How to Calculate Airfoil Ordinates

Part 1 of this series provides some background and provides sources for obtaining airfoil ordinates.

Some airfoils have a large number of ordinates.  I've seen sets of ordinates having over 1,000 points.  If you are manually plotting an airfoil you do not have to plot every ordinate.  You only need enough so that you can draw the airfoil with reasonable accuracy.

I would say plotting 20 points each top and bottom is accurate enough for most airfoils.  In areas where there are tighter curves you should plot points closer together.  Examples are near the leading edge or the reflexed portion of that type airfoil.

Coordinate Standards

Airfoil ordinates are simply points that define the shape of the airfoil.  The numbers are given in percentage of the wing chord.  There is more than one standard, but they are all easy to figure out.

The standards I know of are as follows:

1. Stations from 0% to 100% chord.  In this case, multiply the chord of the airfoil you are plotting times percent of the station/ordinate pairs in percent.  In other words, if the number given is 1.25 then multiply times 1.25%.  If your calculator does not have a percent key, then multiply times 1.25 and then divide by 100.

Ordinates of this type are presented in two sets of ordinate pairs - one for the upper portion of the airfoil and one for the lower.

2. Stations from 0 to 1.  In this case it is straight multiplication of the chord times each of the station/ordinate pairs.  This standard also differentiates between the top and the bottom of the airfoil.

3. The last example is the style used for computer programs.  This is listing of ordinate pairs with no differentiation between the top and bottom of the airfoil.  Numbers are from 0 to 1.  The listing starts at the trailing edge of the airfoil and moves forward defining the underside of the airfoil and then the leading edge, the top of the wing and back to the trailing edge again.

It sounds more complicated than it is - again, it is simple multiplication.

Calculating the Ordinates to be Plotted

For this example I will be plotting a NACA 2412 airfoil.  The NACA 2412 is a semi-symmetrical airfoil (cambered) that is stable and somewhat fast although it would not be the best choice for an extreme speed aircraft.  It would be a good choice for a one-design club racer because it has no bad habits and will not get to speeds that the average pilot can't handle.

The first table below is the set of ordinates for the NACA 2412.  The listing uses standard (1) above.

I will be calculating ordinates for and plotting an airfoil having a 9" chord.  Multiply all stations and ordinates by the chord.  Again, the numbers given in the ordinate listing are percentages.  That means you multiply the chord by the station or ordinate in percent.

To find the second station for example, multiply 9" x 1.25%.

The leading edge (L.E.) radius is also multiplied by the chord to get the actual radius.  This is also a percentage.

The second table contains the resulting numbers after multiplying them by the wing chord.  All numbers are in inches for this example.  Calculating and plotting works the same regardless of your number system.

This particular airfoil has stations that are identical for both the upper and lower surfaces but that is not always true.  Be sure to pay attention to what you are doing.  I have made the mistake of assuming the stations were the same when they weren't which resulted in some strange airfoil plots.

Now that you have the numbers they need to be plotted on paper.  The ordinate/station pairs are simply (x, y) coordinates.  The Station is X and the Ordinate is Y.

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Copyright © 2004 Paul K. Johnson