An optimal Space Shuttle ascent trajectory for the first orbital flight test

An optimal solution of the ascent trajectory of the Space Shuttle for the first orbital flight test is presented; the optimization is a minimum propellant, four-control problem in yaw angle, roll angle, pitch angle and vacuum thrust of each Space Shuttle main engine. Piecewise linear segments with juncture points treated as parameters are employed to model the controls. Equations of motion for a three-dimensional flight with pitch plane moment balance about an oblate are integrated numerically with a fourth-order Runge-Kutta method; two- and one-dimensional cubic spline function curve fits of aerodynamic coefficients are used during the first and second stages, respectively. The constraint minimization problem is solved with the Davidon-Fletcher-Powell function method.