Computation of NACA Airfoil Coordinates

The program naca456 is a public domain program in modern Fortran for computing and tabulating the coordinates of the 4-digit, 4-digit modified, 5-digit, 6-series and 6A-series of NACA airfoils. This program is a complete revision of the NASA Langley programs for computing the coordinates of NACA airfoils. The NASA 1996 program was used as a guide for the development of a program that is highly modular and contains several features that were requested by user of the older programs. This program is a console application for which the user prepares an input file that is read by naca456. An output file (called naca456.out) containing the airfoil geometry is generated by the program. A file for graphical examination is also produced.

All NACA airfoils are produced by combining a thickness distribution and a mean line into a definition of the upper and lower surfaces of the airfoil.

There are three different thickness families of NACA airfoils. I have separate pages describing the computing equations for family.

• 4-digit
• 4-digit (modified)
• 6-series (includes 6A-series)

There are several families of NACA mean lines. I have separate pages describing the computing equations for family.

• 2-digit
• 3-digit
• 3-digit reflex
• 6-series
• 6A-series

By NACA practice,

• Four-digit airfoils use 4-digit thickness and 2-digit camber lines.
• Four-digit (modified) airfoils use 4-digit (modified) thickness and 2-digit camber lines.
• Five-digit airfoils use 4-digit thickness and 3-digit or 3-digit(modified) camber lines.
• 6-series airfoils use 6-series thickness and 6-series camber lines.
• 6A-series airfoils use 6A-series thickness and 6A-series camber lines.
• 16-series airfoils use 4-digit (modified) thickness and 6-series mean lines with A=1.

• Input to naca456
• Sample cases (input and output) for naca456
• Corrected appendices to the book Theory of Airfoil Sections by Abbott and von Doenhoeff