“sky rockets in flight”
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“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. - PowerPoint PPT PresentationTRANSCRIPT
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“Sky Rockets in Flight”
Experimental Engineering
Section 1,Team 3
Student 1, Student 2, Student 3, Student 4
May 5, 2008
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Objectives
• Develop problem solving and critical thinking skills
• Utilize various disciplines of engineering
• Analyze and predict the flight of a rocket.
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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
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Flight Modeling
• Calculate instantaneous acceleration:– Thrust Curve– Gravity– Lift (from wind)– Drag– Weather Cocking
• Euler’s Method to find trajectory
• Algorithm checked using RockSim
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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
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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
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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
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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
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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
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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
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Integration Errors
Acceleration
•Euler’s Method•Dead Reckoning Error
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Pressure Altimeter
• Pressure decreases with altitude
• (1)
• No Dead Reckoning Error
• Poor Sensitivity
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛−××=1902.
5
325.1011104544.1
kPa
Ph
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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
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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
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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.
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…Failed Flight
• Gyroscopes: unexpected activity before and after launch
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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
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Recommendations
• GPS
• Higher sampling frequency in IMU and RDAS
• Looking at all 15 strain gauges at once
• Use the same IMU all semester
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Acknowledgements
Student ProctorsRocket Development Team
Professor SpjutProfessor Miraghie
The Rest of the Engineering FacultySystem Admin
Stockroom Curator
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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.
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Questions?
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Calibration equations
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The Failed IMU Rocket (Accel)
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The Failed IMU Rocket (Gyros)
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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
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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
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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)