oblique-shocklisted

Use when you must analyze an oblique shock in supersonic compressible flow: compute the wave angle beta from the upstream Mach number M1 and the flow deflection angle theta with the theta-beta-M relation, find the weak and strong solutions, the maximum deflection angle for an attached shock, and the downstream Mach number, static pressure, density, temperature, and stagnation pressure ratios across the shock. Covers shock polar basics: the weak branch keeps the flow supersonic with little stagnation pressure loss, the strong branch goes subsonic, and a deflection above the limit detaches the shock. Produces the wave angle, downstream state, and deflection limit for wedge, compression-corner, and inlet analyses. Trigger: oblique shock, shock wave, wave angle, deflection angle, theta-beta, wedge, compression corner, detached shock, shock polar, weak solution, strong solution, supersonic flow.
ashfordeOU/aero-agent-skills · ★ 0 · AI & Automation · score 78

Install: claude install-skill ashfordeOU/aero-agent-skills

# Oblique Shock Relations (aerodynamics/high-speed/oblique-shock) Use when the task is an oblique shock in supersonic flow: the wave angle from the theta-beta-M relation, the weak and strong solutions, the deflection limit for an attached shock, and the downstream state. ## Domain quick reference - Geometry: a supersonic flow deflected into itself by the angle theta (wedge half-angle or compression-corner turn) forms an attached oblique shock inclined at the wave angle beta to the upstream flow, with the Mach angle mu = asin(1/M1) < beta <= 90 deg. - Only the Mach component normal to the shock changes across it: M1n = M1 * sin(beta); the tangential component passes through unchanged. All downstream ratios come from the normal shock relations applied to M1n. - theta-beta-M relation: tan(theta) = 2 * cot(beta) * (M1^2 * sin^2(beta) - 1) / (M1^2 * (gamma + cos(2*beta)) + 2). theta = 0 at both beta = mu (Mach wave, isentropic) and beta = 90 deg (normal shock). - Two solutions for theta < theta_max: the weak solution (small beta, downstream flow usually still supersonic, the branch physically realized on a wedge) and the strong solution (large beta, downstream flow subsonic). - Deflection limit theta_max: the apex of the shock polar, where the two branches merge. Above it no attached oblique shock exists and the shock detaches. theta_max grows with M1 toward about 45.6 deg (gamma = 1.4); at M1 = 2 it is 22.9735 deg. - Downstream Mach: M2 = M2n / si