| The study of forces and moments on a spinning pointed body at an angle of attack is extremely important in ballistics. Previous work has been mostly experimental. This is because the governing Navier-Stokes equations are nonlinear and fully three dimensional, making analysis impossible and direct numerical solutions impractical.; The most promising theoretical technique is the unsteady cross flow analogy. Considering the axial direction as timelike, the pressure and the flow field can be obtained from the impulsive starting of a two-dimensional cylinder. Although the analogy is heuristic, the results do correlate well with experimental data on slender bodies for subsonic through supersonic free stream speeds.; In this study we investigate the impulsive starting of expanding, rotating cylinders. The results are used to calculate the force and moment coefficients for projectiles by means of the unsteady cross-flow analogy. We solve the unsteady Navier-Stokes equations using matched asymptotic inner-outer perturbation method and comparing these results with the solution obtained using numerical methods. Excellent agreement between the two methods has been established in the region where both solutions are valid.; The results obtained are consistent with existing experimental work. For example, a pair of secondary recirculating zones has been predicted, in addition to the well-known primary pair for high Reynolds numbers. The numerical scheme used showed stability and robustness in the integration of the full Navier-Stokes equations. |
