A NACA 4-digit airfoil, its 3D wing, and its full aerodynamic polars — solved live in your browser from thin-airfoil theory and cross-checked against XFoil. Not a screenshot of one.
True NACA 4-digit equations, computed live — not a table of pre-rendered shapes.
Thin-airfoil theory with Glauert & Prandtl–Glauert corrections and Reynolds-scaled drag.
Nine reference profiles cross-checked against precomputed XFoil polars at Re = 1×10⁶.
Every coefficient carries an uncertainty band; post-stall values are flagged as approximate.
Every slider redraws the wing, the airflow and all four polar charts instantly.
No paywall, no signup. Runs entirely client-side. Export your data any time.
Build intuition for camber, thickness and stall before touching XFoil or a CFD suite.
Compare candidate airfoils for a build without a full simulation pipeline.
Explore how thickness and camber trade lift against drag at low speed.
A visual, interactive companion to thin-airfoil theory — works in any browser.
Set one or more constraints. Leave a field blank to skip that filter. Results are ranked by best L/D at the target AoA. Note: uses L1 thin airfoil theory — accurate to ±5% in linear regime.
An airfoil (or aerofoil) is the cross-sectional shape of a wing. When air flows over it, the wing generates lift — the upward force that keeps an aircraft flying.
The key idea is simple: a wing works by turning the oncoming air downward. By Newton's third law, pushing that much air down produces an equal and opposite upward reaction on the wing — that's lift. Camber and angle of attack both increase how sharply the wing deflects the flow, which is why lift climbs as you tilt the wing up.
The same lift can be seen through pressure: the air accelerates over the upper surface and slows underneath, so by Bernoulli's principle the pressure on top is lower than below, and that pressure difference is the lift. (A common myth says the top air must "catch up" with the bottom air because it travels farther — that's not true, and it isn't needed. Even a flat plate or a symmetric wing like NACA 0012 makes lift once it's tilted, because it still turns the flow.)
The three sliders under Geometry control the cross-sectional shape. Move them and watch the 2D profile and 3D wing update in real time.
The angle of attack (AoA, or α) is the angle between the wing's chord line and the direction the aircraft is flying. It is the single most important variable in generating lift.
As you increase AoA, the wing presents a steeper face to the oncoming air, generating more lift. You can see Cl rise on the chart. This works well up to a point — but keep tilting and the airflow on the upper surface can no longer follow the curve and it separates from the wing. This is called a stall.
The same airfoil shape can behave very differently depending on how fast the air is moving and what size the wing is. That's what the Reynolds number and Mach number capture.
All the numbers in the At current AoA panel are dimensionless coefficients — they describe the wing's behaviour independent of its actual size or speed. To get a real force, you multiply by air density, velocity, and area (which is what the Lift Calculator does).
Cl max and α stall are global properties of the airfoil, not just at the current AoA. They appear in the readout strip at the top of the main view and update whenever you change the shape.
The four charts below the 3D/2D views show the airfoil's full aerodynamic behaviour across the entire range of angles. Greyed-out regions are post-stall and unreliable — treat them as approximate only.
Here are a few starting points depending on what you're trying to learn or design:
Built by Aritra Parekh · AS-level aerospace student · Questions or corrections? The methodology and references are in the About tab.
AS-level student pursuing aerospace engineering. This tool was independently built as a passion project — a browser-based aerodynamic analysis platform that makes airfoil data genuinely accessible to students and researchers.
If you have questions about the tool, found a bug, or just want to talk aerospace, reach out.
Reveal email →NACA Airfoil Explorer computes aerodynamic polars for any NACA 4-digit airfoil using thin airfoil theory with Glauert thickness correction, Prandtl-Glauert compressibility, and Reynolds-number drag scaling. The 9 preset profiles include precomputed XFoil data at Re = 1×10⁶ for direct comparison.
The 3D wing viewer uses Three.js with real NACA geometry — same cosine-spaced coordinates used for the aerodynamic model. Every number shown has a calibrated uncertainty estimate. Post-stall values are explicitly flagged as extrapolations.
[1] Abbott, I.H., von Doenhoff, A.E. (1959). Theory of Wing Sections. Dover.
[2] Katz, J., Plotkin, A. (2001). Low-Speed Aerodynamics, 2nd ed. Cambridge UP.
[3] Anderson, J.D. (2010). Fundamentals of Aerodynamics, 5th ed. McGraw-Hill.
[4] Drela, M. (1989). XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils. LNEF 54.
[5] Schlichting, H. (1979). Boundary Layer Theory, 7th ed. McGraw-Hill.
[6] Abbott, I.H., von Doenhoff, A.E., Stivers, L.S. (1945). NACA TR-824.
Explore any NACA 4-digit airfoil in 3D and 2D simultaneously with live aerodynamic polar charts. The Fidelity mode overlays thin airfoil theory against precomputed XFoil data and your own CFD results — the workflow for a multi-fidelity research paper.
Aerodynamic model (L1): Thin airfoil theory with Glauert thickness correction, numerically-integrated zero-lift angle and quarter-chord moment (200-point quadrature), Prandtl-Schlichting Re drag correction, and Prandtl-Glauert Mach compressibility. Good for qualitative comparison — not a substitute for XFoil or CFD.
NACA 4-digit code: digit 1 = max camber % chord, digit 2 = camber position (tenths chord), digits 3–4 = max thickness % chord. NACA 2412 → 2% camber at 40% chord, 12% thick.
Geometry: Sharp trailing edge enforced via TE coefficient −0.1036 (vs NACA standard −0.1015 which leaves a 0.252%c gap). Cosine chordwise spacing. Verified against Abbott & von Doenhoff (1959).
Fidelity mode (L2): Precomputed XFoil-calibrated polars at Re = 1×10⁶ for all 9 preset profiles. drag bucket calibrated to NACA TR-824 Table II. Stall angles and Cl_max match published experimental data within ≤5%. Post-stall values (greyed on charts) are parametric extrapolations only — XFoil itself diverges past stall.
Scientific honesty: Post-stall polar regions are greyed and marked invalid. Stall angle shown as α ± uncertainty. Precision is limited to what the model accuracy justifies. No fake confidence percentages.
References
[1] Abbott, I.H., von Doenhoff, A.E. (1959). Theory of Wing Sections. Dover.
[2] Katz, J., Plotkin, A. (2001). Low-Speed Aerodynamics, 2nd ed. Cambridge UP.
[3] Anderson, J.D. (2010). Fundamentals of Aerodynamics, 5th ed. McGraw-Hill.
[4] Drela, M. (1989). XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils. LNEF 54.
[5] Schlichting, H. (1979). Boundary Layer Theory, 7th ed. McGraw-Hill.
[6] Abbott, I.H., von Doenhoff, A.E., Stivers, L.S. (1945). NACA TR-824.
Three.js r128Chart.js 4.4 NACA TR-824Thin airfoil theory Prandtl-GlauertXFoil Re=1×10⁶
Built by Aritra Parekh, an AS-level student pursuing aerospace engineering. This tool was independently developed as a browser-based aerodynamic analysis platform for students and researchers.