AAE450 Spring 2009 Lunar Impact Analysis Korey LeMond Structures GL Korey LeMond STRC GL 1

AAE450 Spring 2009 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. Korey LeMond STRC GL 2

AAE450 Spring 2009 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 inch thin corrugated aluminum core Shear Failure Shear Modulus ~ 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. Korey LeMond STRC GL 3

AAE450 Spring 2009 BACKUP SLIDES Korey LeMond STRC GL 4

AAE450 Spring 2009 Korey LeMond STRC GL FΔt = mv impact σ zz = F/A F = Force, Δt = Time of Impact, m = lander mass, v = impact velocity, A = Area of Impact, σ zz = compressive Stress Impulse Momentum Theorem 5

AAE450 Spring 2009 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 = 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 psi According to Calculations – we could hit a rock with 0.05 meter diameter without failing by shear at about 6 m/s Korey LeMond STRC GL 6

AAE450 Spring 2009 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 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 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. Korey LeMond STRC GL 7

AAE450 Spring 2009 Korey LeMond STRC GL How Impact Time Affects Velocity at Impact Aluminum 5056, Diameter = 1.5 meters 8

AAE450 Spring 2009 Aluminum 5056, Diameter = 1 meter Korey LeMond STRC GL 9

AAE450 Spring 2009 Korey LeMond STRC GL Square Structure (Edge = 36 in.) Impact Analysis for Aluminum

AAE450 Spring 2009 Korey LeMond STRC GL Shear Analysis for Aluminum 5056 for rock of radius 0.05 meters 11

AAE450 Spring 2009 Sources: Sun, C.T. Mechanics of Aircraft Structures. New York: John Wiley and Sons, “Properties of Materials.” Purdue University. Doyle, James & Sun, C.T. Theory of Elasticity. Purdue University, Callister, William & Rethwisch, David. Fundamentals of Materials Science and Engineering Korey LeMond STRC GL 12