The Sonic Creep — AE 302 Module 6

You never have to fly at Mach 1 for the sound barrier to find you. Air accelerating over the wing goes supersonic long before the airplane does — at the critical Mach number. Push each airfoil as fast as you dare and 🔒 LOCK your speed as close to M_cr as possible without waking the red sonic bubble. Go too far and meet drag divergence (and the buffet). Thin wings win — you'll feel why.

🚀 Flight Mach M∞ 0.50

Cp,min (compressible): —

Cp needed for sonic: —

Peak local flow: subsonic

Best locks: — · — · —

Two curves race as M∞ grows (Anderson §11.6):
Compressibility inflates the suction peak — Prandtl–Glauert: Cp = Cp₀ / √(1 − M∞²).
Meanwhile the Cp needed to reach LOCAL Mach 1 shrinks: Cp,cr = 2/(γM∞²) · [((2 + (γ−1)M∞²)/(γ+1))^{γ/(γ−1)} − 1].
Where they cross: M∞ = M_cr, the critical Mach number. Beyond it a supersonic pocket forms, terminated by a shock → boundary-layer separation → drag divergence near M_dd ≈ M_cr + 0.05…0.08. Thinner airfoil → smaller |Cp₀| → later crossing → higher M_cr. That's why transonic jets have thin, swept wings (and why the 747 cruises at ≈ M 0.85, not 0.99).

Creep up on the sound barrier… the bubble appears the instant your peak Cp crosses the critical line.

Module 6 · The Sonic Creep