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

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

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

Pressure Theory Relate altitude to pressure:

Pressure

Flight Model

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

Flight Model

Numerical integration Explicit Euler Compounds error sources

Flight Model

Inertial Measurement R

Procedure

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

Results: Pressure Medium rocket, G67R

Results: Pressure Medium rocket, G69N

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

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

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

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

Results: Medium IMU G69N Apogee992.8 ft Time of Apogee 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

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

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± ±98± Med.G69N1540±7010.4± ±85.3± SmallG104T

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

Analysis Flight Model Assumptions Load cell

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

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

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

3D Plot of G67R IMU

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

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

Offset

Thermo-Mechanical Noise

3D Plot of Small IMU G104T

Altitude and Temperature vs. Time for G69N

Altitude and Temperature vs. Time for G67R

Correlation between Altitude and Temperature(G67R)

Correlation between Altitude and Temperature(G69N)

Thermistor 1 Temperature for different flights

Thermistor 2 Temperature vs. Time for different flights

Load Cell Discrepancies

Thrust curve analysis