cl = 2π (α − α_L0)
Thin-airfoil theory, for an inviscid incompressible two-dimensional section, gives a constant lift-curve slope of 2π per radian and a lift coefficient cl = 2π (α − α_L0). Five degrees on a flat plate is therefore cl ≈ 0.548. Real sections are a little less steep (closer to 0.1 per degree) because of thickness and viscosity, and they stall; this page does not invent a stall angle. The aerodynamic center is at the quarter chord, and a flat plate has no quarter-chord pitching moment in the theory.
For a finite wing the slope is reduced by aspect ratio — see the aspect-ratio lift-slope calculator. To turn a force, speed, and area into a coefficient, or the other way around, use lift and drag coefficients.
Sources
- Thin-airfoil theory, cl = 2π(α − α_L0) (Glauert; Abbott and von Doenhoff, Theory of Wing Sections).
- Anderson, Fundamentals of Aerodynamics.
Frequently asked questions
Why is my measured slope less than 2π per radian?
Thickness, viscosity, and a finite span all reduce the slope. 2π is the inviscid, two-dimensional, infinitely thin limit.
What zero-lift angle should I use?
Zero for a symmetric section. For a cambered section, α_L0 is negative and comes from a catalog or a computation, not from this thin-plate default.
Does this predict stall?
No. Thin-airfoil theory has no stall. Stay well below the section’s published stall angle.