PDAS home > Contents > NACA Airfoil > Thickness > 4-Digit (modified) > Calculation
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The thickness distribution is given by the following equation ahead of the maximum thickness:

y = A0 sqrt(x) + A1 x + A2 x**2 + A3 x**3

where ** denotes exponentiation, (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:
 m D1 0.2 1.000 t 0.3 1.170 t 0.4 1.575 t 0.5 2.325 t 0.6 3.500 t

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.

PDAS home > Contents > NACA Airfoil > Thickness > 4-Digit (modified) > Calculation
Public Domain Aeronautical Software (PDAS)