German Modifications to NACA Airfoils

I am interested in defining the airfoils for the A-4 Skyhawk. The wing root is a NACA 0008-1.1-25 and the tip is a NACA 0005-.825-50. I have read your previous explanations on modified four and five digit aifoils and still have a hard time defining it. Can you help me out?
- question from Ted Schmidt

I'm currently working on plans to build an example of the S-3 Viking. However I'm totally stumped on the 4 Digit NACA numbers for the S-3. Could you explain the following NACA names?
Wing root: 0016.3-1.03 32.7/1.00
Wingfold: 0013.9-1.10 40/1.00
Wing tip: 0012-1.10 40/1.00
Horizontal Stabilizer root/tip: 2410-0.8 45/1.575 (inverted)
Vertical Stabilizer root: 0012-1.10 20/1.312
- question from Curtis Chance

According to Theory of Wing Sections, the airfoil names you've provided are modifications to the NACA four-digit series developed by researchers in Germany. They devised a new naming system that includes some additional adjustments to the airfoil geometry.

NACA airfoil geometrical construction

As discussed previously, the basic NACA Four-Digit airfoils are described by four numbers. The first digit specifies the maximum camber in percentage of the chord (airfoil length), the second indicates the position of the maximum camber in tenths of chord, and the last two numbers provide the maximum thickness of the airfoil in percentage of chord. All but one of the examples mentioned above are symmetric airfoils with no camber, so the first two digits are both zero.

We have described the first series of numbers, but what of the remaining values after the dash? These digits describe the modifications made by German researchers. These changes are similar to those used in the modified NACA Four and Five Digit Series, but the Germans went further by specifying even more modifications. Let us first explain the names provided for the A-4 Skyhawk since these are a simplified version of the full designation system.

The first number after the dash specifies a leading-edge radius parameter. This parameter is defined as being equal to the radius of the leading edge divided by the square of the airfoil thickness. The value given after the second dash is the location of the maximum airfoil thickness in percentage of chord aft of the leading edge. For example, the NACA 0008-1.1-25 is thickest 25% back from the leading edge while the NACA 0005-.825-50 reaches maximum thickness halfway (50%) along its length.

The airfoil sections provided for the S-3 Viking demonstrate yet more examples of the modification system devised by the Germans. For this example, we will pick the wing root airfoil and more fully explain the purpose of each set of values.

NACA 0016.3-1.03 32.7/1.00

The meanings of these values are specified below:

0016 = NACA 0016 airfoil shape, a symmetric airfoil with no camber and a maximum thickness of 16%

.3 = the same basic NACA 0016 airfoil shape that has been scaled up to 16.3% thick

1.03 = the leading edge radius parameter (LERP). This variable describes how rounded the nose of the airfoil is. LERP is equal to the radius of the nose divided by the square of the thickness (r/t2). Since the thickness is known to be 0.163, solve for the radius r:

r = LERP * t2 = 0.0274

The radius is defined in fractions of chord, so this airfoil has a nose radius equal to 2.74% of the length of the airfoil.

32.7 = the location of the maximum thickness in percentage of chord from the leading edge. In other words, the thickest point on the airfoil is located 32.7% chord back from the leading edge.

1.00 = trailing-edge angle parameter (TEAP). This variable describes the thickness of the trailing edge. It is determined by the following equation:

TEAP = (1/t) * (tan τ/2)

where

t = thickness
τ = the angle (in radians) between the tangents to the upper and lower surfaces at the trailing edge

Since TEAP and t are both known, solve for τ:

τ = 2 * arctan (TEAP * t)

In this case, t is 0.163 and TEAP is 1.00, so τ is equal to 0.323 radians (18.516 degrees).

Even these examples, however, do not illustrate all of the modifications available under the German system. The following example provided in Theory of Wing Sections explains additional variations that can be made to the airfoil camber.

NACA     1.8     25     14-1.1     30/0.50

The meanings of these values are specified below:

1.8 = the maximum camber in tenths of chord
25 = location of the maximum camber in percentage of chord back from the leading edge
14 = maximum thickness in percentage of chord
30 = location of maximum thickness in percentage of chord back from the leading edge
0.50 = trailing edge angle paramter, defined as (1/t)(tan τ/2)
where
t = thickness ratio, or maximum thickness divied by chord
τ = trailing edge angle, or the included angle between lines tangent to the upper and lower surfaces of the trailing edge
The relationships described above can be used to decipher the meanings of airfoil designations of this form. Unfortunately, I have so far been unable to find a source describing exactly how to convert these parameters into complete airfoil coordinates. There are a number of programs to generate NACA airfoil coordinates available on the web, but none appear to be capable of handling the variables described by the German modification system. We will continue to investigate this subject and hopefully provide that additional information in the future. In any event, most of these modifications are so minor and subtle that they should have little discernible impact on the final shape.
- answer by Jeff Scott, 25 April 2004

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