1. Jeff Stuart 2/28/2008 Dynamics and Controls, CAD Spin Stabilization of Third Stage (200g Payload)
AAE 450 Spring 2008

2. Pointing Error Goal and Spin Rate
Figure from code developed by A. Chaney
Thrust Deflection angle: 0.5 deg
From data provided by A. Guzik,
Spin Rate: 125rpm
AAE 450 Spring 2008
Dynamics and Controls

3. Spin Up Motor Sizing Future Work TVC finalization
For spin-up time of 3.85 sec, from 0 rpm to 125 rpm:
2 motors of total impulse 27.5 N-sec each
Constant thrust: N each
Future Work
TVC finalization
Spin stabilization for initial angular velocity
CAD assembly work
AAE 450 Spring 2008
Dynamics and Controls

4. References
Longuski, J.M., Kia, T., and Breckenridge, W.G. “Annihilation of Angular Momentum Bias During Thrusting and Spinning-up Maneuvers” Journal of the Astronautical Sciences, Vol. 37, No. 4, October-December 1989, pp
National Association of Rocketry
AAE 450 Spring 2008
Dynamics and Controls

5. Table prepared by A. Guzik
AAE 450 Spring 2008
Dynamics and Controls

6. Model Stage 3 Data Model Name: SB-HA-DA-DA Stage 3
Prop Mass = [kg]
Inert Mass = [kg] (nose cone = 4.7 kg)
Engine Mass = 8.92 [kg]
Thrust (vac) = [N]
Burn Time = [s]
Mass Flow Rate = [kg/s]
Exit Area = [m^2]
Exit Pressure = [Pa]
Length Total = [m]
Diameter = [m]
Nose Cone Length = [m] cm S
AAE 450 Spring 2008
Dynamics and Controls

7. Angular Velocities During Spin - Up

8. Rigid Body FBD and Assumptionscp cm ct
Simplifying Assumptions:
Center of gravity is the same as center of mass
Center of mass (cm), center of pressure (cp), and center of thrust (ct) along longitudinal axis of spacecraft
Craft is axisymmetric about cm
AAE 450 Spring 2008
Dynamics and Control

9. Simplified EOMs (Moments about c.m.)
AAE 450 Spring 2008
Dynamics and Control

10. Force Equations Displacement Vectors Aerodynamic Force Definitions
Applied Moment from Spacecraft Stabilization System
Aerodynamic Force Definitions
Displacement Vectors
AAE 450 Spring 2008
Dynamics and Control

11. Moment Equations: Gravity and Spin
Spin Stabilization:
AAE 450 Spring 2008
Dynamics and Control

12. Moment Equations: Aerodynamic
AAE 450 Spring 2008
Dynamics and Control

13. Moment Equations: Thrust
AAE 450 Spring 2008

14. Kinematic Relations Kinematic relations developed by A. Chaney
Moments of inertia about principal body axes