On the Influence of the Geometry of Slender Bodies of Revolution and Delta Wings on Their Drag and Pressure Distribution at Transonic Speeds

Summary

With the help of the area rule the flow around delta wings and swallow-tailed wings in the transonic range is referred to the flow around (equivalent) bodies of revolution. Since the critical Mach-numbers — the limits of the transonic range and the linerarizable subsonic and supersonic region — lie quite near unity, the transonic properties can be determined by the calculation of the critical Mach-numbers, the calculation in the linearized ranges, and at Mach-number 1. For the latter the “parabolic method” [6] is used and applied together with a transonic method of characteristics to various bodies. The lower critical Mach-number is determined with sufficient accuracy by the linear theory. For the upper critical Mach-number the formula of Oswatitsch-Sjödin [15] is used.

After general considerations a geometrical system of bodies of revolution is introduced in the second section. The suitability of this system is checked by applying to the linear range in section 3. Section 4 gives some examples for wings equivalent to the bodies of revolution considered. In the next section the sonic flow is calculated and in the last section the results are given in a most general form by the transonic similarity.

The drag of the forebody (body before the maximum thickness) at M _∞ = 1 is, according to [6], half the linearized supersonic drag. This report shows now that the drag of the afterbody is practically equal to the whole supersonic drag of this part. Therefore the drag of the whole body at M _∞ = 1 lies nearer the supersonic value the greater the contribution of the afterbody is, or the shorter this part is.

It was known to the authors [5] that the linear subsonic theory holds very well for all subcritical Mach-numbers M _∞. The calculations made in connection with the present work show that even the linear supersonic theory holds for all supersonic Mach-numbers. The small subsonic region on the tip at the upper critical Mach-number has no appreciable influence.

The area rule requires a correction if the wings or the equivalent bodies of revolution have too blunt ends. This is not a very serious problem, because in the important Mach-number range the ends of those wings lie in supersonic flow. This matter will be treated later.

This work has been published as a KTH AERO TN at the authors request. The research reported here was sponsored in part by the air research and development command, united states air force, under contract No. AF 61 (514)-811, through the European Office, ARDC.

Reprinted from KTH-AERO TN 42 (1956) with permission.