The NACA airfoil series is a set of standardized airfoil shapes, developed by NACA, which became widely used in the design of aircraft wings.
Origins NACA initially developed the numbered airfoil system which was further refined by the United States Air Force at Langley Research Center. According to the NASA website:
During the late 1920s and into the 1930s, the NACA developed a series of thoroughly tested airfoils and devised a numerical designation for each airfoil — a four digit number that represented the airfoil section's critical geometric properties. By 1929, Langley had developed this system to the point where the numbering system was complemented by an airfoil cross-section, and the complete catalog of 78 airfoils appeared in the NACA's annual report for 1933. Engineers could quickly see the peculiarities of each airfoil shape, and the numerical designator ("NACA 2415", for instance) specified camber lines, maximum thickness, and special nose features. These figures and shapes transmitted the sort of information to engineers that allowed them to select specific airfoils for desired performance characteristics of specific aircraft.
Four-digit series The NACA four-digit wing sections define the profile by:
First digit describing maximum camber as percentage of the chord. Second digit describing the distance of maximum camber from the airfoil leading edge in tenths of the chord. Last two digits describing maximum thickness of the airfoil as percent of the chord. For example, the NACA 2412 airfoil has a maximum camber of 2% located 40% (0.4 chords) from the leading edge with a maximum thickness of 12% of the chord. The NACA 0015 airfoil is symmetrical, the 00 indicating that it has no camber. The 15 indicates that the airfoil has a 15% thickness to chord length ratio: it is 15% as thick as it is long. The maximum thickness of the four-digit series is always located at 30% of the chord.
Equation for a symmetrical 4-digit NACA airfoil
The formula for the shape of a NACA 00xx foil, with "xx" being replaced by the percentage of thickness to chord, is
y t = 5 t [ 0.2969 x − 0.1260 x − 0.3516 x 2 + 0.2843 x 3 − 0.1015 x 4 ] , {\displaystyle y_{t}=5t\left[0.2969{\sqrt {x}}-0.1260x-0.3516x^{2}+0.2843x^{3}-0.1015x^{4}\right],}
where:
x is the position along the chord from 0 to 1.00 (0 to 100%),
y t {\displaystyle y_{t}} is the half thickness at a given value of x (centerline to surface), t is the maximum thickness as a fraction of the chord (so t gives the last two digits in the NACA 4-digit denomination divided by 100). In this equation, at x = 1 (the trailing edge of the airfoil), the thickness is not quite zero. If a zero-thickness trailing edge is required, for example for computational work, one of the coefficients should be modified such that they sum to zero. Modifying the last coefficient (i.e. to −0.1036) results in the smallest change to the overall shape of the airfoil. The leading edge approximates a cylinder with a chord-normalized radius of
r = 1.1019 t 2 . {\displaystyle r=1.1019t^{2}.}
Now the coordinates ( x U , y U ) {\displaystyle (x_{U},y_{U})} of the upper airfoil surface and ( x L , y L ) {\displaystyle (x_{L},y_{L})} of the lower airfoil surface are
x U = x L = x , y U = + y t , y L = − y t . {\displaystyle x_{U}=x_{L}=x,\quad y_{U}=+y_{t},\quad y_{L}=-y_{t}.}
Symmetrical 4-digit series airfoils by default have maximum thickness at 30% of the chord from the leading edge.
Equation for a cambered 4-digit NACA airfoil
The simplest asymmetric foils are the NACA 4-digit series foils, which use the same formula as that used to generate the 00xx symmetric foils, but with the line of mean camber bent. The formula used to calculate the mean camber line is
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