Coefficient of lift vs. angle of attack

Lift Coefficient vs Angle of Attack (CL-α curve)

The CL-α curve (often "lift curve") shows how the lift coefficient CL varies with the angle of attack α. It is the most important characteristic of an airfoil.

Typical course

   CL
   |          *
   |        *           ← α_stall
   |      *  \
   |    *     \
   |  *        \___    ← stall region
   |*
   +-------------- α
   α_0       α_stall

Regions

1. Linear region (small to medium α)

• Slope: dCL/dα ≈ 2π per radian (theoretical, thin airfoil in ideal fluid) or ≈ 0.1 per degree in practice.
• CL = CL₀ + a · α (a ≈ 0.1 /°).
• Symmetric airfoil: CL₀ = 0, so CL = 0 at α = 0°.
• Cambered airfoil: CL₀ > 0, so CL > 0 at α = 0°. NACA 2412 typically CL₀ ≈ 0.2.

2. Near stall (α near α_stall)

• Curve flattens → CL_max reached.
• CL_max for typical GA airfoils: 1.2 to 1.8 (no flaps); with flaps 1.8–2.4.

3. Stall region (α > α_stall)

• CL drops abruptly.
• Boundary layer separates, flow stall.
• Recovery: reduce angle of attack.

Typical values

Why does CL drop after stall?

At small α: flow follows the profile cleanly (laminar/turbulent boundary layer attached).

At critical α (α_stall): adverse pressure gradient on upper surface becomes too large → boundary layer separates.

At α > α_stall: massive separation → large vortex region above airfoil → CL drops dramatically, CD rises sharply.

Wing stall vs airfoil stall

Airfoil (2D): α_stall typically 14–18°. Wing (3D): α_stall typically 10–12°, because wingtip vortices and downwash reduce the effective α at the tips — root stalls first (in a normally designed wing with washout).

Flap influence

Flaps raise CL_max and shift the CL-α curve up and left:

• CL_max can rise from 1.4 to 2.4.
• α_stall can drop from 16° to 12° (flaps "increase" effective airfoil AoA).
• CL₀ becomes more negative (flaps add camber).

Source: FAA AFH Chapter 5.

Practical consequences

1. CL_max sets stall speed: higher CL_max → lower Vs.
2. Flaps for approach/landing: lower Vapp possible.
3. Manoeuvring speed Va: at CL_max the maximum g-factor is also limited.
4. Spin: asymmetric stall (one wing earlier) → autorotation.

What happens exactly in stall? (see lesson "Stall / Flow Separation")

• Nose drops (no lift despite high α).
• Speed falls (at constant pitch).
• Recovery: yoke forward (reduce α), increase power, then pitch up.