16.622 Final Report
Courtesy of Julie Arnold and Paula Echeverri. Used with permission.
Expandable Foam Impact Attenuation for
Small Parafoil Payload Packages
Julie Arnold and Paula Echeverri
November 25th, 2003
Advisor: Christian Anderson
1
Background and Motivation
Impact attenuation for small
payloads delivered by UAV’s
Current mechanisms:
•Airbags/ Parachute Retraction
•Paper Honeycomb
Alternative:
•Expanding Foam Impact
Attenuation (EFIA)
2
Hypotheses
1. 75% less pre-deployment volume and crush thickness efficiency loss of
no more than 30%.
2. Increase in cost of no more than 50% and a decrease in reliability of no
more than 10%.
Objective
Assess the ability of an EFIA to protect a payload having a 50g-impact
shock limit from a 15 ft/s* vertical descent rate.
Compare the pre-deployment volume, crush efficiency, cost and reliability
of the EFIA against paper honeycomb.
Success Criteria
Evaluate the aforementioned metrics for an EFIA and for paper
honeycomb to an accuracy such that the hypotheses can be assessed.
___________________________________________________________
*Impact velocity was 13.5 ft/s during drop tests
3
Hypotheses Assessment
ƒ Confirmed “crush thickness efficiency loss of
no more than 30%”
ƒ Refuted “decrease in reliability of no more
than 10%”
ƒ Uncertain assessment of “75% less predeployment volume”
4
Experimental Overview and Methods
D Choice of Material and
Payload Characteristics
Deployment
Mechanism
D Crush Efficiency
D Cushion Thickness
and Area
Deployment Reliability
D Safety Margin
LEGEND
D Volume
Cost
Path to primary hypothesis
5
Path to secondary hypothesis
Crush Efficiency Test Matrices
• Static
• Dynamic: Same only for ½” samples
6
Test Matrices (Cont.)
Safety Margin
Material: Honeycomb
Material: Expanding Foam
Trial Number
Trial Number
Maximum
Acceleration
1-25
1-25
Expanding Foam Deployment Reliability
Trial Number
Maximum Acceleration
Successful
Deployment
Pre-Deployment
Volume
Material
Volume
Honeycomb
1 - 25
Expanding
Foam
7
Error Mitigation
ƒ Sampled at high data rates on accelerometer
(5000Hz) and high-speed camera (2000Hz)
ƒ Calibrated high speed camera before each
session
ƒ Confirmed impact velocity after each drop
(13.5 +/- 0.3 ft/s)
8
Hypothesis Assessment Results
Efficiency
Hypothesis
Results
Pre-Deployment Reliability
Volume
At least 70%
At most 25%
At least 90%
83.8% (- 11.1)
27% (- 5.4, + 7.5)
83% (95%
confidence)
EF parameters as compared to HC
Hypothesis
100%
80%
60%
% difference
EF
40%
20%
9
0%
Efficiency
Pre-Deployment Volume
Material Reliability
Analysis of Crush Efficiency
Honeycomb
Crush Efficiency
HC Crush Efficiency
Static Test
Samples
0.9
Dynamic Tests
Average
0.7
Linear (Static
Test Samples)
0.5
0.25
0.5
0.75
1
Sample Thickness (in)
- Final cushion thickness of
2.7 inches requires three 1inch pieces of honeycomb
stacked together.
- Used efficiency for 1”
honeycomb
Expanding Foam
EF Crush Efficiency
Samples
Crush Efficiency
1.2
1.1
Lower Bounds
1
Upper Bounds
0.9
0.8
Linear
(Samples)
0.7
Used lower bound to
extrapolate efficiency to final
cushion thickness of 2.5
inches.
Linear (Lower
Bounds)
0.6
0
1
Sample Thickness (in)
2
Linear (Upper
Bounds)
10
Analysis of Safety Margin Tests Results
Paper Honeycomb
Tests show two dominant G-loading modes:
ƒ Buckling (first peak)
ƒ Crushing (~plateau)
S a m p l e F i l te re d H C S a fe ty M a rg i n T ri a l
100
Acceleration (G)
80
60
40
20
0
11
0
0 .0 0 2
0 .0 0 4
0 .0 0 6
0 .0 0 8
T i m e (s )
0 .0 1
0 .0 1 2
0 .0 1 4
0 .0 1 6
Analysis of Safety Margin Tests Results
Paper Honeycomb (Cont.)
Peak Distribution Curves
ƒ Buckling: G-load peak
during drop-tests
ƒ Crush: G-load peak
predicted by theory
Honeycomb Distribution of Secondary Peak Accelerations
Honeycomb Distribution of Primary Peak Accelerations
7
12
Mean Peak Acceleration: 59.0 G
Standard Deviation: 8.0 G
Mean Peak Acceleration: 83.6 G
Standard Deviation: 20.6 G
6
10
Number of Trials
Number of Trials
5
4
3
8
6
4
2
2
1
0
40
45
50
55
60
65
70
Seconday Peak Acceleration (G)
75
80
0
60
70
80
90
100
110
120
Primary Peak Acceleration (G)
130
12 150
140
Analysis of Safety Margin Tests Results
Paper Honeycomb (Cont.)
Sample HC Safety Margin Trial
200
Raw Data
Filtered Data
150
ƒ High Frequency
Vibrations
Solution:
100
Acceleration (G)
Issue:
ƒData filtered above 580Hz
50
Motivation:
0
-50
ƒ 35
-100
σcrush 25
30
20
-150
0
0.002 0.004 0.006 0.008 0.01
Time (s)
0.012 0.014 0.016
15
10
5
0
0
0.2
0.4
0.6
0.8
13
Xcrush
Comparison to Previous Theory:
Analysis of EF Crush Stress
Previous Model: Assumes constant crush stress
ν
τ cushion =
2 gG η t
2
Aσ dynamic = mGg
Findings: Crush stress is not constant
New Model
Crush Stress (psi)
Sample 1" EF Static Test Trial
Actual
Crush
10
Modelled
Behavior
5
Model crush
stress as a
linear function,
solve ODE
Aσ dynamic = m&x&
y = 4.077x - 0.0009
0
0
0.2
0.4
0.6
Displacement (in)
0.8
1
Linear
(Modelled
Behavior)
&x& +
kA
x=0
m
14
Analysis of Safety Margin Tests Results
Expanding Foam
Experiment Results
Errors in Model
Expanding Foam Distribution of Peak Accelerations
7
Mean Peak Acceleration: 62.2 G
Standard Deviation: 6.7 G
6
Number of Trials
5
µ=21 G
4
=
3
calculation error when
determining parameters
µ=159 G
+
modeling error of stress
vs. displacement slope
2
1
0
45
Corrected Model Prediction D
50
55
60
65
70
75
Peak Accleration (G)
µ=65 G
15
Analysis of Volume and Reliability Results
Volume:
¾Use modified models and the results of the Safety Margin Tests to
calculate new Area and Cushion Thickness.
¾Honeycomb Pre-Deployment Volume = Area * Cushion
Thickness
¾Expanding Foam Post-Deployment Volume = Area * Cushion
Thickness, then scale to find pre-deployment volume
Expansion Reliability:
¾Use sample size and number of failures to determine Reliability and
Confidence through Larson’s Binomial Distribution Graph
16
Sources of Error
Honeycomb
Expanding
Foam
Sources of Error
Crush
Efficiency
7.4 %
4.2%
- Instron Machine Error
- Estimating Crush
Displacement
Volume
11%
3.7%
- Impact Velocity
- Acceleration
Measurement
17
Conclusion:
Assessment of Hypothesis
ƒ Confirmed “crush thickness efficiency loss of no more than 30%”
ƒ Refuted “decrease in reliability of no more than 10%”
ƒ Uncertain assessment of “75% less pre-deployment volume”
EF parameters as compared to HC
Hypothesis
100%
80%
60%
% difference
EF
40%
20%
0%
Efficiency
Pre-Deployment Volume
Material Reliability
18
Conclusion:
Summary of Principal Findings
1)
The pre-deployment volume of expanding foam is at most 34.5% the
pre-deployment volume of paper honeycomb, under given test
conditions.
2)
The crush efficiency of expanding foam is at least 72.7% of the crush
efficiency of paper honeycomb, for given test conditions
3)
The expanding foam is 83% reliable (95% confidence) to expand to
expected volume within 30 seconds.
4)
Honeycomb crush efficiency is a function of cushion thickness.
5)
Honeycomb buckling results in peak acceleration during impact.
6)
Expanding Foam crush stress is not constant. Instead behavior
during crush can be characterized using a linear approximation of
crush stress.
19
Conclusion:
Summary of Principal Findings (Cont.)
7) For a given crush stress, payload mass, and impact velocity:
ƒ
Honeycomb volume as a function of maximum acceleration during
impact is constant.
Expanding foam volume as a function of maximum acceleration
during impact is linear.
Pre-Deployment Volume of Attenuation Material vs.
Maximum Acceleration During Impact
35
30
Volume (in^3)
ƒ
25
Expanding
Foam
Honeycomb
20
15
10
5
0
0
50
100
150
Maximum Acceleration (G)
200
20
Recommendations for Future Research
ƒ Experimentally verify and improve the corrected
models of material behavior during impact
ƒ Characterize payload resonance for HC attenuation
ƒ Expand experiment scope:
- lowest pre-deployment volume impact attenuation
material may depend on touch-down conditions
ƒ Design reliable, low-volume, low-weight mechanism to
expand foam onboard
21
Acknowledgements
Christian Anderson
Technical Staff
16.62X Faculty
Questions?
22
Sample EF Safety Margin Test Trial (Raw Data)
70
60
Acceleration (G)
50
40
30
20
10
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
-10
Time (s)
23