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Proceedings of the Bennett Conference on Mechanical Engineering

April 20, 2012, Pittsburgh, PA, USA

LANDING GEAR DESIGN AND STABILITY EVALUATION OF A LUNAR LANDER

FOR SOFT LANDING

Ahmet Sahinoz Mechanical Engineering Carnegie Mellon University Pittsburgh, PA 15213

asahinoz@andrew.cmu.edu

ABSTRACT A stable soft landing is crucial for a lunar roving mission to

maintain structural integrity of the lander to enable payload

operation as well as rover egress. This research develops legs

and evaluates energy absorption methods for an 800kg lander to

maximize landing capabilities for various touchdown scenarios.

Four telescoping legs with aluminum honeycomb cartridges are

utilized for energy absorption to limit the g-force experienced

by the spacecraft, where legs support the lander structure and

provide clearance to avoid impact with rocks.

Full scale landing on the moon is dynamically similar to 1/6

scale on Earth due to similar acceleration/gravity ratios. Drop

tests with a 1/6 scale model are performed in a motion capture

room to verify stability and required honeycomb stroke. A good

correlation is achieved between simulations and experiments.

The design provides a stable landing under the worst case

scenarios that are based on previous lunar missions.

1 INTRODUCTION

Planetary landers require compliant legs to touchdown

undamaged in a stable position, ready for operation. The proper

understanding of the mission requirements, reduced gravity

forces, lander mass properties, worst case touchdown scenarios

and the stowing space limitations of the launch vehicle are of

great importance in order to design an optimal landing system.

Challenges are to design for uncertain landing conditions and to

perform tests on Earth to simulate lunar gravity. Landing gear

must cope with the expected mass, velocity and orientation of

the lander at touchdown, in the expected range of terrains, and

doing so with minimal mass and a margin of safety.

Uncertainties include the mechanical properties of regolith,

slope of the surface and rock distribution.

Fig 1: Scaled model with Astrobotic Griffin lander (mock up

legs) and Red rover

The vertical velocity of the lander will be reduced nearly to

zero as a result of the deceleration provided by the main engine

during descent. Hazard detection identifies obstacles larger than

a threshold value, and finds a landing site. A horizontal velocity

component may be present due to targeting or hazard

avoidance. The main engine cuts off at a predetermined altitude

in the order of a few meters to prevent instability due to surface

effects. The touchdown occurs following a short free fall phase.

The resulting kinetic energy has to be dissipated over a finite

distance while providing sufficient clearance and a stable

landing [4].

A bottom-up design and test approach is utilized, starting

with the characterization of energy absorption materials,

proceeding with leg design and stability simulation, and

concluding with scaled drop experiments.

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2 BACKGROUND

The main configuration types are legged and pod landers.

Pod landers are not viable for the moon because there is no

atmosphere. Griffin lander utilizes four legs due to the geometry

and available connection points of the primary structure.

Energy absorption approaches include spring-damper

systems, airbags, and crushable materials. Any system including

fluids or gases would need hermetic sealing at vacuum. In this

project, crushable materials are considered due to their rigid (no

spring-back), simple, efficient and cost effective nature. Closed

cell materials such as synthetic foams cannot be used since the

air must escape from the crush material during flight as the

atmosphere density rapidly decreases. Aluminum honeycomb

and aluminum foam are available open cell crush materials,

where honeycomb is directional and foam is isotropic. Crush

materials can be incorporated into the struts of the legs, under

the footpads and/or the base of the lander. Force-stroke

characteristics can be adjusted to specific needs by stacking

crushable materials with different densities or cross sections.

Fig 2: Honeycomb, aluminum foam and synthetic foam

Surveyor landers used an inverted tripod leg design with

shock absorbers, where honeycomb under the footpad would

reduce the load if the foot lands on a rock, and the block under

the base provided extra energy absorption capability in case the

shock absorber reaches its limit. The landed mass of Surveyor

landers was about 300kg.

Fig 3: Surveyor landing gear design (one of three legs)

Deformation of the soil is an important aspect for footpad

design. Size of the footpad and the bearing strength of the

regolith determine the penetration distance. Surveyor had a

30cm footpad and penetrated 2 to 10cm with 1 to 4m/s vertical

velocity. Landing conditions are listed in Table 1 [1, 2].

Table 1: Surveyor landing conditions summary [2]

Apollo utilized a cantilever leg design with aluminum

honeycomb cartridges in all three struts of each leg. The main

strut has a compressive stroke only, whereas lower struts

incorporate a tensile stroke because they can experience both

types of loading. Due to space restrictions, legs have a folding

mechanism and they are stowed during launch and flight, and

deployed after separation from the launch vehicle [3].

The cantilever design creates a torque on the telescoping

interface that increases friction force and the design loads

significantly. The inverted tripod configuration eliminates the

bending torque, minimizing the design loads by creating almost

pure axial forces on all struts, but increasing the length of the

lower struts compared to cantilever design. Apollo used

cantilever design to achieve compactness when the legs are

stowed, due to the space restrictions of the launch vehicle [5].

Fig 4: Apollo landing gear and main strut design

Materials used in the design of landing structure are usually

high grades of aluminum such as 6061-T6 and 7075-T6, or

aluminum/titanium alloys. Although carbon fiber composite

structures are available, the brittle nature of these structures

may not be well suited for an application that requires

compensation for uncertainty, possibly with plastic deformation.

In addition, due to extreme temperature conditions, the

difference between the thermal expansion coefficients of

composite and metallic structures would have to be addressed.

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3 DESIGN CONSIDERATIONS

The design problem is defined by the specific requirements

for the mission, including lander properties and lunar

conditions. Landed mass of the spacecraft is in the range of

650-850kg depending on the fuel leftover and payloads. The

vertical acceleration limit of the structure is defined to be 10g’s

for Earth gravity (9.8m/s2). No strict limitation is put on the

horizontal component. Dynamic envelope of the launch vehicle

(Falcon 9) is 4.6 meters in diameter, which means the legs must

be contained within this circle. The hazard avoidance system

can detect rocks larger than 25cm with some error, so the

minimum clearance required is selected to be 30cm. Therefore,

the bottom of the lander is required to stand at least 30cm

higher than the ground after the landing. Slopes that are larger

than 10deg can be detected, so the lander may have a 10deg

angle with respect to the ground during touchdown. Angular

velocity is assumed to be negligible. Although nominal landing

velocities are 2m/s vertical with zero horizontal component, to

be conservative, the worst case scenarios are selected as 4m/s

vertical with 1m/s horizontal velocity, considering Surveyor

landings as a reference. Target mass for one leg is 5kg with a

safety factor of 2 [6].

Fig 5: Lander primary structure (from above and below)

The primary structure of the lander consists of a deck (3x3

meters), upper cone, lower cone and bulkheads illustrated in

gold. A rover sits on top of the upper cone; fuel tanks are

located within four holes on the deck; weight of the tanks is

transferred to the bottom ring through bulkheads, and the lander

is connected to the launch vehicle with a clamp band from the

bottom ring. Rectangular plates near the bottom ring between

the bulkheads alleviate stress concentration at the vertices

where bulkheads are touching the lower cone. They also

provide potential connection points for legs.

Lunar gravity is 1.63m/s2, 1/6 of Earth. Temperature has a

wide range from -100 to 120oC depending on the day time and

the region. The effect of temperature is neglected in this study.

Soil bearing strength increases with depth, starting from

0.2N/cm2 at 1-2mm and reaching 5.5N/cm

2 about 5cm. Friction

coefficient is reported being in the range of 0.3-0.7 [2, 3].

4 LANDING GEAR

Landing gear design concepts are evaluated starting from

the simplest configuration and proceeding to more complex

designs. Integrating crush material under the body is not

feasible because the bottom ring is not wide enough to provide

a stable landing.

The simplest form of landing gear would be four rigid legs

with crush material under the footpads. The novelty of this

design is simplicity, strength and rigidity. Welded connections

between the struts and the footpad eliminate the mass of any

type of connectors and/or hinges.

Fig 6: Rigid leg with crush pad design

Up strut is bolted to the lander via a welded plate at the tip.

Lower struts from two different legs share a triangular bracket

that is welded to them, and the bracket is bolted to the

rectangular plates. 10g acceleration requirement for a 650kg

lander results in an approximate total maximum force of 64kN,

16kN for each leg. The energy that needs to be absorbed is

equal to the kinetic energy of an 850kg (upper limit) lander with

4m/s velocity, and the absorbed energy is equal to the integral

of force-displacement curve of the crush material. Assuming

constant force is applied during the crush, for an ideal vertical

landing parallel to the ground, the stroke required to absorb the

energy would be 10cm.

The up strut is designed to be connected to the edge of the

deck, coming straight down to the footpad, while lower struts

connect to the rectangular plates. Thus, the base width is equal

to 3.5m, the diagonal across the deck. The up strut transfers the

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vertical force from the deck to the honeycomb where lower

struts provide stiffness in the lateral plane. Each footpad is

located 30cm below the bottom ring, providing the required

clearance. The material used in design is AL 6061-T6 due to

availability. Legs are analyzed in Solidworks for static yield and

buckling.

Fig 7: Solidworks static, buckling, modal analysis results

There are two options for materials, aluminum foam and

aluminum honeycomb. Detailed characteristics of these

materials and formulations are illustrated in [7, 8, 10].

Aluminum honeycomb is a directional lightweight energy

absorption material which provides constant force during the

stroke. It can compact as much as 70-80% of its original length.

Since the force is constant, the absorbed energy is equal to the

crush force times the stroke. The major disadvantage of

honeycomb is the drastic loss of strength with increasing crush

angle. When incorporated under the footpad, the energy

absorbed heavily depends on the horizontal velocity, and the

orientation of the lander which determine the crush angle. The

advantage of aluminum foam is its isotropic structure, but the

energy absorption efficiency is much less than honeycomb

which makes the foam significantly heavier [10, 11].

Fig 8: Honeycomb strength vs. crush angle [7]

Considering the bearing strength of the soil, diameter of the

footpad is chosen to be 45cm. In order to achieve 16kN of crush

force, honeycomb with crush strength of 15psi (~0.1MPa) must

be used. This is one of the lowest crush strength honeycombs

available in the market. It is inefficient to use low strength

honeycomb because the specific energy absorption

(energy/mass) increases with crush strength [9]. This design is

also sensitive to the rock distribution. If the footpad lands on a

20cm rock, the engaged cross-section is smaller, and loss of

absorption capacity will be more than 50%. These uncertainties

increase the required stroke from 10cm up to 25cm. There are

two potential issues if the footpad diameter is decreased to use a

higher strength material for efficiency. First, increased

penetration into the soil cuts from the clearance. Second, as the

honeycomb gets taller in height and smaller in diameter, it

becomes prone to breaking off from the footpad. The achieved

mass for one leg was 4.5kg with the crush angle limited to

20deg which is combination of the orientation and the angle of

the velocity vector.

Fig 9: Illustration of lander parameters vx (horizontal

velocity), vy (vertical velocity), planar landing scenarios (2-2

and 1-2-1), center of mass height (h), base width (b),

stability triangle (β), and sample velocity vectors v1 and v2

The higher the ratio between the base width of the landing

gear and the height of the center of mass, the more stable the

lander is against toppling over in the presence of horizontal

velocity and orientation errors. The additional honeycomb

height due to uncertain conditions increase the height and

decreases stability, which will also lead to a higher stance after

the landing, requiring the ramps to be longer to provide a safe

rover egress angle. For the rigid leg design, a rough stability

criterion is defined to give a baseline. The worst case is the

pads getting stuck to the soil. Defining the origin of the velocity

vector as the center of mass, if the vector lies within the stability

triangle illustrated in Fig 9 as v2, the landing is stable. If the

vector is aligned with the side of the stability triangle, the

vehicle is critically stable. If it is above the triangle (v1), the

tailing leg would lift from the ground. The energy required to

reach tip over angle is calculated from the resulting increase in

center of mass height due to the motion. If the energy from

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horizontal velocity is larger than this value, the landing might

be unstable. Assumptions include infinite friction and no

rotational energy absorbed by crush pads which is not realistic.

But since the crush of honeycomb depends on the angle, the

system cannot be evaluated in a realistic way with a simple

model. Issues such as the inefficiency of low strength

honeycomb, high sensitivity to landing conditions and footpad

diameter being tied to the crush force, led to the exploration of

other design options.

A telescoping leg design with honeycomb insert in the main

strut is an option that enables the use of high strength efficient

honeycomb. It also constrains the honeycomb to be crushed

along its main axis, eliminating all the variables that affect the

crush angle. The mechanical difference of this configuration

from the rigid leg is introduction of moving parts. The main

strut consists of two parts sliding in each other, has pin joints at

the top and bottom, with a bushing and a honeycomb insert

incorporated inside the upper part. The material for the bushing

is plastic and the structure is AL 6061-T6. For the lower struts

to rotate about the same axis, pin joints with a 15deg bend are

utilized, and they are connected to the rectangular plates on the

lander. Lower struts are welded to the footpad. All connections

at the strut ends are plugs, and these are designed to be bonded

to the struts with space approved adhesives.

Fig 10: Telescoping leg design (transparent main struts)

Previous missions either used crush materials inside, or

load limiters at the ends of the lower struts to limit horizontal

accelerations. The footpad is designed to be deformable in

order to absorb impact if excessive side loadings are present,

for example hitting a rock while sliding on the ground.

Fig 11: Footpad, lower strut hinge connection, main strut

honeycomb integration and cross section sketch

Center part of the footpad is thicker to keep three struts

connected to each other while the rest of it deforms. The top

section of the footpad is a dome, providing remarkable strength

with the same mass compared to a flat surface. A high strength

honeycomb is placed under the dome and a thin sheet of

aluminum is bonded at the bottom of the honeycomb to

minimize penetration and friction. The honeycomb stays intact

if the landing is on regolith, but partially deforms if there are

rocks on the contact surface, creating a deformable structure.

Fig 12: Footpad cross sections (w/o honeycomb)

Kinematic analysis is performed to determine the required

honeycomb stroke and crush force to produce a vertical

resultant force of 16kN and a displacement of 10cm for each

footpad. The stroke is only related to the leg geometry. But the

crush force is also dependent on the friction coefficient because

as the honeycomb crushes, legs move outward and this creates a

horizontal force, a resistance to the outward movement. The

acceleration experiences by the lander increases with friction.

Honeycomb should provide sufficient energy absorption at the

minimum friction expected and the acceleration should be kept

below 10g at the maximum expected friction. The inside

diameter of the main strut is set to be 63.5mm which provides

the desired forces with 750psi honeycomb, one of the highest

strength values available. It is 5 times more efficient than using

a low strength honeycomb under the footpad. This telescoping

leg configuration enables the footpad design to be independent

from the energy absorption design, and the system is less

sensitive to the uncertainties. Assuming that the lower struts

provide sufficient stiffness in the lateral plane, the main strut is

under pure axial loading. The connection of the main strut to

deck is shifted towards the tank to because when the deck is

loaded at the edge, it acts as a cantilever beam starting from

where the bulkhead ends. Thickness of the strut is reduced to

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0.6mm since the welding consideration does not exist, and the

overall design is optimized to 4.5kg with a safety factor of 2.

6 STABILITY

Tip-over stability and honeycomb stroke are investigated

for telescoping legs in a motion simulation program, Working

Model 2D. The honeycomb crush depending on the crush angle

could not be simulated, but honeycomb inside the strut is

modeled utilizing a constant force spring which displaces under

compression and doesn’t extend. Two separate models are

created to simulate 2-2 and 1-2-1 scenarios, as shown in Fig 13.

Fig 13: Working Model 2D simulations (2-2 and 1-2-1)

The structure is rigid and the ground is an anchored block

with adjustable slope and position. Leg geometry is the same as

the lander. Mass, center of mass and rotational inertia of the

block are defined. The trick to imitate the behavior of

honeycomb is the combination of spring, rope and rod elements

that are available in the program with the right activation

conditions. The spring provides constant force during flight

where the rope holds the leg in place under tension. As long as a

leg hits the ground, spring is decompressed by some amount,

but it should stop acting as a spring as soon as the crush is over

to prevent bouncing. To do that, a rod element overrides the

spring at the instant when the length of the spring is below its

initial length and the velocity crosses zero and enters into the

extension region. The limit is tuned to be 0.05m/s because

setting it very close to zero causes chattering due to numerical

errors. Rods are coincident with the springs, and the ropes are

connected to the body for 2-2 and to the deck for 1-2-1.

Variables including the slope, initial velocity of the lander,

mass, inertia, friction coefficient and the spring force can be

altered. In 2-2 configuration, the springs provide 32kN force as

they are the combination of two legs. The middle leg of 1-2-1 is

also modeled with a 32kN spring, and ropes are placed in a way

that resembles struts. Single legs have 16kN springs. Run time

of each simulation is about 10 seconds at 1000Hz and 0.001m

accuracy.

In the simulation environment, linear and rotational

position, velocity and acceleration of each element, normal and

friction forces acting at the contacts, and reaction forces at pin

joints can be measured and recorded. These values can be

exported to a file which can be imported into Matlab for post

processing. The simulations provided valuable insight on the

kinematics and dynamics of the problem. The lander is proven

to be stable in the worst case conditions, and it is shown that the

honeycomb strokes are sufficient, but physical testing is

required to validate the results.

A full scale test is the most realistic option but it requires

extensive use of resources. Creating a scaled drop test platform

is representative and viable. An Apollo era study proved that the

free body drop tests of a 1/6 scale model on Earth produces

dynamically similar results with a full scale landing on the

moon. This similarity is achieved by adjusting the results from

the experiments with scaling factors (Appendix A). The reason

behind the perfect match of the results is the similarity of

acceleration/gravity ratios of each scenario [12]. Drop tests with

a 1/6 scale model of the lander is a feasible method to validate

simulation results. The parameters that must be considered are

leg geometry, total mass, center of mass height and rotational

inertia.

The inner diameter of the scaled main strut is equal to

12.7mm in which the crush material must be inserted. For this

purpose, samples from three different materials are prepared

and crushed with an Instron compression tester to obtain the

force-displacement curves. A total number of 9 samples, three

from each material are tested for statistical significance.

Fig 14: Instron tester and crush samples

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Materials are 360psi and 690psi aluminum honeycomb

from Plascore, and 215psi Rohacell foam. Honeycomb samples

have a small number of unit cells, 7 cells for 690psi and 3 cells

for 360psi. The foam is tested to use it as a backup plan if the

honeycomb samples crush inconsistently. Samples are inserted

in a piston and the speed of the tester was set to 20mm/min.

Test results showed that the 360psi samples crushed with an

average constant force of 325N (400N expected) and the 690psi

samples crushed with 650N (700N expected), both by 70% of

their initial length (31.75mm) before the force increases rapidly.

Foam crushed with an average force of 185N (240N expected)

with a 60% stroke. Other plots are located in Appendix B.

Fig 15: Force-displacement plots of pre-crushed samples

The time frame of the landing is about 10ms for the scaled

drop with 690psi honeycomb cartridges that are equivalent to

10g on the full scale lander. To extend the time period of crush

for the purpose of having more data points with a finite

resolution measurement method, 360psi honeycomb is chosen

which would create about 5g’s on the full scale lander.

Fig 16: Scaled lander sketch and Solidworks model

The scaled lander is designed to satisfy the desired mass

property values within ±20% error. Legs and the body are made

of aluminum with bronze bushings and plastic footpads. The

body is a 275x275mm square which corresponds to the height

of the deck. Center of mass should be located 2cm above the

top surface of the body. The lower struts are solid rods that are

bolted to the footpad. The maximum available honeycomb

stroke is 45mm. The top part of the main strut is threaded onto

the clevis plug for quick honeycomb reload.

Fig 17: Scaled lander leg parts and assembly

Preliminary drop tests are done with springs, foam and

honeycomb. After the telescoping legs are proven to be strong

enough and the crush material is sufficient for energy

absorption, a counterweight is designed and positioned to

achieve desired mass properties.

Fig 18: Scaled lander (first version) with real lander

Desired mass properties of the scaled lander are calculated

with the scaling factors presented evaluated in Solidworks.

Large diameter holes are drilled to the body of the lander to

achieve desired inertia values with a total mass which falls

between 3-4kg that corresponds to a 650-850kg landing mass.

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There are venting holes at the top of the main strut plug which

lets the air escape to minimize the force increase due to viscous

damping. After the counterweight is mounted, the total mass is

measured. The final form of the prototype is 4kg. Other

properties are evaluated only in Solidworks.

Fig 19: Scaled lander final version (w/o holes on prototype)

The drop rig consists of a stand with an adjustable height,

and a four bar mechanism with pitch adjustment to give an

initial angle and a horizontal velocity to the lander while

keeping the orientation the same throughout the swing. An

electromagnet with a switch is attached to the four bar swing as

a quick release to drop the lander.

Fig 20: Four bar illustration

Fig 21: Drop rig with the scaled lander attached

The experiments are conducted in CMU’s Motion Capture

Room, equipped with 15 high speed infrared cameras

distributed around the room that can track coordinates of the

markers on the lander at 480fps with 0.1mm resolution.

Cameras can be seen in Fig 22 as blue light emitting objects.

The shiny surfaces of the lander are covered with a blue tape to

eliminate reflections. Bolt heads are also covered to prevent

errors because the system is trained to detect spherical surfaces.

Fig 22: CMU Motion Capture Room (MOCAP)

Friction coefficient on the ground is measured by dragging

the lander with a spring scale. It is 0.5 on the ground and 0.3 on

plywood. The floor of the lab is plastic and has compliance.

Structural elasticity is present, different from the simulation.

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9 markers are placed on the lander: 4 on each footpad, 4 at

the corners of the body and 1 on the counterweight in an

asymmetric position. Legs on the lander are named on the blue

tape from I to IV in a clockwise order.

Fig 23: Marker locations (note the asymmetry on top)

Honeycomb cartridges are pre-crushed to a desired length

in order to eliminate the peak load (Appendix B) and achieve a

tight fit. They are inserted into the main struts and the strut is

threaded onto the clevis plug which can be seen in Fig 24 as a

part sticking out diagonally from the corner of the deck.

Fig 24: Honeycomb reloading into the main strut

Honeycomb inserts are crushed with variable heights as can

be seen in Fig 25, depending on the landing configuration (2-2

or 1-2-1), velocity and orientation. A few of the cartridges

crushed significantly less than the expected value during the

experiments. The presumed reason is the lack of pre-crush.

The markers on the footpads are used to determine the

contact instant since they instantly stop when they hit the

ground. Markers on the body is utilized to extract the height,

velocity and acceleration of each corner, and to calculate the

center of mass accelerations by taking the average. Although the

center of mass is located 2cm above the surface of the body, this

method provides very close results and is sufficient. The marker

on the counterweight is used to identify the orientation of the

lander, and it can be used to calculate accelerations around the

rover if desired.

Fig 25: Leg view, crushed honeycomb samples, a marker

Pitch angle is calculated from two markers on the body

using the height difference and the known distance, between the

footpads (different for 2-2 and 1-2-1 orientations). Angular

velocity and acceleration are derived from the pitch angle with a

finite difference method. Presence of roll and yaw angles due to

the imperfect structure of the drop mechanism are neglected in

all calculations for practical purposes.

A total number of 10 landing scenarios with different

configurations, velocities and pitch angles are tested. Pitch

angles are disturbed at release due to the imperfection of the

swing mechanism. The predetermined angles are different than

real values. Thus, experiment results are generated, and pitch

angle and velocities are imitated in the simulations to compare

the results. Scenarios listed in the table below show the actual

touchdown conditions of five selected experiments.

Table 2: Landing conditions achieved in experiments

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Fig 26: Result comparison for Landing 5

The time scale of the experiment is multiplied by 6, the

linear accelerations and the angular velocity are divided by 6,

and the angular acceleration is divided by 36 due to scaling

factors in order to correlate with the full scale simulation

results. Results are plotted, the continuous line being the

experiment where the discrete line shows the simulation results.

The comparison of simulations results to the drop test for

Landing 5 is illustrated above. Comparison values include pitch

angle (deg), angular velocity (deg/s), angular acceleration

(deg/s2); horizontal velocity (m/s) and acceleration (m/s

2);

vertical velocity (m/s) and acceleration (m/s2). The acceleration

values are lightly filtered in MATLAB to reduce cripples.

A full list of drop experiment landing conditions and the

results of other selected scenarios are in Appendix A.

7 CONCLUSION

Two landing gear configurations are designed, analyzed

and evaluated. Telescoping legs are preferred to rigid legs due

to energy absorption efficiency and robustness against uncertain

landing conditions.

Stability of the landing is investigated by a 2D motion

simulation. The lander is stable and the honeycomb strokes are

sufficient in worst case conditions. A scaled model of the lander

is prototyped and drop tests are conducted with various landing

conditions to verify the simulation results. Pitching motions,

center of mass velocities and accelerations were in good

agreement. The scaled prototype adequately reproduces 2D

landing dynamics and it is suitable for detailed studies.

Future work includes scaled drops on a lunar simulant with

high velocities to determine the bounds of stability. The effect

of structural elasticity could also be investigated. Manufacturing

full scale legs and performing drop tests with the real lander

would verify the structural integrity of the landing gear.

ACKNOWLEDGMENTS

The author thanks Red Whittaker, Uriel Eisen, Justin

Macey, Steve Huber, Kevin Peterson, Jason Calaiaro, William

Pingitore, Jason Hallack, Eric Benson, Kevin Fulton and Katy

McKeough for their support.

REFERENCES

[1] A. Ball, J. Garry, R. Lorenz and V. Kerzhanovich, 2007,

Planetary Landers and Entry Probes, Part I, Chap. 7.

[2] NASA, Surveyor Program Results, pp. 141-163

[3] Bryan, C., Strasburger, W., “Lunar Module Structures

Handout IM-5”, NASA LSG 770-154-10, May 1969

[4]Buchwald, R., Witte, L., Schroder, S., “Verification of

Landing System Touchdown Dynamics”, IAC-11.A.3.1.3, 2011

[5] Rogers, W.F., “Apollo Experience Report - Lunar Module

Landing Gear Subsystem”, NASA TN D-6850, June 1972

[6] Astrobotic Technology, “System Definition Review”, 2010

[7] Hexcel, “HexWeb Honeycomb Energy Absorption Systems

Design Data”, March 2005

[8] Hexcel, “Honeycomb Attributes and Properties”, 1999

[9] Plascore, 2012, “Crushlite Lightweight Energy Absorption”,

http://www.plascore.com/pdf/Plascore_CrushLite.pdf

[10] ERG Aerospace, “Duocel Foam Energy Absorption”,

http://www.ergaerospace.com/Energy-Absorbtion.html

[11] Chu, B., Jetson, O., Parkhurst, N., “Crash Absorption

Structure for Formula Ford, Use of ROHACELL in Motosport

Crash Worthiness”

[12] Blanchard, U., “Evaluation of a Full-Scale Lunar-Gravity

Simulator by Comparison of Landing-Impact Tests of a Full-

Scale and a1/6-Scale Model”, NASA TN D-4474, June 1968

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APPENDIX A: SCALED DROP EXPERIMENT

Table 3: Scaling factors [2]

λ = Geometric model scale, β = Gravitational ratio

Table 4: Lander parameters (1/6 scale model, corresponding full scale, real lander values)

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Table 5: Landing scenarios of all drop tests (pitch angle is affected by drop rig)

Test Results

- Accelerations are filtered; this enables the reader to see clear output, but decreases correlation at peak points

- Flat tests do not show correlation at angular and horizontal plots (on the left hand side) due to low signal/noise ratio

- Oscillations occur in real experiment due to compliance of ground and structure, simulations are rigid

- Position and height are shown as a reference, not compared with simulation

Fig 27: Landing 1 (Flat, µ = 0.5, Vx = 0, Vy = 3.3m/s)

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Fig 28: Landing 2 (Flat, µ = 0.3, Vx = 0, Vy = 3.3m/s)

Fig 29: Landing 3 (Configuration: 2-2, Pitch = 7.5deg, µ = 0.5, Vx = 0, Vy = 3.25m/s)

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Fig 30: Landing 4 (Configuration: 1-2-1, Pitch = 7.5deg, µ = 0.5, Vx = 0, Vy = 3.25m/s)

Fig 31: Landing 5 (Configuration: 2-2, Pitch = 11deg, µ = 0.5, Vx = 0.4, Vy = 3.25m/s)

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APPENDIX B: CRUSH MATERIALS

Fig 32: Representative aluminum honeycomb behavior [9]

Fig 33: Representative aluminum foam behavior [10]

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In-strut Crush Test Results

Initial length: 31.5mm

Units: Force (N), Displacement (mm)

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