Lunar Impact Analysis
Korey LeMond
Structures GL
1
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.
2
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.
3
AAE450 Spring 2009
Korey LeMond
STRC GL
BACKUP SLIDES
4
AAE450 Spring 2009
Korey LeMond
STRC GL
Impulse Momentum Theorem
• FΔt = mvimpact
• σzz = F/A
• F = Force, Δt = Time of Impact, m =
lander mass, v = impact velocity, A = Area
of Impact, σzz = compressive Stress
5
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
6
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.
7
AAE450 Spring 2009
Korey LeMond
STRC GL
How Impact Time Affects Velocity at Impact
Aluminum 5056, Diameter = 1.5 meters
4
Impact Stress on Circular Structure (Rad = 0.75) for Various Times of Impact
x 10
4.5
dt = 0.00001
dt = 0.00002
dt = 0.00003
dt = 0.00004
dt = 0.00005
dt = 0.00006
dt = 0.00007
dt = 0.00008
dt = 0.00009
dt = 0.00010
dt = 0.00015
dt = 0.00020
dt = 0.0003
Compressive Limit
4
3.5
Stress (psi)
3
2.5
2
1.5
1
0.5
0
10
20
30
40
Velocity (m/s)
AAE450 Spring 2009
50
60
70
8
Korey LeMond
STRC GL
Aluminum 5056, Diameter = 1 meter
4
Impact Stress on Circular Structure (Rad = 0.5) for Various Times of Impact
x 10
5
dt = 0.00001
dt = 0.00002
dt = 0.00003
dt = 0.00004
dt = 0.00005
dt = 0.00006
dt = 0.00007
dt = 0.00008
dt = 0.00009
dt = 0.00010
dt = 0.00015
dt = 0.00020
dt = 0.0003
Compressive Limit
4.5
4
3.5
Stress (psi)
3
2.5
2
1.5
1
0.5
0
0
10
20
30
40
Velocity (m/s)
50
60
70
9
AAE450 Spring 2009
Korey LeMond
STRC GL
Square Structure (Edge = 36 in.) Impact Analysis for Aluminum 5056
4
Impact Stress on Square Structure (Edge = 36in.) for Various Times of Impact
x 10
dt = 0.00001
dt = 0.00002
dt = 0.00003
dt = 0.00004
dt = 0.00005
dt = 0.00006
dt = 0.00007
dt = 0.00008
dt = 0.00009
dt = 0.00010
dt = 0.00015
dt = 0.00020
dt = 0.0003
Compressive Limit
4
3.5
3
2.5
Stress (psi)
2
1.5
1
0.5
0
-0.5
-1
5
10
15
20
25
Velocity (m/s)
AAE450 Spring 2009
30
35
40
45
10
Korey LeMond
STRC GL
Shear Analysis for Aluminum 5056 for rock of radius 0.05 meters
6
Impact Stress on Circular Structure (Rad = 0.05) for Various Times of Impact
x 10
5
4
Stress (psi)
3
2
1
0
-1
2
4
6
8
Velocity (m/s)
AAE450 Spring 2009
10
12
14
dt = 0.00001
dt = 0.00002
dt = 0.00003
dt = 0.00004
dt = 0.00005
dt = 0.00006
dt = 0.00007
dt = 0.00008
dt = 0.00009
dt = 0.00010
dt = 0.00015
dt = 0.00020
dt = 0.0003
Compressive L
Shear Limit
11
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.
12
AAE450 Spring 2009
Korey LeMond
STRC GL