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

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

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

Data-Collection Two main avenues of data recording: Rocket Data- Acquisition System (R-DAS) and video telemetry 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) 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 Gyroscopes and accelerometers for inertial measurement unit rocket Thermistors for temperature and pressure rocket Thermistors for temperature and pressure rocket Strain Gauges for vibration rocket Strain Gauges for vibration rocket Cameras on rocket transmit clear in flight videos Cameras on rocket transmit clear in flight videos

Rocket Simulation Developed 2D model of rocket flight using motor thrust curves and rocket dimensions Developed 2D model of rocket flight using motor thrust curves and rocket dimensions Compared with professional rocket simulation software, Rocksim Compared with professional rocket simulation software, Rocksim Medium VibMedium IMUSmall IMU Apogee (m) Apogee Time (s) Apogee (m) Apogee Time (s) Apogee (m) Apogee Time (s) 2D Model Rocksim

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 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)] Created frequency response function (FRF) using [output]/[input (sensor 11)] Using FRF, plotted magnitude versus frequency and recorded resonant aliased peaks( later unaliased). Using FRF, plotted magnitude versus frequency and recorded resonant aliased peaks( later unaliased). Constructed 1 st, 2 nd, and 3 rd modal shapes Constructed 1 st, 2 nd, and 3 rd modal shapes

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

1 st Modal Frequency: R-DAS Hz Non-Aliased Frequency: Hz

2 nd Modal Frequency: R-DAS Hz Non-Aliased Frequency: Hz

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

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

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

4 thermistors are onboard acting as variable resistors (nominal resistance of 10 kΩ) in a voltage divider 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. Temperature

4 sensors are located throughout body of rocket 4 sensors are located throughout body of rocket

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.

Medium IMU

Velocity from Pitot Pressure

Comparative Table Max altitude (m) Max velocity (m/s) Max accel (m/s^2) Time to apogee (s) Velocity at deployment (m/s) 2D Model Rocksim IMU(acc) IMU (Pitot) IMU (Rocksim)

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

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

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

¿Questions?

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

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

Calculating Full Resolution Freq

IMU analysis code for MATLAB dataredux.mimportfile('IMUMG104TS1T2F1_ 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) if t ~= numel(Time) dt = Time(t+1) - Time(t); dt = Time(t+1) - Time(t); else else dt = dt; dt = dt; end end Rt = orient(ADC3(t), ADC4(t), ADC5(t), Rt, dt, orientcal); Rt = orient(ADC3(t), ADC4(t), ADC5(t), Rt, dt, orientcal); a(t,:) = [accel(ADC0(t), ADC1(t), Acc(t), Rt, acccal)]; a(t,:) = [accel(ADC0(t), ADC1(t), Acc(t), Rt, acccal)]; if t ~= 1 if t ~= 1 v(t,:) = [vel(a(t,:), v(t-1,:), dt)]; v(t,:) = [vel(a(t,:), v(t-1,:), dt)]; p(t,:) = [pos(v(t,:), p(t-1,:), dt)]; p(t,:) = [pos(v(t,:), p(t-1,:), dt)]; end endend

orient.m function [Rdt] = orient(wx, wy, wz, Rt, dt, orientcal) wx = *(wx - orientcal(1))*(pi/180); wy = *(wy - orientcal(2))*(pi/180); wz = *(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; C1 = 1; C2 = 0; 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);

accel.m function [ag] = accel(ax, ay, az, Rt, acccal) ax = *(ax - acccal(1)); ay = *(ay - acccal(2)); az = *(az - acccal(3)) ; a0 = [ax ay az]; a = (Rt*a0.').'; a(3) = a(3) ; [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)) ];

Weathercocking

Small IMU Launch Results