1. Rocket Flight Dynamics Section 1, Team 4 Student 1, Student 2, Student 3 May 5, 2008

2. Rockets Analyzed Large IMU rocket Large vibration rocket Small vibration rocket All launches at Lucerne Valley dry lake bed Altitude: 2848 feet

3. How the RDAS functions 6 channels of data Onboard accelerometer Onboard pressure sensor Samples at 200 Hz Runs on 9V battery supply

4. IMU and Vibration Sensors IMU 3 MEMS Accelerometers 3 MEMS Gyroscopes Vibration Piezoelectric strain gauges X axis Y axis Z axis

5. Modal Shapes Model rocket as a uniform beam At natural frequencies, distinct modal shapes Values of natural frequencies depend on beam dimensions and material properties Mode 1: Mode 2: Mode 3:.

6. Large IMU Rocket Launched April 26, 2008 with G339N motor RockSim used to model launch Estimated Apogee of 482.66 ft

7. Large IMU Rocket Approximations Any point before time=0 needs to be set to zero Account for calibration drift Over thrust curve, all other sensors should be zero Noisy x and z gyroscopes have negligible effect Integration error doesn’t affect apogee

8. Large IMU Rocket Apogee at 5.45 seconds Made several approximations to eliminate noise Model only works until apogee

9. Large Vibration Rocket Launched April 19, 2008 with G69N motor Severe weathercock RockSim trajectory portrays weathercock

10. Large Vibration Rocket Six vibration sensors connected to RDAS Sensor 10 assumed as input 72.39cm 60.64cm 46.67cm 31.75cm 15.875 cm 0 cm ADC0 ADC1 ADC2 ADC3 ADC4 ADC5 3 5 6 7 8 10

11. Large Vibration Rocket Applied Fourier transform Treating sensor 10 as input, plotted FRF

12. Large Vibration Rocket Identified three resonant peaks Mode 1 assumed to be at 23.85 Hz

13. Large Vibration Rocket Mode 2 assumed to be at 0.9569 Hz

14. Large Vibration Rocket Higher Mode at 19.65 Hz

15. Small Vibration Rocket Launched April 19, 2008 with G104T motor Camera drew power from battery Parachute did not deploy

16. Small Vibration Rocket Five vibration sensors connected to RDAS Sensor 10 chosen as input 37 in 28 in 22 in 8 in 1 in ADC0 ADC1 ADC2 ADC4 ADC3 1 5 6 8 10

17. Small Vibration Rocket Applied Fourier transform and 50 Hz filter Treating sensor 10 as input, plotted FRF

18. Small Vibration Rocket Identified two resonant frequency peaks Mode 1 assumed to be at 7.997 Hz

19. Small Vibration Rocket Mode 2 assumed to be at 0.5831 Hz

20. Summary Large IMU Apogee at 5.45 seconds Modeled altitude at apogee of 3382 feet Large Vibration Three natural frequencies: 23.85 Hz, 0.956 Hz, 19.65 Hz Small Vibration Two natural frequencies: 7.997 Hz, 0.5831 Hz

21. Acknowledgements E80 lab professors Mary Cardenas, Reza Miraghaie, Erik Spjut, Ruye Wang, and Qimin Yang Lab proctors and Rocket Development Team Reference 1 Reference 2 Reference 3

22. References Miraghaie, Reza, Modal Vibration, http://www.eng.hmc.edu/NewE80/PDFs/ModalVibr ationLecture.pdf Remote Data Acquisition System, http://www.aedelectronics.nl/rdas/index.htm Spjut, Erik, http://www.eng.hmc.edu/NewE80/ Wang, Ruye, Inertial Navigation, http://fourier.eng.hmc.edu/e80/inertialnavigation/