Loads, Structures, and
Mechanisms Design Project
Team C4
Jason Burr, Rebecca Foust, Samantha Johnson, Kiran
Patel, and Dennis Sanchez
Mission Objectives
• Structural Analysis:
– Crew Vehicle
– Lunar Landing Vehicle
• Crew Vehicle
– Earth Launch
•
•
•
•
Pressurization Loads
Docking Loads
Lunar Landing Loads
Earth EDL
• Landing Vehicle
– Basic design
• Inert mass: 2199 kg
• Propellant Mass (N2O4/MMH): 9914 kg
• Payload: 12,110 kg
– Landing Gear Analysis
• Touchdown velocity 3 m/s vertical, 1.5 m/s horizontal
Crew Capsule Selection
• Jason’s crew capsule was selected because it
has no external elements like radiators or
solar arrays
• It also has the highest mass margin, so we
have the most mass available for our
structural design
CREW VEHICLE
Pressurization Stresses in a Conical
Head
“Analogous to the maximum stresses in the
cylinder, there are maximum stresses in the
conical head…However, in contrast to the
cylinder, it is not possible to establish simple
expressions for the three stress indexes…”
Stresses in a Pressure Vessel With a Conical Head
For this reason we will model our cone as a
cylinder to find pressurization loads.
Pressurization Loads
• Cabin Pressure throughout mission = 59.77kPa
• Hoop stress on cabin = 1.067 MPa
• Longitudinal stress on cabin = 533 kPa
– Hoop stress will cause the structure to fail before longitudinal
stress can cause failure
Total Pressurization Stress = 1.067 MPa
Pressurization stress will occur at all times and is
added into all total stress values
Earth Launch
• Use Falcon Heavy to launch to LEO
– Can carry 53,000 kg to LEO
• Max Thrust = 11,200 kN
– Force at payload = 587 kN
• Stress from thrust = 538 kPa
• Random Vibrational Stress = 181 kPa
Temperature Variation in Atmosphere
Earth Launch
• Thermal loading occurs as payload travels
through different layers of the atmosphere.
– Max temperature difference = 80 K
• Thermal stress = 122.5 MPa
Total Stress at Launch = 124.3 MPa
Lunar Landing Loads
• Maximum G force that our capsule will
undergo is 1.125g
– This is determined from the maximum G force the
astronauts can undergo while standing
• Force from Lunar Landing = 186 kN
Total Lunar Stress = 1.24 MPa
International Docking System Standard
(IDSS)
Maximum force exerted during seal closure
Total Docking Stress = 1.16 MPa
Earth EDL - Heat Shielding
• AVCOAT ablative heat
shield
• Total Thermal Loading:
2597.9 MPa
• Used on Apollo crew
modules
• Will diffuse heat into
the air as opposed to
the structure
AVCOAT Shielding
• Will withstand total
thermal loading for EDL
• Epoxy resin in fiberglass
honeycomb matrix
• Above – before EDL
• Below – after EDL
Earth EDL
• Maximum G force that our capsule will undergo is
7.19g
• Force during EDL = 493 kN
• Thermal Stress = 122.5 MPa
– This is from fluctuations in the atmosphere. The heat
shield takes all of the thermal stress during EDL
Total Stress during EDL = 126 MPa
Safety Factors
NASA Technical Standard: STRUCTURAL DESIGN AND TEST FACTORS OF SAFETY
FOR SPACEFLIGHT HARDWARE
Need a safety factor of at least 1.25 to fall
under NASA standards
Highest Stress on Lander
• During EDL the stress reaches 126 MPa
• Based off of the yield stress of different
materials, aluminum will be the best material
for our structure
• With a safety factor of 1.25 the stress is still
well under the yield strength of aluminum,
386 MPa
Yield Stress (Mpa)
Yield Stress vs. Density
1000
900
800
700
600
500
400
300
200
100
0
Aluminum
Steel
Carbon
Titanium
0
2000
4000
6000
Density (kg/m^3)
8000
10000
Total Stresses
Case
Design Stress with SF (MPa)
Pressure
1.33
Launch
155.3
Lunar Land
1.55
Docking
1.45
Earth EDL
157.5
MOS
145.0%
MOS is based off of case of maximum load
LANDING VEHICLE
Lander Strut Configurations
• Three Distinct Design Possibilities
1. Rigid Structure
2. Spring and Damper Attenuation
3. One-Time Energy Dissipation
Lander Strut - Rigid Structure
• Advantages
– Simple analysis
– Re-usable
– Easy deployment
• Disadvantages
– Large loads
• “Crash” landing scenario
– Large magnitude accelerations
• Potentially fatal to astronauts
Lander Strut – Spring and Damper
• Advantages
– Re-usable
– Adjustable maximum
accelerations
• Disadvantages
– Complicated analysis
– Challenging deployment technique
• Springs act to move the struts to their equilibrium positions
Lander Strut – Energy Dissipation
• Advantages
– Relatively simple analysis
– Easy deployment
• Comparable to rigid strut
– Low accelerations
• Disadvantages
– One-time use
Design Choice – Energy Dissipation
• Honeycomb Energy Dissipation
– Wide range of strengths available
– Constant force during crushing
– Reliable energy dissipation
Honeycomb – Energy Dissipation
• Energy Conservation
– Kinetic Energy to Crushing Work
2
1
m
v
 Pcrush  Vcrush
– Lcrush is the total length of
2
Honeycomb required to
m a
Pcrush 
dissipate all of the
Acrush
energy from landing
Vcrush  Acrush  Lcrush
– Acceleration increases with
v 2  v x2  v y2
decreasing stroke length
Lcrush
v v

2 a
2
x
2
y
Honeycomb – Acceleration Limits
• Maximum Acceleration – 1.125g
– Limit imposed on elevators
– Provides low enough acceleration that astronauts
can remain standing in lunar descent
• Maximum Stroke Length – 1.75 m
– Limit to easily store struts in descent stage
– Assume all energy is dissipated in a single strut
(worst case)
• Results in minimum acceleration of 0.328g
Honeycomb – Strength Selection
• Various Honeycombs of
different strengths and
densities
• Performing the worst
case landing, we can
determine the
Honeycomb mass and
diameter to meet our
constraints
Strength Selection Continued
Optimum Honeycomb:
p=8.1 lb/ft3
Pcrush=750psi
Note: All designs from this point on use this Honeycomb
Honeycomb – Landing Scenarios
• Three likely scenarios to arise are:
1. Landing on a single strut
•
Landing on extremely uneven surfaces (rock)
2. Landing on a constant incline
•
Assumed smooth planar surface
3. Landing on a flat surface
•
Specific type of incline
Case 1: Uneven Landing
Landing Scenario – Single Strut
• Worst case – all energy dissipation is in a
single strut
• As before, the length of the crushed section is:
Lcrush

v x2  v y2

2 a
Case 2: Sloped Landing
Landing Scenario – Sloped Landing
• More complicated
• Total length required for energy dissipation
remains the same
• Maximum crushing occurs in the “leading
strut” of the lander, minimum in the “trailing”
one
Assumptions:
– Lander remains horizontal to the surface during descent
– Maximum landing slope is determined where the trailing
leg does not need to absorb any additional energy
Sloped Landing – First Pass
*Maximum crushing
occurs in the “leading
strut”. It never
reaches the
maximum crush
length because the
two struts between
the leading and
trailing one absorb
some of the energy.
Note: assume the lander must make contact with all four struts –
any other configuration is unstable! (This is the cause of the
curves ending)
Sloped Landing – Refined Pass
• Considering only the data points that maximize the slope at
any given acceleration, we can produce the following plot:
•Possible landing
slope is maximized
at the lowest
acceleration, 8.07ᵒ
and 0.328g’s,
respectively
Case 3: Zero-Slope Landing
Landing Scenario – Flat Surface
• Subset of the previous scenario where the
slope is equal to 0
• Energy is dissipated evenly between the four
struts – thus the crush length is as well
v x2  v y2
Lcrush,strut 
8 a
Summary of Landing Crush Lengths
The following table represents the worst crush lengths for
the three main landing scenarios:
Strut
Single Strut Landing
Max. Slope Landing (8.07ᵒ) Min. Slope Landing (0ᵒ)
Leading Strut 1.75 m
1.56 m
0.438 m
Mid-Strut
0m
0.970 m
0.438 m
Mid-Strut
0m
0.970 m
0.438 m
Trailing Strut
0m
0m
0.438 m
*Honeycomb Mass= 2.62 kg/strut
Where:
a = 0.378g’s
m = 16905 kg
Pcrush = 5.17 kPa
Lcrush = 1.75 m
Acrush = 0.011 m2
ρcrush = 130 kg/m3
Landing Strut Analysis
• Source of loads on the landing struts:
1. Earth launch loads
2. Lunar landing loads
3. Thermal loads
• Landing struts are 6 m long before crushing
– Minimum of 4.25 m after crushing
• Model the struts as hollow tubes
– Design varied to minimized margin of safety
• Neglect joint forces
Strut Analysis – Earth Launch
• Stress due to launch forces and moments
• Iteratively solved to minimized mass with:
ax = 8.5g
L=6m
earth
ay = 5.8g
az = 4.85g
ax 2  ay 2  A L


 az  L
g
I
A   r  r
2
out


2
in
4
I  4 rout
 rin4
Strut Analysis – Lunar Landing
• Stress due to landing force and moment
• Assumed the landing force is purely axial and
purely rotational
– Physically impossible to occur at once, but creates
an extreme-upper bound on loading
• Iteratively solved to minimized mass with:
a = 0.328g
L=6m
moon
A 
a
   L  1
 I 
g
Strut Analysis - Thermal
• Rapidly changing temperatures while during
Earth launch
– Greatest temperature variation ~80 K
• Iteratively solved to minimized mass with:
ΔT = 80 K
L=6m
thermal  E L
L    T L
Strut Analysis – Combined Loading
• Consider Earth and thermal loading combined,
as well as lunar landing and thermal loading
• All cases use factors of safety (SF) of 1.4
• Iteratively design with various radii to
minimize mass and the margin of safety
MoS 
 yield
1.4   earth   thermal 
 1 or MoS 
 yield
1.4   moon   thermal 
Depending on which is the limiting (lower) value
1
Strut Analysis – Analyzed Materials
•Consider the following metals for our struts:
Material
E (GPa)
p (g/cm3)
α (μm/m*K)
σ (MPa)
Aluminum 2024
72
2.78
22.2
324
Aluminum 7075
71
2.78
22.2
490
Titanium Ti-6Al-4V
110
4.46
8.6
869
Steel AISI4340
200
7.8
13
1483
Steel 300M
200
7.8
13
1520
•These materials are used with the preceding
formulas to find the optimum strut design that
1. Minimizes strut mass
2. Keeps an external strut diameter below 20 cm
3. Has a MoS = 0
Strut Analysis – Optimization
Titanium appears to be the best metal, but…
Strut Analysis – Optimization Cont.
When we consider the
constraint of less than
20 cm (external)
diameter, we see that
Steel 300M at this point
is 68.24 kg/strut,
whereas titanium at an
external diameter of 20
cm is 72.78 kg/strut
Strut Analysis – Summary
Landing Strut
• Total length
• Outer radius
• Inner radius
• Material
• MoS
• Strut Mass
6m
10 cm
9.5 cm
Steel 300M
0
68.24 kg/strut
Honeycomb
• Max crush length
• Min crush length
• Honeycomb Mass
1.75 m
0m
2.62 kg/strut
Strut Storage and Articulation
• The landing struts are divided
into three 2-meter segments:
two hollow tubes and one
honeycomb piston
• During launch, the three
segments are stored side by
side as shown here
• Rotary actuators at the joints
align the segments and lock
them into place for lunar
descent
Actuators
• The landing struts will be stored folded into 3
sections during launch
• Before lunar descent, the landing struts will
deploy using the space-rated rotary actuator
shown below
• This actuator was chosen because it can produce
high torque at low speeds. Lower speeds will
reduce vibrational loads on the spacecraft
Supplemental Ladder
• The honeycomb piston is designed for worst-case
scenario loading, so a best-case load would result
in significantly less compression
• Because of this, a supplemental ladder is
attached to the end of the second segment on
the ladder strut
• The ladder will deploy in all scenarios, but will
only be critical for light load cases where the
astronauts would otherwise be unable to
perform EVAs
Footpad Design
• The footpad needs to be large enough to
remain stable across small variations in
surface depth
• We chose a radius of 0.5 m because this
covers a total area of 0.7854 m2, which should
be sufficient to ameliorate the effects of an
undesirable landing site
• The footpads are mounted with a ball joint to
allow them to rotate as needed for various
surface slopes
PROPULSION MODULE
Engine Mount Structure
• We are using a truss
design to mount the
engine to the module
• Needs to handle a
maximum thrust load of
15568 N from engine
• The design is composed
of 8 criss-crossing
trusses which distribute
the weight evenly
amongst them
Engine
Top View of Truss Engine
Mount
Side View of Truss Engine Mount
Truss Mount
Engine
Truss Analysis
In the analysis the truss was scaled by .2 and the force
applied at each joint was (1/8)(Maximum Thrust)/10 or
195 N
Truss Design
• Each truss member is a hollow tube composed of
aluminum and carries a maximum load of about
4070 N
• The radius of each member is 5 cm
• The thickness of each member is chosen to be 1
cm
• Maximum Stress = 1.43 MPa
– Well under the yield stress of aluminum, 386 MPa
Truss Member Stress vs. Thickness
14
Stress (Mpa)
12
10
8
6
Truss
4
2
0
0
0.01
0.02
0.03
Thickness (m)
0.04
0.05
Propulsion Module Requirements
• The full propulsion module is a two meter
long cylinder with a diameter of 3.57 m
– Four 60x30 cm sections are cut from the overall
cylinder to store the landing struts
• Required propellant volumes:
Monomethyl Hydrazine (MMH) Nitrogen Tetroxide (N2O4):
4.333 m3
4.208 m3
• This volume also holds the engine and engine
mount, which occupy a total volume of 0.713
m3
Tank Sizing
• The tanks were cylindrical with ellipsoidal end
caps. The height of the ellipse was modeled as
0.25*radius of cylinder
• Using this equation and the volumes stated
earlier produces the following radii, which fit
well within our design limits:
Monomethyl Hydrazine (MMH) Nitrogen Tetroxide (N2O4):
0.4227 m
0.4165 m
Mass Totals
Component
Crew Systems
Power, Propulsion, Thermal
Aluminum Shell
Propellant
Propulsion Inert Mass
Landing Struts
Total Mass
Mass (Kg)
1500
4795
1687
9914
2199
283.4
20,378
Final Design
References
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Cameron, John R.; James G. Skofronick & Roderick M. Grant.Physics of the Body. Second Edition. Madison, WI:
Medical Physics Publishing, 1999: 182.
http://www.gaudisite.nl/ElevatorPhysicalModelSlides.pdf
http://heroicrelics.org/info/lm/landing-gear-strut-honeycomb.html
http://www.plascore.com/pdf/Plascore_CrushLite.pdf
https://webspace.utexas.edu/jkm343/mikulak/compressive%20and%20lamination%20strenght%20of%20honey
comb%20%20panels%20from%20ASTM.pdf
http://www.sciencedirect.com/science/article/pii/S0020768305003781
http://www.youtube.com/watch?v=q4GAomYWb2M
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720018253_1972018253.pdf
http://www.wolframalpha.com/input/?i=volume+of+a+torus
http://airandspace.si.edu/collections/artifact.cfm?id=A19721346000
http://www.lr.tudelft.nl/en/organisation/departments-and-chairs/space-engineering/space-systemsengineering/expertise-areas/space-propulsion/design-of-elements/rocket-propellants/liquids/
http://dmseg5.cwru.edu/classes/emse201/overheads/Thermal.pdf
http://www.faa.gov/other_visit/aviation_industry/designees_delegations/designee_types/ame/media/Section2
0III.4.1.7%20Returning%20from%20Space.pdf
http://www.spaceaholic.com/apollo_cm_earth_entry.pdf
http://www.dummies.com/how-to/content/mechanics-of-materials-for-dummies-cheat-sheet.html
http://www.internationaldockingstandard.com/download/IDSS_IDD_RevA_Final_051311.pdf
standards.nasa.gov/documents/viewdoc/3315591/3315591
standards.nasa.gov/documents/viewdoc/3314903/3314903