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