E80 Section 3 Team 3

1. E80 Section 3 Team 3 Student 1 Student 2 Student 3 Student 4 May 5, 2008

2. The New and Improved E80 • Nine labs conducted in preparation of rocket launches (on April 19 and 26) • Each lab geared towards analyzing a specific aspect of the rocket. This included: • Basic electrical measurements • Determining rocket motor thrust curves • Finding drag coefficient of rocket body • Investigating modal vibrations of rocket structure

3. Equipment -Medium temperature and pressure rocket (top) -Rocket Data Acquisition System (R-DAS) (left)

4. Data-Collection • Two main avenues of data recording: Rocket Data-Acquisition System (R-DAS) and video telemetry • Rocket equipped with different instrumentations that record and output data using R-DAS (samples at 200Hz resulting in additional problems of aliasing) • Gyroscopes and accelerometers for inertial measurement unit rocket • Thermistors for temperature and pressure rocket • Strain Gauges for vibration rocket • Cameras on rocket transmit clear in flight videos

5. Rocket Simulation • Developed 2D model of rocket flight using motor thrust curves and rocket dimensions • Compared with professional rocket simulation software, Rocksim

6. Medium Vibration Rocket • Took voltage outputs from on-board storage on the R-DAS and ran a fast Fourier transform on each data output from our chosen strain gauges • Created frequency response function (FRF) using [output]/[input (sensor 11)] • Using FRF, plotted magnitude versus frequency and recorded resonant aliased peaks( later unaliased). • Constructed 1st, 2nd, and 3rd modal shapes

7. Theory Diagrams of 1st, 2nd and 3rd expected modal diagrams

8. 1st Modal Frequency: R-DAS 45.93 Hz Non-Aliased Frequency: 445.93 Hz

9. 2nd Modal Frequency: R-DAS 36.36 Hz Non-Aliased Frequency: 1236.36 Hz

10. 3rd Modal Frequency: R-DAS 0.96 Hz Non-Aliased Frequency: 2400.96Hz

11. Pressure & Temperature • Rockets are equipped with altimeters to measure pressure • Voltage reading of the altimeter calibrated in previous lab to reflect pressure in psia. • From pressure results, altitude can be derived.

12. Pressure and altitude are plotted versus time • To eliminate noise, the data are filtered

13. Temperature • 4 thermistors are onboard acting as variable resistors (nominal resistance of 10 kΩ) in a voltage divider • R-DAS voltage readings determine resistance • Using Steinhart-Hart equation, temperature values extracted • The three constants are determined through calibrations at known temperatures.

14. 4 sensors are located throughout body of rocket

15. Medium IMU Took data from rate gyros and accelerometers in local reference frame and, using process below, derived acceleration, velocity, and position in the global reference frame.

16. Medium IMU

19. Velocity from Pitot Pressure

20. Comparative Table

21. IMU Result using z-axis Acceleration Offset + 1 Std. Dev. (approx. 1 mV)

22. Conclusion • Aspects of rocket flight considered • Flight trajectory • Pressure and temperature • Vibrational modes • Recommendations • Increase number of R-DAS channels and increase its sampling frequency • Use of same rocket during earlier labs and actual launch • Method of integration which avoids or filters huge integration errors • Use DAQ analysis to aid in identifying aliased frequencies

23. Acknowledgments • E80 Professors • Professor Erik Spjut • Professor Mary Cardenas • E80 Proctors • Proctor A • Proctor B • Proctor C • Proctor D • Proctor E • Student A for a photo

24. ¿Questions?

25. Rocket Preparation and Launch • On launch day, 6:30 AM departure • Numerous checks conducted before launch • Video Telemetry • R-DAS Programming • Set theoretical drogue and apogee with modeling help from Rocksim • Parachute Loading • Motor and Recovery Charge (student proctors) • Launch Pad Preparation

26. Resonant Freq Calculation Comparing the hollow tube cylinder modal frequencies, a relative modal frequency for the rocket could also be estimated just by comparing the dependent values. Rocket length is longer than hollow cylinder length Second moment of area and area of rocket dependent on radii All other values are approximately the same

27. Calculating Full Resolution Freq

28. IMU analysis code for MATLAB dataredux.m importfile('IMUMG104TS1T2F1_20080426.txt'); Rt = [[1 0 0]; [0 1 0]; [0 0 1]]; p = zeros(length(Time), 3); v = zeros(length(Time), 3); a = zeros(length(Time), 3); orientcal = [ mean(ADC3(1:400)) mean(ADC4(1:400)) mean(ADC5(1:400)) ]; acccal = [ mean(ADC0(1:400)) mean(ADC1(1:400)) mean(Acc(1:400)) ]; for t = 1:numel(Time) if t ~= numel(Time) dt = Time(t+1) - Time(t); else dt = dt; end Rt = orient(ADC3(t), ADC4(t), ADC5(t), Rt, dt, orientcal); a(t,:) = [accel(ADC0(t), ADC1(t), Acc(t), Rt, acccal)]; if t ~= 1 v(t,:) = [vel(a(t,:), v(t-1,:), dt)]; p(t,:) = [pos(v(t,:), p(t-1,:), dt)]; end end

29. orient.m function [Rdt] = orient(wx, wy, wz, Rt, dt, orientcal) wx = -1.326624*(wx - orientcal(1))*(pi/180); wy = -1.449224*(wy - orientcal(2))*(pi/180); wz = -1.036963*(wz - orientcal(3))*(pi/180); beta = (wx^2 + wy^2 + wz^2)^(1/2); sigma = abs(beta*dt); C1 = sin(sigma)/sigma; C2 = (1-cos(sigma))/(sigma^2); if sigma == 0 C1 = 1; C2 = 0; end B = [[0 -wz*dt wy*dt]; [wz*dt 0 -wx*dt]; [-wy*dt wx*dt 0]]; I = [[1 0 0]; [0 1 0]; [0 0 1]]; [Rdt] = Rt*(I + C1.*B + C2.*B^2);

30. accel.m function [ag] = accel(ax, ay, az, Rt, acccal) ax = -0.1614505*(ax - acccal(1)); ay = -0.1841975*(ay - acccal(2)); az = -1.4532265*(az - acccal(3)) + 9.81; a0 = [ax ay az]; a = (Rt*a0.').'; a(3) = a(3) - 9.81; [ag] = a; vel.m function [v] = vel(ag, v, dt) [v] = [ (v(1) + dt*ag(1)) (v(2) + dt*ag(2)) (v(3) + dt*ag(3)) ]; pos.m function [p] = pos(v, p, dt) [p] = [ (p(1) + dt*v(1)) (p(2) + dt*v(2)) (p(3) + dt*v(3)) ];

31. Weathercocking

32. Small IMU Launch Results