Optimal flight paths for a winged supersonic rocket vehicle
Abstract
A simple and reliable method is proposed for defining optimal trajectories of a winged rocket vehicle within the atmosphere. The solution is not analytical and is carried out numerically using distance or path length as the independent variable. It is valid for all speeds and trajectories between sea level and earth orbit. Since there is no integral performance index to be satisfied, modern methods of control system design are not required, and the solution proceeds using only the classical methods of calculus of variations. A particular case is evaluated, namely the placing of a given mass to maximum velocity at a given horizontal distance down range equal to 10 scale heights (70 km). The solution equations are programmed on an interactive digital computer, and the integration technique is fourthorder RungeKutta, and the iteration for velocity uses simple firstorder Newtonian approximation. The optimal programmed thrust required to place maximum mass into earth orbit can also be determined.
 Publication:

Aeronautical Journal
 Pub Date:
 December 1978
 Bibcode:
 1978AeJ....82..517L
 Keywords:

 Flight Paths;
 Rocket Planes;
 Supersonic Aircraft;
 Thrust Programming;
 Trajectory Optimization;
 Calculus Of Variations;
 Differential Equations;
 Equations Of Motion;
 Mass;
 Nonlinear Equations;
 Time Dependence;
 Astrodynamics