Modern aircraft are expected to fly faster and more efficiently than their predecessors. To improve aerodynamic efficiency, designers must carefully consider and handle shock wave formation. Presently, many designers utilize computationally heavy optimization methods to design wings. While these methods may work, they do not provide insight. This thesis aims to better understand fundamental methods that govern wing design. In order to further understand the flow in the transonic regime, this work revisits the Transonic Similarity Rule. This rule postulates an equivalent incompressible geometry to any high speed geometry in flight and postulates a “stretching” analogy. This thesis utilizes panel methods and Computational Fluid Dynamics (CFD) to show that the “stretching” analogy is incorrect, but instead the flow is transformed by a nonlinear “scaling” of the flow velocity. This work also presents data to show the discrepancies between many famous authors in deriving the accurate Critical Pressure Coefficient (Cp*) equation for both swept and unswept wing sections. The final work of the thesis aims to identify the correct predictive methods for the Critical Pressure Coefficient.