Waveriders have been constructed from hypersonic flowfields behind arbitrary three dimensional shock shapes using a special spatial marching finite difference approach. This routine exploits the simplicity and efficiency of spatial marching techniques and the accuracy of the method of characteristics, and greatly simplifies the waverider design process. The stream surfaces behind the shock shapes form the compression surface for a new family of waveriders, providing greatly needed flexibility in the design and optimization of such vehicles. Emphasis is placed on the influence of the shock shape and its relationship to the aerodynamic characteristics of the resulting waverider. A systematic approach based on the direct search Rosenbrock optimization technique is developed in an effort to carve waveriders with optimal aerodynamic quantities for given dimension and free stream conditions. Waveriders carved from arbitrary oblique and axisymmetric shock waves are evaluated and validated against those constructed using conventional numerical techniques. Finally, a new class of waveriders carved from arbitrary three dimensional shock shapes are presented and discussed,
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