ASEN 2003 Introduction to Dynamics and Systems
Spring 2009
Lab 4: Despinning a Satellite
(This lab was originally developed by Prof. Robert Culp and Walter Lund)
ASSIGNED: MONDAY, FEBRUARY 23
DUE: WEDNESDAY, MARCH 11, 2009 (Beginning of lab)
INSTRUCTOR: K. C. Park
OBJECTIVES
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Understand the concept of a spacecraft subsystem
Learn one simple and commonly used method of controlling satellite spin
Observe application of conservation of angular momentum
Learn several experimental techniques useful in rigid body dynamics
Apply safety practice to an energetic dynamics system
Modify an experiment to achieve design objectives
OVERVIEW
The last stage of many launch systems is often spin-stabilized at a high angular speed, perhaps as high as
150 rpm. This spin rate is imparted to the satellite at orbit insertion. Since most satellites operate at a
slow, or zero spin rate, some mechanism is needed to reduce the insertion spin rate to a mission spin
rate. One dependable device for performing this spin reduction is called a yo-yo despinner. It consists of
one or two small masses on the ends of cords wrapped about the spin axis. If one mass is used, it must
be wrapped in the plane containing the satellite center of mass to avoid attitude perturbations. Two
identical masses avoid this problem.
When the mass is released, centrifugal force unwinds the cord and the mass extends gradually from the
satellite. The spin moment of inertia of the system increases, but the spin angular momentum and total
kinetic energy remain constant. This decreases the spin angular speed of the satellite body and transfers
angular momentum to the unwinding mass. Ice skaters use this same technique to control their spin
rate by extending and retracting their arms.
When the cord is completely unwound, it is released and the cord and its attached mass fly away. The
size of the mass and the length of the cord (and perhaps the radius about which it is wound) can be
varied to control the spin rate of the satellite. The system is analyzed by noting that the system angular
momentum and the total system kinetic energy remain constant throughout the process. The attached
derivation is from W. T. Thomson (1986).
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ASEN 2003 Introduction to Dynamics and Systems
Spring 2009
PRELAB
Before recording experimental data from the yo-yo despinner, you will need to analytically determine
the string lengths that you will need to conduct the experiment. You will need to:
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Calculate the moment of inertia of the satellite about its spin axis.
Calculate the string length for a final spin rate of zero for the masses available.
Calculate the string length for the final spin rate of one-half of the initial spin rate for the masses
available.
To calculate the moment of inertia, I, of the yo-yo despinner, we will combine the moments of inertia of
all the component parts. We can determine I to about 1% accuracy if we combine the moments of
inertia about the common axis of symmetry from the 11 cylindrical parts of the despinner listed in
Table1. (Note that some of the parts are “missing” cylinders that we will subtract, i.e., I = I1 – I2 + I3 + …)
1. Write a Matlab function to compute the moment of inertia of a cylinder about its symmetrical
axis, using the radius, height, and density of the cylinder as variables. The equation for moment
of inertia is I = mr2/2, where r is the radius. You can compute the mass, m, of each cylinder by
multiplying the density by the volume of a cylinder (V = r2h).
2. To use your function, you will need to determine the dimensions of all 11 cylinders. Some of the
dimensions that you will need can be found in Table 1. You will need to complete the table by
using the three pages of engineering drawings given.
Table 1: Cylindrical Parts of the Yo-Yo Despinner
Page
Main body (cylinder assembly)
Added section
Figure 1
Subtraction section
Figure 1
Drive Shaft
Thin pin on drive shaft
Figure 2
Wide part of drive shaft
Figure 2
Bottom plate
Missing section of
Figure 3
bottom piece
Top inner plate
Figure 3
Bottom inner plate
Figure 3
Upper outer plate
Figure 3
Upper removal plate
Figure 3
Middle plate
Figure 3
Main plate
Figure 3
Radius
(inches)
Height
(inches)
Add or
subtract
Material
8.500/2
7.625/2
+1
-1
Al
Al
0.400/2
0.875/2
+1
+1
Steel
Steel
0.875/2
-1
Al
2.500/2
3.250/2
7.625/2
6.500/2
7.625/2
8.500/2
+1
+1
+1
-1
+1
+1
Al
Al
Al
Al
Al
Al
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ASEN 2003 Introduction to Dynamics and Systems
Spring 2009
3. Write a Matlab program that calls the moment of inertia function for each of the cylinders listed
in Table 1. Determine the approximate moment of inertia of the entire despinner by combining
the individual moments of inertia using the appropriate additions or subtractions. You can find
the necessary densities on the engineering drawings. Report the final value of I in both English
(lb-in2) and SI (kg-m2) units.
4. Use the attached derivation to calculate a) the string length for a final spin rate of zero for the
masses available and b) the string length for the final spin rate of one-half of the initial spin rate
for the masses available.
EXPERIMENT
 Experimentally determine the string length for zero final spin rate for a specific mass.
 Determine the final spin rate for several combinations of string length and mass for which the
final spin rate is definitely not zero. Try for about one-half initial spin rate, but record anything
between 0.1 and 0.9 initial spin rate.
 Determine friction torque of the spinning satellite by taking data without any masses.
ANALYSIS
In your analysis of the experiment:
 Compare experimental data with theory for the zero spin rate case.
 Compare experimental data with theory for fractional final spin rate cases.
 Explain friction torque from experimental determination. Discuss why it has little or no effect.
 Discuss possible experimental error.
 Discuss possible modeling and assumption weaknesses.
WHAT TO TURN IN:
The following should be included in your lab report:
1. Title page
2. Abstract
3. Description of the experiment
4. A short discussion of the results that addresses the topics listed in the Analysis section
Include the completed Table 1 in your report. You will also need to turn in the Matlab code that you
used to calculate the moment of inertia.
Appendix A List the contributions of each member of the group and have each group member initial
this page. Describe assistance or contributions provided by classmates or others.
REPORT GRADING
5
Abstract
10
Introduction/Description of the experiment
70
Performance (30 pts for calculation of moment of inertia and 40 pts for analysis of experiment)
5
Acknowledgements
_10_ Style and Clarity (includes organization, grammar, spelling, etc.)
100
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Spring 2009
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Spring 2009
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