10 01-01 team cheese-final report_lunar landing gear

Lunar Landing Gear
MECH 460 | QUEEN’S UNIVERSITY, KINGSTON ONTARIO, CANADA

Group 27 | Team Cheese

Nabeil Alazzam – 6na3@queensu.ca
Ben Banks – 5bb7@queensu.ca
James Burke – 7jb25@queensu.ca
Ian Cameron – 6dic@queensu.ca

As part of a student project with Queen’s University, this report contains a documented approach to the
conceptual design of a system to dampen the shock impulse of an unmanned vehicle landing on the
surface of the moon. The project has been adapted from an open task provided by Team FREDNET, a
registered competitor for the Google Lunar X Prize.

http://teamcheese.com
12/7/2009

Lunar Landing Gear

“Ask not what open source can do for you,

but what you can do for open source.”

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MECH 460 – Fall 2009

Special Thanks

Dr. Ronald Anderson

Ryan Weed

Chau Ngai

Sean Casey

Team FREDNET

Dr. Kevin Deluzio

Professor Alan Ableson

Andy Bryson

Eric Benson

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Lunar Landing Gear

EXECUTIVE SUMMARY
The Google Lunar X PRIZE is a thirty million dollar international competition to safely land a robot on
the surface of the Moon, which will travel five hundred meters over the lunar surface and send images
and data back to Earth.

Team Cheese is a group of four mechanical engineering undergraduates at Queen’s University. They
have worked with Team FREDNET, which is a registered official team competing for the Google Lunar X
Prize, over the semester. Team FREDNET is a special competitor as it consists of an international group
of developers, engineers, scientists and other members dedicated to the open source philosophy.

Previous missions to the moon and to mars as well as various energy absorption systems were
investigated which helped to design and gain knowledge on landing mechanisms. Design constraints
such as weight restrictions, absorption methods, operation, reliability and cost were identified. These
constraints helped each analysis on force absorption, strut design, and foot pad design.

There are two design elements that TC analyzed; the energy absorption system and the structural
support system.

The energy absorption system chosen incorporated plastically deforming material. The energy
absorption system would be contained in the secondary struts and these struts would be able to house
crush cartridges .12 m long with cross-sectional diameters of .01905 m. All the acceleration values fall
under the 10 G acceleration constraint, while the energy absorbing structure reduces the penetration
into regolith and the acceleration beyond the results of obtained for a rigid structure if touchdown
occurs on pure regolith, with properties similar to those suggested by data from the Apollo missions.

More accurate mission constraints would have to be put forward for more accurate accelerations
and force values. The error propagated though with unrealistic amounts due to suggested uncertainties
of up to 30%. As design work progresses, the theoretical modeling of the touchdown scenario will
improve. These are all issues that can be investigated during prototyping and testing.

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Through the use of Matlab optimization, along with graphical analysis, key relationships between
design variables were examined. Key relationships were evaluated to determine dimensions. The final
inside diameter of the primary strut was found to be 3cm, and the final outside diameter of the primary
strut was found to be 3.25cm. The angle between the primary strut and the vertical (theta) was found to
be 20o, and the angle between the secondary strut and the primary strut (alpha) was found to be 50O.
The length between the primary strut interface to the lunar module, and the secondary strut interface
to the primary strut (a) was found to be 0.4mm. The inside diameter of the secondary strut was found to
be 1.905cm and the outside diameter was found to be 2.35cm.

The structural system also included foot pads for each strut. They needed to provide stability and
support for each leg while making contact. The foot pads contact area helped reduce the force
transferred to the legs and minimized the penetration into the regolith. These two ensured the
acceleration felt by the landing module was minimal.

The physical areas analyzed included the overall shape including the joint, the area, and the
thickness of the pads. The overall shape incorporated a cup shaped pad with a ball joint welded to the
bottom. To reduce weight, both the ball joint and pad were designed to be made of titanium. The area
was determined to be 0.071m2 which resulted in a penetration of 8cm and a force of 14KN felt by the
landing module. An acceleration of 7 G’s would be experienced by the landing module which was much
less than the required 10G Team FREDNET restriction. Using mechanics of materials knowledge, and
applying methods of superposition, the thickness of each pad was found to be 1.76cm. This was found
to be the maximum the thickness had to be.

With the help of Team FREDNET, Professor Anderson, other faculty members, strong design analysis
processes, and available resources, Team Cheese was able to design a preliminary conceptual lunar
landing gear system. The design incorporated key aspects of energy absorption, structural design, and
foot pad design. A landing gear system was developed to the design constraints proposed by Team
FREDNET. Further analysis and prototyping is needed to finalize the design, make it ready for
manufacturing, and finally incorporate it into Team FREDNET’s final Google X Prize landing module
design.

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Table of Contents
EXECUTIVE SUMMARY................................................................................................................................. iii

LIST OF FIGURES......................................................................................................................................... ix

1 Introduction .................................................................................................................................. 1

1.1 Google Lunar X Prize ................................................................................................................. 1

1.2 Team FREDNET .......................................................................................................................... 1

1.3 Team Cheese ............................................................................................................................. 1

2 Project Description........................................................................................................................ 2

2.1 Constraints ................................................................................................................................ 2

2.1.1 Successful Design .............................................................................................................. 2

2.2 Scope ......................................................................................................................................... 4

3 Research ........................................................................................................................................ 4

3.1 Background ............................................................................................................................... 4

3.2 Energy Absorption Techniques ................................................................................................. 4

3.3 Past Missions............................................................................................................................. 8

3.3.1 Apollo ................................................................................................................................ 8

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3.3.2 Surveyor .......................................................................................................................... 13

3.3.3 Mars ................................................................................................................................ 14

3.4 Lunar Conditions ..................................................................................................................... 15

4 Design.......................................................................................................................................... 16

4.1 Evaluative criteria ................................................................................................................... 16

4.2 Design Methodology ............................................................................................................... 18

4.2.1 Structural System Design Candidates ............................................................................. 19

4.2.2 Energy absorption Design Candidates ............................................................................ 23

4.3 Design Selection ...................................................................................................................... 26

4.3.1 Structural System ............................................................................................................ 26

4.3.2 Energy Absorption System .............................................................................................. 27

4.3.3 Strengths ......................................................................................................................... 27

4.3.4 Weaknesses..................................................................................................................... 28

4.3.5 Combined Design ............................................................................................................ 28

5 Design Refinement ...................................................................................................................... 28

5.1 Impact design .......................................................................................................................... 29

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5.2 Lever Design ............................................................................................................................ 30

6 Design Analysis............................................................................................................................ 32

6.1 Structural System .................................................................................................................... 32

6.1.1 Optimization design and setup ....................................................................................... 33

6.1.2 Optimization analysis ...................................................................................................... 36

6.1.3 Determining optimal wall thickness and diameters ....................................................... 38

6.1.4 Determining optimal position for secondary strut interface .......................................... 41

6.1.5 Optimization Program ..................................................................................................... 45

6.2 Energy Absorption................................................................................................................... 46

6.2.1 System Energy Modeling................................................................................................. 49

6.3 Landing Pad Design ................................................................................................................. 55

6.3.1 Landing Pad Shape .......................................................................................................... 55

6.3.2 Area of landing pads ....................................................................................................... 56

6.3.3 Thickness of Pads ............................................................................................................ 56

6.4 Ball Joint .................................................................................................................................. 58

6.5 Pad Connection ....................................................................................................................... 60

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6.5.1 Other Considerations ...................................................................................................... 60

6.6 Thermal Considerations .......................................................................................................... 61

7 Design Results ............................................................................................................................. 63

8 Prototyping ................................................................................................................................. 65

8.1 Materials ................................................................................................................................. 65

8.2 Manufacturing......................................................................................................................... 66

8.3 Cost ......................................................................................................................................... 66

9 Recommendations ...................................................................................................................... 66

10 Conclusion ................................................................................................................................... 67

APPENDIX A ............................................................................................................................................. 74

APPENDIX B ............................................................................................................................................. 75

APPENDIX C ............................................................................................................................................. 84

APPENDIX D ............................................................................................................................................. 86

APPENDIX E ............................................................................................................................................. 89

APPENDIX F ............................................................................................................................................. 91

APPENDIX G ............................................................................................................................................. 96

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LIST OF FIGURES
Figure 1 - Opened extrusion profile with APM aluminum foam–polymer hybrid filling(12) ................. 6

Figure 2 - Open cell structure with regular geometry (13) .................................................................... 6

Figure 3: Piston connected to suspension strut pushes the hydraulic fluid which compresses the

Nitrogen. ....................................................................................................................................................... 7

Figure 4: Stowed and deployed positions of landing gear for the Apollo 11 landing module(15) ........ 9

Figure 5: Detailed design of landing gear for Apollo 11 lunar landing module(15) ............................. 10

Figure 6: Landing-gear primary strut honeycomb structure.(15) ........................................................ 11

Figure 7 - Landing-gear secondary strut honeycomb structure.(15) ................................................... 11

Figure 8 - Secondary Strut depicting compression and tension stroke(16) ......................................... 12

Figure 9 - Photograph of Aluminum honeycomb shock-absorbing cartridges from full-scale landing-

gear struts before and after impact crush(16) ........................................................................................... 12

Figure 10 - Surveyor 1 Landing Gear Dimensions (18) ......................................................................... 13

Figure 11 - Operation of Surveyor Landing Gear a) During Descent b) Initial Contact and Compressed

Shock Absorber c) Rest Position (18) .......................................................................................................... 14

Figure 12 – Early Structural Lunar Landing Module Concept (3) ......................................................... 18

Figure 13 –QFD Chart for Structural Strut Systems .............................................................................. 23

Figure 14 - QFD Chart for Energy absorption Systems ........................................................................ 26

Figure 15 - Impact Design ..................................................................................................................... 29

Figure 16 - High stress location, impact design .................................................................................... 30

Figure 17 - Lever design........................................................................................................................ 31

Figure 18 - Variability in pod leg position during touchdown .............................................................. 32

Figure 19: Free body diagram for primary strut ................................................................................... 34

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Figure 20: Normal Stress vs. Theta for Primary Strut ........................................................................... 37

Figure 21: Shear Stress vs. Theta for Primary Strut .............................................................................. 38

Figure 22: Outside Diameter vs. Theta for Primary Strut ..................................................................... 39

Figure 23: Thickness vs. theta for primary strut................................................................................... 40

Figure 24: Weight vs. Theta for varying inside diameters .................................................................... 41

Figure 25: Weight vs. theta for varying lengths of a. ........................................................................... 42

Figure 26: Wall thickness of secondary struts for varying lengths of a. ............................................... 43

Figure 27: Plot of 3D Secondary strut length vs. theta ........................................................................ 44

Figure 28: Plot of alpha vs. theta.......................................................................................................... 45

Figure 29 - Column of regolith per strut pad modeled with a spring stiffness .................................... 49

Figure 30 - Complete plastic deformation and densification of crush cartridge ................................. 51

Figure 31 - Simplified cross sectional view of half a lunar pad ............................................................ 57

Figure 32 - Cross-sectional area of foot pad ........................................................................................ 58

Figure 33 - steering link ball joint (Ningbo Pair Industrial Co.)............................................................. 59

Figure 34 - Final landing pad design ..................................................................................................... 61

Figure 35 – Conceptual thermally isolated spherical joint ................................................................... 62

Figure 36 - Three dimensional rendering of entire lunar landing gear assembly (note: dimensions are

not to scale, this rendering is only for an approximate visual representation) ......................................... 63

Figure 37 – Three dimensional rendering of entire landing assembly (note: dimensions are not to

scale, this rendering is only for an approximate visual representation) .................................................... 65

Figure 38 - Rigid Landing Structure Energy Analysis ............................................................................ 84

Figure 39 - Energy Analysis with an Absorbing Structure .................................................................... 85

Figure 40 - Mass conservation of crush cartridge ................................................................................ 85

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Lunar Landing Gear

Figure 41 - Simplified Foot Pad............................................................................................................. 86

Figure 42 - Cross sectional Area of Foot pad ........................................................................................ 86

Figure 43 - Simplified model of landing mechanism ............................................................................ 91

Figure 44 - Spring system modeled at impact ...................................................................................... 92

Figure 45 - Inclined crush spring model ............................................................................................... 93

Figure 46 - Vertical crush equivalent spring system............................................................................. 93

Figure 47 - Combined vertical spring system ....................................................................................... 94

Figure 48 - Equivalent spring system.................................................................................................... 94

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LIST OF TABLES
Table 1 - Lunar Regolith Properties (20)............................................................................................... 15

Table 2 – Evaluative Design Criteria ..................................................................................................... 16

Table 3 – Advantages and disadvantages of vertical static strut structural system design ................. 20

Table 4 - Advantages and disadvantages of vertical dynamic strut structural system design ............. 20

Table 5 - Advantages and disadvantages of angled static strut structural system design ................... 21

Table 6 - Advantages and disadvantages of angled dynamic strut structural system design .............. 22

Table 7 – Advantages and disadvantages of hydro-pneumatic suspension system ............................ 23

Table 8 - Advantages and disadvantages of plastic deformation structure system ............................ 24

Table 9 - Advantages and disadvantages of shock absorber system ................................................... 25

Table 10 - Advantages and disadvantages of hydro-pneumatic suspension in combination with

plastic deformation structure system ......................................................................................................... 25

Table 11 - Landing Characteristics of Lunar Module ............................................................................ 53

Table 12 - Effect of mass and free fall height error for a system with energy absorption .................. 53

Table 13 - Summary of structural dimensions ..................................................................................... 64

Table 14 - Operation Variables ............................................................................................................. 74

Table 15 - Design Variables .................................................................................................................. 74

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Lunar Landing Gear

1 Introduction
MECH 460 is one of three possible capstone project courses for Mechanical and Materials
Engineering students at Queen’s University. The course aims to prepare graduating students for the
engineering workforce by working on real-world team design problems as proposed by industry based
clients. Students will participate as part of an engineering design team to complete a significant
engineering design project while working in a professional manner within the constraints of limited time
and budgets. (1)

1.1 Google Lunar X Prize
The Google Lunar X PRIZE (GLXP) is a thirty million dollar international competition to safely land a
robot on the surface of the Moon, which will travel five hundred meters over the lunar surface and send
images and data back to the Earth. (2)

1.2 Team FREDNET
Team FREDNET (TF(X)) is a registered official team competing for (GLXP). TF(X) is a special
competitor as it consists of an international group of developers, engineers, scientists and other
members dedicated to the open source philosophy. Their goal, besides winning the GLXP, is to bring the
same successful approach used in developing major software systems to bear on the problems
associated with space exploration and research. (3)

1.3 Team Cheese
Team Cheese (TC) is a group of four mechanical engineering undergraduates at Queen’s University
taking part in the MECH 460 Project Course. TC is cooperating with TF(X)’s open effort to design and
build the systems necessary to land a functional rover on the moon. TC has adapted the task of
designing a conceptual landing system that will absorb the impact loading on an unmanned lunar
landing craft during touchdown.

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2 Project Description
The landing gear is a crucial structural component of a lunar landing craft. The system has to absorb
the kinetic energy associated with touchdown in a controlled manner and support the static load of the
landing module in an upright position allowing the deployment of a rover. TF(X) is seeking conceptual
designs to address these issues. (4) TC is pursuing the design of a structural system that will absorb the
energy associated with landing and provide the correct orientation to the landing craft on the lunar
surface.

2.1 Constraints
The nature of the design task will impart constraints on a proposed system. A conceptual design will
have to account for:

• The absorption of an expected impact force and the support and upright orientation of the
landing module within an appropriate safety factor.
• Forces to be reacted against post-landing (i.e. rover deployment, robotic component
operation).
• Appropriate and safe stowing into a launch payload.
• Reliable activation or deployment while in lunar orbit prior to landing if stowing is only
possible with the system in an inactive or stowed configuration.
• Appropriate operation of the system while not conflicting with the function of other landing
module subsystems.
• The expected horizontal and vertical motion and orientation of the landing module during
touchdown.
• Conditions and terrain of the lunar surface.

2.1.1 Successful Design
Considering the constraints, assumptions were implemented to direct the successful design of a
landing system.

1. The static launch payload is cylindrical in geometry (2 meter diameter and 3.3 meter in
height).

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• The landing module will occupy 70% to 75% of this volume.
2. The mass is assumed to be 190kg ± 30%.
• The landing module center of mass will be assumed to be the center of its simplified
volume.
3. The impact force developed must be less than a 10G static load.
• The landing structure must withstand and limit the force of landing.
4. The thrust engine shuts down 1 m above lunar surface.
• The thrust engine will only reduce the impact velocity, it will not remove it. The
landing gear operates in close proximity to the thrust engine. The material will have
to resist large temperature variations.
5. Level support of the landing module with some degree of stability on a flat surface or an
incline is ideal.
• The surface area of the landing module in contact with lunar regolith must spread
the weight out appropriately and prevent slip to a reasonable degree. Uneven
impact may affect the levelness of the final orientation.
6. A clearance of 0.3m ± 30% is required.
• Clearance is needed to restrict contact of the landing module and fuel systems with
the lunar surface. It might be beneficial for rover deployment while mitigating the
potential for minor surface protrusions to affect mission performance.
7. The readiness of the landing system is required by the time the landing module is in lunar
orbit.
• Proper remote or programmed deployment and activation of the landing system
while in lunar orbit is essential if the system involves an inactive or stowed
configuration.

As a consequence of the mission specifications, many components of the landing system can be
sacrificial; the landing module comes to its final rest position after touchdown. Successful performance
of the landing system is geared towards rover deployment and landing an undamaged base station in a
position of rest.

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2.2 Scope
The scope of this project consists of conceiving and justifying a lunar module landing system that will
function within the constraints described. Aspects of the landing gear such as storage, deployment and
the process and mechanics of the absorption of forces created upon impact on the moon will be
analyzed.

3 Research
TC has had assistance from the helpful library staff at Queen’s University. Initial research snowballed
off of the prior work of the TF(X) community documented by Anders Feders in the TF(X) Wiki. TC has
studied the background components or systems of proposed landing mechanisms and several energy
absorption techniques to complement work performed in previous missions. Lunar conditions were
investigated to determine their effect on the conceptual design.

3.1 Background
For the proposed SELENE project, the Japanese Aerospace Exploration Agency will be landing
unmanned probes onto the lunar surface. Simulation of the landing of a 520 kg module with four legs
from a freefall height (engine shutdown) of 3 m at lunar gravity predicted a peak acceleration of 293.3
m/s2 for a maximum impact force of 38.3 kN acting on each leg.(5)

Research into an optimal pod leg configuration suggested that a three-legged structure only
required a slightly larger landing gear diameter than a four-legged structure for a given probability of
stable landing. (6) The smaller leg configuration would better accommodate the mass constraint of the
design.

3.2 Energy Absorption Techniques
An energy absorption system can dissipate the kinetic energy of impact load by employing a damped
elastic structure (i.e. a piston structure), a controlled fluid damper (i.e. an airbag or restricted fluid flow
chamber), electromagnetic magnetic resistance on moving components (i.e. resistive magnetic flux) or
the property of certain materials or structures to plastically deform (i.e. crushing certain materials or
buckling structural components). A combination of several of these techniques may synergize the

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energy absorption capabilities of a whole system. A benefit within the scope of the mission is that the
energy absorption system may be sacrificial; the landing module will not move after arriving at its final
resting location.

The structural benefit of aluminum honeycomb or foam is observed as a reduction in density with
restricted loss of energy absorption capabilities compared to a solid structural member. An increase in
energy absorption is observed after filling a structural element with aluminum foam.(7) The yield stress
of aluminum honeycomb is dependent on the direction of loading. (8) (9) Under dynamic compressive
loading, the escape of trapped air within the structure is suspected for strain-rate dependence. (9) In
design applications, the direction of compression may be controlled within the design. A combined
orientation of honeycomb cells may benefit the overall structure and control the manner of material
buckling.

Concerning the axial crushing of honeycomb material structures, a dynamic (as opposed to quasi-
static) loading increases the crash strength or force transmission by up to 74%. The preservation of
energy absorption capabilities is achieved by using a smaller cell volume. (10) Alternative materials may
provide greater strength also.

Structural foam can be used to remove energy from a system. Work can be done on the structural
foam in terms of the crush force and the distance by which the structure plastically deforms.(11)

Material bonding to the containing structure upon injection is a design concern regarding the use of
structurally internal aluminum foam if it is designed to fail. Closed cell polymer composite aluminum
foam (Figure 1) will not suffer the same shortcoming and will also fill whatever the shape the cells are
poured into while providing high yield strength. (12)

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Figure 1 - Opened extrusion profile with APM aluminum foam–polymer hybrid filling(12)

Open cell structures (Figure 2) employ manufactured imparted geometry to reduce the mass of the
structure and increase the crushability of the substance. The deformation of these structures exhibit
brittle behaviours and the relative stiffness of the structure is dependent on its size. (13)

Figure 2 - Open cell structure with regular geometry (13)

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A proprietary hydro-pneumatic damping system uses nitrogen as a resistive medium in a suspension
system. The nitrogen is approximately six times more flexible than conventional steel, making it very
elastic.

A pump pressurizes the hydraulic fluid. This work can also be used in another system. Since the
hydraulic fluid is pressurized by the car, this system features ride height control. The pressure sinks in
this system consist of one sphere per wheel. These spheres are hollow metal balls that have a hole on
the bottom, with a rubber membrane (usually a flexible desmopan) filling the opening. The top of the
sphere is filled with pressurized nitrogen (up to 75 bar), while the bottom of the sphere is connected to
the hydraulic fluid system of the car (up to 180 bar). This can be seen in Figure 3 below.

Figure 3: Piston connected to suspension strut pushes the hydraulic fluid which compresses the Nitrogen.

The suspension system works by have a rod from the wheel push the hydraulic fluid into the sphere
compressing the nitrogen. The hydraulic fluid flows through a two way leaf valve in and out of the
sphere dampening the system. This type of dampening system is one of the most efficient and simplest.
The hydraulic fluid that is used by Citroën is a mineral oil, similar to automatic transmission fluid.

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Mineral oil is used because it is not hygroscopic, which means it does not absorb water. This prevents
bubbles forming in the hydraulic fluid and corrosion occurring.

Advantages:

• It is a progressive spring-rate suspension since the more it is compressed, the harder it becomes.
As the piston is pushed in, as the volume of the nitrogen halves, the pressure doubles. This
relationship produces a suspension system with an infinite number of elastic rates. The further it is
pushed in the harder it is to further go in. The main benefit is the fact that you can have a very
soft suspension at the beginning yet not bottom out like a soft steel suspension.
• This system adjusts to the weight of the car as passengers load and unload. The hydraulic fluid
can be pressurized and depressurized respectively as the weight increases and decreases. This
allows the car to maintain a constant ride height.
• Ride height is manually adjustable
• Compact suspension design.
• Maintenance is relatively easy, as it doesn't require any specific tools.

Disadvantages:

• Specifically trained mechanic may be required to service certain parts increasing cost of owning
this suspension system.
• Expensive to replace if poorly maintained
• If failure occurs, ride height will drop and the braking power will be reduced. It takes a large failure
before braking power is reduced however.

3.3 Past Missions
There have been thirteen successful missions to the moon involving the landing of manned and
unmanned crafts. (14) The landing mechanism of the Mars Rover landings was also investigated.

3.3.1 Apollo
The NASA Apollo 11 mission was the first manned mission to the lunar surface. The design of the
lunar module initially started out as a static five-legged, inverted-tripod-type landing gear attached to a

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Lunar Landing Gear

cylindrical descent stage.(15) A six-legged landing gear configuration was found to have a lower stability
to weight ratio then the five-legged design, and the four-legged configuration was found to require too
large a diameter for deployment and retraction for stowage. The design of the module was later
changed to a cruciform-type structure and with this change the landing gear was changed to a four
legged structure. (15)The original design of an inverted-tripod-type landing gear was reviewed at this
point and it was found that the use of a cantilever type design provided a smaller overall diameter of the
landing module and due to the availability of stowage space on the rocket this design was chosen.
(15)The final design can be seen below in Figure 4 and Figure 6Figure 5. Figure 4 shows a detailed design
of the stowed and deployed positions of the Apollo 11 landing gear. The truss design can be seen as the
secondary struts are connected approximately half way up the primary strut. In the inverted-tripod
design the secondary struts were connected to the foot of the primary strut in the landing pad area.

Figure 4: Stowed and deployed positions of landing gear for the Apollo 11 landing module(15)

Figure 5 shows a detailed design of the Apollo 11 landing gear components. The secondary struts
can be seen along with a detailed view of the supporting deployment truss designed to provide
structural support while allowing for stowing the landing gear before launch.(15)

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Figure 5: Detailed design of landing gear for Apollo 11 lunar landing module(15)

The energy absorption system for the Apollo 11 Lunar Lander was a collapsible aluminum
honeycomb structure contained in the primary and secondary struts. The design consisted of an inner
cylinder that fitted into an upper outer cylinder to provide compression stroking at touchdown. (15)The
inner cylinder of the main strut was connected the footpad through the use of a ball-joint fitting. Figure
6 shows the cartridge interface for the primary struts.

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Lunar Landing Gear

Figure 6: Landing-gear primary strut honeycomb structure.(15)

For the secondary struts the same method was chosen however the inner cylinder was attached to
the primary strut and the outer cylinder was attached to the deployment truss through the use of a ball-
joint fitting.(15) Figure 7 shows the cartridge interface for the secondary struts.

Figure 7 - Landing-gear secondary strut honeycomb structure.(15)

In testing, non-vertical components of impact force (due to geometric orientation) on the secondary
struts were addressed in compression and tension stroke damping. This configuration can be seen in
Figure 8. (16)

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Figure 8 - Secondary Strut depicting compression and tension stroke(16)

Figure 9 shows images of the aluminum honeycomb shock-absorbing cartridges from the Apollo 11
Lander before and after impact crush testing.

Figure 9 - Photograph of Aluminum honeycomb shock-absorbing cartridges from full-scale landing-gear struts before
and after impact crush(16)

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3.3.2 Surveyor
The surveyor program consisted of seven unmanned lunar landing spacecraft of similar design that
were sent to the moon. Five of the seven spacecraft successfully landed on the lunar surface. (17)

Surveyor 1 landed with a vertical velocity of about 3.6 m/s and a lateral velocity of about 0.3 m/s.
Figure 10 shows dimensions and structure of the landing gear used for the Surveyor spacecraft. Figure
11 depicts the operation of the landing gear. A portion of the impact load was absorbed by crushable
aluminum foam attached on the underside of the landing module and on the footpads of the three pod
legs. The remainder of the landing energy was damped by an elastic shock absorber (11 cm stroke) on
each of three primary pod legs. The spacecraft frame was designed to come to a rest position parallel to
the lunar surface. (18)

Figure 10 - Surveyor 1 Landing Gear Dimensions (18)

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Figure 11 - Operation of Surveyor Landing Gear a) During Descent b) Initial Contact and Compressed Shock Absorber c)
Rest Position (18)

Strain gauges on the shock absorbers indicated the loads of impact and the bounce that some of the
Surveyor crafts experienced. Surveyor 1 rebounded clear of the surface for approximately 500 meters
after initial touchdown before coming to rest. This corresponds to a bounce height of approximately 6
cm. (18)

Surveyor 1 had a mass of 292 kg. The static load needed to support the spacecraft on its three pads
was approximately 3kPa. The initial impact loading of landing acting on each pod leg was about 2.2 kN.
The second impact generated loads of approximately one-quarter initial loads. The footpads exerted
approximately 40 to 70 kPa on the lunar surface during landing. (18)

As a shock absorber was used, the landing module had an oscillation before coming to rest after the
second touchdown.(18)

3.3.3 Mars
As of 2008, there have been fifteen missions involving landing on mars. Of these fifteen, five have
been successful. Device malfunctions have resulted in many of these failures. Three of the last five mars

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missions have used an air bag absorption system for landing. One specific Lander was researched, called
the Mars Pathfinder. [1]

The mars pathfinder relied on air bags to absorb the force of impact on the surface of mars. This
enabled the payload to bounce off the surface without harming the inner components. The air bag
system was made up of 24 inner connected spheres that inflated within half a second right before
impact. The spheres made up a pyramid shape 17 feet tall and 17 feet in diameter, with the payload at
the center of the pyramid. This landing gear system was able to absorb a 20-27 G’s of acceleration and
was able to accomplish this at temperatures as low as -80oC. [3]

The main purpose of this type of landing gear was to eliminate the contamination of the soil and
rock samples that were picked up. It also was a great way of absorbing impact. This sort of design was
able to take much more acceleration compared to other designs used. The Mars Pathfinder was tested
to resist 75 G’s of acceleration. [2]

However this type of landing gear also had its drawbacks. The final resting place of the payload was
never known and such things as slopes and rocks could easily veer it off course. After the initial contact
opportunity, the module bounced 24km away from the intended landing site. The airbags also weighed
a lot. Being made of the same material as space suits, this increased the cost dramatically. (22)

3.4 Lunar Conditions
The moon has a negligible atmosphere. The lunar acceleration is approximately 1/6th terrestrial
acceleration. Lunar surface temperature ranges from 40K to 396K. During the day, the temperature
average is 380K and at night the temperature average is 120 K. (19)

Table 1 - Lunar Regolith Properties (20)

Bulk Density [g/cm3] Lunar Regolith Load Bearing
Strength [N/cm2]
1.15 0.02-0.04
1.9 30-100

Page | 15


Data from surveyor 3 suggest regolith has a bulk density of 1.6 g/cm3 at 2.5 cm depth.(20) The
Apollo 11 mission had a probe that stuck into the lunar surface. Data from this mission suggests that the
lunar regolith has a load bearing strength of 2-3psi/inch penetration.(15)

From a study of rock sizes on the crest of the North Ray crater rim, approximately 20% of surface
protrusions greater than 20 cm in size. This value falls to 10% in the outer eject area of the crater.
(21)The design of a landing system can assume that a clearance of 30 cm will account for all surface
protrusions and that the landing surface will be relatively flat whether angled or level.

4 Design
Dr. Tim Bryant suggested rewording the design challenge so as not to unintentionally restrict design
possibilities to a narrow scope. The original title of the project, the conceptual design of lunar landing
gear, implied an inherent mechanical aspect to the design of a landing mechanism.

Designating the problem as the requirement of a system to dampen the shock impulse of a lunar
landing allowed TC to identify the underlying design conflict with greater ease. The optimal design will
absorb the most energy in a simple and cost effective manner. It will have the lowest mass and the
smallest volume within the constraints of the problem; we are aiming to maximize the ratio of energy
absorption to density. This will minimize launch cost and maximize available room in the launch payload
and lunar landing module itself.

4.1 Evaluative criteria
The evaluative criteria relate to the assumptions integrated into the design effort. Each criterion is
intended to guide design efforts relating to a part of the system.

Table 2 – Evaluative Design Criteria

Design Criteria Description
Mass The mass of a landing system must be minimized in order
to minimize the cost of launch.
Volume The volume of landing system components must be

Page | 16

Lunar Landing Gear

minimized to reduce volume occupancy in the launch
payload and to maximize cargo space available within the
landing module itself
Energy absorption The energy absorption properties of the damping system
must be maximized.
Material Temperature Resistance Structural material must perform within specifications
regardless of large temperature variation. (Lunar surface,
retrorocket fire, )
Support The landing system must provide a reasonable degree of
level orientation after landing and minimize potential slip
and sink in its rest position.
Stability The intended final orientation of the landing module
must be able to withstand moments and anticipated
external forces acting on its structure.
Clearance The landing system must provide adequate clearance
within specifications over a range of possible surface
conditions.
Simplicity Ease of manufacture, operation and implementation in a
landing module.
Reliability Confidence in successful operation, unobtrusive
integration and no interference with landing module
subsystems.
Design Time TC’s design efforts are restricted by time and academic
deadlines. Availability of research pertaining to proposed
design system and design time will play a factor in
choosing a certain design.
Cost Important factor considering an open effort. Cost of
launch and manufacture. This criterion was kept in mind
but omitted in design comparison as it would influence in
the weighting of every other criteria.

Page | 17


4.2 Design Methodology
Several landing mechanisms were explored. TC will seek to optimize a simple and affordable
design, one that an open community can hopefully develop. Ideally the designed system will also easily
integrate with the structural concept of the landing module Figure 12 that has previously been
developed.

Figure 12 – Early Structural Lunar Landing Module Concept (3)

To achieve a soft landing on the surface of the moon, the landing module will have to decelerate
to a reasonable velocity before hitting the moon.

While the balloon mechanism used to land Spirit and Opportunity on Mars is interesting and
thought provoking, the atmosphere on the moon is so thin that a parachute could not be used to slow
descent let alone stabilize a thrust platform. This removes the possibility of using an inflatable balloon
shell as there would be no cheap and readily available alternative to slow or orient the landing module
before impact (heat from onboard thrusters would likely damage the shell). Without negative
acceleration as the landing module approaches the surface of the moon it could possibly crash land or
bounce away at escape velocity depending on its impact angle.

The use of electromagnetic flux to resist the motion due to impact between the landing gear
and the landing module was omitted in the design comparison; a large power source would make for a
high mass and low feasibility.

Page | 18

Lunar Landing Gear

The pod leg concept offers the most versatility; it is a modular design that has a low mass and
volume. The approach has been used successfully in a number of past missions like the Apollo and
Surveyor missions. Conceptual design will look for an optimal pod leg design.

The design was split into two sections for analysis to help identify the best combination of structural
support and energy absorption systems. Individual analysis of the two different systems allows for a
more comprehensive look at each component and will provide a stronger final solution to design. Four
designs were chosen for the structural support analysis, and four designs were chosen for the energy
absorption system analysis.

The four different structural support designs being analyzed consist of a combination of static and
dynamic struts with vertical or angled orientations. Static struts will be rigid bodies protruding from the
landing module while dynamic struts will have a system that allows them to extend from a collapsed
state to a deployed state and that will lock them in this position for landing. A three strut configuration
will be assumed for this process as the majority of research done has shown that this is lightest
configuration while still having a lot of stability.(14) Angled struts will also have two support beams in a
triangle configuration providing extra strength to stop them from deflecting upwards upon landing.

The four different energy absorption systems consist of fluid dampening systems, plastic
deformation structures and elastic dampening systems. The plastic deformation structure system is
considered to be housed entirely in the strut. Other systems may be housed in the strut or designed as
an interface between the strut and the landing module.

4.2.1 Structural System Design Candidates
Design 1 – Vertical Static Strut
The vertical static strut is the simplest of the four designs being considered. It consists of 3 struts
that are oriented vertically from the base of the landing module. Due to the orientation of the struts
and the potential for lateral loading stronger material will be required. During landing there is a
potential for the landing module to have a horizontal velocity which could put a significant amount of
lateral stress on the strut. However, the lateral stress can also occur during static loading after the
landing if the weight distribution is unbalanced, which may occur when the rover disembarks the
landing module.

Page | 19


Table 3 – Advantages and disadvantages of vertical static strut structural system design

Advantages Disadvantages

Simple ( very easy to model, easy to test) Does not support significant lateral loading
Strong vertical support (materials are usually Due to lack of lateral support stronger materials
strongest in compression) will have to be used
Uses little volume in payload Stability is limited in instances of lateral loading

Design 2 – Vertical Dynamic Strut
The vertical dynamic strut is more complex than its static counterpart. It is very similar to the static
design as it consists of three struts oriented vertically from the base of the landing module. However, to
decrease volume used in the payload, a mechanism is used to extend the struts from a collapsed
configuration. Once extended the struts lock into place and act in the same manner as the vertical static
struts. This mechanism would be designed very similar to the Apollo 11 lunar landing gear locking
mechanism. (14)

Table 4 - Advantages and disadvantages of vertical dynamic strut structural system design

Reasonably Simple Design ( very easy to model Does not support significant lateral loading
after extension of struts, easy to test)
Strong vertical support (materials are usually Due to lack of lateral support stronger materials
strongest in compression) will have to be used
Uses little volume in payload Lateral loading capability is reduced even further
with this design due to locking mechanism being
weakest link
Reliability is reduced due to added complexity of
design
Stability is limited in instances of lateral loading
Dynamic mechanism adds extra weight

Page | 20

Lunar Landing Gear

Design 3 – Angled Static Strut
This concept is more complicated to design and analyze than the vertical static, however it provides
the best method of support. The reason to this is the angled design accommodates lateral loading and
as a result material and size requirements decrease significantly. The angled struts also provide greater
stability not only because of their capability to handle lateral loading but also because the base area is
increased. The increase in base area provides a greater resistance to any induced moments that would
cause the module to tip over.

Table 5 - Advantages and disadvantages of angled static strut structural system design

Reasonably Simple Design Harder to model than vertical strut designs
Less materials and size are required due to Uses the most volume in payload of all four
strength designs
Stability exceeds that of vertical strut designs More complicated to model and test

Most reliable design

Design 4 – Angled Dynamic Strut
This concept is the most complicated of all four designs. This type of strut provides all the benefits of
angled static struts with the benefit of reducing the volume used in the payload. Once extended the
struts lock into place and act in the same manner as the vertical static struts. This mechanism would be
designed very similar to the Apollo 11 lunar landing gear locking mechanism. (14)

Page | 21


Table 6 - Advantages and disadvantages of angled dynamic strut structural system design

Uses the least volume in payload of all four designs Most complicated design (testing, modeling, and
designing)
Stability exceeds that of vertical strut designs Locking mechanism will reduce overall strength as
it will be the weakest link
Less materials and size are required due to Reliability is reduced slightly due to added
strength complexity of design

4.2.1.1 Decision Matrix - Structural Systems
A Quality Function Deployment chart, Figure 13, was used to determine the optimal design to
proceed with for the structural section of the landing gear. The requirements were weighted based on
their effect on the evaluative criteria. Mass was considered the most important factor as it not only
significantly affects the cost of launch but the client highlighted the importance of a light weight design.
Since the primary function of the strut design is to support the landing module the structural integrity of
the unit was weighted heavily. Reliability was also one of the most important factors as there is no room
for failure. Material strength is also considered as it significantly affects the cost of the final strut
design. Stability is also important as the landing module may also be used as the antenna to
communicate with Earth. Simplicity is important to increase reliability, decrease cost and most
importantly to increase TC’s probability of success. Design time was also taken into consideration, since
the tight timeline quality, reliability and the probability of success.

Page | 22

Lunar Landing Gear

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Stability 8.8 3 3 9 2.5 2.2 4.0 3.6
Structural 17.6 9 9 3 3 3.0 2.7 4.0 3.5
Simplicty 7.7 3 1 1 1 1 1 3 9 3 9 4.0 2.7 3.8 2.5
Design Time 4.4 1 1 1 1 1 9 9 9 4.0 2.9 3.6 2.6
Reliablity 17.6 1 3 3 3 9 1 1 9 9 9 2.9 2.6 4.0 3.6
100.0 281.2 255.5 322.4 285.3

Figure 13 –QFD Chart for Structural Strut Systems

4.2.2 Energy absorption Design Candidates
Design 1 – Hydro-pneumatic Suspension
The Hydro-pneumatic suspension system is one of the most complex systems being considered. The
design being considered this time is an altered version of the Hydro-pneumatic suspension system used
on cars. A piston pushes on a liquid fluid which alternately pushes on a compressed gas. This system
provides energy absorption however it does not result in oscillation as it has an internal dampening
system.

Table 7 – Advantages and disadvantages of hydro-pneumatic suspension system


No oscillation of system Takes up the most volume
Provides variable resistance to applied load Most complex design
Clearance below structure after landing is Fluid is susceptible to extreme temperature
invariable and controllable variances
One of the least reliable designs due to the
number of components with potential to fail

Page | 23


Design 2 – Plastic Deformation Structure
The Plastic Deformation Structure system is the simplest design being considered as it does not rely
on various interacting components. The deformation structure will be compartmentalized allowing for
changes to easily be made in future design refinements. No oscillation will occur in this system as the
energy is not being absorbed elastically but rather dissipated through the destruction of material.

Table 8 - Advantages and disadvantages of plastic deformation structure system


Provides one of the best energy absorption density Requires a large amount of volume
ratios
Requires the least mass Has the largest variability in clearance after landing
The simplest design (testing, modeling and design Less reliable than other designs due to variable
time) nature of collapsing structures
Has a variable clearance after landing since
amount of plastic deformation that will occur is
unknown

Design 3 – Shock absorber
The Shock Absorber system is a more complex system then the plastic deformation structure
however the design process should be simpler due to the abundance of resources available for
reference. This type of system is used on everything from cars to bikes and provides the most energy
absorption for its volume. The required mass is high due to the need for working fluid as well as spring
material, and a small amount of oscillation will occur since some energy is being absorbed elastically.

Page | 24

Lunar Landing Gear

Table 9 - Advantages and disadvantages of shock absorber system


Requires the least volume as it is a compact design Has more mass due to the requirement of working
fluid as well as surrounding spring
Clearance below structure after landing is Fluid is susceptible to extreme temperature
invariable and controllable fluctuations
Will require the least design time as there are a Oscillation will occur in the spring till the system is
large amount of resources on the subject available fully dampened by the fluid.
Is the most reliable system

Design 4 – Hydro-pneumatic Suspension in combination with Plastic Deformation structure
This system is the most complicated of all four designs and will require the most design time. The
combination of systems allows for each one to be specialized for a certain range of the energy
absorption allowing for a smoother landing. This specialization also allows the individual components to
be smaller than if they were used on their own.

Table 10 - Advantages and disadvantages of hydro-pneumatic suspension in combination with plastic deformation
structure system


Fairly Reliable design as there will be less Complicated design requiring integration of both
systems
No oscillations since there is no elastic absorption Will be very heavy due to the added weight of the
of force. working fluids.
Requires less material then most other designs as Fluid is susceptible to extreme temperature
each system is specialized for certain ranges fluctuations
Will provide the best energy absorption as each Variability in clearance after landing due to
system supports the other unknown amount of plastic deformation occurring

Page | 25


4.2.2.1 Decision Matrix - Energy absorption

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Force Absorption 16.7 1 9 9 1 3 9 1 9 9 3.0 3.8 3.4 4.0
Mass 17.5 9 9 3 1 1 9 9 3 2.0 3.5 1.8 1.5
Volume 10.0 3 1 1 3 3 1 3 3 1.2 1.5 2.2 1.8
Material 10.0 3 9 1 9 9 1 1 3 3 3 2.2 3.5 2.4 2.8
Clearance 8.3 3 9 3 3 4.0 1.5 4.0 2.6
Simplicty 8.3 3 1 1 1 1 1 3 9 3 9 1.6 3.2 2.4 2.2
Design Time 12.5 1 1 1 1 1 9 9 9 3.0 3.0 3.5 2.5
Reliablity 16.7 1 3 3 3 9 1 1 9 9 9 2.6 2.6 3.5 3.0
100 246.50 294.58 289.58 260.17

Figure 14 - QFD Chart for Energy absorption Systems

4.3 Design Selection

Based on the analysis preformed, and after a review of the design constraints, the candidate design
for an analysis is the angled static strut structural system with the plastic deformation structure energy
absorption design. The combination of these two systems will provide the most stable, reliable and
strongest support, while using the least volume and mass and providing the most energy absorption.

4.3.1 Structural System

The structural system will consist of three primary angled struts extending in an equilateral manner
from the landing module. These struts will contain a structural geometry or a material that will
plastically deform to absorb impact load. Two secondary struts will cantilever with the primary legs in a
similar fashion to Apollo 11 design. The angled struts will be fixed in a static fashion to the lunar module
and extend outwards increasing the overall radius of the module.

4.3.1.1 Strengths

The strength of the angled static struts lies in its increase of system stability and resistance to
variable loading conditions. The use of angled struts over vertical struts allows for support of some
horizontal loading in the case of a slightly non uniform vertical landing. This means that if the landing

Page | 26

Lunar Landing Gear

module comes in at a slight angle, or lands on a slight incline the struts will still be able to support the
landing force without failing. The angled aspect of the struts also helps to reduce rotation of the module
upon landing by expanding the base radius. This design is fairly simple to model, and the lack of moving
parts will reduce the probability of a part failing during operation of the landing gear which increases the
probability of a successful mission.

4.3.1.2 Weaknesses

The primary weakness of an angled static strut design is the increase in the amount of space within
the launch payload that the module will occupy. Without the ability to retract the struts increased base
radius caused by the extruding struts will need to be accommodated. The angled strut design will also
require more mass than the vertical strut design due to the need for secondary struts supporting vertical
forces to compensate for the difference in vertical strength between the angled strut design and the
vertical strut design.

4.3.2 Energy Absorption System

The energy absorption system will consist of sacrificial materials contained in each of the primary
angled static struts that will plastically deform.

4.3.3 Strengths

The strength of the plastic deformation materials lies in the amount of force it can absorb relative to
its weight. The impact force is absorbed through the landing pads and transferred to the primary strut
where the impact materials absorb the kinetic energy as they buckle. This design will also not provide
any oscillation as the process does not consist of any elastic damping of force and all the force is
dispersed through buckling or crush of the materials. The structure is also fairly simple and does not
consist of many moving parts meaning there is less probability that something will go wrong causing
failure of the landing gear system which is important as reliability of the landing gear is a strong concern
for the project.

Page | 27


4.3.4 Weaknesses

The weakness of the plastic deformation structure is the large amount of volume it takes up. The
strut diameter will need to be larger to incorporate the absorption material within it and the length of
the strut will need to be long enough to allow for buckling of the absorption material while still
providing the clearance required of the lunar module. There may be variability in the clearance between
the lunar module and the lunar surface with the use of this type of energy absorption system as the
variability in the force of landing will affect the degree of buckling of the absorption material.

4.3.5 Combined Design

The primary strengths of the combined design will be its simplicity, stability and energy absorption
ratio. The plastic deformation of the absorption material will allow large forces to be absorbed while
reducing the force transfer to the lunar module by dissipating the kinetic energy of impact through the
buckling of the honeycomb. The static strut design will allow for energy absorption system to be housed
within the module reducing the overall volume of the craft and the angle of the struts will help to
support a degree of horizontal loading. The combined design is simple with few moving parts increasing
the probability of a successful landing which is important in the design. This design seems easy to
integrate with the current conceptual design of the module’s structure without significant change. The
weakness in the design will be in the increased base radius that the angled static struts will require
leading to an increased volume that the landing gear will take up in the launch payload. The mass
required for the primary and secondary struts will also be a weakness however integration of the
landing gear into the structural aspects of the module may account for this.

5 Design Refinement
Prior work justified three angled pod legs fixed in a static manner such that no deployment would be
necessary for use. Each primary leg is cantilevered by two secondary struts (projecting outwards and
upwards) in order to stabilize the primary strut against non-axial forces. In this regard, the selected
impact design was refined into a lever design.

Page | 28

Lunar Landing Gear

5.1 Impact design
The impact design consists of the angled primary strut housing the energy absorption system below
its connection to two rigid secondary struts. The primary strut mates with the landing pad cylinder so
that the impact at touchdown accelerates the landing pad strut into the energy absorption system as in
Figure 15. The joints for the impact design can be pinned or fixed. Apart from the energy absorption, the
structure is rigid.

Figure 15 - Impact Design

This design is capable of absorbing vertical forces. The energy absorption component is located
bellow the secondary strut connection. Note that during touchdown, the landing pad will be accelerated
at an angle whereby its final position is less extended; the landing pad will essentially drag inwards
across the surface until the landing module has reached its rest position ultimately reducing the base
diameter. This dynamic constraint will create bending where the landing pad cylinder mates with the
landing structure cylinder as in Figure 16.

Page | 29


Figure 16 - High stress location, impact design

Further the combination of three pod legs with the impact design will not adequately address
horizontal forces that may develop in non-ideal touchdown scenarios. These forces will induce further
bending forces in the high stress location depicted in Figure 16. The final clearance of the impact design
will depend upon the deflection of the energy absorption component easily resolved into a vertical
component, and the compression of the lunar regolith.

5.2 Lever Design
Due to the shortcomings of the impact design it evolved into a new design. The lever design makes
use of pin joints, universal, spherical or any other type imparting a larger range of motion to the landing
structure, to allow the primary strut to act as a lever. The energy absorption system is contained within
each secondary strut and used to restrict the lever motion of the primary strut as in Figure 17. With this
in mind, the whole structure will be dynamic until it is rigid in its final rest position under load.

Page | 30

Lunar Landing Gear

Figure 17 - Lever design

While any axial force developed on the primary strut will be transmitted to the landing module, this
situation is unlikely due to the ability for the landing pad to slip outwards along the regolith extending
the base diameter of the landing module. The lever design is better suited to accommodate both vertical
and non-vertical forces that may develop during touchdown. Each leg regardless of it touchdown
position relative to the acting forces will be able to dampen both horizontal and vertical force. This
design makes the landing structure more versatile and capable of dealing with a variety of touchdown
scenarios. However, its final rest position is variable depending on what forces develop during
touchdown and the angle at which the secondary struts are connected; an incline at rest could develop
due to non-symmetric crush of the energy absorption cartridges and the angle of the pod legs is then
likely to change as in Figure 18, a top perspective.

Page | 31


Figure 18 - Variability in pod leg position during touchdown

The impact will increase the base diameter as the primary strut levers outward, increasing the final
stability of the landing module. The sweep of the primary legs will be to the extent of the resolved
deflection lengths of the crush material and will not be extreme so instability is not likely. An extreme
tilt of the landing module is also not likely for the same reasons.

6 Design Analysis
Analysis was done into three main areas. The structural design analysis looked at determining
optimal angles, lengths and the thickness of the primary and secondary struts. The footpad design
analysis looked at determining the optimal shape and thickness of the footpad and determining the
optimal attachment mechanism of the footpad to the primary strut. Energy absorption design analysis
looked at removing the most acceleration from the system within the limits of the structural design.
These sections had to be designed with the primary design constraints taken into account.

6.1 Structural System
The structural design incorporated key aspects in determining how the landing pads and struts
would be oriented and located. Methods of statics and solid mechanics along with optimization
techniques were used to determine optimal angles, lengths and diameters of the primary strut and
secondary struts.

Page | 32

Lunar Landing Gear

6.1.1 Optimization design and setup
The first method discussed for optimizing the structural design was to create a program that
optimized all the design variables on its own. This program would be designed in conjunction with the
impact design outlined in the design selection section. The struts would be designed as a rigid body with
known variables such as material properties input into the program, and inequality constraints defined
to optimize the structure. This method however had some key problems. The structure would be
statically indeterminate and would require a Finite Element Analysis program to determine the optimal
design. Allowing the program to optimize the variables on its own would hide the cost of changing
variables. One design could be optimal, but the cost of halving weight might be a minimal increase in
angle above the set boundary and this cost would not be shown. The design is not feasible within the
given constraints however, changes could be made to the design to allow this slight increase, but this
case could not be analyzed since this information would not be outputted from the optimization.

With the design selection changed to the lever design, the method chosen for analysis of the
structural design was also changed. Instead of creating a program to optimize the structure, a program
was created to output graphs of key design variables. In this way trends between variables could be
analyzed to come up with a favorable design. This new method would allow easy comparisons between
variables, and allow slight changes to the design with large effects on highly valued weightings to be
identified.

To begin the analysis, free body diagrams were created for the primary and secondary struts.
Figure 19 shows the free body diagram for the primary strut with area 1 being the interface between the
footpad and the primary strut, area 2 being the interface between the secondary strut and the primary
strut and area 3 being the interface between the lunar module and the primary strut. Key forces were
determined for each of the free body diagrams and statics methods were used to find the unknown
forces. Firstly, the forces in the x and y directions were found and set equal to zero. These equations
can be seen in Equation 6-2 and Equation 6-3. The second moments of area about the x-y axis for the
primary and secondary struts were then determined using the equation for a hollow cylinder. The sum
of the moments about point 1 were found and set equal to zero and this can be seen in Equation 6-1.

Page | 33


L

Y y

L

��
X 3
x
P

��

2

G 1

x

G

y
Figure 19: Free body diagram for primary strut

Equation 6-1

� ��1 = �� sin �� (�� − ��) + �� sin �� × �� − �� cos �� × �� = 0

Equation 6-2

� �� = �� − �� − �� sin(�� − ��) = 0-
-

Equation 6-3

� �� = �� − �� − �� cos(�� − ��) = 0-
-

Using these force and moment balance equations, equations for the unknown design variables
were built. These equations could be used to build trend graphs of variables. The equation for the force

Page | 34

10 01-01 team cheese-final report_lunar landing gear

10 01-01 team cheese-final report_lunar landing gear

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