Dispersion of a Ground-Launched Rotating Missile

Abstract : From the equations of motion of a rotating rocket, closed solutions are obtained for the ballistic dispersion during boost under the assumption that the angular acceleration is constant - Part II and Appendix A. These solutions are evaluated numerically for the two cases: (a) launching spin zero; (b) angular acceleration zero, and the results are presented and discussed in Part I. By comparing the dispersion with that of a non-rotating round, the effectiveness of spin as a means of reducing dispersion can be assessed in each case. In case (a) it is found that reductions in the dispersion by a factor of 3 are theoretically possible by off-setting the nozzles of a multiple boost system tangentially by less than 5 deg. To achieve larger reductions by this method, the nozzle off-set must be increased in proportion to the square of the reduction sought. In case (b), the constant spin case, it is found that a spin of just less than 1 rev/sec is in general sufficient to reduce the dispersion by a factor of 3. For higher spins the reduction varies linearly with the spin. In Part III closed solutions are obtained for the dispersion of the dart due to unclean separation and aerodynamic misalignments. From these solutions the maximum dispersions that can arise are then deduced. The results are presented in Part I, and it is concluded that dispersion of the dart from these causes will be small compared with the dispersion at the end of boost.