5.
3.
4.
UNDERGRADUATE CURRICULUM COMMITTEE
NEW COURSE PROPOSAL FORM
Does this proposal affect Liberal Learning requirements? Yes __X_ No _____
1. Title of Course: Mathematics of Powered Flight
Proposed Course Number (cleared with Registrar): MATH 121
Prerequisite Courses: None
(if you require a minimum acceptable grade greater than the default of D- , please indicate the grade you require) _________
Catalogue Description (including credits, lecture, and lab hours):
Application of mathematics to airplane flight. Wind and its effect on airport design and aircraft operations. Maps. Magnetic variation.
Navigation systems. Lift, drag, thrust, gravity.
(3, 3, 0)
Is the course cross-listed? If so, what is the number of the other course?
This is not a cross-listed course.
**A proposed syllabus, including complete text and/or reference information, as well as any relevant information to this decision, must be appended.
NOTE: All affected department chairs must sign approval on last page.
2. For whom is the course primarily intended? Explain why it should be added to the curriculum.
This course is intended to broaden the options available to satisfy the
Liberal Learning Core requirement in mathematics. Topics are quite different than what is usually found in a math course. Subject matter should offer an attractive course.
If this course is required, append a description of how the course fits into the curriculum. Indicate how it affects hours required for graduation.
This is not a required course.
Has this course been offered previously as a special topics course? If so, when? What course number was used?
No, this course has not been offered previously as a special topics course.
6.
Has this course, or one closely related to it, been offered at CNU previously?
If so, is that course currently being offered? How does the proposed course differ? When is the last term the old course will be offered?
No, this course has not been offered at CNU previously.
What is the anticipated enrollment per offering for the next three years? 70
During which term will this course first be offered?
Fall 20 __ Spring 2006 __ Summer 20___

During which semesters will this course regularly be offered?
Spring 20XX __ Summer 20___ Fall 20XX
Print in the 2006-2007 (academic year) Undergraduate Catalog.
How will the course be staffed? 7.
For the Spring semester of 2006, the course will be taught by Julie
Young (an adjunct), who has taught the course several times for the
College of William and Mary, and by Prof. Ron Persky of CNU’s
Mathematics Department, who sat through this course at William and
Mary during the Spring semester of 2005. During subsequent semesters, MATH 121 will be taught by regular and adjunct faculty as needed.
8.
Does the course involve a particular classroom, special equipment, or costs beyond those usually associated with a course at CNU? If so, please explain.
In addition to the textbook, high altitude charts are needed by each student (cost approx. $15). The department needs to purchase handheld global positioning instruments (3 or 4 at approx. $150 each).
9. Is the course repeatable for additional credit? If so, is there a limit to the number of times the course can be repeated? (e.g., applied music courses)
10.
No, this course is not repeatable for credit.
If this course is for an Area of Inquiry a. Identify the Area of Inquiry _________________________________________ b. Demonstrate how your course will meet the objectives of this Area of Inquiry
This course was approved by:
(Liberal learning core courses must be reviewed by BOTH academic Deans.) Concur Do Not
| Concur**
Department(s): (1)
(2)
Brian Bradie, Chair, Mathematics
Date:
____9/1/2005__
__
Date: ________
X
College Curriculum
Committee: Date: ________
Dean: Date: ________
Dean: Date: ________
Undergraduate Curriculum
Committee: Date: ________
Changes to the Liberal Learning requirements must be reviewed by the Faculty Senate.

Faculty Senate President: Date: ________
Provost Date: ________
Distribution by Provost Office following approval:
Department Chair(s), UCC Chair, Deans, Registrar
** If “Do Not Concur” is checked, please attach a statement of explanation.

Course Materials: 1) Fear of Flying, by the Numbers, by George Rublein. 2) Aeronautical Charts – these are available at the book store. 3) A scientific calculator with sin, cos, tan, log and exp functions or a graphing calculator.
Instructional Methods: The course content will be taught primarily through a series of lectures with example problems to supplement the course textbook.
Homework: Complete the assigned problems immediately after the corresponding lecture. You may collaborate on homework. Although homework is not collected for grading, successful completion of each problem is essential to your success in the course. Homework will be reviewed in class.
Quizzes: During weeks when there is not a test, you can expect an open-note quiz. The lowest quiz score is dropped; if you miss a quiz, it is your lowest score. There are no make-up quizzes. Quizzes will be averaged to count as one 100 point test.
Tests: There will be 3 100-point tests taking the complete period and announced at least one week in advance. You have four week days to complete a make-up. Tests are closed notes and closed book.
However, you will be given a formula sheet to use.
GPS (Global Positioning System Assignment: The class will be divided into teams. Each team will
“check-out” a hand-held GPS which will be used to establish coordinates of and distance between two points. This will be worth 10 points.
Final Exam : A cumulative 200 point exam will be given. You will be given a formula sheet that you may use during the exam.
Attendance: Regular attendance is critical for your success in this course. I expect your presence at all lectures. Attendance will be taken.
To determine your grade:
Possible points: In class tests 300 points
Find your percentage:
Quiz Results 100 points
GPS 10 points
Final Exam
Total Possible
200 points
610 points your total points X 100
610
Grades will be assigned according to the following scale.
A
A-
B+
B
93-100%
90-92
87-89
83-86
B-
C+
C
C-
80-82
77-79
73-76
70-72
D+
D
D-
F
67-69
63-66
60-62
< 60%

1.
Trig Review (provided through supplemental material)

General introduction to triangles (define sides and angles, talk about what it means to refer to the angle opposite of a side, the sum of the angles equals 180

, define what a right triangle is, we will only be working
 in degrees)
Introduce trig ratio (make it clear that these are only used for right triangles, define the six ratios though put particular emphasis on sine, cosine and tangent)


Solve problems using sine, cosine and tangent
Introduce the Law of Cosines and solve numeric problems (i.e., non-application problems) - The Law of
Cosines is used in solving the Great Circle problems in Chapter 7.

Introduce the Law of Sines and solve numeric problems (i.e., non-application problems) – The Law of Sines is actually used in solving the indicated heading problems.

Vector addition/subtraction using the Parallelogram Method and solve numeric problems.

Introduce sin -1 , cos -1 and tan -1 and solve calculator problems.
2.
Introduction to the Wind and Velocity Vectors (provided through lecture notes)

A vector has direction and magnitude. (Real life examples of a vectors: wind and velocity)

Direction is identified using compass direction not the standard coordinate reference frame. Practice drawing vectors of different magnitudes and directions. Define head and tail of the vector.

Introduce the wind vector. (Direction is given in the direction that the wind is coming from . The tail shows

 where the wind is coming from. The head shows where the wind is blowing to.)
Air Traffic Control Language (ATC) referring to the wind vector.
Define direct headwind and direct tailwind. (in-line vector addition/subtraction)

Define velocity (solve right triangle problems involving velocity, i.e., the moving incline belt)

Introduce the aircraft velocity vector (Direction is given in the direction at the aircraft is flying to .)

Unit conversions between ft/sec and knots (nm/hr)
3.
General Flight Information (provided through lecture, and Private Pilot manual reference)

Basic principles of flight (Pilots take-off into the wind and land into the wind)

Runway layout, runway numbers, parallel runways

Explain using an airport diagram (symbols, nomenclature and downloading these from the web)
 Explain choosing the “ideal” runway based on wind conditions (choose runway number closest to ATC wind direction to minimize cross-wind)
 Since the “ideal” runway doesn’t usually exist the wind vector must be broken down into the headwind and crosswind components. (solve right triangle problems using runway, wind and aircraft)
4.
Ground Track/Ground Speed Problem (provided through lecture, though Chapter 1 eludes to this)

Define indicated airspeed (IAS), indicated heading (IH), ground speed (GS), ground track (GT)

Solve parallelogram problems (wind and aircraft vector addition and subtraction problem)
5.
Navigation (Chapter 3 and supplement with the Private Pilots manual)

Introduction to the high altitude charts (open them up and explain symbols)

Brief introduction to types of Navigation Systems (VOR, TACAN, VORTAC)

Basic principles of VOR (how it works)

Using VOR, OBI and ADF information to determine where you are (excellent example problems in the
Private Pilots Manual – this involves plotting radial directions and determining intersection)

Dead Reckoning Problems (using your velocity and heading to mathematically determine where you are).
This is NOT covered in the textbook but has very good math application (trig). Basic physics equations

Indicate Heading Problems (uses the Law Of Sines to determine what heading you should be on to overcome

the wind direction to get to your desired location)
6.
Center of Gravity (Luggage/System of Weight and Balances) – Chapter 5 in the textbook

Weight is a force. A system of forces can be replaced by one overall force acting the center of gravity. An aircraft has two balancing points (nosewheels and main undercarriage wheels). The center of gravity acts between these two points.
 Solve balancing problems (the “seesaw” problems) using the proportionality rule. (L
1
W
1
=L
2
W
2
) The balancing point is the center of gravity.

Determine center of gravity of an aircraft when luggage is added/removed.

Determine the change in center of gravity with multiple luggage changes.

Determine how much luggage must be added or removed, forward or aft to have the aircraft within the limitation of the manufacturer’s specified center of gravity.
7.
True North, Magnetic North and Runway Directions (Chapter 6 in the textbook)

True North is defined as the point where the longitude lines converge

Magnetic North is based on north being at 0

(also know as “compass north”) and differs from True North
(show migration of Magnetic north over time)

Define magnetic variation as the difference in degrees between magnetic north and true north

Runways are numbered based on magnetic north (rules for rounding)

Solve algebraic type equations to determine true direction, magnetic direction, rate of variation between true and magnetic, what will the magnetic direction be in future years, when will runway numbers need to be changed.
8.
Propulsion (Chapter 13 in the textbook)

Define four forces acting on an aircraft (lift, drag, thrust and gravity).


Learn to interpret charts giving coefficients of lift and drag.
Learn to interpret Standard Atmospheric Air chart to determine density at a given altitude.

Calculate density at a given altitude based on the decay equation (log equation)

Compare calculated density to density in Standard Atmospheric Air chart. (could determine % error)

Solve the lift equation to determine velocity based on known aircraft weight, wing surface area, altitude and angle of attack. Unit conversion between ft/sec to knots.

Solve the drag equation for required thrust.

Discuss difference between maximum thrust at sea level and maximum thrust at altitude. (ratio equation to solve) Maximum available thrust decreases with altitude.

Calculate percent throttle.

Determine resulting aircraft altitude if the pilot gives the aircraft too much throttle.
9.
The Shortest Path (Chapter 7 in the textbook)

Review orientation on the globe (lines of latitude, longitude, Equator, Prime Meridian, numbering)

Calculate distance traveled along a meridian (always the shortest distance between any location and a pole).
Each degree equals approximately 60 nautical miles (nm). (could calculate this exactly using ratios). Each minute equals approximately 1 nm.

Given the circumference of the Earth at the Equator, calculate the circumference at a specific latitude.
Calculate the radius of the Earth at specified latitude.

Calculate the distance traveled along a line of latitude (parallel). Use the charts to calculate the distance between real cities.

Define “Great Circles”. Meridians are great circles. Great circles at the largest circle that can be drawn on the Earth.


Calculate the distance along the great circle route for two points at the same latitude.
Calculate the distance along the great circle route for two points that have no common coordinates. (this is the
 most difficult calculation)
Use a computer program to compute the distance between 2 points (available on the web) and have students compare to there hand calculations.
10.
Falling Bodies/Parachuting (Chapter 8 in the textbook)


Galileo’s Formula for falling bodies

Define and calculate the average velocity of a falling object

Define and calculate the terminal velocity of a falling object (the object is neither accelerating or decelerating)

Solve parachute problems using terminal velocity.
11.
Global Positioning Systems (GPS)

Introduction to GPS (satellite system that gives you latitude, longitude and altitude)

Given two sets of data (latitude, longitude and altitude) conduct a coordinate transformation to determine the distance between 2 points.

Incorporate a “lab” assignment whereby students “check-out” hand-held GPS.