transonic-similaritylisted

# Transonic Similarity Corrections (aerodynamics/high-speed/transonic-similarity) Use when the task is compressibility corrections for high-subsonic flows: the Prandtl-Glauert and Karman-Tsien pressure coefficient corrections, the transonic similarity parameter, and critical Mach estimation. ## Domain quick reference - Prandtl-Glauert (linearized thin-airfoil theory, valid below M ~ 0.7): perturbation quantities scale with the factor 1 / sqrt(1 - M^2). Pressure coefficient C_p = C_p0 / sqrt(1 - M^2), lift coefficient C_L = C_L0 / sqrt(1 - M^2), and section lift-curve slope a = a0 / sqrt(1 - M^2), where subscript 0 marks the incompressible value. - Karman-Tsien (extended, usable toward M ~ 0.85): C_p = C_p0 / (sqrt(1 - M^2) + (M^2 / (1 + sqrt(1 - M^2))) * C_p0 / 2). The denominator shrinks less than the Prandtl-Glauert factor alone, so the correction stays finite closer to M = 1. - Transonic similarity parameter: K = (1 - M^2) / tau^(2/3), with tau the thickness ratio (sweep enters through the effective Mach M * cos(Lambda)). Two thin configurations with equal K have similar pressure fields near M = 1. - Critical pressure coefficient (isentropic sonic limit at freestream Mach M, gamma = 1.4 default): C_p* = (2 / (gamma * M^2)) * (((1 + (gamma - 1) / 2 * M^2) / (1 + (gamma - 1) / 2))^(gamma / (gamma - 1)) - 1). Local flow is sonic where C_p equals C_p*. - Critical Mach number M_cr: solve C_p0 / sqrt(1 - M^2) = C_p*(M) for the smallest M; the p