Bodies of Revolution for Minimum Drag at High Supersonic Airspeeds Page: 2 of 47
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NACA RM A51K27
a
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
RESEARCH MEMORANDUM
BODIES OF REVOLUTION FOR MINIMUM DRAG
AT HIGH SUPERSONIC AIRSPEEDS
By A. J. Eggers, Jr., David H. Dennis,
and Meyer M. Resnikoff
SUMMARY
Approximate shapes:6f nonlifting bodies having minimum pressure
foredrag at high supersonic= airspeeds are calculated. With the aid of
Newton's law of resistance, the investigation is carried out for various
combinations of the conditions of given body length, base diameter, sur-
face area, and volume. In general it is found'that when body length is
fixed, the body has a blunt nose; whereas, when the length is not fixed,
the body has a sharp nose. In the case of a body of given length and
base diameter, the additional effect of curvature of the flow.over the
surface is investigated to determine its influence on the shape for min-
imum drag. The effect is. to increase the bluntness of the shape in the
region of the nose and the curvature in the region downstream of the nose.
Several bodies of revolution of fineness ratios 3 and 5, including
the calculated shapes of minimum drag for given length and base diameter
and for given base diameter and surface area, were tested in the Ames
10- by 14-inch supersonic wind tunnel at Mach numbers from 2.73 to 5.00.
A comparison of theoretical and experimental foredrag coefficients indi-
cates that the calculated minimum-drag bodies are reasonable approxima-
tions to the correct shapes. It is verified, for example, that the body
for a given length and base diameter has as much as, 18 percent less fore-
drag than a cone of the same fineness ratio.
INTRODUCTION
The shapes of nonlifting bodies of revolution having minimum pres-
sure drag at supersonic speeds have been the subject of numerous theo-
retical investigations. Krman (reference 1) determined the shape Qf
such a body (neglecting base drag) with given length and base diameter.
Somewhat later Haack (reference 2), Ferrari (reference 3), Lighthill
(reference 4), and Sears (reference 5) calculated body shapes having
minimum pressure drag for various other given conditions using methods
similar to those first employed by Karman. In all these investigations
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Eggers, A. J., Jr.; Dennis, David H. & Resnikoff, Meyer M. Bodies of Revolution for Minimum Drag at High Supersonic Airspeeds, report, February 25, 1952; (https://digital.library.unt.edu/ark:/67531/metadc59933/m1/2/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.