Boundary layer equations are developed and incorporated into an implicit finite-difference technique solving non-similar, axi-symmetric boundary layer equations for both laminar and turbulent flow. The new equations match all the boundary layer properties with the variation of the inviscid solution near the edge, except for the normal velocity. In this way entropy layer swallowing effects are automatically included in the solution. The method also incorporates more inviscid flowfield information into the boundary layer solution than other methods at a negligible increase in run-time. Results show that the new technique can provide improved heating rates and skin friction predictions for preliminary design of vehicles where shear layers and entropy layer swallowing are important. Solutions are presented for three sphere-cone configurations at high Mach number and comparisons are made with the SABLE boundary layer code, Navier-Stokes solutions, and Viscous Shock Layer solutions. Use of a new L'Hôpital rule-based inviscid velocity gradient provides better prediction of stagnation-point heating rates. Heating rates are predicted more accurately in both the nose region and areas near the sphere-cone juncture than SABLE's final iteration. Shear stress results are also improved in the sphere-cone juncture area. The new technique's impact is seen readily in cases where the inviscid flowfield experiences velocity and enthalpy gradients near the wall. Little effect was seen on cases where the inviscid velocity ratios at the boundary layer edge was less than 1.5 and the enthalpy ratio greater than 0.9.
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