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Method & Assumptions

NACA 4-digit geometry and classical thin-airfoil theory

NACA geometry

The first digit defines maximum camber, the second its chordwise location, and the last two digits define maximum thickness.

NACA MPXX → m = M/100, p = P/10, t/c = XX/100

Lift

Classical thin-airfoil theory is used to determine the zero-lift angle from the mean camber line.

CL = 2π (α − αL=0)

Vortex panel method

The actual airfoil contour is discretized into straight panels. A Hess-Smith potential-flow system solves source strengths and one global vortex/circulation degree of freedom.

[A] {q, γ} = {b}

Pressure coefficient

The panel solution gives the tangential surface velocity and therefore the inviscid pressure distribution.

Cp = 1 − (Vt/V∞)²

Kutta condition

The circulation is selected so that the upper- and lower-surface flow leaves the trailing edge smoothly.

Vt,upper,TE + Vt,lower,TE = 0

Applicability

  • 2D, incompressible flow
  • Thin airfoil
  • Attached flow
  • Small to moderate angle of attack
  • No viscous profile drag or stall prediction
Preliminary analysis only. Thin-airfoil theory and the panel method are both inviscid. The panel method resolves profile shape and Cp, but it still does not predict viscous drag, transition, separation or stall.
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Parameters

Airfoil designation and operating point

Airfoil

Example: 0012, 2412, 4415.

Analysis method

Even number. 80 is a good default.

Operating point

CL

Results

Geometry, lift, moment and inviscid pressure distribution
Vortex Panel Method
Lift coefficient
–
Zero-lift angle
–
Moment Cm,c/4
–
Thickness t/c
–

Airfoil Geometry

NACA profile
0 c

Pressure Distribution

Surface pressure coefficient Cp(x/c)
Upper surface Lower surface

Aerodynamic convention: negative Cp (suction) is plotted upward.

Lift Curve

α [deg] CL

Airfoil Properties

Quantity Value Unit
Maximum camber m/c – –
Camber position p/c – –
Maximum thickness t/c – –
Lift-curve slope dCL/dα – 1/deg

Thin Airfoil Theory

CL–
αL=0–
Cm,c/4–

Vortex Panel Method

CL–
αL=0–
Cm,c/4–