Jet damping of a solid rocket - theory and flight results

Abstract

The angular motion of a spin stabilized solid rocket is computed, considering the effect of jet damping about axes normal to the spin axis. The approximate formula used is chosen for computational accuracy and to fit the rocket geometry. Results are compared with measurements of body angular acceleration made during the rocket's flight in space. The comparison indicates that the jet damping is a very strong effect in this case, and that the approximate formula gives adequate accuracy for computing the reduction in conical precession motion due to jet damping. It is probable that the same formula can be used to estimate jet damping for other solid rockets. I. Introduction T HE term jet damping refers to the change in the angular rates of a thrusting rocket due to the torques exerted by the gases flowing out the nozzle. The jet damping effect is especially important in spin stabilized rockets where it acts to reduce the amplitude of the conical free precession motion and, therefore, to reduce the motion to a steady spin. It is important to know what the cone angle is at staging, as this strongly influences the attitude error of the next stage. In rockets operating in air, jet damping is usually second in importance to aerodynamic moments. In vacuum, however, the jet damping can be the most important torque acting on the rocket. Several simplified theories have been proposed to give estimates of the rate of damping for a particular rocket.15 In general, these theories use one-dimensional gas flow in the rocket and characterize the thrust chamber and nozzle by certain approximate dimensions. Proper verification of these approximate theories has been difficult to obtain because of the lack of experimental data on the attitude of a spinning rocket in vacuum flight. In the present paper, a formula for pitch jet damping is derived from the general rocket equations in a body-fixed coordinate system assuming one-dimensional flow. The formula is selected to use quantities that are known accurately and to be compatible with the geometry of the rocket considered. The formula, a modification of the one presented in Ref. 4, is evaluated to give the predicted rate of cone angle damping for a particular frequently used spin-stabilized rocket, the Allegany Ballistics Laboratory! X-248 with a satellite payload. The resulting prediction of jet damping is then compared with measurements of the angular motion made in actual flight.