What the tunnel shows. A fan pulls air through a honeycomb, screens and a contraction so the air in the test section is smooth and uniform. A model on a force balance feels lift L = q c b Cl and drag D = q c b Cd, where the dynamic pressure is q = ½ ρ V². A Pitot tube measures q directly and gives the speed V = √(2q/ρ) (Bernoulli, valid for low-Mach, incompressible air).
Reynolds number. Re = V c / ν with air density and viscosity from the ideal-gas law and Sutherland's law. It controls the boundary layer: low Re means laminar flow that separates early, high Re means a thinner, turbulent layer that clings longer.
Flow solver (real). The section is replaced by 160 flat panels carrying constant-strength sources plus one constant vortex strength (Hess and Smith 1967). Zero normal velocity at each panel midpoint gives 160 equations, and the Kutta condition (equal speed on both sides of the trailing edge) gives the last one. The 161 x 161 system is solved by LU decomposition in your browser. Surface speed gives Cp = 1 − (Vs/V)², forces come from integrating pressure, and the same velocity field drives the smoke. This potential-flow model has no viscosity and no wake: it is exact for the inviscid problem but cannot predict drag or stall.
Thin-airfoil theory. Cl = 2π(α − αL0) for a thin, lightly cambered section. A section of thickness ratio t/c lifts about (1 + 0.77 t/c) times more, so the panel result for a 12 % section is roughly 9 % above thin theory, which is expected.
Kutta-Joukowski. Lift per unit span is L' = ρ V Γ where Γ is the circulation around the section. The page checks that integrating the surface pressures gives the same lift as ρ V Γ from the vortex strengths.
Viscous part (empirical, labelled). Boundary-layer behaviour is estimated from the inviscid surface speed: Thwaites' method (laminar growth, separation at λ = −0.09), Michel's criterion for transition, and Stratford's criterion for turbulent separation (constant scaled by a calibration factor of 1.32 because the panel pressure recovery is optimistic). The separation point f (fraction of chord) reduces lift with Kirchhoff's model Cl = Cl,pot ((1 + √f)/2)², and boundary-layer displacement trims the lift slope by about 8-10 %. Friction drag uses flat-plate laws (laminar 1.328/√Re, turbulent 0.074/Re0.2, combined at the transition point) times Hoerner's form factor 1 + 2t/c + 60(t/c)4; separated flow adds a pressure-drag term. These are engineering estimates: expect Cl,max in the 1.4-2.0 range depending on camber, not wind-tunnel-grade numbers, and no hysteresis, no laminar bubbles, no Mach effects.
Blockage. The solver is for free air. Real closed walls squeeze the flow past the model; the readout uses a one-dimensional continuity estimate Veff = V / (1 − B) where B is the model's frontal height over the test-section height. Real corrections (Pope and Rae) are smaller; treat it as an upper bound.
Smoke. Particles are released from 25 ports and moved with the computed velocity field. For steady flow, streaklines, streamlines and pathlines coincide. The smoke is slowed down (slow-motion slider) because real air crosses the section in a fraction of a second.
Sources: Hess and Smith (1967) panel method; Abbott and von Doenhoff, Theory of Wing Sections (1959) for NACA 4-digit shapes and typical data; Thwaites (1949); Michel (1952); Stratford (1959); Kirchhoff separated-flow model.