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

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

AAE 450 Spring 2008 TVC Analysis Dynamics and Control TVC Angle (deg)123 Time to Vertical (s) G Forces (g's)  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

AAE 450 Spring 2008 References  Klaurans, B. “The Vanguard Satellite Launching Vehicle,” The Martin Company. No , April 1964  Vick, Charles P., Berman, Sara D., “Pegasus,” Federation of American Scientists: Military Space Programs, April 23, 1997, Dynamics and Control

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 m/s^2 to achieve a g force. Example (2 Degree TVC) 3.0 rad/s^2 * 8.36 m = m/s^ m/s^2 / m/s^2 = g’s

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