MINI SLED CRASH PROJECT

Jayneel Gajjar, Madhu Kandampadath | Vehicle Crash Dynamics | December 19, 2015
Mini Sled Project
GROUP 11

Objective -:
Conduct a crash reconstruction of collision of bullet object with target object which is fit with a cup. Generate a
mathematical model to find the Pre Impact Velocity and Post Impact Velocity of both bullet and target object.
Compare the values obtained with the values obtained from accelerometer reading and using the crash analysis
software TEMA and give your conclusion.
Data Available -:
We need to make a calibration curve for Ecrush Vs Crush and coefficient of restitution (e) vs Crush. In order to
make the curves the data which is required is given below
Crush Length
(in.) Sled Weight (lb) Air Pressure (psi)
0.53 14.0 40
0.95 14.0 50
0.93 14.0 60
0.67 19.7 40
1.05 19.7 50
1.26 19.7 60
0.54 25.4 30
1.60 25.4 40
2.02 25.4 50
The above data is obtained by conducting a full frontal collision with rigid barrier. The cup is attached to the
barrier. In the experimental setup, the bullet is made to move using compressed air which makes piston move
which in turn pulls the bullet sled. So the test is conducted at different air pressure which will provide different
Pre Impact velocity and different crush length.
Test Condition -: The test is recorded by using a camera which can record at speed of 1000 frames per second.
The lighting used in the lab is direct current since alternating current has frequency of 60 Hz it will cause
fluctuation in brightness while video is recorded.
TEMA -:
TEMA is a crash analysis software which makes use of the video recorded to analyze the crash. The basic input
which are required for the TEMA software -:
1.) Recording Speed ( frames per second)
2.) Gamma Value
3.) Distance of the reference plane from camera
4.) Distance of setup from reference plane
5.) Scale distance between stationary points.
Upload the video of the 9 experiments conducted one by one and follow the mentioned procedure.

Once the video is opened on the software we need to set T0. After that locate the bullet, target and reference
points using add point tool. Using the quadrant geometry locate the points correctly and set size for the object.
Once the points the located we need to provide distance of the reference plane from camera and Scale distance
between stationary points which help TEMA to analysis the motion. The data is -:
Distance from Camera Lens to Reference Frame (in.) 38.25
Scale Distance between Stationary Targets (in.) 3
Distance from Reference Frame to Sled Target (in.) -3.25
Select the point on the bullet to obtain the velocity vs time graph and acceleration time graph. From the velocity
time graph we obtain the Pre Impact velocity and Post Impact Velocity. Also we know the crush depth for each
case. We obtain the coefficient of restitution by taking the ratio of Post impact velocity to Pre Impact Velocity.
The corresponding values are tabulated below -:
Test
Air
Pressure
(psi)
Vpre(m/s) Vpost(m/s) e Crush
Sled
Weight
(lb)
Sled
Wt.(kgs)
Ecrush(J)
TEST
1 40 2.6 -0.206 0.079 0.53 14 6.3 21.301
TEST
2 50 2.38 -0.205 0.086 0.95 14 6.3 17.829
TEST
3 60 2.0923 -0.196 0.094 0.93 14 6.3 13.760
TEST
4 40 1.4 -0.1 0.071 0.67 19.7 8.9 8.701
TEST
5 50 2.25 -0.162 0.072 1.05 19.7 8.9 22.472
TEST
6 60 1.88 -0.154 0.082 1.26 19.7 8.9 15.665
TEST
7 30 2.2 -0.174 0.079 0.54 25.4 11.5 27.671
TEST
8 40 1.95 -0.126 0.065 1.60 25.4 11.5 21.785
TEST
9 50 1.48 -0.115 0.078 2.02 25.4 11.5 12.526
The only input value which we have with us is the crush depth. Therefore we make a calibration plot of
Coefficient of restitution vs Crush Depth

Also we know that
Epre=Epost+Ecrush
Since we know the pre impact velocity and post impact velocity from the graphs we can obtain Ecrush for each
case. Therefore we make another calibration curve of Ecrush vs Crush Depth.
Since we have the calibration curves with us we can use the data from calibration curve to obtain Ecrush and
Coefficient of restitution for our experiment.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.00 0.50 1.00 1.50 2.00 2.50
e(Coefficientofresitution)
Crush Depth (inch)
E Vs Crush Depth
0
5
10
15
20
25
30
0.00 0.50 1.00 1.50 2.00 2.50
Ecrush(J)
Crush Depth (inch)
Ecrush(J)

Actual Setup -:
Distance of reference plane from camera -: 43.5 inch
Distance between two points on reference plane -: 12 inch
Distance between reference plane and setup -: 7 inch
Using the steps shown above we setup the case in TEMA. Then we plot acceleration vs time and velocity vs time
curve for our actual experiment.
The yellow curve shows the velocity of bullet and red curve shows the velocity of target. From the graph we see
that the bullet approaches the target with velocity of around 3 m/s. We chose the point just before the velocity
starts to decrease therefore the pre impact velocity of bullet is 2.91 m/s. Whereas the target is at rest therefore the
pre impact velocity of the target is 0 m/s. The post impact velocity of bullet is 1.15 m/s and for the target it is 1.52
m/s. From the graph we see that the velocity of bullet tends to increase at time 135 msec. This might be because
vibration in the table which must have caused the reference points to move a bit causing error in reading the pixel
in TEMA. Velocity of bullet does not become negative which means that there is no change in direction of its
motion.

Accelerometer
The accelerometer are fit on the bullet and target which measures the deceleration during impact. From the data
obtained we plot acceleration vs time graph for bullet and target.
For Bullet Sled
From the graph we can see that initially the accelerometer reads zero. Then when it starts to accelerate we find the
value in accelerometer changes. At around 0.1 sec the bullet reaches a constant velocity so again the
accelerometer reads zero. At around 0.18sec it impacts the targets and we see that accelerometer reads the data.
On integrating the acceleration curve we obtain the velocity curve.
From the velocity time graph we see that the bullet sled speed increases from zero to 3.25 m/s between 0.2 sec to
0.8 sec. It remains constant till around 0.18 sec and as soon as it impact it decelerates so its velocity decreases and
reaches 1.3 m/s.
-150
-100
-50
0
50
100
150
-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Acceleration(g's)
Time (sec)
Acceleration vs time for bullet
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
-0.05 0.05 0.15 0.25 0.35 0.45
Velocity(m/s)
Time (sec)
Velocity of Bullet sled

For Target Sled
The target sled is initially at rest. There are small reading in acceleration curve from 0.02 sec to 0.05 sec because
of minor vibration in the setup. As the bullet sled impacts the target at around 0.18 sec, we see that accelerometer
shows reading. The target sleds accelerates till 0.25 secs and maintains a constant velocity.
-70.000
-50.000
-30.000
-10.000
10.000
30.000
50.000
70.000
-0.05 0.05 0.15 0.25 0.35 0.45
Acceleration(m/s^2)
Time(sec)
Acceleration vs Time graph of Target Sled
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
-0.05 0.05 0.15 0.25 0.35 0.45
Velocity(m/s)
Time(secs)
Velocity v/s Time graph for Target Sled

Fig : i. Before Crush ii. After Crush
Mathematical Model
Our mathematical model is based on 3 important equations. From our experiment which we conducted we get the
value of the crush depth. We measure crush depth at four different points on the cups. The original length of the
cup is 4.5 inch. The length of cup after impact at four different region are 86 mm, 92.3 mm, 91 mm and 93 mm.
We take average of the four values and we get average length of cup after crash as 90.575 mm or 3.566 inch. The
crush depth is
Crush depth = Original Length before impact – Length after impact
Crush depth = 4.5 – 3.566 = 0.934 inch
Using the calibration curve which we made of Coefficient of restitution vs crush depth and Ecrush vs crush Depth
we obtained the coefficient of restitution and Ecrush for our crush depth of 0.934 inch. The corresponding value
of coefficient of restitution (e) = 0.08 and Ecrush =20 J.
Since we have to find the pre and post impact velocity of bullet and target sled. We have 4 unknown out of which
𝑣2
𝑝𝑟𝑒
= 0. Therefore we are left with 3 unknowns. We require three equations to solve
Basic governing equations for solving the Mathematical model

1. Conservation of Momentum Eq:
𝑚1 𝑣1
𝑝𝑟𝑒
+ 𝑚2 𝑣2
𝑝𝑟𝑒
= 𝑚1 𝑣1
𝑝𝑜𝑠𝑡
+ 𝑚2 𝑣2
𝑝𝑜𝑠𝑡
m1 =7.67 kgs (Mass of bullet sled) m2= 7.83kgs (Mass of Target Sled)
𝑣2
𝑝𝑟𝑒
= 0 (Since the target sled is in rest initially)
7.67𝑣1
𝑝𝑟𝑒
= 7.67𝑣1
𝑝𝑜𝑠𝑡
+ 7.83𝑣2
𝑝𝑜𝑠𝑡
----- i
2. Conservation of Energy Eq :
1
2
𝑚1 𝑣1
𝑝𝑟𝑒2
+
1
2
𝑚2 𝑣2
𝑝𝑟𝑒2
=
1
2
𝑚1 𝑣1
𝑝𝑜𝑠𝑡2
+
1
2
𝑚2 𝑣2
𝑝𝑜𝑠𝑡2
+ 𝐸2𝑐𝑟𝑢𝑠ℎ
𝑣2
𝑝𝑟𝑒
= 0
3.835𝑣1
𝑝𝑟𝑒2
= 3.835𝑣1
𝑝𝑜𝑠𝑡2
+ 3.915𝑣2
𝑝𝑜𝑠𝑡2
+ 20𝐽 ------ ii
3. Coefficient of Restitution Eq :
𝑒 = −(
𝑣2
𝑝𝑜𝑠𝑡
− 𝑣1
𝑝𝑜𝑠𝑡
𝑣2
𝑝𝑟𝑒 − 𝑣1
𝑝𝑟𝑒
)
𝑒 = 0.08
−0.08𝑣1
𝑝𝑟𝑒
= −𝑣2
𝑝𝑜𝑠𝑡
+ 𝑣1
𝑝𝑜𝑠𝑡
------ iii
Simplifying equations:
𝑣1
𝑝𝑟𝑒
= 𝑣1
𝑝𝑜𝑠𝑡
+ 1.02𝑣2
𝑝𝑜𝑠𝑡
−0.08(𝑣1
𝑝𝑜𝑠𝑡
+ 1.02𝑣2
𝑝𝑜𝑠𝑡
) − 𝑣1
𝑝𝑜𝑠𝑡
+ 𝑣2
𝑝𝑜𝑠𝑡
= 0
𝑣2
𝑝𝑜𝑠𝑡
= 1.176𝑣1
𝑝𝑜𝑠𝑡
3.835(𝑣1
𝑝𝑜𝑠𝑡
+ 1.02𝑣2
𝑝𝑜𝑠𝑡
)2
− 3.835𝑣1
𝑝𝑜𝑠𝑡2
+ 3.915(1.176𝑣1
𝑝𝑜𝑠𝑡
)2
+ 20𝐽
9.355𝑣1
𝑝𝑜𝑠𝑡2
= 20
𝑣1
𝑝𝑜𝑠𝑡
= 1.46 𝑚/𝑠
𝑣1
𝑝𝑟𝑒
= 3.2 𝑚/𝑠
𝑣2
𝑝𝑜𝑠𝑡
= 1.71 𝑚/𝑠

Observations-:
MODE
BULLET (m/s) TARGET(m/s)
V1pre V1post V2pre V2post
TEMA- VIDEO ANALYSIS 2.91 1.15 0 1.52
ACCELEROMETER 3.25 1.3 0 1.6
MATHEMATICAL MODEL 3.2 1.46 0 1.71
ERROR of Mathematical model
w.r.t Accelerometer 1.538462 -12.3077 NA -6.875
Error of Tema w.r.t
Accelerometer
10.46154 11.53846 NA 5
Possible Error sources in TEMA are
1. Anomalous output from Video analysis.
When the setup vibrate the position of the reference points in the video tend to change which affects the
tracking ability of the software. As we can see from the velocity vs time curve after collision the bullet
tends to accelerate. This cannot not be possible without any force applied on the bullet. We expect that the
table was shaking so the position of reference points changed which resulted in the error. This causes
error in taking the right Vpost values. This accounts for the maximum error in the Vpost. The Vpost value
fluctuates between 1.15 to 1.3 m/s. We took Vpost as 1.25 m/s. So the relative error in taking the Vpost
value ranges from -4.2% to 8.3%.
2. Reference Error
If the actual distance between camera and reference points and what we measure is off by some value it
can result in error. It will basically offset the values.
For the given conditions with a slight reference plane value offset of 0.25” ~6.34mm the value of the
velocity changes by 0.15m/s which gives an error up to 3%.
3. Human Reading error
This error is accountable along with the error in the output from the TEMA software. The error in reading
the values can occur like if the reading is taken 2 times then the probability of getting two different values
are bit high as the TEMA software doesn’t give that much precise curve and the variations in the curve
makes difficult to get exact values.
For a variation in getting V values form the graph is slightly off by 0.05m/s then the % error in the value
of V Is 1.36%. We can say reading error will be around 1.5%
4. Processing Error
The TEMA works by tracking the pixel as it updates the pixel matrix displacement with respect to its
previous location and the with the help of reference plane it calculates the Angle thus the variation in
angle gives the desired value of velocity(triangulation/trilateration). Due to its high velocity and low
frame capture there happens to have the offset in the pixels thus causes the variation in speed thus results
in cumulative error in the tracking.

This error is reduced by using the 2 Camera tracking system which is widely used in photogrammetry
nowadays to reduce the error.
This error accounts for the error % ranging about <1%.
Possible error in Mathematical Modelling
1. Calibration Curve Fit Error.
The calibration curve is made using TEMA software which again returns about 2.4% error in the values.
Also the calibration values are plotted by the number of similar experiments. It can occur some of the
points shows the anomalous behavior thus that point doesn’t give to the prover curve fit. Which
eventually gives an error to the “ e “ and “ Ecrush “ values . Thus the error is carried and multiplied in the
Vpre and Vpost calculations.
For 2 different curve fits for Ecrush even if value of Ecrush is varies by +/- 1 Joule the error in velocity
ranges from 5 to 8%.
2. Inability of Mathematical model to process the actual scenario.
From the values of V pre and V post we observe that major error occurs in the Vpost value of the bullet. It
is because when the bullet crushes target the accelerometer reads the deceleration whereas the
mathematical model is unable to read this. This results in higher value of Vpost of the bullet. This error
ranges between 3 to 4%
3. Reading error from the Graph
There is a probability of the reading error form the graph. For e.g. from the calibration graph there is
chance of taking up value with error 1- 2.5% error.
Possible error from the Accelerometer
Accelerometer gives the best approximation of the values w.r.t to the other methods still it can carry some error
such as
1. Vibration of the system
The vibration of the system on which the accelerometer is mounted is subject to rapid acceleration and
deceleration due to crush and external force which can induce many internal vibration to the
accelerometer which adds up to the accelerometer reading of its own.
This causes and error in the graph which causes error in the velocity curve which is obtained by
integrating the acceleration graph thus the cumulative error is estimated up to 1.5% to the actual values.
2. Aliasing
Aliasing is a type of sampling error in which frequencies that do not actually exist appear in the data.
Since nearly all data acquisition devices are digital, they have a sample rate: the rate at which samples are
collected and stored. If you use the wrong sampling rate the sampled waveform will differ significantly
from original.
Thus the common error is accounted upto 1%.

Error Chart in Accelerometer
% Internal Error
Vibration of System Aliasing
Reading Unaccounted Error
Error Chart in Mathematical
Modelling % Error w.r.t. accel
Calibration Fit Curve
Inability to process actual sc.
Human Reading error
Unaccounted Error
3. Time delay
The third biggest source of error is not accounting for the impact of the time delay between sampling the
data and the application software processing that information.
Error Sources Error Estimation -:
Considering the maximum of every error possible we have plotted the below pie chart -:
1. Accelerometer -:
Error Chart in Accelerometer
Error sources
% Internal
Error
Cumulative
Error
Vibration of System 1.5 36.31961259
Aliasing 1 24.21307506
Reading 0.33 7.99031477
Unaccounted Error 1.3 31.47699758
Total error 4.13 100
2. Mathematical Modeling -:
Error Chart in Mathematical Modelling
Error sources
% Error
w.r.t. accn
Cumulative
Error
Calibration Fit Curve 8 48.48484848
Inability to process
actual sc. 3 18.18181818
Human Reading
error 2.5 15.15151515
Unaccounted Error 3 18.18181818

Error Chart in TEMA
modelling % Error w.r.t Accel
Anomalous Output Reference Error
Reading Error Unaccounted Error
3. TEMA
Error Chart in TEMA modelling
Error sources
% Error
w.r.t Accel
Cumulative
Error
Anomalous Output 12 64.86486486
Reference Error 3 16.21621622
Reading Error 1.5 8.108108108
Unaccounted Error 2 10.81081081
Conclusion -:
Mini Sled project was conducted using three platform accelerometer values, TEMA and mathematical model. The
accelerometer gives the most accurate values even though there are some errors associated with it. Possible causes
for the error has been above mentioned for the data obtained. Our mathematical model gives us the second most
accurate values followed by TEMA. In mathematical model, the calibration curve fit error can be reduced by
including more sampling point and eliminating the ones with abnormal values. The calibration curve values are
obtained from TEMA. Other way to reduce the error can be done by obtaining the values of each experiment
using accelerometer rather than TEMA thereby reducing the error carried forward to mathematical model. The
second error which is the inability of mathematical model to replicate the actual scenario we can consider some
correction factor which will reduce the error. This can be taken into account by conducting several experiment
and deciding the empirical value of the correction factor.

MINI SLED CRASH PROJECT

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