Transcript E80 Presentation

Characterization of
Model Rockets in Flight
Section 4, Team 1
Student 1, Student 2, Student 3 and
Student 4
Introduction
Using prototypes can prevent costly
errors in complicated systems
 Different types of sensors are required
to collect a wide variety of data
 The current set of rockets follow in the
footsteps of Mudd I and Mudd II

Preparation: Rocket Launch

Following a series of
checklists:




Configure R-DAS
and Video
Load parachute and
ejection charge
Install motor
Followed NAR and
Tripoli guidelines
http://mpcardenas.smugmug.com/gallery/4805272_ZJqsr#285517109_ANAvP
Procedures: Data Collection
R-DAS - Rocket Data
Acquisition System
Three batches of sensors:
 IMU
 Strain Gauges
 Thermistor and Pressure
Transducers





These batches are used to model:
© Bruce Yan
 Velocity and position
 Vibration and response
 Atmospheric variables
Calibration curves are used to convert from digital signals to
physical variables
Video camera
Theory:
Rocket Flight Simulation


The MATLAB script numerically integrates
acceleration given by an experimental thrust
curve
It makes several simplifying assumptions:




The rocket only moves in two dimensions
The wind exerts a constant lift force
The rocket travels straight for 6 feet along
the rail. Then it instantaneously changes
direction towards the wind
The coefficient of drag is .75
Theory: IMU





The IMU contains:
 Accelerometers
 Gyroscopes
Sensors are mutually orthogonal to
create a local set of axes
Can convert between local axes to
global variables by using a rotational
matrix
Data were used to recreate the
rocket flight path
The global variables can be found
from the local variables by using
 a
rotation matrix.
 

u  R(t )  a
 1


R(t )    z
  y

 z
1
x
y 

 x 
1 
  



u (t )  R(t )S (t )a(t  t )  R(t  t )a(t  t )
 sin 
1 cos 2 
R(t t)  R(t)I 
B
B 



2
 0


B(t )  R(t )t    zt
  zt
 2  (x 2 y 2 z2 )t 2
  zt
0
 xt
 yt 
  xt 
0

Theory: IMU
IMU Calibration Curve
Medium Rocket: IMU




A variety of engines were used
Theoretical models were created using MATLAB and
RocSim
Flights were modeled using the IMU data in conjunction
with a MATLAB script
Both the theoretical models overestimated the altitude of
the apogee
Flight
Engine
1
2
3
4
G67R
G79W
G69N
G104T
Theoretical Theoretical
Apogee
Time to
(m)
Apogee (s)
287.8501
7.4350
259.4868
7.2150
413.6383
8.9850
N/A
N/A
RocSim
Apogee
(m)
293.096
301.98
427.29
197.79
RocSim
Time to
Apogee (s)
8.32
8.300
9.95
5.595
Experimental
Apogee
(m)
211.3246
201.4885
297.1816
137.0017
Experimental
Time to
Apogee (s)
6.975
7.005
8.405
5.595
Rocket Flight Model:
Medium IMU
Experimental Modeling of IMU Rocket Flight 2 (Motor G79W, 4/26/2008)
Rocket Flight Model:
Medium IMU
Experimental 3D Modeling of IMU Rocket Flight 2 (Motor G79W, 4/26/2008)
Rocket Flight Video:
Medium IMU
© Masanori Honda
Small Rocket: IMU
Tragedy Strikes!
 The R-DAS did not detect apogee and
deploy the parachute
 Data was irrevocably damaged by the
fall

© Masanori Honda
Rocket Flight Model:
Small IMU
Theory: Thermistors

The locations of the Thermistors are shown
below
3
1

2
4
Temperature can be found as a function of the
resistance of the thermistor using the Steinhart –
Hart (S-H) Equation displayed below.
1
3
 C1  C 2  lnR   C 3  lnR 
T
Theory: Pressure Sensors



The rocket has two pressure sensors
 R-DAS
 IMU
The two pressure sensors were calibrated with
an desiccation chamber
The altitude of the rocket can be calculated using
the relationship between altitude and the
atmospheric pressure shown below.
 dT  R 

dh
 P g 
T0
h
 1   

dT
P


dh   0 




Smoothing Function
Medium Rocket:
Temperature and Pressure

Apogee


R-DAS: 199.8 m
IMU: 199.7 m
3
1
2
4
Medium Temperature and Pressure Flight 1(Motor G67R, 4/19/2008)
Theory: Vibration

The Modal shape of a linear objects can be
given by the following equation
y n  Sin (


nx
)
L
The first three Modal shapes should have the
shapes below
The following diagram displays the location of
the strain gauges on the rocket
Medium Rocket: Vibration
Plot of time vs raw data for 3-4 seconds
Plot of time vs raw data for 4-4.5 seconds
Medium Rocket: Vibration
Medium Rocket: Vibration
Medium Rocket: Vibration
Deflection At 1.99 Hz From 3 to 4 Seconds
Deflection At 42.79 Hz From 3 to 4 Seconds
1.2
1.8
1.6
1
Corrected Magnitude
Corrected Magnitude
1.4
0.8
0.6
0.4
0.2
1.2
1
0.8
0.6
0.4
0.2
0
0
10
20
30
40
0
50
-0.2
-0.2
0
10
Positions of The Sensors (in)
20
30
40
50
Positions of The Sensors (in)
Deflection At 43.56Hz From 4 to 4.5 Seconds
Deflection At 1.99 Hz From 4 to 4.5 Seconds
0.9
1
0.8
0.8
0.7
Corrected Magnitude
Corrected Magnitude
0.6
0.4
0.2
0
0
10
20
30
40
50
0.6
0.5
0.4
0.3
0.2
0.1
-0.2
0
0
10
20
30
-0.1
-0.4
Positions of The Sensors (in)
Position Of The Sensors (in)
Plots of sensor positions to corrected magnitude
40
50
Conclusions



The IMU rocket showed:
 Theoretical models consistently
overestimate the actual apogee by
30-40%
The temperature pressure rocket:
 Consistency between two pressure
sensors
 Temperature of the rocket during
flight
The vibrational rocket:
 Only the first mode was observed
 The first resonance occurred at 43
Hz
© Masanori Honda
Further Work

Suggestions for design improvement:
 Change from the R-DAS to
another type of data acquisition
system due to issues:
• The R-DAS altitude sensor
does not reliably detect
apogee due to low resolution
• The R-DAS doesn’t sample
at high enough of a
frequency to detect higher
vibration modes
 Further rocket flights to determine
any inefficiencies in the rocket
design
© Masanori Honda
Acknowledgements
Professor Spjut
 Professor Cardenas
 Professor Miraghaie
 Professor Yang
 Professor Wang
 Proctor 1
 Proctor 2

Acknowledgements

And the E80
students who
have risked their
lives for the
course
© Med Temp. Press. Rocket
Questions?