  Compressible flows around blunt objects have diverse applications, but
present analytic treatments are inaccurate and limited to narrow parameter
regimes. We show that the flow in front of an axisymmetric body is accurately
derived analytically using a low order expansion of the perpendicular gradients
in terms of the parallel velocity. This reproduces both subsonic and supersonic
flows measured and simulated for a sphere, including the transonic regime and
the bow shock properties.
