“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
Fthrust
A *  * cd * V 2 * cos( )
ay 
cos( )  g 
mass
2 * mass

 * c L *W 2 * d
2Ix
Fthrust=Instantaneous thrust from motor cD=drag coefficient
θ=angle from vertical
 from gravity
g = acceleration
cL=lift coefficient
V=velocity
A = cross sectional area
α=angular acceleration
ρ=air density
W=wind speed
Ix=Moment of Inertia about x axis
d= distance between CM and CP
200
0
-200
0
2
4
6
8
10
12
x acceleration(m/s 2)
y acceleration(m/s 2)
Rocket y Acceleration
400
Rocket x Acceleration
2
1
0
-1
0
2
4
0
-100
0
2
4
6
8
10
8
10
12
8
10
12
Rocket Tilt
2
0
0
2
4
6
time(sec)
x Displacement(m)
6
4
radians
y Displacement(m)
0
4
8
10
12
10
12
-2
0
2
4
6
Rocket x Displacement
100
2
12
0
Rocket Altitude
0
10
2
-4
12
200
-100
8
Rocket x Velocity
100
x velocity(m/s)
y velocity(m/s)
Rocket y Velocity
6
10
0
-10
-20
0
2
4
6
time(sec)
8
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
Vx   a x   wz  a y   wy  a z
V y   a y   wx  a z   wz  a x
Vz   a z   wy  a x   wx  a y
• Calibration for IMU
a x  (0.17855)vax  91.596
a y  (0.21392)vay  109.483
 x  (1.43681)v wx  730.179
 y  (0.683)v wy  417.313
a z  (1.62784674)vaz  838.381  x  (1.92815)v wz  640.3745
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
•Euler’s Method
•Dead Reckoning Error
Acceleration
Pressure Altimeter
• Pressure decreases with altitude
.1902

P

 
5 
• h  1.4544 10  1  
 
  101.325kPa  
• No Dead Reckoning Error
• Poor Sensitivity
(1)
Vibration Analysis
• Periods with limited external influence
• Analyze short segments with FFT
Sensor 1, 7, 12 Detrend Sampled Data
200
Sensor 1
Sensor 7
sensor 12
150
Strain Voltage Output
100
50
0
-50
-100
-150
0
0.05
0.1
0.15
Time (sec)
0.2
0.25
Frequency Analysis
• Sampling frequency too low (200 Hz).
• Fundamental frequency folded.
Magnitude and Phase of FFT for Sensor 1
Magnitude
15
Frequency
(Hz)
1
141.5
6
135, 137
7
140
10
135.5
12
141.5
10
5
0
-100
-50
0
50
100
5
Phase (radians)
Sensor
0
-5
-10
-15
-100
-50
0
Frequency (Hz)
50
100
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 Proctors
Rocket Development Team
Professor Spjut
Professor Miraghie
The Rest of the Engineering Faculty
System 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:
f aliased  f  nf s  f aliased  f s
Sensor
Dominant Frequency
(Hz)
Sensor
Frequency (Hz)
1
58.5
1
141.5
6
65, 67
6
135, 137
7
60
7
140
10
64.5
10
135.5
12
58.5
12
141.5
Detrend Data
Sensor 10 Detrend Sampled Data
Sensor 10 Sampled data
8
25
Sensor 10
20
6
15
4
Strain Output Voltage
Strain Output Voltage
Sensor 10
10
5
0
-5
2
0
-2
-4
-10
-6
-15
-8
-20
0
0.5
1
Time (sec)
1.5
-10
0
0.5
1
Time (sec)
1.5
FFT
Magnitude and Phase of FFT for Sensor 10
Magnitude
0.1
0.05
0
-50
0
50
100
-50
0
Frequency (Hz)
50
100
Phase (radians)
50
0
-50
-100
-100