NACA Wing on a Test Rig: Panel-Method Lift, Induced Drag and Stall

What you see. A NACA wing on a test rig with an angle scale. White particles follow the flow around the section, the wing surface is coloured by pressure (blue = suction, red = high pressure), and the readout gives lift, drag, lift-to-drag and Reynolds number for the chosen airspeed.

Section flow. The section is the closed NACA 4-digit contour (120 panels). A Hess–Smith panel method puts a constant-strength source on every panel plus one common vortex strength Γ, requires zero normal velocity at each panel midpoint and applies the Kutta condition (equal and opposite tangential speeds at the two panels meeting at the trailing edge). The pressure coefficient is Cp = 1 − (Vt/V∞)²; lift comes from integrating it, and independently from the circulation CL = −2 Γ Σl / c (Kutta–Joukowski).

Finite wing and stall. The tips shed a downwash that reduces the effective angle of attack by αi = CL / (π e AR) (e = 0.92), so the wing solves CL = CL,sec(α − αi) and adds the induced drag CL² / (π e AR). Real sections stall, which a potential flow cannot show: below the stall angle the lift is rolled off smoothly so that it reaches the approximate textbook maximum lift coefficient (1.50, 1.65, 1.80 for NACA 0012, 2412, 4412 at Reynolds number about 3 million) at the stall angle; beyond it the Viterna–Corrigan post-stall formulas continue the curve to a flat plate at 90°.

Honest simplifications. Potential flow has no boundary layer: viscous drag is the simple fit 0.0065 + 0.006 (CL − 0.2)², not a computed value; the stall angle, maximum lift and the roll-off shape are approximate and independent of Reynolds number; the red-blue pressure picture after stall is an illustrative plateau, not a computed separated flow; the particles are a two-dimensional section flow shown on three spanwise planes (no wing-tip vortices); one constant span efficiency; incompressible air (fine below about Mach 0.3); the negative-angle branch mirrors the positive one around the zero-lift angle. Use it for trends, not for design. Educational physics only.

Checks. (1) pressure-integrated lift equals Kutta–Joukowski lift and the potential-flow pressure drag is zero; (2) the panel lift slope matches thick-airfoil theory for the symmetric section and the zero-lift angle of the cambered section matches the thin-airfoil integral; (3) the closed contour has zero net source strength and the stagnation pressure coefficient is 1; (4) the stall model is continuous in lift and drag, reaches the flat-plate limit, and the finite wing reduces to the section at infinite span.