Supersonic flow only turns two ways. Turn it INTO itself (wedge up) and it snaps through an oblique shock; turn it AWAY (wedge down, negative angle) and it relaxes through a smooth expansion fan. Steer the wedge, watch β chase θ — and find the angle where the shock says "no" and detaches. Then hit 🎯 for design challenges.
tan θ = 2 cot β · (M₁² sin²β − 1)/(M₁²(γ + cos 2β) + 2) — we solve it for the weak shock, like nature usually does.Mₙ₁ = M₁ sin β feeds the normal-shock relations, then M₂ = Mₙ₂ / sin(β−θ).ν(M) = √((γ+1)/(γ-1)) · tan⁻¹√((γ−1)(M²−1)/(γ+1)) − tan⁻¹√(M²−1), with ν(M₂) = ν(M₁) + |θ| — isentropic, zero total-pressure loss. Free turning!