ASEN 3200 Orbital Mechanics and Attitude Dynamics
Spring 2006
ASEN 3200 LAB A-1 Attitude Sensors and Actuators
Assigned:
Report Due:
17 March 2006
4 April 2006
OBJECTIVES
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Investigate two types of rate gyros and measure their capabilities for sensing angular position and angular
velocity.
Investigate a reaction wheel actuator and measure its angular momentum storage capability.
Operate and qualitatively understand how a control moment gyro works.
PRELIMINARY QUESTIONS
1) Suppose you are given a data file containing samples of rate gyro measurements at equally-spaced time
increments of t sec, for rotation about a fixed axis aligned with the gyro sensitive direction. The measurements
are in volts, and the gyro sensitivity is K [V/(rad/sec)]. How would you calculate angular position in [rad]
versus time from this data?
2) A spacecraft in low Earth orbit has a constant torque disturbance due to aerodynamic drag of Md [Nm]. A
reaction wheel is being angularly accelerated to produce a counter torque to keep the spacecraft from tumbling.
If the reaction wheel has a moment of inertia about its spin axis of Iw [kg m^2], what is the rate of change of the
angular velocity of the reaction wheel?
3) You are sitting on a stool, free to rotate about the vertical, holding the spinning bicycle wheel in front of you
with the spin axis horizontal. Describe how the spin axis should be moved so that a torque is obtained about the
vertical axis, i.e. so that you are rotated on the stool.
EQUIPMENT
Spacecraft mockup with spinning and MEMS rate gyros, Labview Gyro.VI, Labview Torque.VI, rim-loaded
bicycle wheel, spin-up motor, bicycle wheel speed sensor, low-friction lab stool.
PROCEDURE
There are multiple sets of hardware for this experiment, but groups will need to take turns observing and measuring
data for each of the parts below.
1) Measure the sensitivity of both types of rate gyro.
a. Measure the sensitivity of both the spinning and MEMS rate gyro by moving the spacecraft back and
forth by hand and capturing voltage versus angular velocity data using the Labview Gyro.VI. Note that
abrupt changes in angular velocity can cause “looping” in this relationship. Move the spacecraft so that
a good linear relationship between voltage and angular rate can be observed.
b. Import this data into Matlab and find the best fit straight line to this data. Report the resulting gyro
sensitivity in [V/(rad/sec)] for each type of gyro.
c. Record an angular rate data set where the spacecraft is moved back and forth between two precisely
known angles, e.g. 90 deg. rotation between landmarks on the module table.
2) Measure the torque constant and moment of inertia for the reaction wheel.
a. Measure the moment of inertial of the reaction wheel about its the spin axis by applying a constant
torque and recording the angular velocity data as the wheel accelerates using the Labview Torque.VI.
Be careful to limit the speed of the wheel, since applied torque is limited at high speeds, resulting in a
non-linear relationship between apparent applied torque and speed.
b. Import this data into Matlab and find the best fit straight line. Report the moment of inertia of the
wheel in [kg m^2].
c. What is the maximum speed for which the relationship between apparent applied torque and speed is
linear?
Lawrence ASEN3200_LabA1_2006
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ASEN 3200 Orbital Mechanics and Attitude Dynamics
Spring 2006
3) Experiment with the bicycle wheel control moment gyro.
a. Stand on the swivel board, or sit on the swivel stool with feet on the support rung . Hold the bicycle
wheel in front of you with arms straight and wheel axle horizontal. Have another group member spin
up the wheel using the electric motor. Experiment with moving the wheel spin axis. Try to obtain
reaction torques that cause you to rotate about the stool vertical axis.
b. Use the wheel to point your horizontal body axis (e.g. the axis described by our outstretched arms) to
track a moving reference point (e.g. a walking group member). Try this with more than 1 group
member and note any differences in performance.
ANALYSIS
1) Using the data from the procedure part 1) c., calculate the angular position change from the initial position
from the angular rate data. Comment on the relative accuracy of the two types of gyros in measuring
angular position.
2) Using the data obtained in the procedure part 2), calculate how long the reaction wheel could resist an
aerodynamic torque of 1e^-4 Nm before the wheel speed exceeds the limit of 150 rad/sec. What is the
angular momentum capacity of this wheel in [Nms]?
3) Explain qualitatively how you were able to obtain pointing torque using the bicycle wheel as a control
moment gyro. Draw a diagram showing the momentum vector and its vector rate of change, as well as the
resulting moment vector.
REPORT OUTLINE & GRADING
Title Page (1 pt) – Lab, Course Number, Group Members, Date
Abstract (5pts)– short summary of objectives, experiment, results, and analysis
A. Rate Gyro Characterization (30 pts)
 Experiment – list equipment, detailed procedures
 Results – give table of results (including units), observations made during the experiment
 Analysis – present your computations of expected precession, compare with experimental results, describe
and quantify possible sources of error
B. Reaction Wheel Characterization (30 pts)
 Experiment – list equipment, detailed procedures
 Results – give qualitative results of this experiment, observations made during the experiment
 Analysis – explain the results you obtained; use diagrams to show what results you expected compared to
what was obtained
C. Control Moment Gyro Experiment (20 pts)
Conclusions and Recommendations (5 pts)
 What did you learn from this experiment?
 What would you recommend to improve the experiment or to extend it beyond the given objectives?
Acknowledgements (1 pt) Who did what in the group and what outside assistance you received
References
[Style & Clarity 8 pts]
Organization (2) – clear flow, follows required outline, numbered pages
Figures (2) – clear figures, appropriate axes, informative titles
Tables (2) – clear tables, significant figures, headings, informative titles
Spelling & Grammar (2)
Lawrence ASEN3200_LabA1_2006
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