The problem at hand is to guide a re-entry vehicle safely back to Earth starting from speeds approaching Mach 25. The vehicle has thrust and glide capability. The red solid line shows a pre-planned trajectory for the vehicle to follow. At several way points along this path, the vehicle may need to change course, divert, and re-program its path. The blue solid lines show the maximum possible cross-range diversion the vehicle could achieve from each of the way points.
This type of calculation is not only useful in mission planning, the sophistication of the method enables new metrics in the vehicle design loop. The next figure compares the reachable footprint at each way point for a powered (line) and unpowered vehicle (solid).
This work was published in the AIAA Journal of Spacecraft and Rockets:
Range Improvements in Gliding Reentry Vehicles from Thrust Capability