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With the recent development of capabilities for predicting the damping derivatives, it is now possible to predict the stability characteristics and free-flight motion for projectiles using data that are derived solely from computational fluid dynamics (CFD). As a demonstration of the capability, this report presents results for a family of axisymmetric projectiles in supersonic flight. The particular configuration selected for this computational study has been extensively tested in aeroballistic ranges, and high-quality experimental data have been obtained. Thin-layer Navier-Stokes techniques have been applied to compute the attached viscous flow over the forebody of the projectile and the separated flow in the projectile base region. Using the predicted aerodynamics coefficients, parameters that characterize the in-flight motion are subsequently evaluated, including the gyroscopic and dynamic stability factors, and the projectile's fast and slow mode frequencies and damping coefficients. These parameters are then used to predict the free-flight motion of the projectile. In each case, the computational approach is validated by comparison with experimental data, and very good agreement between computation and experiment is found. It is believed that this demonstration represents the first known instance of a viscous CFD approach being applied to predict all the necessary data for performance of linear aerodynamics stability and trajectory analyses.