AIAA Design, Build, Fly Competition 2006/2007 Purdue Black Team

AAE 450 Spring 2008Adam Waite03/06/2008Dynamics and ControlSplines and 1 kg CaseAAE 450 Spring 2008Splines Dynamics and Control

Figure by Adam WaiteThanks to D&C group Splines attempt to optimize trajectorys steering law Uses Excel equations to create new trajectory for all three stages Attempts to smooth the transition between stages For 1kg case, used linear steering law in upper stages to create a constant change in pitch rate Performance is very sensitive to changes in spline and control gainsAAE 450 Spring 20081 kg Case (115%) Dynamics and ControlFuture WorkOptimize spline and gains for 5kg caseRun Monte Carlo for all cases

Red TrajectoryBlue - Actual Results using all average values: Periapsis: 365 km Apoapsis: 2,392 km Eccentricity: 0.131 Figure by Adam WaiteThanks to D&C groupAAE 450 Spring 2008ReferencesDynamics and Control groupTrajectory GroupMain D&C codeEverybody else that contributed to design and sizing of rocket Dynamics and ControlAAE 450 Spring 2008Excel Sheet for 1kg CaseBlack Line Actual PathYellow Line SplineBlue Line Trajectorys Steering LawFigure by Adam WaiteAAE 450 Spring 2008Logic Behind Splines in ExcelFirst, trajectorys steering law was plotted using arctangentSharp changes in steering law were notedThose points were eliminated from the plot and a polynomial curve fit was used in its placeThese polynomial equations are then input into the main configuration file for the rocket to follow with the times for each spline also being inputThe upper stages undergo a scalar adjustment in the positive or negative direction to either increase or decrease the radial velocityPeriapsis is determined and the spline is adjusted accordinglyAAE 450 Spring 2008Earlier Test Spline for 200g CaseBlack line Actual PathYellow line Trajectorys Steering LawBlue line- SplineFigure by Adam WaiteAAE 450 Spring 2008Earlier Test Spline for 5kg CaseBlack Line Actual PathColored Lines - SplineFigure by Adam WaiteAAE 450 Spring 2008Alternative Orbit Views

Red Line Trajectorys OrbitBlue Line Actual OrbitFigures by Adam Waite with thanks to D&C group