Legacy narration is unverified. This app uses authored algebraic coefficients and separate sketch/export velocity expressions. Its flag is a fixed rule above 15 degrees, not solved boundary-layer separation or a validated stall limit. Read the sourced lesson for the formula, units and visual/export boundaries.
Compare the equations, the sketch and the exported grid
Which quantities come from the formula, and which are only an illustrative visual treatment?
Explore an authored airfoil coefficient model, animated flow sketches and sampled algebraic velocities. This is not a NASA tool, validated CFD calculation, wind-tunnel polar or operational flight predictor. NASA references below explain the physical concepts; they do not validate this implementation.
No mesh-based conservation solver, solved surface boundary condition, boundary layer, calibrated separation model, viscosity, compressibility, finite-wing geometry or experimental coefficient dataset is provided. The fixed 15° threshold and coefficient constants are authored assumptions. Aircraft safety, stall limits and airfoil design cannot be established from these outputs.
Try a worked example
The initial 2412-labelled setup uses 12° angle, 65 m/s speed, 15° flap and density 1.225 kg/m³. The app returns CL 1.86836, CD 0.187085, lift per span 4834.97 N/m and circulation 60.7218 m²/s, assuming a 1 m reference chord. At unchanged coefficient/density, doubling speed quadruples that lift per span. Reset instead selects the cruise preset (2.5°, 95 m/s,zero flap), not the initial setup, and retains visibility toggles.
Trace the authored coefficients before interpreting force
Before the threshold, CL = 2π(α + δ), with angles in radians, plus 0.035×flap degrees. δ is an authored 0°, 0.25° or 0.45° shift for the three choices; it is not a measured camber effect. Above 15° only, CL is multiplied by exp[−0.2(αdegrees−15)]. Negative angles, even −10°, never set the stall flag. CD = 0.015 + 0.001×flap + 0.045CL², plus 0.012(αdegrees−15)² when flagged. These constants are not an experimentally fitted polar supplied with this page.
NASA presents lift and drag as coefficient×dynamic pressure×reference area, and notes that coefficient determination depends on conditions and often experiments. This app uses q=ρU²/2 and a 1 m chord to report lift per unit span, then Γ=L′/(ρU). It does not calculate total aircraft lift, actual drag force or measured circulation. The drag coefficient and screen arrows are illustrative: arrow lengths are capped and remain aligned to screen axes. NASA Glenn: Lift EquationNASA Glenn: Drag Equation
Recognize a threshold, not solved separation
With the cruise profile at 15°, CL≈1.67235 and the flag is off; at 15.5°, CL≈1.56282 and the flag turns on. CD initially falls from≈0.140854 to≈0.127908 because the CL² term decreases more than the added threshold penalty. Thus even this authored rule does not mean drag always rises immediately. The animation adds a sine perturbation in a fixed region; it does not solve turbulence or boundary-layer separation. NASA’s ideal-flow panel-code example explicitly cannot predict stall; its explanation is a useful boundary, not certification of this simpler sketch. NASA Glenn: Panel Code Performance Prediction
Do not equate the three flow representations
The exported 117-point grid uses r²=x²+y²+0.01, u=U(1+0.1/r²)+Γy/(2πr²), v=Uα−Γx/(2πr²), then Cp=1−(√(u²+v²)/U)². It does not exclude points inside the profile or enforce its surface condition. The colored field instead uses a 0.15/r² term and one scalar velocity; animated particles use a different clipped denominator and cosine/sine terms with visual scaling. Their colors and paths are not the same dataset displayed three ways.
The silhouette uses a thickness polynomial with 12% or 15% thickness and a shared triangular camber treatment for both cambered choices; it is not the complete named NACA geometry. The displayed model label does not establish exact section coordinates. Reynolds number depends on density, speed, length and viscosity; this app has no viscosity input or Reynolds calculation. Its former 2.1e6 label was static. NASA Glenn: Reynolds Number
Export and restore with the limits attached
JSON contains inputs, toggles, derived coefficients/lift/circulation and the sampled grid with scope metadata. CSV contains only rounded x,y,u,v,speed magnitude and Cp columns, without the input setup, density, coefficients, toggles or timestamp. Neither file is a CFD mesh, experiment or importable saved project. Browser local storage retains inputs and toggles and reload recomputes derived values; presets and Reset retain the display toggles. Keep the selected configuration alongside CSV when comparing cases. The polar sketch clips negative CL and CD above 0.25, so the graph can hide magnitude/sign while JSON retains them.