Connecting gravity turn guidance dynamics to near planar missile motion geometry

Abstract

The dynamic pressure on a rocket body caused by atmospheric drag must be kept small to prevent the missile from breaking up during its trajectory in the earth's lower atmosphere. Gravity turn guidance minimises this dynamic pressure load on the body structure by aligning the rocket's thrust in the direction opposite to the drag force, along the direction of the missile's inertial velocity relative to the inertial velocity of the earth's atmosphere. In this study, the authors first show why the trajectories of ballistic missiles under gravity turn guidance are accurately approximated by motion that is closely confined to an earth-centred, earth-fixed plane. They then introduce a new cylindrical coordinate trajectory profile model that exploits this inherent near planar motion. It is shown that this model interpolates the numerically integrated solution to the rocket equations of motion down to centimetres of position accuracy and tenths of centimetres per second in velocity error.