NACA 4 Digit Series

NACA Aerofoil 4 Digit Series  The NACA four-digit wing sections define the profile by 1. One digi digitt descr describi ibing ng maxim maximum um camber as percentage of the chord chord.. 2. One One digi digitt desc descri ribi bing ng the the dist distan ance ce of maxi maximu mum m camb camber er from from the the airf airfoi oill leading edge in tens of percent's of the chord. 3. Two Two digits digits describ describing ing maximu maximum m thick thicknes ness s of the airfoi airfoill as percent 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. Fourdigit series airfoils by default have maximum thickness at 30% of the chord (0.3 chords) from the leading edge.  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. 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: where: 

c is the chord length,

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x  is the position along the chord from 0 to c,

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y  is the half thickness at a given value of  x  (centerline to surface), and

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t  is the maximum thickness as a fraction of the chord (so 100 t  gives the last two digits in the NACA 4-digit denomination).

Note that in this equation, at (x/c) = 1 (the trailing edge of the airfoil), the thickness is not quite quite zero. zero. If a zero-t zero-thi hickn ckness ess trailing trailing edge is requi required red,, for example 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) will result in the smallest change to the overall shape of the airfoil. The leading edge approximates a cylinder with a radius of:

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: is :[2]

Equation for a cambered 4-digit NACA airfoil

Where: 

m is the maximum camber (100 m is the first of the four digits),

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p is the location of maximum camber (10  p is the second digit in the NACA xxxx description).

For this cambered airfoil, the coordinates ( x U, y U) and ( x L, y L), of respectively the upper and lower airfoil surface, become: [5]

Where:

 The four-digit NACA airfoil sections are the oldest and simplest NACA airfoils to generate. The camber of a four-digit airfoil has made up of two parabolas. One parabola generates the camber geometry from the leading edge to the maximum camber, and another parabola produces the camber shape from the maximum camber to the trailing edge. In a Four-digit NACA airfoil, the first digit indicates the maximum camber in percent chord. The second digit indicates the position of maximum camber in tenths of chord length. The last two digits represent the maximum thickness-to-chord ratio. A zero in the first digit means that this airfoil is asymmetrical airfoil section. For example, the NACA 1408 airfoil section in the figure has 8 percent (t/c) max (the last two digits), its maximum camber is 10 percent, and its maximum camber is located at 40 percent of the chord length. Although these airfoils are easy to produce, but they generate high drag compared with new airfoils.

Five Sample Aerofoil Shapes