow
Coefficient Definitions (2)


Pout
1



 Pin     1  1
1

2 

.
C A 2 
C A 2 
 Pin  Pout 
d
Q STP   d
 P

  let...N1Cv  
  STP Rg  in  T0




  STP Rg 
.
P P
Q STP  N1Cv Pin  in out
 T0



Rg any 
gas
MWair
MWair
Ru
R
1
 u 
 Rg air 
 Rg air 
MW
MWair MW
MW
Gs
any
gas
any
gas
any
gas
For gases other than air
 Pin , Pout  psia 


T0  o R


.

English Units  Q STP  SCFH ft 3 
(
)
hr


 N1  1360 3 o 
ft
R 


hr psia 

.
UnChoked Flow
 Cv 
.
Cv 
Q STP
1360
P P 
Pin  in out 
 T0 
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Q STPany
P P 
Pin  in out   Gs  " specific gravity "
 GsT0 
gas
1360
.
P P 
Q STPany  1360Cv Pin  in out 
gas
 GsT0 
79
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Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Flow Coefficient Definitions (4)
Flow Coefficient Definitions (5)
For choked flow
For metric units
.
Kv 
Q STPany
gas
4.17
 1
.
.
Q STP 
P P 
P P 
 4.17 K v Pin  in out 
Pin  in out  Q STPany
gas
 GsT0 
 GsT0 
.
m
 STP

Cd Ain*
 STP
 1
Cd Ain*
 Pin , Pout  kPa 


T0  o K


.

Metric Units  Q STP  SCMH mt 3 
(
)
hr 

 N1  4.17 3 o 
m
K 


hr kPa


 STP
 Pin 
Pin  2   1 Cd Ain*
1
P 

 
RgT0    1 
 STP in GsT0

*
.
C A
Q STP   d in

 STP

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Stephen A. Whitmore, USU MAE Dept.
 2   1
 
  1 
 Pin  in 
 1

  2   1  
1
  Pin 


Rg    1   
GsT0

 1
  2   1


Rg    1 


1
  N 2Cv  Pin 
GsT0


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


82
Stephen A. Whitmore, USU MAE Dept.
20
6/14/2009
Flow Coefficient Definitions (6)
Flow Coefficient Definitions (6)
For choked flow
For Metric Units
.

1
Q STPany  N 2Cv  Pin 
G
gas
sT0

 Pin , Pout  psia 


T0  o R


 .

English Units   Q STP  SCFH ft 3 
(
)
hr 

 N1  640.56 3 o 
ft
R 


hr psia 

.

1
Q STPany  N 2 K v  Pin 
G
gas
sT0




.
Cv 
Q STPany
gas
640.56
P P 
Pin  in out 
 T0 
ANSI/ISA–75.01.01–2002
(IEC 60534-2-1 Mod)
 Pin , Pout  kPa 


T0  o K


.

Metric Units  Q STP  SCMH mt 3 
(
)
hr 

 N1  1.964 3 o 
m
K 


hr kPa 




.
Kv 
Q STPany
gas
1.964
P P 
Pin  in out 
 T0 
ANSI/ISA–75.01.01–2002
(IEC 60534-2-1 Mod)
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83
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84
Example Flow Rate Calculation
Flow Coefficient Definitions (7)
For Metric Units
Tescom Control Valve-
Unchoked Flow Formula :
.
Q STPany  1360Cv
gas
 Pin  4500 psia 
 P  285 psia 
 out

P P 
Pin  in out    Gs  1.0 


 GsT0 
 T0  300 K 


Cv  2
44-1300 Series
.
Q STPany 
gas
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85
= 11,398.9 SCFM
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Stephen A. Whitmore, USU MAE Dept.
21
6/14/2009
Example Flow Rate Calculation (2)
Example Flow Rate Calculation (3)
Clark Cooper Solenoid valve
Tescom Control Valve-
Choked Flow Formula :
Choked Flow Formula :
.
Q STPany
gas
 Pin  4500 psia 




1  
 640.56Cv  Pin 
   Gs  1.0 
GsT0  


 T0  300 K 


Cv  2
.
Q STPany
gas
44-1300 Series
.
Q STPany 
 Pin  4500 psia 




1  
 640.56Cv  Pin 
   Gs  1.0 
G
T


s
0


 T0  300 K 
 Cv  4.5 
.
Q STPany 
gas
gas
= 12,481.7 SCFM
= 5547.41 SCFM
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Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Liquid Rocket Example, Injector Design
Injector Design (2)
• Injector Geometry
• Solve for V2
A1
A2
V2 
• Continuity  A1V1   A2V2
1
 p  p2 
2 1
  
Friction
effects
V•2 actual
 V2 ideal
 V2inactualorifice
 CvVwill
2 ideal 
• Assume Liquid Propellants are incompressible (=const)
1
1
• Momentum p1  V12  p2  V2 2
2
2
1
  A  2 2
1   2  
  A1  
cause
 A 
1
p1  p2  V2 2 1   2 
2
  A1 
2



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V2 actual 
Cv
  A 2
1   2  
  A1  
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1
2
 p  p2 
2 1
  
A1
A2
• Define “Discharge
Coefficient”
Cd 
Cv -->
“velocity coefficient”
Cv
1
  A  2 2
1   2  
  A1  
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90
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Injector Design (3)
Injector Design (4)
 p  p2 
V2 actual  Cd 2  1
  
• Define Volumetric Flow as
Qv  A2V2 actual  A2Cd
A1
A2
 p  p2 
2 1
  
• Finally Massflow is
•
m  Qv  A2Cd 2  p1  p2 
QuickTime™ and a
TIFF (LZW) decompressor
are neede d to see this picture.
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Stephen A. Whitmore, USU MAE Dept.
ReD
• For Turbulent Flow the Velocity profile is considerably different than laminar
• Turbulent
Flow
• Turbulent
Flow
4Cf =
Re
D
92
Line Losses (2)
Line Losses for Turbulent Flow
• For Turbulent Flow the Velocity profile is considerably different than laminar
ReD
Stephen A. Whitmore, USU MAE Dept.
91
• Pressure
gradient
proportional
to skin friction
• Pressure
_
gradient
U  mean velocity in channel
proportional
to skin friction
• Solve for mean velocity
_
U
-- Typically tube flow is
turbulent when ReD > 4000
1
_
2U
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_ 2 C
p
4
1 _ 2 Cf
f
  0  4  U
 2  U

dx
D
2
D
D
p

1
p
1
p


_
C f dx
C dx


2 Re D C f 2 dx
2  U D f2
D
D
D
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94
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6/14/2009
Line Losses (3)
Line Losses (4)
• Calculate Volumetric flow rate thru orifice?
Qv 
D
4
• Calculate Volumetric flow rate thru orifice?
a
 D2
2 _
U 
Qv 
r
p
D
1
p


8 Re D C f dx
2 Re D C f 2 dx
D
4
4
R
 D2
4
 D2
U 
Qv  
P1  P2
 D4
1
p  D 4
1
Qv  

8 Re D C f dx 8 Re D C f
L
.
_
r
R
P1  P2
 D4
1
p  D 4
1

8 Re D C f dx 8 Re D C f
L
Qv  m 
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a
p
 D4
1
p

 dx
8 Re D C f dx
2 Re D C f 2
D
4
P1  P2
 D4
1
 D4
1  P1  P2   P1  P2 
 


8 Re D C f
L
8 Re D C f  L  2  Rg  T
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Line Losses (5)
96
Line Losses (6)
• Collect terms
• Calculate Volumetric flow rate thru orifice?
  D4
m
 16  R  T
g

.
P
2
1

 2
1
P  P2 2 

 Re C L   1
 D f 
• Turbulent flow skin friction formulae ,… smooth line
a
r
Prandtl :
R
.
.
16  Rg  T  
 16  Rg  T  


2
2 
 P2 2   
  Re D  C f  L  m   P2  P1  
  Re D  C f  L  m 
4
4


 D

 D

.
 16  Rg  T  

P2  P12  
  Re D  C f  L  m   P  P1  P2
4

 D

4C 

f
1
2
  
1
2


 =average wall


1 0.3164 
Blasius : C f = 
1

4
4
R
e
  D  
roughness height
• Turbulent flow skin friction formulae ,… rough orifice
 
Colebrook : 4C f

Haaland : C f =
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
 ReD 4C f
 2 log10 
2.51

1
2

2.51
  
 2 log10 

 3.7D 
ReD 4C f

1
2
 




1

   1.11 6.9  
12.96 log10 

 +
ReD  

 3.7D 
2
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6/14/2009
Working with Saturated Liquids
Working with Saturated Liquids (2)
Allows greater Mass
storage than working
with pure gasses
Li uid exists in
saturated state, vapor
pressure and density
are purely a function
of fluid temperature
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99
100
Working with Saturated Liquids (3)
Questions?
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101
102
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6/14/2009
“Design Friday”
Demo of Pneumatic “head-Loss’ program
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ESDM Senior
Design Project
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Measurement Error
Measurements and Uncertainty Analysis I
Classification of Measurement
Errors, Calibration, Trend Lines,
and Data Presentation
All measurements contain error. This may be difficult for you
perfectionist types to come to grips with, but you will have error,
and it is not a sin. The sin is not knowing how big your error can
be. Or as Clint Eastwood says “A man’s got to know his
limitations,” or something like that.
Mechanical Measurements, 6th Edition, 2006
Authors: Thomas G. Beckwith,
Roy D. Marangoni, John H. Lienhard, V
Prentice-Hall
In this chapter, we will learn how to estimate the size of the error
in a given measurement. The theory is obtuse, but important,
and will be clarified with hands-on examples in the lab.
This is an extremely important topic (perhaps the most important
topic in the course). It is also one that many people, including
many experimentalists, do not fully understand.
www.nasa.gov
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Classification of Errors
Stephen A. Whitmore, USU MAE Dept.
1
Instrument Performance Ratings
1) Bias or systematic error
•
Calibration Error
•
Recurring Human Errors
•
Defective Equipment Errors
•
Loading Errors
•
Resolution Limitations
2) Precision or random errors
a) Human errors
b) Equipment disturbance errors
c) Fluctuating condition errors
d) Insufficient sensitivity errors.
e) Fundamental accuracy of sensor / Sampling Resolution
3) Illegitimate errors
a) Experimental mistakes
b) Computational errors
4) Errors that can appear as bias or precision
a) Backlash, friction, hysteresis
b) Calibration drift
c) Errors from variations in procedure among experimenters
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2
Accuracy
The difference between the measured value and the
actual value, reported as a maximum.
Precision
The difference between the instrument’s reported
values during repeated measurements of the same
Resolution
The smallest increment of change in the measured value
that can be determined from the instruments read out.
Usually similar or smaller than precision.
Sensitivity
The change in the output of an instrument per unit
change in the input.
Hysterysis
As a general term, hysteresis means a lag between
input and output in a system upon a change in
direction.
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quantity.
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3
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6/14/2009
Measurement Resolution (1)
Precision versus Accuracy (1)
• Precision is the smallest number that can be
Repeatedly reproduced by a measurement System
• Resolution determines the ability to see fine details in the
measurement.
• Precision and Accuracy are NOT! The same
• Defined as the smallest incremental value that can be
Discerned by a system
• Typically a consequence of
data sampling
Accuracy without Precision Precision without Accuracy
small bias,
large random error
significant bias,
small random error
Accuracy and Precision
small bias and
small random error
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4
Measurement Resolution (2)
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5
Measurement Resolution (3)
• Example: 8-bit word encoding
• Sampled Signals are typically represented by Binary numbers or “digital
words”
• Full scale range of Sensor: … 0-10 volts
• Range divided unto 28=256 parts or “counts”
Digital
encoding
• Least significant bit = 10volts/256 = 0.039 volts/count
• --> Analog output from sensor … 2.3575 volts
• Sampled signal …
 10 volts 
60counts  
 2.344volts
 256 count 
• Digitized Sine Wave
with a Resolution of Three Bits
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2.3575volts
 60.352counts  truncate  60counts
10volts / 256counts
“resolution error”
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6/14/2009
Measurement Resolution (4)
Measurement Sensitivity (1)
• Example: 16-bit word encoding
• Example: unamplified Load cell … 3mv/volt output
• Full scale range of Sensor: … 0-10 volts
• Range divided unto 216=65536 parts or “counts”
• Least significant bit = 10volts/65536 = 0.000153 volts/count
• --> Analog output from sensor … 2.3575 volts
2.3575volts
• 500 lbs full scale reading
• Sampled signal …10volts / 65536counts  15450.112counts  truncate  15450counts
•3mv full scale output per
Excitation voltage input
 10 volts 
60counts  
 2.35748volts
 65536 count 
“resolution error” is
Two orders of magnitude less
• 15Volt excitation ….
3mv / v 15v  0.09mv / lbs  output 
500lbs
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Measurement Sensitivity (2)
not very sensitive
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9
Hysteresis (1)
• Example: amplified Load cell output …gain =
100
• 500 lbs full scale reading
Many sensors have the undesirable characteristic of giving a
different value when the input is increasing than when it is
decreasing. This is called hysteresis.
•3mv full scale output per
Excitation voltage input
As a general term, hysteresis means a lag
between input and output in a system upon a
change in direction.
• 15Volt excitation ….
3mv / v 15v  100  9mv / lbs  output 
500lbs
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Anyone who's ever driven an old automobile
with "loose" steering knows what hysteresis is:
to change from turning left to turning right (or
visa-versa), you have to rotate the steering
wheel an additional amount to overcome the
built-in "lag" in the mechanical linkage system
between the steering wheel and the front
wheels of the car.
better!
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10
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6/14/2009
Hysteresis (2)
The Trend Line of a Measurement
• In a magnetic system, hysteresis is seen in a ferromagnetic
material that tends to stay magnetized after an applied
field force has been removed.
• Typically a measurement will have a mean “trend line”
With a variability about that trend line
10
1
Error
0.5
5
P [kPa]
0
0
-0 .5
% fs error
Cross lines of
flux counter
clockwise
-1
-5
Cross lines of
flux clockwise
Example: Aviation
Magnetometer
(Compass) Lag
-10
-0.3
-2
-0.2
-0.1
0
12
0.3
13
Non-linear Calibration Example
Many types of sensors have linear
input/output behavior, along a defined
range of inputs. The sensor thus follows
an input/output relation like
Velocity[m/s]
error
60
0.4
0.2
50
yL(x) = a0 + a1x.
Velocity[m/s]
40
-0 .2
30
-0 .4
20
error (% of reading)
0
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0.2
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Linearity
These will often be marketed as linear,
and the only calibration data you get is
the slope of the input/output relation (a1)
and the zero input value (a0). For these
types of sensors, the deviation from
linear behavior is reported in the
specifications. This deviation can be
calculated: eL(x) = y(x) - yL(x). The spec
is usually the percentage error relative to
full scale,
0.1
Volts
Stephen A. Whitmore, USU MAE Dept.
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-1 .5
Trend line
• Many times
the trend is
Not a line but a
“curve” .. And
We describe the
Trend as a
“calibration” curve
-0 .6
10
-0 .8
0
-1
-3
-2
-1
0
1
2
3
Volts
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14
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6/14/2009
Example of Measurement
Calibration Error (1)
Zero-shift and Sensitivity Errors
Variations in the trend parameters a0 and a1 are called zero
errors and sensitivity errors, respectively . Zero errors are handled rather easily by
measuring the zero input response before measurements are started. These two
errors are often sensitive to temperature fluctuations in electronic equipment.
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Spin table
• Rate Gyro calibration
16
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Example of Measurement
Calibration Error (2)
17
Quantification of Error
• Three different
Sensors
of same make were
tested using
Same spin table
as the reference
• Whenever possible, systematic errors are taken out
Of a measurement system using trend lines and calibration
Curves …
• The remaining errors are unknown and must be quantified
Using statistical means ….
(zero shift)
Variability Of each is
Nearly identical
Stephen A. Whitmore, USU MAE Dept.
Our best tools for this quantification are the Mean and
Standard deviation
Random error
Offsets are Very different
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Mean Value of a Random Sample
Standard Deviation of a Random Sample
• The mean value () of a random population is what is commonly
Referred to as the “average” … it is the most likely value to occur
… more on this in the next section
• A random sample will always vary about the mean .. And a
Quantification of this variability is referred to as the “standard
Deviation” … the square of the standard deviation is called the
“variance”… for a sample of n members, selected at random from the
population we can true variance by the “sample variance”
… for a sample of n members, selected at random from the
population we can Represent the mean by the “Sample mean”
x
2
x1  x2  x3  ...xn
x
 i
n
i 1 n
Stephen A. Whitmore, USU MAE Dept.
2
 x  x_ 
 i

 n 1
i 1
2
n
• … standard deviation is used to quantify the random error
In a measurement
• For error quantification … mean error can be considered as bias
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2
 x  x_    x  x_   ... x  x_ 
 1
  2

 n

  Sx 

n 1
n
20
Mean and Standard Deviation of a Random Sample
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Stephen A. Whitmore, USU MAE Dept.
21
Bias and Random Error (1)
x(t)



• Error
Systematic
Random
• Random error is caused by any factors that randomly affect
measurement of the variable across the sample.
•Systematic error is caused by any factors that systematically affect
measurement of the variable across the sample.
… trend line and
unknown errors
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6/14/2009
Bias and Random Error (2)
Bias and Random Error (3)
• Random Error Example
• Systematic Error Example
The important thing about random error is that it does not have consistent effects across
the entire sample.
Systematic error is caused by any factors that systematically affect measurement of the
variable across the sample. For instance, if there is loud traffic going by just outside
of a classroom where students are taking a test, this noise is liable to affect all of the
student's scores -- in this case, systematically lowering them. Unlike random error,
systematic errors tend to be consistently either positive or negative -- because of this,
systematic error is sometimes considered to be bias in measurement.
For example, a person's mood can inflate or deflate their performance on a test score. For
a particular test, some students may be feeling in a good mood and others may be
depressed. If mood affects performance, it may artificially inflate the observed scores for
some “happy students” and artificially deflate them for “unhappy students”. In this case
one would expectThe moods to be randomly distributed and will push observed scores up
or down randomly.
Summary … Two Major Classes of Errors:
1) Bias (systematic)
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2) Noise (random)
24
Random (Noise) Error
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Stephen A. Whitmore, USU MAE Dept.
Cannot be treated statistically
Very bad if you don’t know it exists
Typically if we add up all of the random effects in a given population they would sum to 0
-- there would be as many negative errors as positive ones. The important property of
random error is that it adds variability to the data but does not affect average performance
for the group. Because of this, random error is sometimes considered noise.
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Can be treated statistically for a population
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25
Systematic (Bias) Error
26
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6/14/2009
The Trend Line: Linear least Squares (2)
The Trend Line: Linear least Squares (1)
• Linear trend line
y = a1x +a0
• Consider a set of calibration data for an instrument
• How de we
Calculate this line?
{x1,x2,x3,…xn}
{y1,y2,y3,…yn}
instrument
Stnd. Dev in error
We want to model the input/output relationship
By a straight line of the form • Given the calibration
Data set {xi,yi} we want
y(x)  a1x  a0
To compute a0,a1 so that we
Get the best overall “fit” to data
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29
The Trend Line: Linear least Squares
The Trend Line: Linear least Squares (3)
(4)
• Look at Matrix Solution
• We want to minimize the fit variance
…. The “squared error” or …
“Least squares” of the
Collected data set
n
2
^
^
J    yi  yi   yi  a1 xi  a0

i 1 
from calculus
 J

J
J min  
 0,
 0
a0
 a1

We can solve as
n
n
^   a x  a 
J
1 i
0
 2  yi  yi  
  2  yi  a1 xi  a0  xi  0
a1
a1

i 1 
i 1

n
n
^   a x  a 
J
1 i
0
 2  yi  yi  
  2  yi  a1 xi  a0  1  0
a0
a0

i 1 
i 1


1
 a1    x1
T
T
A   X X  X Y     
 a0    1


 n
2
 xi 
 a1   i 1

a   n
 0 
  xi 
2x1
i 1
1
 
n
 x1
... xn   x2

... 1   ...

 xn
x2
1
i 1
n
2x2
i i



1

 x
1

  1


x2
1
 y1 
... xn   y2 
 
... 1   ... 
 
 yn 

n
 x    x y 
i
1
1

1

1
 i 1n



  yi  
11
2i x
Reduces to a 2-by
element system
2 equations in two unknowns (a1,a0)
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
30
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
31
8
6/14/2009
The Trend Line: Linear least Squares (5)
The Trend Line: Linear least Squares (6)
• Solve for slope and intercept
• Long winded answer but a nice result
• Given the noisy data set …
  y1   x1  
    
 y2 x2 
{input, output}     ,     best fit  yi  a1 xi  a0
  ...   ...  
  yn   xn  
n


n
  xi 

i 1
 n

n
 n

2

   xi   xi     xi yi 
 a1 
i 1
i 1
 i 1n

a    n
2

 0
 n
 
2
 n xi     xi     yi  
 i 1
  i 1
 i 1
a1 
n
n
n
i 1
i 1
i 1
n xi yi    xi  yi 
n
 n

2
n xi     xi 
 i 1

i 1
2
n
 "slope"  a0 
n
n
n
 x   y   x  x y 
2
i
i 1
i
i 1
i
i 1
i i
i 1
2
n
 n

2
n xi     xi 
 i 1

i 1
a1 
 "intercept"
n
n
n
i 1
i 1
i 1
n xi yi    xi  yi 
n
n xi 
i 1
2
 n

   xi 


2
n
... a0 
i 1
n
n
n
 x   y   x  x y 
2
i
i 1
i
i
i 1
n
i 1
n xi 
i 1
2
i i
i 1
2
 n

   xi 


i 1
“careful with book keeping indices”
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
32
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
33
Trend Curve:
Polynomial Least Squares (1)
Linear Fit Example Revisited
• Unbiased …But
noisy calibration
• Reduced error
… obviously
What appeared to be
Random error was
Actually systematic
• Parabola trend line
y=a2 x2 +a1x +a0
Stnd. Dev in error
bias
precision
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
34
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
35
9
6/14/2009
Trend Curve:
Polynomial Least Squares (2)
Trend Curve:
Polynomial Least Squares (3)
 ^ 
2
 y1  y2   y1  a2 x1  a1 x1  a0
 y   ^   y  a x 2  a x  a0

2
2
2
2
1 2
y
    2  
 ...   ...  
...



 
 yn   ^   yn  a2 xn 2  a1 xn  a0
yn 
• Use same approach as linear fit derivation
{x1,x2,x3,…xn}
{y1,y2,y3,…yn}
instrument
• Given the calibration
Data set {xi,yi} we want
To compute a0,a1,a2 so that we
Get the best overall “fit” to data
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
  y   x
   y    x


 ^ 
y2 
 x12
 y1 
 ^ 
 2
y 
^
x
2
y





2
Y
Y 
X 2
 ... 
 ...
 ... 


 2
 
 yn 
 ^ 
 xn
yn 
We want to model the input/output relationship
By a now use polynomial of the form
y(x)  a2 x 2  a1 x  a0


36


2
1
1
2
2
2
 ...   ...
   2
 yn   xn
x1 1 
  a2 
^
x2 1   
a1  Y  Y  Y  XA
... ...  
  a0 
xn 1 
x1 1 
 a2 

x2 1 
 A   a1 
... ...
 a0 

xn 1 
1
A   X T X  X T Y
Can be solved in
Closed form but easier
To use Numerical
Methods
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
37
Trend Curve: Polynomial Least
Squares (5)
Trend Curve:
Polynomial Least Squares (4)
• In general for an “mth” order fit
 ^ 
y2 
 x1m
 y1 
^ 

 m
y 
^
x
2
Y     Y  y2   X   2
 ... 
 ...
 ... 


 m
 
 yn 
 ^ 
 xn
yn 
1
A   X T X  X T Y
National Aeronautics and Space Administration
... x12
... x2 2
... ...
.. xn 2
 am 
x1 1 
 ... 

 
x2 1 
 A   a2  

... ...
 

 a1 
xn 1 
 a0 
1
A   X T X  X T Y
• Labview fit VI
• Numerical
Methods required for
Solution to this system
• Solution Algorithms
• Numerical
Methods required for
Solution to this system
Stephen A. Whitmore, USU MAE Dept.
38
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
39
10
6/14/2009
The Trend Curve: Polynomial Least
Squares (6)
Second Order Fit Revisited
• 10th order curve fit
• Are we starting
to over fit the
data here?
Definitely a
better fit
• The curve inflections
Are matching random
Components in the data
And not systematic trends
bias
precision
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
40
41
Trend Curve: Polynomial Least
Squares (8)
The Trend Curve: Polynomial Least
Squares (7)
• 10th order curve fit
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Second Order Fit
• 2nd order curve fit
Higher Order Fit
is not
Necessarily
better
Tenth Order Fit
Use Minimum
Order Fit that
De-trends Data
• Which fit de-trends the data best?
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
42
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
43
11
6/14/2009
Error Propagation (1)
Error Propagation (2)
Calculate dz2
2
f (x, y)
 f (x, y)

d x 
d y 
y
 x

More often then not, the quantity we are interested in measuring is a
function of a several other independent sensed variables .. And the
end result is calculated from these independent variables .. How do
we account for the errors in the independent variable measurements?
d z2  
• LOOK AT CHAIN RULE FOR DIFFERENTIATION
…approximate infinitesimal d by finite d
dz 
2
2
 f (x, y) 
 f (x, y) 
 f (x, y)   f (x, y) 
2
 d y2  2 

d x d y

 d x  
 x   y 
 y 
x 
example  z  f (x, y)....x, y are noisy measurements
...what can we say about error in z ?
• Now .. Assume we collected N measurements
N
f (x, y)
f (x, y)
d x 
d y
x
y
 d z 
2
i
i=1
2
2
N
N
 f (x, y)  N
2
2
 f (x, y) 
 f (x, y)   f (x, y) 

 d xi   
  d yi   2 

 d xi  d yi 
 x  
 x   y  
 y  i=1
i=1
i=1
For now assume unbiased measurements d x  d y  0
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
44
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Error Propagation (3)
45
Error Propagation (4)
For now assume unbiased measurements d x  d y  0
Argument can be generalized for biased data ...
• in the limit as N becomes very large
2
2 N
N
1 N

 N
2
2
 f (x, y)  N
2
2
2
 f (x, y) 
 f (x, y)   f (x, y) 
  d z  N  1  d zi    d zi    x    d xi    y    d yi   2  x    y    d xi  d yi 
i=1
i=1
i=1
i=1

 i=1


1 N
2
2
 dx 
 d xi  
N  1 i=1




1 N
2
2
d yi  
dz2 
 dy 


N  1 i=1


2
2
 f (x, y) 
f (x, y) 

 f (x, y)   f (x, y) 
N


2
1
 dx  
  d y2  2 


 d xd y 
d xi  d yi   x 
 x   y  d xd y

 y 

N  1 i=1


zi  f (xi , yi ,...)  d z 
d z  lim
N
1
N
N
z
i
i1

f (x, y)
f (x, y)
d x 
d y
x
y
f (x, y)
f (x, y)
 d x 
 d y
x
y
2
1
 f (x, y)
 f (x, y)
 
f (x, y)
f (x, y)
2
1
lim   
 d xi 
 d yi  
 d x 
 d y    
 d zi  d z    N
 x
 
y
y
N
 N  x

 z2  lim 
N
2
1
 f (x, y)
 
f (x, y)
lim   
 d xi  d x 
 d yi  d y  
 
y
 N  x
N
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
46
National Aeronautics and Space Administration


Stephen A. Whitmore, USU MAE Dept.
47
12
6/14/2009
Error Propagation (5)
Error Propagation (6)
• Expand and collect terms
1
 z2  lim 
N
 N
2
 f (x, y)
 
f (x, y)
 d xi  d x 
 d yi  d y  
 
x
y

 
2

1
2  f (x, y) 
 lim  d xi  d x  
 d yi  d y
N N
 x 



y) 
  f (x,
y 
2
2
 d2xd y  lim

2
dx
1
 lim 
N  N
 d x
 d x 
2
i


 d2y  lim   d yi  d y  
N  N

1
2


 2 d xi  d x  d yi  d y
N
1
N
 d x
i

 d x d xi  d x 
• Applying the general
definitions for variance, covariance
2
2
f 
f 
f f 
  d2y    L  2 d2xd y    
  x 
 x   y 
 y 
 d2z   d2x 

2
2
 f (x, y)   f (x, y)  

 x   y  

Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
48
f 
f 
f f 
  d2y 
 L  2 d2xd y 
  x 
  x    y 
  y 
 d2z   d2x 

Generalized Error Propagation Formula. In the first two terms,
the variance of the uncertainty  is the uncertainty of a
fundamental quantity while the partial derivative comes from
the relation between z and x,y.
The last term, called the uncertainty covariance, accounts for
the extent that fluctuations in x are correlated to fluctuations in
y. We will generally assume that this is not significant. If x
and y occur randomly and independently, then this last
term is zero.
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
49
Error Propagation Example (1)
Error Propagation (7)
In general if z = f(x,y,u,v, …)
2
2
2
More often then not, the quantity we are interested in measuring is a
function of a few variables. The book cites the example of estimating
volume flow rate by measuring the time it takes to fill a bucket of
known volume. Q = V/t If you knew the uncertainty of V and the
uncertainty of t, how do you find the uncertainty of Q?
2
f 
f 
f 
f 
f f 
  v2 
  u2 
  v2    2 xy2 
 ...
  x 
  u 
 v 
  x    y 
  y 
 z2   x2 
We will ignore the covariance (last) term and assume that
our uncertainties behave like standard deviations. Thus
• LOOK AT CHAIN RULE FOR DIFFERENTIATION
 z  f (  x ,  y , u ...)
2
2
Q =  V/t  =
2
2
f 
f 
f 
f 
 d y2    d u2 
 d v2 
L
  x 
  u 
  v 
 y 
Q
Q
 Q   1
 Q 
V
 V 
 t  

 
  2 
 V   t 
 t 
t 
V
t
d z2  d x2 

2
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2
2
 Q 
 1
 Q 
V
 
   
 2
 V 
t
 t 
t 
Eqn. 3.35 in B.M.L.
50
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2
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51
13
6/14/2009
Error Propagation Example
Overall Measurement Uncertainty
(2)
• The overall uncertainty of a measurement will be a
combination of the bias uncertainty and the precision
uncertainty
Assuming unbiased measurements of V and t, and that
errors in these measurements are uncorrelated
• Substitute in
 t 2   d t 2 
for

   d tdV   0
2
2
2
2
 Q 
 1
 Q 
V
 2  dV 2 
 

    
  2
 V

 V 
2
t
 t 
• If we can account for the bias we take it out …
otherwise bias is modeled as an uncertainly
t 
• The overall uncertainty is the Root-sum-square (RSS)
of the Bias and random uncertainty + other classifiable
errors like hysterysis, calibration, etc.
2
 Q 
 Q 

 2
2
 V  V  t  t
 Q2
2
Ux = (Bx2 + Rx2+… )1/2
2
 1
V
2
2
    V   2    t
t
t
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52
Uncertainty Analysis Procedure (1)
Uncertainty Analysis Procedure (2)
1) Find the functional form of what you will measure (e.g. Re = Ud/v)
5)
Root sum square the bias and precision uncertainty for each quantity.
2) Identify all variables to be measured (U, d, v)
6)
Propagate the uncertainty. If component uncertainties are provided as
percentages (relative uncertainties, as opposed to absolute uncertainties), and if
the functional form is multiplications, divisions and powers, it may be
convenient to write the propagation equation in terms of relative uncertainties
by dividing through by the function.
3) For each of these quantities, determine the bias error based on
instrument specs and calibration information
E.G., the velocity probe has an accuracy of 2% of reading (0.02U)
or perhaps 1% of full scale. The diameter is known to the
resolution of the measuring caliper, which is 0.001”.
2
2
 Re 2
2
2  Re 
2  Re 
uRe
 uU2 
  ud 
  uv 

 U 
 d 
 v 
d 2
U 2
 dU 2
2
uRe
 uU2    ud2    uv2  2 
v 
v 
 v 
4) For each of the quantities, if repeated measurements produce
different results, sample the quantity until the desired precision
uncertainty is obtained. ENSURE ALL SAMPLES ARE
INDEPENDENT. If not, your precision error is larger than you have
estimated. A desirable precision uncertainty is similar to the bias
uncertainty.
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2
2
• Compute total error
Ux = (Bx2 + Rx2)1/2
2
2
u  u  u 
uRe
  U    d    v 
Re 2 U   d  v 
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55

14
6/14/2009
Experimental Design Tips
Graphical Presentation of Data (1)
A graph should be used when it will convey information and portray
significant features more efficiently than words or tabulations.
1) Avoid approaches that require two large numbers to be measured in
order to determine the small difference between them. For example,
large uncertainty is likely when measuring d = (x1 - x2) if d << x1.
Graphs should:
2) Design experiments that amplify the signal strength to improve
sensitivity.
1) Require minimal effort from the reader in understanding and
interpreting the information it conveys
3) Build “null designs” in which the output is measured as a change
from zero rather than a change in a non-zero value. This reduces
both bias and precision errors. Such designs often make the output
proportional to the difference of two sensors.
2) The axes should have clear labels that name the quantity plotted,
its units, and its symbol
3) Axes should be clearly numbered and should have tick marks for
significant numerical divisions. Typically, ticks should appear in
increments of 1, 2, or 5 units. Not every tick need be numbered.
Too many will clutter the axis.
4) Avoid experiments where large correction factors are applied
5) Attempt to minimize loading errors
4) Use scientific notation to avoid placing too many digits on the
graph.
6) Calibrate the entire system rather than the individual components.
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56
Graphical Presentation of Data (2)
57
11) Minimize lettering on graphs
12) Labels on the axes and curves should be oriented to be read from
the bottom or from the right. Avoid forcing the reader to rotate the
figure to read it.
6) Axes should usually include 0.
7) The choice in scales and proportions should be commensurate
with the relative importance of the variations shown in the
results.
13) The graph should have a descriptive but concise title.
8) Use symbols, Not dots, for data points. Open symbols should
be used before closed.
Bottom Line- You want to communicate information to your reader.
The burden to get your point across falls to you. The chances of
successfully communicating your point are improved considerably
when you make it easy on the reader. Never think of your plot as
pretty graphics. If that is all it is, you should remove it.
9) Either place error bars on the plot that indicate uncertainty or
use symbols that are the size of the uncertainty.
10) When several curves appear on the same plot, use different line
styles to distinguish them. Avoid using colors.
Stephen A. Whitmore, USU MAE Dept.
Stephen A. Whitmore, USU MAE Dept.
Graphical Presentation of Data (3)
5) When plotting on logarithm axes, place ticks at powers of 10 and
minor ticks at 10, 20, 50, 100, 200, etc.
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Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
Finish
Questions??
Stephen A. Whitmore, USU MAE Dept.
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ESDM Senior
Design Project
60
Sample Mean and
Standard Deviation (1)
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 is the true mean of the distribution, or the actual value without any error. If we
Measurements and Uncertainty Analysis II
take a sample and average the results, we obtain the most probable value of the
mean: sample mean
n
Probabilistic Assessment of
Experimental Uncertainty
x
x1  x2  x3  ...xn
x
 i
n
i 1 n
Define the deviation to be the the sample mean and any value
Mechanical Measurements, 6th Edition, 2006
Authors: Thomas G. Beckwith,
Roy D. Marangoni, John H. Lienhard, V
Prentice-Hall
di = xi - 
The mean squared deviation can be approximated by averaging the squared
deviation of the sample: (sample standard deviation)
2
www.nasa.gov
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62
2
2
 x  x_    x  x_   ... x  x_ 
 1
  2

 n

  Sx 

n 1
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 x  x_ 
 i

 n 1
i 1
2
n
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16
6/14/2009
Sample Mean and
Standard Deviation (2)
Estimation of Uncertainty (1):
Sample Statistics
For the Sample standard deviation … n-1 is the degrees of freedom (number of
samples minus what we calculate from them) …. Since the sample mean is
already computed from the samples, the degrees of freedom are reduced by 1
2
2
2
• Based on
Measurements of
a hand full of
Marbles what can
We conclude
About the
Diameters
Of the marbles
in the bag?
2
 x  x_    x  x_   ... x  x_ 
 x  x_ 
n
 1
  2

 n

 i

  Sx 
 
n 1
n 1
i 1
• If the samples within the population are independent of each other
(as in Gaussian population) … then
2
n
 xi 2 
 xi 2 
n  x 
2
  n  1   xi    x    n  1  "mean square"
i 1  n  1 
i 1
i 1 

n
 2  Sx 2   
Sx 2   x 2 
n  _
x
n  1 
2
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64
Estimation of Uncertainty (2)
• In real life we deal with samples of a population and NOT the entire
population itself … thus we must use averages From the sample to infer
the properties of the population
65
• If an error is purely random … then it will tend to give a different
Value each time … and the occurrence of a given value is
Just as likely as the occurrence of another value
• As the sample population
gets very large … not a
problem … But for smaller
samples … its a bit trickier
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Stephen A. Whitmore, USU MAE Dept.
Probabilistic Description of Error (1)
Sample Statistics
• Which sample would you
Expect provides the
best information about
the population of
marbles in the bag?
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• Flipping a coin is a good example … 50% probability of
Heads, 50% probability of tails
Big! Sample
Small! Sample
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66
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67
17
6/14/2009
Probabilistic Description of Error (2)
Probabilistic Description of Error (3)
• What is the probability that a coin 4 times in a row and having
Them all be heads? … look at sample space …
• Example of Non-uniform probability distribution
• How many ways to get
Seven?
{1,6},{2,5},{3,4}
{6,1},{5,2},{4,3}
(H,H,H,H), (H,H,H,T), (H,H,T,H), (H,H,T,T), (H,T,H,H),
(H,T,H,T), (H,T,T,H), (H,T,T,T), (T,H,H,H), (T,H,H,T),
(T,H,T,H), (T,H,T,T), (T,T,H,H), (T,T,H,T), (T,T,T,H),
(T,T,T,T)
How about four?
{1,3},{2,2},{3,1}
P(H,H,H,H)=N(H,H,H,H)/Npossible =1/16
• As a shortcut, we could say that the probability of
getting heads on any one throw is 1/2. The probability of
getting four heads in a row therefore is
(1/2)(1/2)(1/2)(1/2) = or (1/2)4 = 1/16.
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… so seven is twice
As likely as 4!
68
Probabilistic Description of Error (4)
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69
Probabilistic Description of Error (5)
• For three or more die rolls, the curve becomes more bell-shaped
with each additional die added to system … central limit theorem
• The “Bell-shaped” curve is referred to as the Normal or
Gaussian distribution
• “7” is Most likely
• The Gaussian distribution describes the population of possible
Outcomes when a large number of independent sources contribute
To the final outcome
• “2” is least likely
• It is typically used for a probabilities description of
uncorrelated errors … empirical result based on observation
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6/14/2009
Gaussian Probability Density Function
Central Limit Theorem
p(x) 
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1
2 
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e

x   2 • --> “mean” most likely value
2 2
• --> “standard deviation” …
Describes likelihood of deviation
from the mean --> = “variance”
Stephen A. Whitmore, USU MAE Dept.
73
Probability Density versus Distribution (2)
Probability Density versus Distribution (1)
• Probability of an occurrence with in a given range is the integral
Of the density function over that range
x2 
x    

1
2
Px  x1 & x  x2    
e 2  dx
 2 

x1 
2
• Integral cannot
Be analytically
evaluated
Density
p(x) 
1
2 
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e

x   2
2 2
Distribution
x   
 1

2
Px    
e 2

2 
 
x
2
Stephen A. Whitmore, USU MAE Dept.
• Numerical
Calculation
Is used

 dx

74
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6/14/2009
Tabulation of Normal Data
p z  
z =(x - )/ 
1
 2
e z
2
Labview Code
/2
“not very
convenient”
Stephen A. Whitmore, USU MAE Dept.
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77
Probabilities of Deviation (2)
Probabilities of Deviation (1)
2- ”two-sigma"
1- "one-sigma"
z
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z
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6/14/2009
Probabilities of Deviation (3)
Probabilities of Deviation (4)
3- ”three-sigma"
z
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81
Example 3.6.1 (2)
Example 3.6.1 (pp. 52-53 B.M.L)
• # of Pressure readings
Taken that line within
+ 0.005 Mpa of listed value
n
x 
i 1
• Histogram of Data
(number of occurrences
Within each bin)
• Compared with Normal
Distribution based on sampled
Mean and standard deviation
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• Sample mean and
standard deviation
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xi
 4.008Mpa
n
2
 x  x_ 
 i

Sx  
 0.014Mpa
n 1
i 1
n
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21
6/14/2009
Example 3.6.1 (3)
Confidence Intervals for Finite Samples
2
n
x 
i 1
xi
 4.008Mpa
n
 x  x_ 
n
 i

Sx  
 0.014Mpa
n 1
i 1
1 n
x   xi
n i1
• Sample
“Not quite”
Gaussian

• How much
“not quite”?
 n 2 
2
 x i  nx
n
1
2
i1 
 x i  x  
n 1 i1
n 1
Sx 
Estimate of
the mean

Estimate of the
Standard
Deviation
Based on a finite sample, we would like to:
1) Estimate the mean and standard deviation, and their
uncertainty
2) Infer the probability distribution of the data
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84
Confidence Intervals (1)
Confidence Intervals (2)
• For a Gaussian distributed population … the sum of any selected
sample is also Gaussian distributed … consequently … the sample
mean (for n points)
… more data you use … the better your estimate
… is a Gaussian distributed variable  2 _   (x)
x
n
with a standard deviation given by
2
x
1 n
 xi  
n i1
• Our estimate of the mean
Stephen A. Whitmore, USU MAE Dept.
1 n
 xi  
n i1
In terms of
Normalized
_
_ value
x 
x 
z

_
/ n
x

Of course if we take another equally large, but different random
sample from The population … we will get another equally valid
estimate of the mean …Which estimate is “more correct”
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x
is a Gaussian distributed variable
with
 (x)2
Variance …
2_ 
x
n
… more data you use … the better your estimate

85
1 n
x   xi  
n i1
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86
_
z
_
x 

 x    z
/ n
n
Stephen A. Whitmore, USU MAE Dept.
87

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6/14/2009
Confidence Intervals (3)
Confidence Intervals (4)
x
We’d like to be able to say how sure we are of this estimate. Let’s
look at the probability that our estimate of the mean is within some bound.
We can say that there is a c% chance that our estimate of the mean lies
within
  zc /2

n
x  zc / 2

n
   x  zc / 2


n
   x  zc / 2

n

c/2
zc/2

n
Stephen A. Whitmore, USU MAE Dept.
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x  zc / 2
The larger we make the confidence interval c …. the larger zc/2 becomes
… and the larger the range for the mean estimate

 

    zc /2 
 x    zc /2 
n
n 

• Or Alternatively
1 n
 xi  
n i1
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88
89

Confidence Intervals (6)
Confidence Intervals (5)
This means that we are c% confident that the true mean  lies within
the interval about our measurement:
x  zc / 2

n
   x  zc / 2
x

x  zc / 2
n


Sx 
z = 1.96 = zc/2
Sx
n
Stephen A. Whitmore, USU MAE Dept.
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Sx
S
   x  zc /2 x
n
n
0.4750 - area Under
curve between lines
Sx
S
   x  zc / 2 x
n
n
Standard Error of the Sample Mean
x  zc /2
Same effect using computer code … i.e .. For 95% confidence level … c/2
z=0
= 0.475
The only trouble is that we don’t know the value of  either. If n is large
enough, we can use our estimate Sx, so

1 n
 xi  
n i1
x  1.96
90
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Sx
S
   x  1.96 x
n
n
Stephen A. Whitmore, USU MAE Dept.
91

23
6/14/2009
Confidence Interval for
Example 3.6.1 (1)
n
x 
i 1
Confidence Interval for Example 3.6.1 (2)
• Or use your numerical program
xi
 4.008Mpa
n
What is 99%
confidence
level for this
sample mean?
2
 x  x_ 
 i

Sx  
 0.014Mpa
n 1
i 1
n
• Can use table 3.2 with c = 49.5%
Which is kinda Kludgy
What is 99%
confidence
level for this
sample mean?
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
zc/2=2.575
92
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Confidence Interval
for Example 3.6.1 (3)
• or more directly use two sided probability
99% confidence level
c/2 = 0.495
93
Confidence Interval
for Example 3.6.1(4)
99% confidence level
--> c = 0.99
What is 99%
confidence level
for this sample
mean?
99% confidence level zc/2=2.575
Sx
S
   x  zc /2 x 
n
n
0.014
0.014
4.008  2.575
   4.008  2.575

100
100
x  zc /2
Z0.99=2.575
4.004395    4.01165    4.008  0.003605
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94
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95
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6/14/2009
Confidence Intervals for Small
Samples
Confidence Interval for
Example 3.6.1(4)
Or Using the tables
We do not always have the luxury of taking large samples (n > 30). For
smaller sample sizes, we cannot assume that  ~ Sx. If we derive the
distribution of the quantity
Easier to mechanize using
Computer .. And less error
c = 0.99, c/2 = 0.495 …
t
x 
Sx / n
• Dependent upon the number of
Degrees of freedom, v=n-1
assuming that the population is Gaussian,we get the Student t-distribution
  zc / 2
z0.495 = 2.575
The derivation of the t-distribution was first

published in 1908 by William Sealy Gosset,
while he worked at a Guinness brewery in
Dublin. He was not allowed to publish
under his own name, so the paper
was written under the pseudonym Student.

n
 = 4.008 ± 2.575 (0.014)/10 = 4.008 ± 0.003605 (99%)
Stephen A. Whitmore, USU MAE Dept.
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96
Stephen A. Whitmore, USU MAE Dept.
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97

Student’s-t distribution (1)
Student’s-t distribution (2)
• The Student's t-distribution is a probability distribution that arises in
the problem of estimating the mean of a normally distributed population
when the sample size is small. It is the basis of the popular Student's ttests for the statistical significance of the difference between two sample
means, and for confidence intervals for the difference between two
population means.
• Gosset studied a related quantity, for small samples

n


i 1
x
x1, x2 , x3 ,...xn   var iance :  2   sample mean : x   ni
_
• The variable z 
x 

_
x
t2 
  
     1  

 2 
x 
/ n

(x)   u x 1eu du 
0
is normally distributed with mean 0 and variance 1
National Aeronautics and Space Administration
  1

 2 

p(t) 
_

Stephen A. Whitmore, USU MAE Dept.
“t” distribution
And showed that it had the probability density function
• Given a sample set …
 mean : 
x 
Sx / n
t
98
National Aeronautics and Space Administration
 1
2
  n 1




   "gamma function"


e-0.5772156649 x   e x /i 



x
x
i 1
 1  
i
Stephen A. Whitmore, USU MAE Dept.
99
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6/14/2009
Student’s-t distribution (3)
Small-Sample Confidence Interval (1)
• The Student's t-distribution is a probability distribution that arises in the problem
of estimating the mean of a normally distributed population when the sample size is
small. It is the basis of the popular Student's t-tests for the statistical significance of
the difference between two sample means, and for confidence intervals for the
difference between two population means.
Density
function
• Done exactly in the same was as for large samples … only
Now you use the “t-distribution” for  = n-1 degrees of freedom
and not the Gaussian distribution
• Want to evaluate …. To evaluate precision of
estimate
At some c --> confidence level
Probability
function
x  zc /2,
Sx
S
   x  zc /2, x
n
n
• Sx --> sample standard deviation
Stephen A. Whitmore, USU MAE Dept.
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100
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Small-Sample Confidence Interval (2)
Small-Sample Confidence Interval (3)
• example … for a sample with 8 data points estimate precision
Bounds for 95% level of certainty
• compare to “large population” Gaussian  =infinity
For 95% confidence level
= n-1 = 7 -->
c/2,=7=0.475
x  2.2364
zc/2,=7 =2.2364
x  2.2364
zc/2,=7
=2.2364
Sx
S
   x  2.2364 x
n
n
101
Area under
Curve
Between
lines
x  1.96
Sx
S
   x  2.2364 x
n
n
Sx
S
   x  1.96 x
n
n
8 of data points
( --> 7)
“lots” of data points
( --> infinity)
“uncertainty is obviously larger for small sample”
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102
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103
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6/14/2009
Small-Sample Confidence Interval (4)
Small-Sample Confidence Interval (5)
• Example 3.6 in B.M.L.
• Example 3.6 in B.M.L.
Postal scale calibration …. 14 one-ounce weights chosen & weighed
Value x
dx
dx2
dx2
1.080
1.030
0.960
0.950
1.040
1.010
0.980
0.990
1.050
1.080
0.970
1.000
0.980
1.010
0.071
0.021
-0.049
-0.059
0.031
0.001
-0.029
-0.019
0.041
0.071
-0.039
-0.009
-0.029
0.001
0.005
0.000
0.002
0.003
0.001
0.000
0.001
0.000
0.002
0.005
0.002
0.000
0.001
0.000
0.005
0.005
0.008
0.011
0.012
0.012
0.013
0.014
0.015
0.020
0.022
0.022
0.023
0.023
1.080
2.110
3.070
4.020
5.060
6.070
7.050
8.040
9.090
10.170
11.140
12.140
13.120
14.130
95 % confidence
level -->
c/2,=0.475 -->
= n-1 = 13
Sample Statistics
zc/2,=13 =
2.160
x =1.00929
Sx =0.04178
x =1.00929
Sx =0.04178
• Compute
Area under
Curve
Between
lines
Sx
S
   x  2.160 x
n
n
95% confidence
interval
(precision) for
population mean
Stephen A. Whitmore, USU MAE Dept.
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x  2.160
104
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Stephen A. Whitmore, USU MAE Dept.
105
Bias and Single Sample
Uncertainty
Small-Sample Confidence Interval (6)
• Example 3.6 in B.M.L.
95 % confidence level --> c/2=0.475 --> = n-1 = 13
x =1.00929
Sx =0.04178
Sx
S
   x  2.160 x 
n
n
0.04178
0.04178
1.00929  2.160 
   1.00929  2.160 
14
14
0.098517    1.03341
x  2.160
What can you do about estimating the your precision
uncertainty if you only take 1 or 2 samples?
You can use the instruments specs (non repeatability) to
estimate the uncertainty and treat it like it is a bias error.
---> Measurement precision …. At 95% confidence level
Px  zc /2,
National Aeronautics and Space Administration
Better approach is to “take more samples”
Sx
S
(c%) = 2.160 x  0.02412
n
n
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106
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107
27
6/14/2009
The t-Test Comparison (2)
The t-Test Comparison (1)
If we take two small samples, and we wish to determine whether or
not the resultant means are statistically identical, we use this test.
x 
t
Sx / n
• At 95% confidence level Is there any statistical difference?
x1  x 2
t
S12 /n1 S22 /n2 
We find t by choosing a confidence interval. In order to do that, we need to know
the number of degrees of freedom. In general, the number of samples in 1 and 2
may be different. The effective degrees of freedom can be approximated by:
 S 2 /n  S 2 /n 2
 1 1  2 2 


S
2
1
/n1 
2
n1 1

S
2
2
/n 2 
2
n 2 1
to the nearest integer. If the computed value of t lies inside of the interval ±ta/2,n
, then the two means are statistically identical within the confidence assumed.

Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Lifetime, months
Brand B
Brand A
7.2
7.6
6.9
8.2
7.3
7.8
6.6
6.9
5.5
7.4
5.7
6.2
108
7.5
8.7
7.7
7.5
6.7
11.2
7.0
10.7
7.0
8.6
6.1
6.3
7.8
8.7
6.1
National Aeronautics and Space Administration
7.5
8.7
7.7
7.5
6.7
11.2
7.0
10.7
7.0
8.6
6.1
6.3
7.8
8.7
6.1


 
 


x=7.84
Sx=1.53
n=15
Stephen A. Whitmore, USU MAE Dept.
109
For 95% --> c/2=0.475
effective ~ 22
 0.822 1.532  2


+
 12
15 
2
 S12 / n1  S22 / n2 
 

2
2
S12 / n1
S22 / n2

n1  1
n2  1
x=6.94
Sx=0.82
n=12
The t-Test Comparison (4)
• At 95% confidence level
Is there any statistical difference?
Lifetime, months
Brand B
Lifetime Statistics , months
Brand A
Brand B
National Aeronautics and Space Administration
The t-Test Comparison (3)
Brand A
7.2
7.6
6.9
8.2
7.3
7.8
6.6
6.9
5.5
7.4
5.7
6.2
• Want to determine lifetimes of
two different Brands of light bulbs






 1.532  2 

 
 15  
+

12  1
15  1 

zc/2=0.475,=22 = 2.074
 0.822  2


 12 
= 22.213 .. Round to 22
Stephen A. Whitmore, USU MAE Dept.
110
• Look at test statistic
t
S
2
1
x1  x2
 
/ n1  S22 / n2
National Aeronautics and Space Administration






6.94  7.84


  0.822 1.532  0.5 



+
  12
15  
= 1.954 < 2.074
At 95% level no
Statistical significance
111
Stephen A. Whitmore, USU MAE Dept.
28
6/14/2009
c2 Distribution (1)
c2 Distribution (2)
• Consequently, the
Sample variance is
A random variable
Distributed as c2.
• As we saw earlier … For a Gaussian distributed population
… the sum of any selected sample is also Gaussian distributed
… consequently … the sample mean (for n points) … is a Gaussian
… distributed variable
 1 2
    1  x
2
pc 2 (x) 
x 2  e 2

 
 2
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112
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
c2 Distribution (3)

2
n

• However the sum of the squares of any set of points is NOT
Gaussian distributed .. The distribution is instead described
By a c2 distribution for  = n-1 degrees of freedom.
National Aeronautics and Space Administration
 x  x_ 
 i

Sx  
n 1
i 1
2
113
c2 Distribution (4)
Cumulative Distribution
function

 1 2

 2   2 1  a2
Pc 2 ( ,  )  
a
e da

  
 2 
 1 2
    1  x
2
pc 2 (x) 
x 2  e 2

 
 2

 x  x_ 
 i

• For a Gaussian Distributed population with =0, 2=1 Sx  
n 1
i 1
2
• Tables of c2
probability
2
n
• One-sided density function … because of “squared” components
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Stephen A. Whitmore, USU MAE Dept.
114
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115
29
6/14/2009
c2 Significance testing (2)
c2 Significance Testing (1)
• Example 1 … 8 data points … =7, 95% confidence level
• Recall that the Gauss/Student’s-t distributions allow us to
Assess the precision of an estimate of the population
Mean
 (x)2
1 n
2_ 
x
xi
x
n
n
•  = 1-0.95 = 0.05-->

c2 (1-/2) = 1.689
i1
1) large sample .. Gaussian distribution
2) small sample … Student’s t distribution
c2 (/2) = 16
• The c2 distribution allows up to perform the same evaluation For the
 variance (square of the standard deviation)
sample
Sx2 
1 n
2
xi  x 
n  1 i 1
7Sx2
7Sx2
 2 
.....(95%)
16
1.689
 n 2
2
  xi   nx
 i 1
n 1
n  1Sx2   2  n  1Sx2 .....(c%)
2
2
c /2
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
116
c2 Significance testing (3)
/2 = 0.025
1- /2 = 0.975
c2 (1-/2) = 32.33
c2 (1-/2) = 32.33
c2 (/2) = 70.75
c2 (/2) = 70.75
50Sx2
50Sx2
 2 
.....(95%)
70.75
32.33
n  1Sx2   2  n  1Sx2 .....(c%)
2
2
n  1Sx2   2  n  1Sx2 .....(c%)
2
2
c /2
117
• Example 2 … 51 data points … =50, 95% confidence level
•  = 1-0.95 = 0.05-->
/2 = 0.025
1- /2 = 0.975
50Sx2
50Sx2
 2 
.....(95%)
70.75
32.33
National Aeronautics and Space Administration
c1 /2
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
c2 Significance testing (34)
• Example 2 … 51 data points … =50, 95% confidence level
•  = 1-0.95 = 0.05-->
c% = 1 - 
/2 = 0.025
1- /2 = 0.975
c /2
c
 MAE
/2 Dept.
Stephen A. Whitmore, 1
USU
118
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c1 /2
Stephen A. Whitmore, USU MAE Dept.
119
30
6/14/2009
c2 Significance testing (4)
Other uses for c2 distribution
• Example 2.. 251 data points … =250, 95% confidence level
•  = 1-0.95 = 0.05-->
/2 = 0.025
1- /2 = 0.975
c2 (1-/2) = 207.35
We can use Chi-squared to estimate our confidence in our estimate of the standard
deviation Sx. However, there is seldom much call for this. A more useful application of
Chi-squared is to check our assumption that the data we are dealing with fits a certain
distribution. We are going to assuming in this class that our data fits a normal (gaussian)
distribution. If we have a set of data and we want to make sure this is a good fit, we use
20
this test.
Thermo II 2002
15
N=64
K=7
c2  
c2 (/2) = 276.2
n
nj
Count
j
250Sx2
250Sx2
 2 
.....(95%)
276.2
207.25
 n' j 
2
j
n 'j
10
j = 1, 2,… K

5
0
Stephen A. Whitmore, USU MAE Dept.
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120
0.3
0.4
0.6
0.7
National Aeronautics
and Space 0.5
Administration
ou t of 1
0.8
0.9
1
Stephen A. Whitmore, USU MAE Dept.
121
Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
“Design Friday”
Finish
Questions??
National Aeronautics and Space Administration
Demonstration of
Probability Analysis Labview
Codes, Go Through FADS
Confidence Interval Assessment
Example
Stephen A. Whitmore, USU MAE Dept.
122
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
123
31
6/14/2009
ESDM Senior
Design Project
National Aeronautics and
Space Administration
Measurements and Uncertainty Analysis
Appendix, c2 Example
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
Other uses for c2 distribution
“Design Friday”
We can use Chi-squared to estimate our confidence in our estimate of the standard deviation Sx.
However, there is seldom much call for this. A more useful application of Chi-squared is to
check our assumption that the data we are dealing with fits a certain distribution. We are going to
assuming in this class that our data fits a normal (gaussian) distribution. If we have a set of data
and we want to make sure this is a good fit, we use this test.
Demonstration of
Probability Analysis Labview
Codes, Go Through FADS
Confidence Interval Assessment
Example
20
Thermo II 2002
2
N=64 c  
j
K=7
Count
15
nj
126
 n' j 
2
j
'
nj
j = 1, 2,… K
0
0.3
Stephen A. Whitmore, USU MAE Dept.
n
10
5
National Aeronautics and Space Administration
125

0.4
0.5
0.6
0.7
0.8
0.9
1
ou t of 1
National Aeronautics and Space Administration
Stephen A. Whitmore, USU MAE Dept.
127
32
6/14/2009
c2 Hypothesis Testing Example (1)
c2 Hypothesis Testing Example (2)
X-33
• Suborbital Spacecraft
For “Space Tourism”
XP-1
• Extremely steep
Reentry Profile
• Angle of attack and Dynamic
Pressure
Are critical at Atmospheric
interface
For keeping vehicle Stable and
within
Loads limits … and for energy
management for reaching landing
site
Stephen A. Whitmore, USU MAE Dept.
X-43
FA-18 SRA
X-34
• Other Vehicles with FADS
• Flight and mission critical
system
National Aeronautics and Space Administration
X-38
128
c2 Hypothesis Testing Example (3)
Stephen A. Whitmore, USU MAE Dept.
National Aeronautics and Space Administration
129
c2 Hypothesis Testing Example (4)
• “Flush Airdata Sensing System” …multiple pressure ports
On Nosecap
Background: Orbiter (SEADS)
• 5 flights on Columbia
• Niobium inserts into C/C TPS
• Accurate airdata to 280K feet
+y
• 0.5˚ ,b
Nose cap Front View Look ing Aft
Nose cap Left Side View Look ing Inboard
y=0
• 5% qbar
Aerodynamic OML
TP S Nominal
Thickness 5 cm
Nosecap Tile / Blanket Interfac e
• Semi-empirical, iterative
method
Structural OML
o
28.9
Structural Nosecap
radius~17.8 cm
5
z=0
45
4
o
1
6
o
o
45
f
7
6.4
o
16.1
2
4) Larson, T erry J., Whitmore, St ephen A., Ehernburger, L. J., Johnson, J. B., and Siemers, Paul M., II,
Qualitative Evaluation of a Flush Air Data System at Transonic Speeds and High Angles of Attack,
NASA TP 2716, April 1987
o
38.6
3
+z

8
o
61.1
x=0
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+x
o
90
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c2 Hypothesis Testing Example (5)
c2 Hypothesis Testing Example (6)
• Multiple Minima Instabilities
 ind 
b 
ind 
X FADS  
 qc 2 


 p 
p() = qc
cos2  + e sin2  + p
cos i  cos  ind cos bind cos fi 
sin bind sin i sin fi  sin  ind cos bind cos i sin fi
• Failed Sensors can result in
Catastrophic Instabilities in solver
….
• Need System Health Monitor
• Pressures related to airdata state via Mathematical Model
• Complex Set of Non-linear
Equations, Solve Via Non-Linear
Regression
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c2 Hypothesis Testing Example (7)
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c2 Hypothesis Testing Example (8)
• Since residuals are ~ Gaussian,
sum square is approximately
c2 with N-5 degrees of freedom
• FADS algorithm is basically a (nonlinear) least squares fit
• Residuals are random, with Gaussian Distribution
d pi  Pi  P i  Pi  qc cos2   e sin 2   p ...i  1, N ports 
^
10
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c2 Hypothesis Testing Example (10)
c2 Hypothesis Testing Example (9)
• Hypothesis test
• c2 is good
tool for system health
n 1
c 2d p  
p  qc cos   e sin    p 
2
i
2

i0
2
2
i
i

2
dp
• 2dp ---> derived “a priori” from large population data base
c2dp --> distributed as chi-square variable with n-5 DOF
In general, the higher the value of c2dp computed, the worse the system
is performing. To test the hypothesis “the system is healthy and
performing properly” we compare the parameter c2dp against tables of
c2 for n-5 degrees of freedom. If one plots 1-Prob[c2] versus c2 then c2dp
can be used to predict the relative “health” of the system.
Compare against
probabilities tables
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c2 Hypothesis Testing Example (12)
c2 Hypothesis Testing Example (11)
Thus for a 95% health
indicator we want
n 1
2
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s2  c 2   2 
n 1
c2
s2 
7  11.7  51
0.2
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c2 Hypothesis Testing Example (14)
c2 Hypothesis Testing Example (13)
• Healthy FADS
• Evaluating the c2dp parameter as a part of the FADS
algorithm calculation allows the system health to be easily
and quickly monitored. Assuming that a single pressure
value has caused the failure trip, this technique allows
the isolation of a bad (but undetected) pressure port by
sequentially weighting out individual ports.
When the bad port has been weighted out of the algorithm,
the computed c2dp value will drop dramatically, isolating
the bad sensor in the system.
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Understand Space: An Introduction to Astronautics, Jerry Jon Sellers, 3th ed., McGraw-Hill, 2005., ISBN 9780073407753
c2 Hypothesis Testing Example (15)
Finish
• “Belly-up” FADS
Questions??
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