An approximate method for the efficient calculation of stagnation-streamline quantities in hypersonic flows about spheres or cylinders is suggested. Based on the local similarity of the flow field the two-dimensional Navier-Stokes equations are simplified to a one-dimensional approximation for the stagnation streamline. These equations are solved with an implicit finite-volume scheme. Comparisons with fully two-dimensional Euler and Navier-Stokes calculations for flows about spheres are presented, that include perfect gas flows and flows in chemical non-equilibrium. Comparisons with a number of experiments conclude this report.