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Analysis of Rocket Flights. Section 4, Team 4 Student 1, Student 2, Student 3, Student 4. Temperature Predictions. Decrease in temperature upon ascent Rise in temperature upon descent Further increase after landing. Thermistor 3 (middle of rocket body, on surface). Thermistor 2 (on fin).

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## Analysis of Rocket Flights

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**Analysis of Rocket Flights**Section 4, Team 4 Student 1, Student 2, Student 3, Student 4**Temperature Predictions**• Decrease in temperature upon ascent • Rise in temperature upon descent • Further increase after landing**Altimeters**• Expect decrease in pressure with increase in altitude, and vice versa • Used barometric equation to find altitude • Calibrated sensors in lab using vacuum chamber**Flight Modeling (2-D)**T T z z y θ y CG CG r r CP Wind CP Wind mg mg D D**Euler’s Integration**• Method for numerical integration • Iterative • For given a(t) and initial conditions for x and v: v(t+Δt)=v(t)+a(t)*t x(t+Δt)=x(t)+v(t)*t**az**Az y ay az ax ax Ax Ay ay IMU Analysis: Mudd IIIC (Large) Rocket • Rotation from local to global axes • Euler integration of rotation matrix**Processing Algorithm (Matlab)**Calibrations Acceleration Filtering (optional) Raw RDAS Data (counts) Local Acceleration (m/s2) Global Acceleration (m/s2) Filtered Global Acceleration (m/s2) Euler integration Calibrations Rotation Matrix (radians/sec) Global Velocity (m/s) and Position (m) Local Rotation Rate (radians/sec) Euler integration Local Rotation Angle (degrees)**z**wind E80 teams Acceleration Filtering (Descent Plot)**Bad Data**• Mudd IIIA IMU rocket • Failure to eject parachute • Flat spin crash after apogee • WHY? http://www.tribuneindia.com/2002/20020715/world.htm**Acceleration Data…**• Very pronounced 0.2149 Hz oscillations • Possible causes: camera interference, camera overpowering • Band-stop filter might be able to retrieve data**Theoretical Analysis**• Tap tests on hollow tube are inaccurate • Mass spring damper system**Spring-Mass-Damper Model**• Rocket can be modeled as a single degree of freedom spring-mass-damper system. • Effective mass, m • Spring constant, k • Damping • Half-Power Bandwidth Predicted Resonance Frequency**Analysis**• No control variables! • Treat Sensor 10 as input. • Create FRFs of other sensors to see relative peaks Sensor 10**FRF plots**• Removed DC offset • fdomain.m used to generate Fourier Coefficients • Relative Amplitudes • First set of data is not trustworthy • Second set of data has more coherent peaks • Used 1st second of data, short motor burn time**1st Set of Data Results**• Peak around 60 or 70 Hz • Other peaks are inconsistent • Sensor 15 seems to be malfunctioning • Locally, 3 sensors show local peaks between 60-80 • No video**2nd Set of Data Results**• Consistent peaks at 64 Hz • Possible peaks around 30 Hz, but not consistent • Sensors 1, 3, and 8 are 13 show peak frequencies • Sensor 13 farther away from the input source**Noises**• Only 64 Hz showed in every FRF • Others are jumbled by the noise • Running averages smoothes out the data too much. • Too little data during the 1st second of input • Ineffective way of removing noise**Mode Shapes**• Absolute magnitude of Fourier Coefficients vs Relative Sensor Distances • Sensor 10 was normalized as “0” point.**Results from FRF**• Not enough frequencies to test all 3 mode shapes • Does not deal well with noise, especially with highly aliased data**Problems with FFT**• Using just FFT coefficients to calculate Frequency Response Functions assumes a clean periodic signal. • The rocket data is neither. • A better estimator is Power Spectral Density (PSD).**Power Spectral Density**Auto power spectral density Cross power spectral density Frequency Response Function**H(jw)**PSD and Noise x(t) v(t) y(t) n(t) Assume n(t) is unrelated to v(t) 0**Hamming Window**Time Domain Frequency Domain**Averaging Overlap**Overlapping windowed segments by 50% minimizes attenuation of time domain signal near the end of segment**Waterfall Analysis**FRF of Sensor 5 over time magnitude (dB) time (.1 sec) freq (Hz)**Conclusions**• Thermistor behavior depends on location • Euler Integration Method not sufficient to model whole flight path • Spring-Mass-Damper model can simplify system to find theoretical resonance • FFT method of finding FRF is not consistent due to large noise component • PSD method gives much sharper peaks in FRF**Interesting Precautions...**• Check battery…sensors are sensitive! • Wait until last moment to turn on R-DAS and video camera…otherwise, ejection charge could go off early! • Don’t try to catch rocket…it may have a chute, but it’s still falling fast!**Acknowledgements**• The professors and proctors who helped to make this beta-test a success. • All of our classmates for their infinite support and advice during this semester • Student A for a discussion on the causes of small rocket IMU corruption • Student B for his help with setting up the Single Degree of Freedom model**References**• E80 The Next Generation Spring 2008, http://www.eng.hmc.edu/New E80/index.html. • R. Wang, http://fourier.eng.hmc.edu/e80/inertialnavigation/ • Q. Yang, http://www.eng.hmc.edu/NewE80/PDFs/Lecture_PressureSensor Thermistors.ppt • H. Buchholdt, Structural Dynamics for Engineers (Telford, 1997), pp. 17-22. • The Hanning Window, http://www.dliengineering.com/vibman/thehanning window.htm

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