1. Analysis of the Mudd III Rockets
By: Student 1
Student 2
Student 3
Student 4

2. Introduction: Rocket Types
Medium Vibration (G104T)
Determine resonant frequencies of rocket
Medium Temperature and Pressure (G104T)
Determine altitude and temperature
Medium IMU (G79W)
Convert from local to global coordinates
Determine flight path from on-board data
Small IMU (G104T)
Analyze bad data

3. Introduction: Data Collection
RDAS unit
On-board data storage
200Hz sampling rate
6 channels
Interfaces with thermistors, pressure sensors, gyroscopes, accelerometers, and strain gauges

4. Medium Vibration: Theory
Modal shapes and frequencies
Resonance
Modeling as a free-free beam
Assumptions within the model
Mode
ωn (rad/s)
Frequency, fn (Hz) 1
414.02
65.89 2
181.63 3
356.12
Assumptions: the rocket has no internal support structures, no cut-out sections on the surface, no camera mounted to its side, and no additional mass other than the mass of its polycarbonate outer frame.

5. Medium Vibration: Laboratory
LabView and DAQ
Frequency Response Function
Bode plots
Sensor positions
Mode
Frequency, fn (Hz) 1 80 2
260 3
360

6. Medium Vibration: Flight
R-DAS
Nyquist Theorem
FRF at ignition and parachute deployment
Resonant Frequencies due to ignition and parachute deployment

7. Medium Vibration: Conclusions
Mode
Theoretical Modal Frequencies
(Hz)
Laboratory Modal Frequencies
Flight
Modal Frequencies 1
65.89 80 85 2
181.63
260
258 3
356.12
360
348

8. Medium Temperature and Pressure: Theory
Altimeters and thermistors
RockSim model
Predictions

9. Medium Temperature and Pressure: Flight
Pressure-Altitude relationship
R-DAS and IMU altitudes
Temperature readings from thermistors

10. Medium IMU Rocket: Theory
Inertial Measurement Unit (IMU)
Accelerometers
Rate gyros
Modeling with RockSim
Projected apogee
theoretical prediction shows an apogee of 223m should occur at t=7.3s.

11. Medium IMU Rocket: Flight
Conversion method
Major flight events on graphs
multiplied the accelerations by the rotation matrix to convert from local to global variables.
Three major points of acceleration occur: the launch at t = 0s, the parachute deployment at t = 7.035s, and the landing at t = 29.9s.
the velocity in the z-direction increases dramatically as the motor burns up until roughly t = 1.595s. Then, once the motor is done burning, the velocity decreases until it reaches zero, at t = 6.96s. Lastly, the velocity once again reaches zero for a brief second when the rocket hits the ground, at time t = 29.92s.

12. Medium IMU Rocket: Flight
The position along the z-axis as measured from the IMU unit is consistent with the data measured from the RDAS unit. However, while they both have a curve shape that fits very well with prediction, the actual values for apogee height differ slightly from prediction. Additionally, the y-positions of the rocket are consistent with what was observed at the launch.
The x positions of the rocket, however, differ from observation beginning at roughly t = 10s onward, slightly after apogee. The discrepancy between measured and observed landing locations is thus due to the double integration of a constant only along the x-axis, as a result of the wind.
Discrepancy between IMU data and actual position

13. Medium IMU Rocket: Conclusions
Theoretical Altitude
(meters)
IMU
Altitude
RDAS
223
195.56
196.77
In flight data is consistent with theoretical prediction. Deviation between two most likely caused by several factors: a non-ideal motor, stronger wind than expected, more drag than anticipated, and unaccounted for friction along the launch pad.

14. Small IMU Rocket: Theory
Predicted apogee
Flight events and life of the rocket
Discrepancies in acceleration
An apogee of roughly 285m is expected to occur after approximately 7.75s

15. Small IMU Rocket (continued)
Affects of bad acceleration data
Problems with IMU data
Possible reasons for inaccurate readings

16. Conclusions
Modal vibrations of experiment and actual flight are consistent
On-board pressure data accurate with predicted
Temperature data not quantitatively useful
Medium IMU on-board data fairly accurate to describe flight
Small IMU data was faulty

17. Recommendations Multiple flights using same motor
Multiple rockets with more sensors
Additional data channels in RDAS
Higher sampling frequency in RDAS
Method of accounting for sensor drift

18. Acknowledgements E80 Proctors: Proctor 1 and Proctor 2 Professor Spjut
Professor Yang
Everyone in E80

19. Questions?

20. References
1. Analog Technologies. (2007). High Stability Miniature Thermistor, Retrieved 3 May , from
2. Freescale Semiconductor. (2007). High Temperature Accuracy Integrate Silicon Pressure Sensor, Retrieved 3 May 2008, from
3. Freescale Semiconductor. (2007). Integrated Silicon Pressure Sensor, Retrieved 3 May 2008, from
4. Murata Manufacturing. (2007). NTC Thermistors, Retrieved 3 May , from
5. Spjut, Erik, et, al. (2008). The Lectures, Retrieved 4 Apr. 2008, from
6. Spjut, Erik, et, al. (2008). The Labs, Retrieved 4 Apr. 2008, from
7. Tedesco, Joseph and Addision Wesley. (1999). Dynamic Beam Analytical Solution, Retrieved 4 Apr. 2008, from

21. Equations
Temperature and Pressure
Modal Frequencies