Power law shapes for leading-edge blunting with minimal shock standoff

The application of power law shapes to the blunting of sharp leading-edged vehicles is investigated. Newtonian results have shown that power law shapes exhibit aerodynamic properties similar to geometrically sharp shapes, and power law shapes are close to minimum drag forms for axisymmetric bodies. Power law shapes have, for certain power law exponents, zero radius of curvature (a property of geometrically sharp objects) and infinite slope (a property of geometrically blunt objects) at the nose. These qualities have seemed promising for the design of blunted Leading edges with minimum shock detachment distance (and, hence, low drag), which might also have acceptable heating rates. To investigate this, comparisons based on geometry, equivalent drag, equivalent heating, and equivalent shock detachment distance are made between power law configurations and circular cylinder shapes. Two-dimensional computational and analytical results are provided that question the results of Newtonian analysis for power law leading-edge geometries. The analysis also shows that, despite the seeming advantages of power law geometries, circular cylinders provide smaller shock standoff and drag for equivalent stagnation point heating under the range of conditions investigated.