Angle of Attack Labα
Pick any airfoil, tilt it, and watch the flow respond. A panel method solver with a boundary layer model predicts lift, drag, pitching moment and stall, live in your browser.
Pressure distribution
Plotted with suction upward, as engineers do. The area between the two lines is the lift. A tall spike near the nose means a strong suction peak, which the boundary layer must recover from.
Polar
How it works
Each angle of attack runs a chain of classic methods that an aerodynamicist would recognise from a first year graduate course. Everything is solved from scratch in about a millisecond.
- Geometry. NACA 4- and 5 digit sections are generated from their defining equations. Library and imported coordinates are splined and re panelled with cosine spacing, which clusters panels at the leading and trailing edges where the flow changes fastest.
- Inviscid flow. A Hess and Smith panel method places a constant strength source on every panel plus a uniform vortex sheet, with the Kutta condition closing the system. Solutions at α = 0° and 90° are superposed, so any angle costs one vector sum.
- Compressibility. The Kármán and Tsien rule corrects surface pressures for Mach number, and the critical Mach number is found where the suction peak reaches sonic speed.
- Boundary layer. Each surface is marched from the stagnation point. Thwaites' method handles the laminar region, Michel's criterion (or a trip) sets transition, and laminar separation forces transition through a short bubble. Head's entrainment method tracks the turbulent layer until the shape factor reaches 2.4.
- Drag. The Squire and Young formula converts the trailing edge momentum thickness into profile drag. Lost leading edge suction adds pressure drag once flow separates.
- Stall. The separation point feeds a Kirchhoff trailing edge separation model, as used in the Leishman and Beddoes family. A displacement thickness correction reduces the inviscid lift slope to a realistic viscous value.
Use it for learning and early design trades, not certification. The boundary layer does not feed back into the outer flow, so maximum lift usually differs from published wind tunnel data by up to about 15%, and post stall values are indicative only. Results above the critical Mach number, and below Re ≈ 2×10⁵ where laminar bubbles dominate, should be treated with caution.
Verification
A Kármán and Trefftz section (thickness 0.10, camber 0.05, 10° trailing edge angle) has an exact potential flow lift coefficient. The table compares the panel solution at α = 4° as the panel count is refined.
| Panels | Panel CL | Exact CL | Error | Solve time |
|---|---|---|---|---|
| Running study… | ||||
The error falls steadily as panels are added, which is the expected behaviour for a correctly implemented first order panel method.
Sources
- Hess, J. L. & Smith, A. M. O. (1967). Calculation of potential flow about arbitrary bodies. Progress in Aerospace Sciences 8.
- Thwaites, B. (1949); Head, M. R. (1958); Michel, R. (1951); Squire, H. B. & Young, A. D. (1938): integral boundary layer methods.
- Leishman, J. G. & Beddoes, T. S. (1989). A semi empirical model for dynamic stall. J. American Helicopter Society 34(3).
- Abbott, I. H. & von Doenhoff, A. E. (1959). Theory of Wing Sections. Dover.
- Library coordinates: UIUC Airfoil Coordinates Database (M. Selig), via the AeroSandbox project.