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E80 Final Report
Section 4 Team 2Student 1Student 2Student 3Student 4May 5, 2008
Introduction Goals:
Simulate rocket flights Analyze rocket flight data Compare simulation to analysis and explain
discrepancies Three analyses
Large Inertial Measurement Unit (IMU) Large Vibration Small IMU Rocket—fatal flat spin
Background IMU
Placed the IMU board on a turntable
Measured distance from center to IMU
Spun at several different frequencies
Plotted ADC values as a function of known angular velocity and linear acceleration
IMU calibration
y = 4.5054x + 540.35
400
500
600
700
800
900
1000
0 10 20 30 40 50 60 70 80 90 100
Acceleration
Ay
Background Vibration
Placed strain gauges on a hollow cylinder Performed a tap test with an impulse hammer Created Bode plots of output compared to force
Flight Modeling Created 2-dimensional model of flight path using
thrust curves and coefficient of drag Predicted time to apogee and height at apogee
Flight Preparation Set the configuration on the R-DAS unit Check transmission channel and settings Checked R-DAS and video telemetry
Two flights did not have working video Loaded parachute and wadding Proctor loaded motor Proctor loaded ejection charge Loaded rocket on launch pad Turned on R-DAS unit to transmit Launch
IMU Analysis Procedure MATLAB code used calibration curves to
convert ADC values to acceleration and angular velocity
Numerically integrate angular velocities to find angles at each time step
Create rotation matrix to convert local acceleration to global
Numerically integrate in 3-dimensions to find velocity and position
Large IMU Analysis
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−−
−=
0
0
0
)(
xy
xz
yz
t
ωω
ωω
ωω
Ù
( ) ( ) ⎟⎠
⎞⎜⎝
⎛ −++=⎥⎦
⎤⎢⎣⎡=+ ∫
+ 22
))(()cos(1
)()sin(
)()(exp ttttItdttttttt
tδ
σ
σδ
σ
σδ
δÙÙRÙRR
localz
y
x
global
ta
ta
ta
tRt
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
)()()(
)()(a
Large IMU Simulation Analyzed and launched
with G339N Motor Rocksim predicted
Time to apogee: 6.627 s Height at apogee: 701.7 ft Burnout: 0.360 s Distance from launch pad:
254.44 ft
Large IMU Data—Flight 1 Only able to
analyze to apogee Too much error
accumulated past apogee to analyze the data
Time to apogee: 6.220 s
Height at apogee: 522.22 ft
Burnout: 0.35 s
-2 -1 0 1 2 3 4 5 6 7-500
0
500
timez acceleration
-2 -1 0 1 2 3 4 5 6 7-100
0
100
time
z velocity
-2 -1 0 1 2 3 4 5 6 7-200
0
200
z position
time
0 50 100 150 200 0 50 100 150 200-20
0
20
40
60
80
100
120
140
160
yx
z
Large IMU Data—Flight 2 Only able to
analyze to apogee Too much error
accumulated past apogee to analyze the data
Time to apogee: 5.2150 s
Height at apogee: 454.35 ft
Burnout: 0.34 s
-2 -1 0 1 2 3 4 5 6-500
0
500
timez acceleration
-2 -1 0 1 2 3 4 5 6-100
0
100
time
z velocity
-2 -1 0 1 2 3 4 5 6-200
0
200
z position
time
0
50
100
0204060801001201400
20
40
60
80
100
120
140
xy
z
Large IMU Analysis Sensitivity to calibration curves Bias changes due to temperature Propagation of error
Large Vibration Flight Data Collected data for
6 sensorsUsed the
sensor closest to the motor as the input
Graphed plots of the output of each sensor vs. the designated input 10 7 6
12
1
15
1.5”13”
17”33.25”
Large Vibration Analysis Sampling at 200 Hz gave frequencies
between 0 and 100 Hz Based on Fourier transform and hollow
cylinder results expected frequencies ~10 Hz and ~50 Hz within window
Observed frequencies matched expected frequencies at both liftoff and apogee
Mode shapes were arbitrary because of limited sensor resolution
3D Analysis
0 10 20 30 40 50 60 70 80 90 100
5
10
15
20
25
Frequency (Hz)
Sensor 1 - Spectrogram
Time
Small IMU Simulation Analyzed and flown with
G104T motor Analysis performed without
parachute Rocksim predicted:
Time to apogee: 7.864 s Height at apogee: 938.31 ft Burnout: 0.901 s Distance from launch pad:
126.91 ft Time to impact: 15.68 s
Small IMU Flight Data Data was corrupted throughout
flight No distinct impulse and landing
curves as in other plots Signal present only noise
MATLAB analysis gave useless data
From visual and video analysis: Height at apogee: ~850 ft Time at apogee: ~7.8 s
Small IMU Analysis Cause of data corruption may be low voltage to R-DAS
and IMU Could have also led to failure of parachute to open at
apogee From video, rocket experienced greater weather
cocking than predicted by Rocksim Traveled nearly twice the predicted distance from
launch pad Also likely due to higher wind gusts than predicted
Noise in acceleration signal prevents accurate numerical analysis of flight path
Conclusions RockSim Simulations were relatively
accurate when compared to flight data Variable winds and launch conditions
contribute to discrepancies High amount of error after apogee for all
IMU flights Resonant peaks for vibration rocket were
observed during liftoff as expected Mode shapes could not be resolved
Acknowledgments Professors Spjut, Wang, Cardenas,
Miraghie, and Yang Proctor A, Proctor B, Proctor C, and Proctor
D
Questions?
Extra Figures
0 10 20 30 40 50 60 70 80 90 100
-140
-120
-100
-80
-60
-40
-20
0
20
40
Frequency (Hz)
Sensor 1 - Spectrogram without a High Pass Butterworth Filter
Amplitude
Modal Shape
0 5 10 15 20 25 30 35 400
5
10
15
Magnitude vs. Position, with theoretical mode on top Sensor 10 as input, 7, 6, 1 as outputs 80 Hz
Large IMU Day 1 : Without Rotation
0 10 20 30 40 50 60
-2000
200400600
timez acceleration
0 10 20 30 40 50 60
-50
0
50
100
time
z velocity
0 10 20 30 40 50 60
-400-200
0200400
z position
time
VI Front Panel
First Modal Shape
0 5 10 15 20 25 30 35 400
50
100
150
Position along Rocket (in)
Mag
nitu
de o
f V
ibra
tion
(dB
)
Second Modal Shape
0 5 10 15 20 25 30 35 400
50
100
150
200
250
300
350
Position along Rocket (in)
Mag
nitu
de o
f V
ibra
tion
(dB
)