Accuracy Limits of Fast Analytical Methods for the Lift and Wave Drag of Supersonic Double-Wedge Airfoils

Fast analytical methods matter in early supersonic design because they answer in milliseconds questions that CFD answers in hours. This paper quantifies how far two such methods can be trusted for a double-wedge (diamond) airfoil: linearised supersonic theory (Ackeret) and shock- expansion theory. Both were implemented in Python and verified in three layers: exact closed- form anchors, machine-precision satisfaction of the Rankine–Hugoniot conservation laws, and spot checks against published tables. Predictions were then compared with three independent reference datasets digitised from the literature: RANS CFD at Mach 1.2 to 3.5 (Prasad et al., 2017), RANS CFD at Mach 2 for thickness ratios 0.1 to 0.5 (Dhungana et al., 2026), and pressure- integrated wind-tunnel measurements at Mach 1.166 to 1.377 near shock attachment (Vincenti et al., 1954). In the attached-flow, moderately supersonic core the fast methods are accurate: shock-expansion theory matches CFD lift to a median 2 % (Prasad) and 6.5 % (Dhungana), consistently ahead of linearised theory. Accuracy degrades with thickness and incidence, and both methods fail near Mach 1, in different ways: shock-expansion theory stops answering when the shock detaches, while linearised theory keeps answering and is wrong. Finally, the validated solver was used to design for minimum wave drag at fixed lift and fixed structural thickness: the optimum diamond carries its maximum thickness aft of mid-chord (x/c≈0.52–0.62), an effect the linearised formulation cannot capture, since its wave-drag expression is symmetric about mid-chord.