1. Trajectory Analysis Student 1 Student 2 Student 3 Student 4 E80: Section 4 Team 3 Harvey Mudd College 5 May 2008

2. Goals Deep vs. broad Trajectory Practical application Relates many types of data Vibration

3. Trajectory Analyses 3 Methods: 1-D: Pressure 2-D: Flight Model 3-D: Inertial Measurement

4. Pressure Theory Relate altitude to pressure:

5. Pressure

6. Flight Model

7. C L <<C D Lift forces negligible θ Initially vertical Tangent to Trajectory dm Mass of fuel small compared to rocket body Flight Model: Assumptions

8. Flight Model

9. Numerical integration Explicit Euler Compounds error sources

10. Flight Model

11. Inertial Measurement R

14. Procedure

15. Sensor Data Voltage Raw (binary) to Voltage (decimal) Voltage to desired value Calibration curves

16. Results: Pressure Medium rocket, G67R

17. Results: Pressure Medium rocket, G69N

18. Results: Flight Model Medium rocket, G67R Apogee at 1004 ± 16 ft

19. Results: Flight Model Medium rocket, G69N Apogee at 1540 ±70 ft

20. Results: Flight Model Small rocket, G104T Apogee at 1013.8 ft RockSim Thrust curve

21. Results: Medium IMU G67R Apogee672 ft Time of Apogee6.9 s Landing time12.5 s Maximum Acceleration 223.4 ft/s 2 at 0.24 s Thrust Duration0 s to 1.16 s IMU Summary

22. Results: Medium IMU G69N Apogee992.8 ft Time of Apogee 8.425 s Landing time16.25 s Maximum Acceleration 190 ft/s 2 at 0.12 s Thrust Duration 0 s to 1.75 s IMU Summary

23. Results: Small IMU G104T Apogee: 409.9 ft Time of Apogee: 6.9 s IMU Summary:

24. Results: Apogee Compared apogee altitude and time as calculated by 3 methods and RockSim SizeMotor Flight ModelIMUPressureRockSim Alt. (ft) Time (s) Alt. (ft) Time (s) Alt. (ft) Time (s) Alt. (ft) Time (s) Med.G67R1004±168.26±0.06671.96.86642±98±0.5940.28.2 Med.G69N1540±7010.4±0.2993.18.48436±85.3±0.21358.69.8 SmallG104T1013.758.262409.96.9-- 925.67.8

25. Analysis Flight Model vs. RockSim Motor% Difference in apogee% Difference in time G67R6.86%0.388% G69N13.4%6.14% G104T9.53%10.21%

26. Analysis Flight Model Assumptions Load cell

27. Analysis Pressure vs. Theoretical Flight Model, RockSim Severe Weathercock Temperature

28. Analysis: IMU (Assumptions) Assume IMU stationary Calibration Expressions: A=Slope·(Raw Output – Offset)

29. Analysis: IMU (Errors) Offset Thermo-Mechanical Noise Shift in Offset Temperature Variation Numerical Integration Accelerometers and Rate Gyros

30. 3D Plot of G67R IMU

31. Conclusion Major sources of error Damage Compounded error from integration Future work Assumptions Drift due to Accel, Rate Gyro IMU vs. Temperature

32. Acknowledgements E80 Professors E80 Proctors Student A Student B Student C E80 rocket production team

33. Offset

34. Thermo-Mechanical Noise

35. 3D Plot of Small IMU G104T

36. Altitude and Temperature vs. Time for G69N

37. Altitude and Temperature vs. Time for G67R

38. Correlation between Altitude and Temperature(G67R)

39. Correlation between Altitude and Temperature(G69N)

40. Thermistor 1 Temperature for different flights

41. Thermistor 2 Temperature vs. Time for different flights

42. Load Cell Discrepancies

43. Thrust curve analysis