1. “Sky Rockets in Flight” Experimental Engineering Section 1,Team 3 Student 1, Student 2, Student 3, Student 4 May 5, 2008

3. Objectives Develop problem solving and critical thinking skills Utilize various disciplines of engineering Analyze and predict the flight of a rocket.

4. Prior to Launch Sensors Need to be Calibrated –Accelerometers, Gyroscopes, Pitot Tube, Pressure Sensor Physical Characteristics –Coefficients of Lift and Drag –Natural frequencies of rocket body Motor Quantities –Thrust Curve and Total Impulse for Modeling

5. Flight Modeling Calculate instantaneous acceleration: –Thrust Curve –Gravity –Lift (from wind) –Drag –Weather Cocking Euler’s Method to find trajectory Algorithm checked using RockSim

6. Algorithm F thrust =Instantaneous thrust from motor θ=angle from vertical g = acceleration from gravity A = cross sectional area ρ=air density I x =Moment of Inertia about x axis c D =drag coefficient c L =lift coefficient V=velocity α=angular acceleration W=wind speed d= distance between CM and CP

8. Launches Lucerne Valley, CA --- dry lake bed 4/19 - Large IMU & Small IMU –Windy (15-25 mph) 4/26 - Large IMU & Large Vibration –No wind

9. IMU Sensors Getting global coordinates from local coordinates Calibration for IMU

10. 4/19/08 IMU Height Graph: Apogee @ 5.20 sec & 166 m Predicted (RockSim): Apogee @ 6.17 sec & 183 m Predicted (MATLAB): Apogee @ 5.94 sec & 171 m

11. 4/26/08 IMU Height Graph: Apogee @ 4.98 sec &181 m Predicted (RockSim): Apogee @ 6.17 sec & 183 m Predicted (MATLAB): Apogee @ 5.97 sec & 172 m

12. Integration Errors Acceleration Euler’s Method Dead Reckoning Error

13. Pressure Altimeter Pressure decreases with altitude (1) No Dead Reckoning Error Poor Sensitivity

15. Vibration Analysis Periods with limited external influence Analyze short segments with FFT 00.050.10.150.20.25 -150 -100 -50 0 50 100 150 200 Sensor 1, 7, 12 Detrend Sampled Data Time (sec) Strain Voltage Output Sensor 1 Sensor 7 sensor 12

16. Frequency Analysis Sampling frequency too low (200 Hz). Fundamental frequency folded. SensorFrequency (Hz) 1141.5 6135, 137 7140 10135.5 12141.5

17. Failed Flight… Small IMU parachute did not deploy, rocket went into a fatal flat spin. Pitot, Pressure: No activity. Accelerometers: Activity stops at t=0.

18. …Failed Flight Gyroscopes: unexpected activity before and after launch

19. Conclusions IMU: Accurate measurement, but limited by the low sampling frequency Vibration: Shows the expected reaction –vibration occurred at same frequency as dynamic beam experiment

20. Recommendations GPS Higher sampling frequency in IMU and RDAS Looking at all 15 strain gauges at once Use the same IMU all semester

21. Acknowledgements Student Proctors Rocket Development Team Professor Spjut Professor Miraghie The Rest of the Engineering Faculty System Admin Stockroom Curator

22. References 1. Anonymous "Model Rocket Safety Code," http://www.nar.org/NARmrsc.html. 2. Qimin Yang, “Pressure sensors and thermistors,” http://www.eng.hmc.edu/NewE80/PresTempLec.html. 3. Student 5, E80 Section 4, Team 2 4. Phillip D. Cha and John I. Molinder, Sampling and Data Acquisition, in Fundamentals of Signals and Systems: A Building Block Approach, edited by Anonymous (Cambridge University Press, New York, 2006), pp. 86-88. Anonymous, “Accelerometer and Gyroscope Calibration,” http://www.eng.hmc.edu/NewE80/AccelGyroLab.html. Anonymous, “Integrated Dual-Axis Gyro,” http://www.eng.hmc.edu/NewE80/PDFs/IDG_300_Datasheet.pdf http://www.eng.hmc.edu/NewE80/PDFs/IDG_300_Datasheet.pdf Anonymous, “Analog Devices,” http://www.eng.hmc.edu/NewE80/PDFs/ADXL320.pdf Colin Holland, “Tri-axi inertial measurement unit combines seven sensors,” http://www.eetimes.eu/industrial/199905290 Mary Cardenas, “Rocket Dynamics,” http://www.eng.hmc.edu/NewE80/PDFs/rocket_dynamics.pdf.

23. Questions?

24. Calibration equations

25. The Failed IMU Rocket (Accel)

26. The Failed IMU Rocket (Gyros)

27. Aliasing Sampling Theorem: SensorDominant Frequency (Hz) 158.5 665, 67 760 1064.5 1258.5 SensorFrequency (Hz) 1141.5 6135, 137 7140 10135.5 12141.5

28. Detrend Data

29. FFT