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)
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
Altimeter vs. Models for Flight
Flight Modeling (2-D) CGCG CPCP mg D T y z r Wind T CGCG CPCP mg r Wind D y z θ
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
IMU Analysis: Mudd IIIC (Large) Rocket Rotation from local to global axes Euler integration of rotation matrix azaz axax ayay AyAy AzAz AxAx y azaz ayay axax
Processing Algorithm (Matlab) Raw RDAS Data (counts) Local Acceleration (m/s 2 ) Calibrations Global Acceleration (m/s 2 ) Global Velocity (m/s) and Position (m) Local Rotation Rate (radians/sec) Rotation Matrix (radians/sec) Calibrations Euler integration Local Rotation Angle (degrees) Filtered Global Acceleration (m/s 2 ) Acceleration Filtering (optional)
Principle Axis Rotation: Plot vs. Video
1-D Model Comparison (launch 2) day 1 2 nd launch (13-20 mph winds) IMU dataR-DAS pressure altimeter % difference from altimeter Student model % difference from model Rocksim model % difference from model Apogee height meters m+3.759% m (lies within range) m-3.001% Apogee time 6.38 sec sec % sec %5.888 sec+8.356% Max z vel m/sN/A m/s (lies within range) m/s-5.049% Max z accel m/s 2 N/A m/s %202.5 m/s %
Acceleration Filtering (Before)
Acceleration Filtering (After)
Acceleration Filtering (Descent Plot) E80 teams wind z
Bad Data Mudd IIIA IMU rocket Failure to eject parachute Flat spin crash after apogee WHY?
Principle Axis Rotation Plot vs. Video, Round 2
Acceleration Data… Very pronounced Hz oscillations Possible causes: camera interference, camera overpowering Band-stop filter might be able to retrieve data
Vibration Analysis
Tap tests on hollow tube are inaccurate Mass spring damper system Theoretical Analysis
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 1 st second of data, short motor burn time
1 st 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 No video
2 nd 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 1 st 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
PSD and Noise H(j x(t)v(t)y(t) n(t) Assume n(t) is unrelated to v(t) 0
Hamming Window Time DomainFrequency Domain
Averaging Overlap Overlapping windowed segments by 50% minimizes attenuation of time domain signal near the end of segment
Frequency Response Function
Waterfall Analysis freq (Hz) time (.1 sec) magnitude (dB) FRF of Sensor 5 over time
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!
Extra: Altimeter Plots
Extra: Why We Didn’t Do 2-D Model Comparison
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, E80/index.html. R. Wang, Q. Yang, Thermistors.ppt H. Buchholdt, Structural Dynamics for Engineers (Telford, 1997), pp The Hanning Window, window.htm