## A Generalized Orthogonal Coordinate System for Describing Families of Axisymmetric and Two-dimensional Bodies |

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0max 0r-plane analytic body shapes angle of attack Approximation to Spherically axisymmetric and two-dimensional axisymmetric body base radius body surface body-oriented coordinate system boundary conditions calculated circular disks computational space conditions along line cone angle constant 9 coordinate in transformed cosh Curvilinear Coordinate curvilinear orthogonal coordinate cylinders with rounded cylindrical coordinate system defined direction of increasing Families of Triangular figure 23 flat-faced cylinders flow field forebody governing equations hemispherical afterbody infinite radius Langley Research Center line of constant maximum body radius mesh points metric coefficients nAnenr cos(n0 nAnenr sin(n0 natural coordinate system Navier-Stokes equations Newton's method nose radius obtained orthogonal coordinate system outflow boundary planetary probe vehicles Planetary probe-vehicle approximation problem radius of curvature radius to base ratio of nose rectangular coordinate system rounded corners sinh specified spherically capped cones stagnation line substituted into equations system to describe triangular shapes two-dimensional body shapes uniform velocity field vector xy-plane Ymax