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Analysis of the Mudd III Rockets

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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


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