78 Related Airfoil Sections from Tests in the Variable-Density Wind Tunnel

DESCRIPTION OF AIRFOILS

Well-known airfoils of a certain class including the Göttingen 398 and the Clark Y, which have proved to be efficient, are nearly alike when their camber is removed (mean line straightened) and they are reduced to the same maximum thickness. A thickness variation similar to that of these airfoils was therefore chosen for the development of the N.A.C.A. airfoils. An equation defining the shape was used as a method of producing fair profiles.

If the chord is taken along the x axis from 0 to 1 the ordinates y are given by an equation of the form

The equation was adjusted to give the desired shape by imposing the following conditions to determine the constants:

Maximum ordinate 0.1 at 0.3 chord

x =0.3 y =0.1
dy /dx =0
Ordinate at trailing edge

x =1 y =0.002
Trailing-edge angle

x =1 dy /dx =–0.234
Nose shape

x =0.1 y =0.078

The following equation satisfying approximately the above-mentioned conditions represents a profile having a thickness of approximately 20 percent of the chord.

This equation was taken to define the basic section. The basic profile and a table of ordinates are given in figure 1. Points obtained by removing the camber from the Göttingen 398 and the Clark Y sections, and applying a factor to the ordinates of the resulting thickness curves to bring them to the same maximum thickness, are plotted on the above figure for comparison. Sections having any desired maximum thickness were obtained by multiplying the basic ordinates by the proper factor; that is

where t is the maximum thickness. The leading-edge radius is found to be

When the mean lines of certain airfoils in common use were reduced to the same maximum ordinate and compared it was found that their shapes were quite different. It was observed, however, that the range of shapes could be well covered by assuming some simple shape and varying the maximum ordinate and its position along the chord. The mean line was, therefore, arbitrarily defined by two parabolic equations of the form

where the leading end of the mean line is at the origin and the trailing end is on the x axis at x =l. The values of the constants for both equations were then expressed in terms of the above variables; namely (1) Mean-line extremities

(2) Maximum ordinate of mean line

x =p (position of maximum ordinate)

The resulting equations defining the mean line then became

(forward of maximum ordinate) and

(aft of maximum ordinate)

The method of combining the thickness forms with the mean-line forms is best described by means of the diagram in figure 2. The line joining the extremities of the mean line is chosen as the chord. Referring to the diagram, the ordinate y, of the thickness form is measured along the perpendicular to the mean line from a point on the mean line at the station along the chord corresponding to the value of x for which y, was computed. The resulting upper and lower surface points are then designated:

Stations x _u and x _l

Ordinates y _u and y _l

where the subscripts u and l refer to upper and lower surfaces, respectively. In addition to these symbols, the symbol Ø is employed to designate the angle be-tween the tangent to the mean line and the x axis. This angle is given by

The following formulas for calculating the ordinates may now be derived from the diagram:

Sample calculations are given in figure 2. The center for the leading-edge radius is placed on the tangent to the mean line at the leading edge.

A family of related airfoils was derived in the manner described. Seven values of the maximum thickness, 0.06, 0.0B, 0.12, 0.15, 0.18, 0.21, and 0.25; four values of the camber, 0.00, 0.02, 0.04, and 0.06; and six values of the position of the camber, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7 were used to derive the related sections of this family. The profiles of the airfoils derived are shown collectively in figure 3.

For the purposes of this investigation the construction and tests were limited to 68 of the airfoils. Tables of ordinates at the standard stations are given in the figures presenting the aerodynamic characteristics. These ordinates were obtained graphically from the computed ordinates for all but the symmetrical sections. Two sets of trailing-edge ordinates are given. Those inclosed by parentheses, which are given to facilitate construction, represent ordinates to which the surfaces are faired. In the construction of the models the trailing edges were rounded off.

Three groups of supplementary airfoils were also constructed and tested. The derivation of these airfoils will be considered later with the discussion.