AAE450 Spring 2009 Korey LeMond STRC GL

Lunar Impact Analysis

Korey LeMondStructures GL

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AAE450 Spring 2009 Korey LeMond STRC GL

Impact Analysis done via use of Impulse - Momentum Theorem

• Aluminum 5056 can withstand 22 ksi of compressive stress before failure

• What Velocity can Aluminum withstand at a certain Δt (Time of impact)?

• For 1.5 meter diameter cylinder ~ 43 m/s at 50 μs• For 1 meter diameter cylinder ~ 19 m/s at 50 μs• For 36 inch side square ~ 20 m/s at 50 μs• As can be seen, this depends on geometry.

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AAE450 Spring 2009 Korey LeMond STRC GL

• Honeycomb structure increases impact time and compressive strength:

•Compressive Strength increases by 6500 psi• Impact time increases by ~ 100 μs• Additional 80 m/s of impact velocity allowable• Extra 35 pounds of weight needed on Lander• 0.006 inch thin corrugated aluminum core

• Shear Failure• Shear Modulus ~ 4000000 psi• Hitting a rock 0.05 meters in diameter could result in shear failure at 30 m/s or greater for 50 μs impact• The probability is very low that this could happen.

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AAE450 Spring 2009 Korey LeMond STRC GL

BACKUP SLIDES

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AAE450 Spring 2009 Korey LeMond STRC GL

• FΔt = mvimpact

• σzz = F/A

• F = Force, Δt = Time of Impact, m = lander mass, v = impact velocity, A = Area of Impact, σzz = compressive Stress

Impulse Momentum Theorem

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AAE450 Spring 2009 Korey LeMond STRC GL

Failure Modes:• Have to slow down enough that lander wont compressively fail – this parameter determines impact speed to great degree.

• Compressive Strength of Aluminum 5056 = 22000 ksi.• Can approximately double compressive strength with steel or other metals, but at weight penalty, approx. 4X.• Can change by either lengthening time of impact or increasing contact area.

• Have to design lander thick enough that it wont shear, rupture, or fracture. For instance, If we hit a rock, this greatly perturbs the loading scenario, and will result in failure if not designed to accommodate.

• Shear Modulus 4000000 psi• According to Calculations – we could hit a rock with 0.05 meter diameter without failing by shear at about 6 m/s

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AAE450 Spring 2009 Korey LeMond STRC GL

Key to surviving a hard/semi-hard impact is increasing the time of impact, as the only other way to increase survivability is to increase the size of the lander.

• Increasing time of impact by even a tenth of a tenth of a millisecond provides an increase of 9 m/s in impact speed for a 1.5 meter in diameter lander.

How do we increase our time of Impact? - Honeycomb or Sandwich structures (Crumple zones) - Sandwich structures with 0.006 inch thick corrugated aluminum foil with up to 0.25 inch thick Aluminum face plates. This type of structure can increase our compressive strength by up to 6500 psi, while increasing our impact time by a more conservative estimate of up to a tenth of a millisecond. - Using a sample size of 0.625 inch thick Aluminum 5052 corrugated honeycomb, this provides an extra 80 m/s of potential impact speed for 1 meter in diameter lander, with an addition of 35 pounds.- About $200 in raw material costs, with a standard shop rate used for processing the sheets into corrugated aluminum.

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AAE450 Spring 2009 Korey LeMond STRC GL

10 20 30 40 50 60 700

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

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Velocity (m/s)

Stre

ss (p

si)

Impact Stress on Circular Structure (Rad = 0.75) for Various Times of Impact

dt = 0.00001dt = 0.00002dt = 0.00003dt = 0.00004dt = 0.00005dt = 0.00006dt = 0.00007dt = 0.00008dt = 0.00009dt = 0.00010dt = 0.00015dt = 0.00020dt = 0.0003Compressive Limit

How Impact Time Affects Velocity at ImpactAluminum 5056, Diameter = 1.5 meters

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AAE450 Spring 2009 Korey LeMond STRC GL

Aluminum 5056, Diameter = 1 meter

0 10 20 30 40 50 60 700

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4

Velocity (m/s)

Stre

ss (p

si)

Impact Stress on Circular Structure (Rad = 0.5) for Various Times of Impact

dt = 0.00001dt = 0.00002dt = 0.00003dt = 0.00004dt = 0.00005dt = 0.00006dt = 0.00007dt = 0.00008dt = 0.00009dt = 0.00010dt = 0.00015dt = 0.00020dt = 0.0003Compressive Limit

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AAE450 Spring 2009 Korey LeMond STRC GL

5 10 15 20 25 30 35 40 45

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

x 104

Velocity (m/s)

Stre

ss (p

si)

Impact Stress on Square Structure (Edge = 36in.) for Various Times of Impact

dt = 0.00001dt = 0.00002dt = 0.00003dt = 0.00004dt = 0.00005dt = 0.00006dt = 0.00007dt = 0.00008dt = 0.00009dt = 0.00010dt = 0.00015dt = 0.00020dt = 0.0003Compressive Limit

Square Structure (Edge = 36 in.) Impact Analysis for Aluminum 5056

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AAE450 Spring 2009 Korey LeMond STRC GL

Shear Analysis for Aluminum 5056 for rock of radius 0.05 meters

2 4 6 8 10 12 14

-1

0

1

2

3

4

5

x 106

Velocity (m/s)

Stre

ss (p

si)

Impact Stress on Circular Structure (Rad = 0.05) for Various Times of Impact

dt = 0.00001dt = 0.00002dt = 0.00003dt = 0.00004dt = 0.00005dt = 0.00006dt = 0.00007dt = 0.00008dt = 0.00009dt = 0.00010dt = 0.00015dt = 0.00020dt = 0.0003Compressive LimitShear Limit

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AAE450 Spring 2009 Korey LeMond STRC GL

Sources:

Sun, C.T. Mechanics of Aircraft Structures. New York: John Wiley and Sons, 2006.

“Properties of Materials.” 2009. Purdue University. http://www.lib.purdue.edu/eresources/wts/result.html?WTSAppName=Lib_edupack.

Doyle, James & Sun, C.T. Theory of Elasticity. Purdue University, 2008.

Callister, William & Rethwisch, David. Fundamentals of Materials Science and Engineering. 2007.

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