1. E80 Final Report Section 4 Team 2 Student 1 Student 2 Student 3 Student 4 May 5, 2008

2. 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

3. 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

4. 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

5. 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

6. 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

7. Large IMU Analysis

8. 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

9. 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

10. 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

11. Large IMU Analysis Sensitivity to calibration curves Bias changes due to temperature Propagation of error

12. Large Vibration Flight Data 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 1076 1212 1 15 1.5” 13” 17” 33.25”

13. 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

14. 3D Analysis

15. 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

16. 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

17. 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

18. 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

19. Acknowledgments Professors Spjut, Wang, Cardenas, Miraghie, and Yang Proctor A, Proctor B, Proctor C, and Proctor D

20. Questions?

21. Extra Figures

22. Modal Shape Magnitude vs. Position, with theoretical mode on top Sensor 10 as input, 7, 6, 1 as outputs 80 Hz

23. Large IMU Day 1 : Without Rotation

24. VI Front Panel

25. First Modal Shape Position along Rocket (in) Magnitude of Vibration (dB)

26. Second Modal Shape Position along Rocket (in) Magnitude of Vibration (dB)