1. AAE 450 Spring 2008 Adam Waite January 24, 2008 Dynamics and Control Thrust Vector Control Analysis for an Air Launched Rocket

2. AAE 450 Spring 2008 Outline of Air Launch  TVC offsets the thrust vector by an input angle which creates a moment about the center of gravity and pitches the rocket up to vertical  Assumptions  Constant TVC angle  Constant thrust, mass flow  No drag or atmospheric forces  No controller  Minimum Rise Time  Vanguard Model with Full Thrust Dynamics and Control

3. AAE 450 Spring 2008 TVC Analysis Dynamics and Control TVC Angle (deg)123 Time to Vertical (s)5.9954.3253.564 G Forces (g's)1.2792.5573.58  Pegasus pulled 2.5 g’s  Recommend combination of TVC and lifting surface for air launched rocket Future Work  Add drag and atmospheric forces to the current model  Develop a controller

4. AAE 450 Spring 2008 References  Klaurans, B. “The Vanguard Satellite Launching Vehicle,” The Martin Company. No. 11022, April 1964  Vick, Charles P., Berman, Sara D., “Pegasus,” Federation of American Scientists: Military Space Programs, April 23, 1997, http://www.fas.org/spp/military/program/launch/pegasus.htm Dynamics and Control

5. Calculation of G Force AAE 450 Spring 2008  Along with Alfred Lynam and Mike Walker, a simulation was created for a 6 DOF rigid body rocket  This simulation was then analyzed for a horizontal air launch  In the EOMs portion of the simulator, angular acceleration is output in rad/s^2  This value was multiplied by the distance from the thrusters to the center of gravity (8.36 m for this simulation)  The new value is then divided by 9.80665 m/s^2 to achieve a g force. Example (2 Degree TVC) 3.0 rad/s^2 * 8.36 m = 25.08 m/s^2 25.08 m/s^2 / 9.80665 m/s^2 = 2.557 g’s

6. Added Figures AAE 450 Spring 2008 Exact Data Points for Time to Vertical See attached Matlab and Simulink Files for configuration code and EOM solver with angular acceleration