Calculating the Thickness of a NACA 4-Digit (Modified)Airfoil

The thickness distribution is given by the following equation ahead of the maximum thickness:

y = A₀ sqrt(x) + A₁ x + A₂² + A₃ x³

where (t/c) is the maximum thickness to chord ratio of the airfoil, x is the position as fraction of chord, and y is the half-thickness as fraction of chord.

and by the following equation from maximum thickness to trailing edge:

y = D₀ + D₁(1-x) + D₂ (1-x)² + D₃ (1-x)³

The constants A₀, A₁, A₂, A₃, D₀, D₁, D₂, D₃ are calculated from the values of maximum thickness, position of maximum thickness, and leading edge radius that are specified by the user.

The airfoil must satisfy the following constraints:

• y = one half the maximum thickness when x/c = m, the specified location of maximum thickness (as fraction of chord).
• The leading edge radius = 1.1019/36.0*((t/c)*leIndex))² [ see p.117 in Abbott & von Doenhoff]
• The first and second derivatives of the forward function and the aft function match exactly at the point of maximum thickness.
• The coefficient D₁ is given by the following table:

D₁ is the negative of the trailing edge slope.

These conditions are sufficient to determine all of the A and D terms in the polynomial equations.