Navier-Stokes predictions of pitch damping for axisymmetric projectiles

An approach for predicting the pitch-damping coefficient sum for axisymmetric flight bodies is presented. The approach utilizes a specific combination of spinning and coning motions that allows the pitch-damping force and moment coefficient to be directly related to the aerodynamic side force and moment. The use of combined spinning and coning motion represents an improvement over existing techniques that utilize lunar coning motion for predicting the pitch-damping coefficients. A parabolized Navier-Stokes approach that utilizes a missile fixed, noninertial rotating coordinate frame is applied to predict the flowfields about axisymmetric projectiles undergoing steady coning motion. The governing equations are modified to include the centrifugal and Coriolis force terms due to the rotating coordinate frame. From the computed flowfield, the side force and moment due to coning motion, spinning motion, and combined spinning and coning motion are used to determine the pitch-damping coefficients. Computations are performed for a generic shell configuration (with and without boattail), and the predictions show good agreement with an existing inviscid code. The comparisons of computational results for a family of ogive-cylinder configurations with aerodynamics range data show excellent agreement and further validate the approach.