Transcript E80 Stupid Presentation

E80 Final Report
Section 4 Team 2
Student 1
Student 2
Student 3
Student 4
May 5, 2008
Introduction

Goals:
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


Simulate rocket flights
Analyze rocket flight data
Compare simulation to analysis and explain
discrepancies
Three analyses
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
Large Inertial Measurement Unit (IMU)
Large Vibration
Small IMU Rocket—fatal flat spin
Background
IMU
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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
1000
900
800
Ay

700
600
500
400
0
10
20
30
40
50
Acceleration
60
70
80
90
100
Background

Vibration

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
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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
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Created 2-dimensional model of flight path using
thrust curves and coefficient of drag
Predicted time to apogee and height at apogee
Flight Preparation
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Set the configuration on the R-DAS unit
Check transmission channel and settings
Checked R-DAS and video telemetry
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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
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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

Ω(t )    z
  y

t t
Rt  t   Rt  exp
t

 z
0
x
y 

 x 
0 
sin( )
1  cos( )

2

Ω(t )dt  R(t ) I 
Ω(t ) t 
(
Ω
(
t
)

t
)

2





 a x (t ) 
a global (t )  R (t ) a y (t )
 a z (t )  local
Large IMU Simulation
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
Analyzed and launched
with G339N Motor
Rocksim predicted
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
Time to apogee: 6.627 s
Height at apogee: 701.7 ft
Burnout: 0.360 s
Distance from launch pad:
254.44 ft



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
0
-500
-2
-1
0
1
2
3
4
5
6
7
3
4
5
6
7
3
4
5
6
7
100
0
-100
-2
-1
0
1
2
time
200
0
-200
-2
-1
0
1
2
time
160
140
120
100
80
z

500
time
z velocity
Only able to
analyze to apogee
z position

z acceleration
Large IMU Data—Flight 1
60
40
20
0
-20
0
50
100
150
200
0
100
50
y
x
150
200
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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
0
-500
-2
-1
0
1
2
time
3
4
5
6
-1
0
1
2
time
3
4
5
6
-1
0
1
2
time
3
4
5
6
100
z velocity

500
0
-100
-2
200
z position
Only able to
analyze to apogee
0
-200
-2
140
120
100
80
z

z acceleration
Large IMU Data—Flight 2
60
40
20
100
0
140
50
120
100
80
60
40
y
20
0
0
x
Large IMU Analysis
Sensitivity to calibration curves
 Bias changes due to temperature
 Propagation of error
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Large Vibration Flight Data
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Collected data for
6 sensors
 Used the
sensor closest
to the motor as
the input
Graphed plots of
the output of each
sensor vs. the
designated input
15
10
7
6
1
1
2
1.5”
13”
17”
33.25”
Large Vibration Analysis
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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
Sensor 1 - Spectrogram
25
Time
20
15
10
5
0
10
20
30
40
50
60
Frequency (Hz)
70
80
90
100
Small IMU Simulation
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Analyzed and flown with
G104T motor
Analysis performed without
parachute
Rocksim predicted:
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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
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No distinct impulse and landing
curves as in other plots
Signal present only noise
MATLAB analysis gave useless
data
From visual and video analysis:
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Height at apogee: ~850 ft
Time at apogee: ~7.8 s
Small IMU Analysis
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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
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RockSim Simulations were relatively
accurate when compared to flight data
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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
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Professors Spjut, Wang, Cardenas,
Miraghie, and Yang
Proctor A, Proctor B, Proctor C, and Proctor
D
Questions?
Extra Figures
Sensor 1 - Spectrogram without a High Pass Butterworth Filter
40
20
0
Amplitude
-20
-40
-60
-80
-100
-120
-140
0
10
20
30
40
50
60
Frequency (Hz)
70
80
90
100
Modal Shape
15
10
5
0
0
5
10
15
20
25
30
35
Magnitude vs. Position, with theoretical mode on top
Sensor 10 as input, 7, 6, 1 as outputs 80 Hz
40
z acceleration
Large IMU Day 1 : Without
Rotation
600
400
200
0
-200
0
10
20
30
40
50
60
40
50
60
z velocity
time
100
50
0
-50
0
10
20
30
z position
time
400
200
0
-200
-400
0
10
20
30
time
40
50
60
VI Front Panel
First Modal Shape
Magnitude of Vibration (dB)
150
100
50
0
0
5
10
15
20
25
Position along Rocket (in)
30
35
40
Second Modal Shape
Magnitude of Vibration (dB)
350
300
250
200
150
100
50
0
0
5
10
15
20
25
Position along Rocket (in)
30
35
40