Reynolds-averaged Navier-Stokes and detached eddy simulations are performed on a 0.50 caliber spinning projectile for three yaw angles over the Mach number range of 0.6-2.7. The simulations are compared with the experimental data of McCoy (McCoy, R. L., The Aerodynamic Characteristics of 0.50 Ball, M33, API, MS, and APIT, M20 Ammunition," U.S. Army Ballistic Research Lab. BRL-MR-3810, Aberdeen Proving Ground, MD, Jan. 1990) and the Reynolds-averaged Navier-Stokes results of Silton (Silton, S., "Navier-Stokes Computations for a Spinning Projectile from Subsonic to Supersonic Speeds," Journal of Spacecraft and Rockets, Vol. 42, No. 2, 2005, pp. 223-231). Unlike the Reynolds-averaged Navier-Stokes simulations, the detached eddy simulations are shown to predict unsteady base and wake flows, which affect the predicted aerodynamic behavior of the projectile. There are some notable differences between the predictions of the present Reynolds-averaged Navier-Stokes simulations and those of Silton; they are most likely a result of the different turbulence models used. This further illustrates the sensitivity of the results to the turbulence modeling approach, for both Reynolds-averaged Navier-Stokes and detached eddy simulations. The largest difference between Reynolds-averaged Navier-Stokes and detached eddy simulations is found for the Magnus moment coefficient at small yaw angles. Analysis shows that this moment is particularly sensitive to the unsteady wake and shock motion predicted by detached eddy simulations.