e80 section 3 team 3
DESCRIPTION
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) Each lab geared towards analyzing a specific aspect of the rocket. This included: Basic electrical measurements - PowerPoint PPT PresentationTRANSCRIPT
E80 Section 3 Team 3E80 Section 3 Team 3
Student 1Student 1Student 2Student 2Student 3Student 3Student 4Student 4
May 5, 2008
The New and Improved The New and Improved E80E80
Nine labs conducted in preparation of Nine labs conducted in preparation of rocket launches (on April 19 and 26)rocket launches (on April 19 and 26) Each lab geared towards analyzing a Each lab geared towards analyzing a
specific aspect of the rocket. This specific aspect of the rocket. This included:included: Basic electrical measurementsBasic electrical measurements Determining rocket motor thrust curvesDetermining rocket motor thrust curves Finding drag coefficient of rocket bodyFinding drag coefficient of rocket body Investigating modal vibrations of rocket Investigating modal vibrations of rocket
structurestructure
EquipmentEquipment
-Medium temperature -Medium temperature and pressure rocket and pressure rocket (top)(top)
-Rocket Data Acquisition -Rocket Data Acquisition System (R-DAS) (left)System (R-DAS) (left)
Data-CollectionData-Collection Two main avenues of data recording: Rocket Two main avenues of data recording: Rocket
Data-Acquisition System (R-DAS) and video Data-Acquisition System (R-DAS) and video telemetrytelemetry
Rocket equipped with different instrumentations Rocket equipped with different instrumentations that record and output data using R-DAS that record and output data using R-DAS (samples at 200Hz resulting in additional (samples at 200Hz resulting in additional problems of aliasing)problems of aliasing) Gyroscopes and accelerometers for inertial Gyroscopes and accelerometers for inertial
measurement unit rocketmeasurement unit rocket Thermistors for temperature and pressure rocketThermistors for temperature and pressure rocket Strain Gauges for vibration rocketStrain Gauges for vibration rocket
Cameras on rocket transmit clear in flight videosCameras on rocket transmit clear in flight videos
Rocket SimulationRocket Simulation
Developed 2D model of rocket flight Developed 2D model of rocket flight using motor thrust curves and rocket using motor thrust curves and rocket dimensionsdimensions Compared with professional rocket Compared with professional rocket
simulation software, Rocksimsimulation software, Rocksim Medium Vib Medium IMU Small IMU
Apogee
(m)ApogeeTime (s)
Apogee(m)
ApogeeTime (s)
Apogee(m)
Apogee Time (s)
2D Model 280.86 8.18 176.1 6.29 286.67 7.86
Rocksim 283.01 8.22 194.71 6.59 279.91 7.78
Medium Vibration Medium Vibration RocketRocket
Took voltage outputs from on-board storage Took voltage outputs from on-board storage on the R-DAS and ran a fast Fourier on the R-DAS and ran a fast Fourier transform on each data output from our transform on each data output from our chosen strain gaugeschosen strain gauges
Created frequency response function (FRF) Created frequency response function (FRF) using [output]/[input (sensor 11)]using [output]/[input (sensor 11)]
Using FRF, plotted magnitude versus Using FRF, plotted magnitude versus frequency and recorded resonant aliased frequency and recorded resonant aliased peaks( later unaliased).peaks( later unaliased).
Constructed 1Constructed 1stst, 2, 2ndnd, and 3, and 3rdrd modal shapes modal shapes
TheoryTheory
0 1 2 3 4 5 6
-1
-0.5
0
0.5
1
0 1 2 3 4 5 6
-1
-0.5
0
0.5
1
0 1 2 3 4 5 6
-1
-0.5
0
0.5
1
Diagrams of 1st, 2nd and 3rd expected modal diagrams
1st Modal Frequency: R-DAS 45.93 Hz
Non-Aliased Frequency: 445.93 Hz
-35
-30
-25
-20
-15
-10
-5
0
0 5 10 15 20 25 30 35
Distance of each strain gauge relative to front of rocket(in)
First Modal Shape (Freq=445.93 Hz)
2nd Modal Frequency: R-DAS 36.36 HzNon-Aliased Frequency:
1236.36 Hz
Second Modal Shape (Freq=1236.36 Hz)
-20
-10
0
10
20
30
40
50
60
70
0 5 10 15 20 25 30 35
Distance of each strain gauge relative to the front of rocket (in)
Amplitude
3rd Modal Frequency: R-DAS 0.96 HzNon-Aliased Frequency:
2400.96Hz
-150
-100
-50
0
50
100
150
200
250
300
350
0 5 10 15 20 25 30 35
Distance of each strain gauge relative to front of rocket (in)
Third Modal Shape (Freq=2400.96Hz)
Pressure & TemperaturePressure & Temperature
Rockets are equipped with altimeters to Rockets are equipped with altimeters to measure pressuremeasure pressure Voltage reading of the altimeter calibrated in Voltage reading of the altimeter calibrated in
previous lab to reflect pressure in psia.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 Pressure and altitude are plotted versus timeversus time
0 5 10 15 20 25 30 3512.9
13
13.1
13.2
13.3
13.4
Pressure (Psia)
0 5 10 15 20 25 30 352800
3000
3200
3400
3600
Time (sec)
Altitude (ft) 0 5 10 15 20 25 30 35
12.9
13
13.1
13.2
13.3
13.4
Pressure (Psia)
0 5 10 15 20 25 30 352800
3000
3200
3400
3600
Time (sec)
Altitude (ft)
To eliminate noise, the data are filteredTo eliminate noise, the data are filtered
4 thermistors are onboard acting as variable 4 thermistors are onboard acting as variable resistors (nominal resistance of 10 kresistors (nominal resistance of 10 kΩΩ) in a ) in a voltage dividervoltage divider R-DAS voltage readings determine resistance Using Steinhart-Hart equation, temperature values
extracted
The three constants are determined through calibrations at known temperatures.
TemperatureTemperature
4 sensors are located throughout 4 sensors are located throughout body of rocketbody of rocket
0 5 10 15 20 25 30 35299
299.5
300
Inside Sensor
(K)
0 5 10 15 20 25 30 35290
295
300
Fin Sensor
(K)
0 5 10 15 20 25 30 35295
300
305
Outside Sensor
(K)
0 5 10 15 20 25 30 35295
300
305
Time (sec)
Base Sensor
(K)
Medium IMUMedium IMUTook data from rate gyros and Took data from rate gyros and
accelerometers in local reference accelerometers in local reference frame and, using process below, frame and, using process below, derived acceleration, velocity, and derived acceleration, velocity, and position in the global reference frame.position in the global reference frame.
Medium IMUMedium IMU
0 5 10 15 20-500
0
500Global Vertical Acceleration, Velocity, and Position (Time scale on x-axis is in seconds)
Acceleration (m/s
2)
0 5 10 15 20-100
0
100
Velocity (m/s)
0 5 10 15 20-400
-200
0
200
Altitude (m)
-0.5 0 0.5 1 1.5-20
0
20
40
60
80
100
Time (s)
Acceleration (m/s
2)
Global Vertical Acceleration (close up of motor firing)
5.5 6 6.5 7-400
-300
-200
-100
0
100
200
300
400
500
Time (s)
Acceleration (m/s
2)
Global Vertical Acceleration (close up of ejection charge and parachute opening)
0 1 2 3 4 5 6 7 8 9 10-500
0
500Global Vertical Acceleration, Velocity, and Position (Time scale on x-axis is in seconds)
Acceleration (m/s
2)
X: 0.35Y: 87.72
X: 5.7Y: -366.5
0 1 2 3 4 5 6 7 8 9 10-50
0
50
100
X: 0.82Y: 55.86
Velocity (m/s)
X: 5.7Y: -1.96
X: 5.9Y: -1.581
X: 6.59Y: -9.067
0 1 2 3 4 5 6 7 8 9 100
100
200
Altitude (m)
X: 5.7Y: 161.3
X: 5.9Y: 160.9
X: 6.59Y: 156.9
Velocity from Pitot Velocity from Pitot PressurePressure
0 1 2 3 4 5 6 7 8 9 10-10
0
10
20
30
40
50
60
X: 0.82Y: 56.55
X: 0.755Y: 39.93
X: 0.96Y: 39.93
Global Vertical Velocity from Pitot Pressure and IMU Data
Time (s)
Velocity from Pitot Pressure (Blue) and IMU Data (Green)
(m/s)
Comparative TableComparative Table
Max Max altitude altitude
(m)(m)
Max Max velocity velocity
(m/s)(m/s)
Max Max accel accel
(m/s^2(m/s^2))
Time to Time to apogee (s)apogee (s)
Velocity at Velocity at deployment deployment
(m/s)(m/s)
2D 2D ModelModel
176.1 43.49 87.4487.44 6.29 0.020.02
RocksiRocksimm
196.27196.27 59.5459.54 87.4687.46 6.596.59 3.733.73
IMUIMU
(acc)(acc)161.3161.3
55.8655.86 87.7287.72
5.75.7 -1.96-1.96
IMU IMU (Pitot)(Pitot) 160.9160.9 5.95.9 -1.581-1.581
IMU IMU (Rocksi(Rocksi
m)m)156.9156.9 6.596.59 -9.067-9.067
IMU Result using z-axis Acceleration Offset + 1 Std. Dev. (approx. 1 mV)
0 1 2 3 4 5 6 7 8 9 10-500
0
500Global Vertical Acceleration, Velocity, and Position (Time scale on x-axis is in seconds)
Acceleration (m/s
2)
X: 5.7Y: -366.2X: 0.35
Y: 88.11
0 1 2 3 4 5 6 7 8 9 10-100
0
100
Velocity (m/s)
X: 5.7Y: 0.7685
X: 5.9Y: 1.201
X: 6.59Y: -6.043
X: 0.82Y: 56.93
0 1 2 3 4 5 6 7 8 9 100
100
200
X: 5.7Y: 172.3
Altitude (m)
X: 5.9Y: 172.4
X: 6.59Y: 170.4
ConclusionConclusion Aspects of rocket flight consideredAspects of rocket flight considered
Flight trajectoryFlight trajectory Pressure and temperaturePressure and temperature Vibrational modesVibrational modes
RecommendationsRecommendations Increase number of R-DAS channels and increase Increase number of R-DAS channels and increase
its sampling frequencyits sampling frequency Use of same rocket during earlier labs and actual Use of same rocket during earlier labs and actual
launchlaunch Method of integration which avoids or filters huge Method of integration which avoids or filters huge
integration errorsintegration errors Use DAQ analysis to aid in identifying aliased Use DAQ analysis to aid in identifying aliased
frequencies frequencies
Acknowledgments Acknowledgments
E80 ProfessorsE80 Professors Professor Erik SpjutProfessor Erik Spjut Professor Mary CardenasProfessor Mary Cardenas
E80 ProctorsE80 Proctors Proctor AProctor A Proctor BProctor B Proctor CProctor C Proctor DProctor D Proctor EProctor E
Student A for a photoStudent A for a photo
¿Questions?¿Questions?
Rocket Preparation and Rocket Preparation and LaunchLaunch
On launch day, 6:30 AM departureOn launch day, 6:30 AM departure Numerous checks conducted before Numerous checks conducted before
launchlaunch Video TelemetryVideo Telemetry R-DAS ProgrammingR-DAS Programming
Set theoretical drogue and apogee with modeling Set theoretical drogue and apogee with modeling help from Rocksimhelp from Rocksim
Parachute LoadingParachute Loading Motor and Recovery Charge (student Motor and Recovery Charge (student
proctors)proctors) Launch Pad PreparationLaunch Pad Preparation
Resonant Freq Resonant Freq CalculationCalculation
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 Calculating Full Resolution FreqResolution Freq
IMU analysis code for MATLABIMU analysis code for MATLAB
dataredux.mdataredux.mimportfile('IMUMG104TS1T2F1_20080426.txt');importfile('IMUMG104TS1T2F1_20080426.txt');Rt = [[1 0 0]; [0 1 0]; [0 0 1]];Rt = [[1 0 0]; [0 1 0]; [0 0 1]];p = zeros(length(Time), 3);p = zeros(length(Time), 3);v = zeros(length(Time), 3);v = zeros(length(Time), 3);a = zeros(length(Time), 3);a = zeros(length(Time), 3);orientcal = [ mean(ADC3(1:400)) mean(ADC4(1:400)) orientcal = [ mean(ADC3(1:400)) mean(ADC4(1:400))
mean(ADC5(1:400)) ];mean(ADC5(1:400)) ];acccal = [ mean(ADC0(1:400)) mean(ADC1(1:400)) mean(Acc(1:400)) ]; acccal = [ mean(ADC0(1:400)) mean(ADC1(1:400)) mean(Acc(1:400)) ]; for t = 1:numel(Time)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); elseelse dt = dt;dt = dt; endend 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 ~= 1if 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)]; endendend end
orient.morient.mfunction [Rdt] = orient(wx, wy, wz, Rt, dt, orientcal)function [Rdt] = orient(wx, wy, wz, Rt, dt, orientcal)wx = -1.326624*(wx - orientcal(1))*(pi/180);wx = -1.326624*(wx - orientcal(1))*(pi/180);wy = -1.449224*(wy - orientcal(2))*(pi/180);wy = -1.449224*(wy - orientcal(2))*(pi/180);wz = -1.036963*(wz - orientcal(3))*(pi/180);wz = -1.036963*(wz - orientcal(3))*(pi/180);beta = (wx^2 + wy^2 + wz^2)^(1/2);beta = (wx^2 + wy^2 + wz^2)^(1/2);sigma = abs(beta*dt);sigma = abs(beta*dt);C1 = sin(sigma)/sigma;C1 = sin(sigma)/sigma;C2 = (1-cos(sigma))/(sigma^2);C2 = (1-cos(sigma))/(sigma^2);if sigma == 0if sigma == 0 C1 = 1;C1 = 1; C2 = 0;C2 = 0;endendB = [[0 -wz*dt wy*dt]; [wz*dt 0 -wx*dt]; [-wy*dt wx*dt 0]];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]]; I = [[1 0 0]; [0 1 0]; [0 0 1]]; [Rdt] = Rt*(I + C1.*B + C2.*B^2);[Rdt] = Rt*(I + C1.*B + C2.*B^2);
accel.maccel.m
function [ag] = accel(ax, ay, az, Rt, acccal)function [ag] = accel(ax, ay, az, Rt, acccal)
ax = -0.1614505*(ax - acccal(1));ax = -0.1614505*(ax - acccal(1));
ay = -0.1841975*(ay - acccal(2));ay = -0.1841975*(ay - acccal(2));
az = -1.4532265*(az - acccal(3)) + 9.81;az = -1.4532265*(az - acccal(3)) + 9.81;
a0 = [ax ay az];a0 = [ax ay az];
a = (Rt*a0.').';a = (Rt*a0.').';
a(3) = a(3) - 9.81;a(3) = a(3) - 9.81;
[ag] = a;[ag] = a;
vel.mvel.m
function [v] = vel(ag, v, dt) function [v] = vel(ag, v, dt)
[v] = [ (v(1) + dt*ag(1)) (v(2) + dt*ag(2)) (v(3) + dt*ag(3)) ]; [v] = [ (v(1) + dt*ag(1)) (v(2) + dt*ag(2)) (v(3) + dt*ag(3)) ];
pos.mpos.m
function [p] = pos(v, p, dt)function [p] = pos(v, p, dt)
[p] = [ (p(1) + dt*v(1)) (p(2) + dt*v(2)) (p(3) + dt*v(3)) ];[p] = [ (p(1) + dt*v(1)) (p(2) + dt*v(2)) (p(3) + dt*v(3)) ];
WeathercockingWeathercocking
Small IMU Launch Small IMU Launch ResultsResults
-5 0 5 10 15 20 25788
788.5
789
789.5
790
790.5
791
Time (s)
R-DAS value for R-DAS Altitude Pressure
R-DAS Altitude Pressure Data from Small IMU Launch