“Sky Rockets in Flight”

Experimental Engineering

Section 1,Team 3

Student 1, Student 2, Student 3, Student 4

May 5, 2008

Objectives

• Develop problem solving and critical thinking skills

• Utilize various disciplines of engineering

• Analyze and predict the flight of a rocket.

Prior to Launch

• Sensors Need to be Calibrated– Accelerometers, Gyroscopes, Pitot Tube, Pressure Sensor

• Physical Characteristics– Coefficients of Lift and Drag– Natural frequencies of rocket body

• Motor Quantities– Thrust Curve and Total Impulse for Modeling

Flight Modeling

• Calculate instantaneous acceleration:– Thrust Curve– Gravity– Lift (from wind)– Drag– Weather Cocking

• Euler’s Method to find trajectory

• Algorithm checked using RockSim

Algorithm

mass

VcAg

mass

Fa dthrusty *2

)cos(****)cos(

2 θρθ −−=

€

α =ρ *cL *W 2 * d

2Ix

Fthrust=Instantaneous thrust from motor

θ=angle from vertical

g = acceleration from gravity

A = cross sectional area

ρ=air density

Ix=Moment of Inertia about x axis

cD=drag coefficient

cL=lift coefficient

V=velocity

α=angular acceleration

W=wind speed

d= distance between CM and CP

0 2 4 6 8 10 12-200

0

200

400

y acceleration(m/s

2)

Rocket y Acceleration

0 2 4 6 8 10 12-1

0

1

2

x acceleration(m/s

2)

Rocket x Acceleration

0 2 4 6 8 10 12-100

0

100

y velocity(m/s)

Rocket y Velocity

0 2 4 6 8 10 12-100

0

100

200

y Displacement(m)

Rocket Altitude

0 2 4 6 8 10 12-4

-2

0

2

x velocity(m/s)

Rocket x Velocity

0 2 4 6 8 10 12-20

-10

0

10

time(sec)x Displacement(m)

Rocket x Displacement

0 2 4 6 8 10 120

2

4

time(sec)

radians

Rocket Tilt

Launches

• Lucerne Valley, CA --- dry lake bed

• 4/19 - Large IMU & Small IMU– Windy (15-25 mph)

• 4/26 - Large IMU & Large Vibration– No wind

IMU Sensors• Getting global coordinates from local coordinates

• Calibration for IMU

381.838)62784674.1(

483.109)21392.0(

596.91)17855.0(

+−=

+−=−=

azz

ayy

axx

va

vava

€

ωx = (1.43681)vwx − 730.179

ωy = (0.683)vwy − 417.313

ωx = (1.92815)vwz − 640.3745

∫ ∫∫∫∫∫ ∫∫∫∫∫ ∫∫∫∫

++=

+−=

+−=

yxxyzz

xzzxyy

zyyzxx

awawaV

awawaV

awawaV

4/19/08 IMU Height

Graph:Apogee @ 5.20 sec& 166 m

Predicted (RockSim):Apogee @ 6.17 sec& 183 m

Predicted (MATLAB):Apogee @ 5.94 sec& 171 m

4/26/08 IMU Height

Graph:Apogee @ 4.98 sec &181 m

Predicted (RockSim):Apogee @ 6.17 sec& 183 m

Predicted (MATLAB):Apogee @ 5.97 sec& 172 m

Integration Errors

Acceleration

•Euler’s Method•Dead Reckoning Error

Pressure Altimeter

• Pressure decreases with altitude

• (1)

• No Dead Reckoning Error

• Poor Sensitivity

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛−××=1902.

5

325.1011104544.1

kPa

Ph

Vibration Analysis

• Periods with limited external influence• Analyze short segments with FFT

0 0.05 0.1 0.15 0.2 0.25-150

-100

-50

0

50

100

150

200Sensor 1, 7, 12 Detrend Sampled Data

Time (sec)

Str

ain

Vol

tage

Out

put

Sensor 1Sensor 7sensor 12

Frequency Analysis

• Sampling frequency too low (200 Hz).• Fundamental frequency folded.

-100 -50 0 50 1000

5

10

15

Magnitude

Magnitude and Phase of FFT for Sensor 1

-100 -50 0 50 100-15

-10

-5

0

5

Frequency (Hz)

Phase (radians)

Sensor Frequency (Hz)

1 141.5

6 135, 137

7 140

10 135.5

12 141.5

Failed Flight…• Small IMU parachute did not deploy,

rocket went into a fatal flat spin.

• Pitot, Pressure: No activity.

• Accelerometers: Activity stops at t=0.

…Failed Flight

• Gyroscopes: unexpected activity before and after launch

Conclusions

• IMU: Accurate measurement, but limited by the low sampling frequency

• Vibration: Shows the expected reaction– vibration occurred at same frequency as

dynamic beam experiment

Recommendations

• GPS

• Higher sampling frequency in IMU and RDAS

• Looking at all 15 strain gauges at once

• Use the same IMU all semester

Acknowledgements

Student ProctorsRocket Development Team

Professor SpjutProfessor Miraghie

The Rest of the Engineering FacultySystem Admin

Stockroom Curator

References• 1. Anonymous "Model Rocket Safety Code," http://www.nar.org/NARmrsc.html.

• 2. Qimin Yang, “Pressure sensors and thermistors,” http://www.eng.hmc.edu/NewE80/PresTempLec.html.

• 3. Student 5, E80 Section 4, Team 2

• 4. Phillip D. Cha and John I. Molinder, Sampling and Data Acquisition, in Fundamentals of Signals and Systems: A Building Block Approach, edited by Anonymous (Cambridge University Press, New York, 2006), pp. 86-88.

• Anonymous, “Accelerometer and Gyroscope Calibration,” http://www.eng.hmc.edu/NewE80/AccelGyroLab.html.

• Anonymous, “Integrated Dual-Axis Gyro,” http://www.eng.hmc.edu/NewE80/PDFs/IDG_300_Datasheet.pdf

• Anonymous, “Analog Devices,”

• http://www.eng.hmc.edu/NewE80/PDFs/ADXL320.pdf

• Colin Holland, “Tri-axi inertial measurement unit combines seven sensors,” http://www.eetimes.eu/industrial/199905290

• Mary Cardenas, “Rocket Dynamics,” http://www.eng.hmc.edu/NewE80/PDFs/rocket_dynamics.pdf.

Questions?

Calibration equations

The Failed IMU Rocket (Accel)

The Failed IMU Rocket (Gyros)

Aliasing

• Sampling Theorem:

Sensor Dominant Frequency (Hz)

1 58.5

6 65, 67

7 60

10 64.5

12 58.5

saliasedsaliased ffnfff ≤⇒+=

Sensor Frequency (Hz)

1 141.5

6 135, 137

7 140

10 135.5

12 141.5

Detrend Data

0 0.5 1 1.5-10

-8

-6

-4

-2

0

2

4

6

8Sensor 10 Detrend Sampled Data

Time (sec)

Strain Output Voltage

Sensor 10

0 0.5 1 1.5-20

-15

-10

-5

0

5

10

15

20

25Sensor 10 Sampled data

Time (sec)

Strain Output Voltage

Sensor 10

FFT

-50 0 50 100

0

0.05

0.1

Magnitude and Phase of FFT for Sensor 10

Magnitude

-100 -50 0 50 100-100

-50

0

50

Frequency (Hz)

Phase (radians)