A Description of the NACA 4-Digit System

The National Advisory Committee for Aeronautics (NACA), NASA's predecessor, used a four digit numbering system to describe a large number of airfoil sections. They later introduced a five digit numbering system as well as several other systems.

This page explains how the four digit system describes an airfoil section. Refer to the diagram below for the explanation that follows. Most of this material comes from the reference given at the bottom of this page.

The first family of NACA airfoil sections, developed in the 1930s, was the "four-digit" series. Following are some definitions of airfoil section characteristics, followed by a description of how the NACA "four-digit" series specifies these characteristics.

The mean camber line is the locus of points midway between the upper and lower surfaces as measured perpendicular to the chord line.

The most forward point of the mean camber line is the leading edge.

The most rearward point of the mean camber line is the trailing edge.

The straight line connecting the leading and trailing edges is the chord line of the airfoil.

The actual distance between the leading and trailing edges, measured along the chord line, is the chord, c.

The maximum camber is the maximum distance between the mean camber line and the chord line, measured perpendicular to the chord line.

The thickness is the distance between the upper and lower surfaces, also measured perpendicular to the chord line.

Having defined these fundamental characteristics, additional properties are now defined, before proceeding to an explanation of the NACA system. Because airfoil sections vary in size, the following properties are generally stated in terms of the chord, c.

The shape of the airfoil section at the leading edge is usually circular, with a radius of approximately 0.02c.

The digits in NACA's four digit numbering system are defined as follows:
the first digit denotes the maximum camber, C_max, as a percent of the chord;
the second digit denotes the chordwise position of the maximum camber, X_Cmax, in tenths of the chord;
the last two digits denotes the maximum thickness of the airfoil section, t, as a percent of the chord.

Consider a specific example, the airfoil designated NACA2412.
The first digit, 2, specifies that this airfoil section has a maximum camber of 0.02c.
The second digit, 4, specifies that the maximum camber of this airfoil section is located 0.4c behind the leading edge.
The last two digits, "12" specify that the maximum thickness of this airfoil section is 0.12c.

Using these numbers, the final shape of the airfoil section can be calculated.
These numbers provide a means to calculate the mean camber line. Once the shape of the mean camber line is determined, the final shape of the airfoil section is found by adding a specified symmetrical thickness distribution around the mean camber line. Here is how it is done:

Assume an x-y coordinate system with origin at the leading edge of the airfoil section
The x-axis is aligned along the chord, positive toward the trailing edge.
The y-axis is perpendicular to the x-axis, positive up (see the diagram above).

Calculate the curve of the mean camber line for the two regions:

y_c  : =   [C_max/(X_Cmax²)][(2)(X_Cmax)(x) - (x²)]     for     0   <=   x   <=   X_Cmax

y_c  : =   [C_max/(1 - X_Cmax²)][(1 - 2X_Cmax) + 2(X_Cmax)(x) - (x²)]     for     X_Cmax   <=   x   <=   c

Now calculate the thickness distribution, positive for the upper surface and negative for the lower surface:

(+ or -)   y_t   =   (5t)[0.2969 √ x - 0.1260x - 0.3516x² + 0.2843x³ - 0.1015x⁴]

Determine the final coordinates for the airfoil section upper surface (x_u, y_u) and lower surface (x_l, y_l) using the following relationships:

x_u   =   x - y_t sin(θ)

y_u   =   y_u + y_t cos(θ)

x_l   =   x + y_t sin(θ)

y_l   =   y_c - y_t cos(θ)

where θ   =   arctan(dy_c/dx)

References:

Anderson, John D., Jr.
          "Fundamentals of Aerodynamics. Third Edition"
          McGraw-Hill, New York.
          2001