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

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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

)