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NACA 4 digit airfoil generator (NACA 2412 AIRFOIL)


Airfoil NACA 2412 Airfoil M=2.0% P=40.0% T=12.0%

Dat file

NACA 2412 Airfoil M=2.0% P=40.0% T=12.0%
  1.000000  0.001260
  0.998459  0.001579
  0.993844  0.002529
  0.986185  0.004092
  0.975528  0.006241
  0.961940  0.008935
  0.945503  0.012126
  0.926320  0.015759
  0.904508  0.019774
  0.880203  0.024103
  0.853553  0.028679
  0.824724  0.033430
  0.793893  0.038286
  0.761249  0.043173
  0.726995  0.048022
  0.691342  0.052761
  0.654508  0.057319
  0.616723  0.061627
  0.578217  0.065618
  0.539230  0.069226
  0.500000  0.072385
  0.460770  0.075035
  0.421783  0.077122
  0.383277  0.078574
  0.345492  0.079203
  0.308658  0.078957
  0.273005  0.077832
  0.238751  0.075842
  0.206107  0.073015
  0.175276  0.069397
  0.146447  0.065047
  0.119797  0.060040
  0.095492  0.054458
  0.073680  0.048395
  0.054497  0.041945
  0.038060  0.035205
  0.024472  0.028266
  0.013815  0.021212
  0.006156  0.014114
  0.001541  0.007031
  0.000000  0.000000
  0.001541 -0.006723
  0.006156 -0.012893
  0.013815 -0.018496
  0.024472 -0.023521
  0.038060 -0.027955
  0.054497 -0.031788
  0.073680 -0.035016
  0.095492 -0.037640
  0.119797 -0.039668
  0.146447 -0.041119
  0.175276 -0.042022
  0.206107 -0.042413
  0.238751 -0.042342
  0.273005 -0.041864
  0.308658 -0.041043
  0.345492 -0.039946
  0.383277 -0.038644
  0.421783 -0.037174
  0.460770 -0.035446
  0.500000 -0.033496
  0.539230 -0.031379
  0.578217 -0.029148
  0.616723 -0.026846
  0.654508 -0.024516
  0.691342 -0.022192
  0.726995 -0.019903
  0.761249 -0.017674
  0.793893 -0.015525
  0.824724 -0.013474
  0.853553 -0.011536
  0.880203 -0.009725
  0.904508 -0.008055
  0.926320 -0.006539
  0.945503 -0.005190
  0.961940 -0.004021
  0.975528 -0.003044
  0.986185 -0.002272
  0.993844 -0.001712
  0.998459 -0.001373
  1.000000 -0.001260
First digit. 0 to 9.5%
Second digit. 0 to 90%
Third & fourth digit. 1 to 40%
20 to 200
Cosine or linear spacing
Open or closed TE
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NACA 4 digit airfoils in the database

NACA 0006 NACA 0008
NACA 0009 NACA 0010
NACA 0012 NACA 0015
NACA 0018 NACA 0021
NACA 0024 NACA 1408
NACA 1410 NACA 1412
NACA 2408 NACA 2410
NACA 2411 NACA 2412
NACA 2414 NACA 2415
NACA 2418 NACA 2421
NACA 2424 NACA 4412
NACA 4415 NACA 4418
NACA 4421 NACA 4424
NACA 6409 NACA 6412

NACA 4 digit airfoil specification

This NACA airfoil series is controlled by 4 digits e.g. NACA 2412, which designate the camber, position of the maximum camber and thickness. If an airfoil number is
NACA MPXX
e.g.
NACA 2412
then:
  • M is the maximum camber divided by 100. In the example M=2 so the camber is 0.02 or 2% of the chord
  • P is the position of the maximum camber divided by 10. In the example P=4 so the maximum camber is at 0.4 or 40% of the chord.
  • XX is the thickness divided by 100. In the example XX=12 so the thiickness is 0.12 or 12% of the chord.

NACA 4 digit airfoil calculation

The NACA airfoil section is created from a camber line and a thickness distribution plotted perpendicular to the camber line.

The equation for the camber line is split into sections either side of the point of maximum camber position (P). In order to calculate the position of the final airfoil envelope later the gradient of the camber line is also required. The equations are:

NACA 4 digit airfoil camber line calculation

The thickness distribution is given by the equation:

NACA 4 digit airfoil thickness calculation

  • The constants a0 to a4 are for a 20% thick airfoil. The expression T/0.2 adjusts the constants to the required thickness.
  • At the trailing edge (x=1) there is a finite thickness of 0.0021 chord width for a 20% airfoil. If a closed trailing edge is required the value of a4 can be adjusted.
  • The value of yt is a half thickness and needs to be applied both sides of the camber line.

Using the equations above, for a given value of x it is possible to calculate the camber line position Yc, the gradient of the camber line and the thickness. The position of the upper and lower surface can then be calculated perpendicular to the camber line.

Coordinate calculation

The most obvious way to to plot the airfoil is to iterate through equally spaced values of x calclating the upper and lower surface coordinates. While this works, the points are more widely spaced around the leading edge where the curvature is greatest and flat sections can be seen on the plots. To group the points at the ends of the airfoil sections a cosine spacing is used with uniform increments of β

Cosine spacing

References