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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

TECHNICAL MEMORANDUM 1227

MOMENTS OF CAMBERED ROUND BODIES

By Glinthe r Kempf

Translation of "Momente von gekrllinmten Rundkorpern." Ludwig Prandtl zurn 70. Geburtstag, Schriften der

Deutschen Aki-demie der Luftfahrtforschung.

Washington

August 1949

https://ntrs.nasa.gov/search.jsp?R=19930080717 2020-07-09T07:24:31+00:00Z

NATIONAL ADVISORY COMMI'ITEE FOR AERONAUTICS

TECHNICAL MEMORANDUM 1227

MOMENTS OF CAMBERED ROUND BODIES*

By GUnther Kempf

The rotationally symmetrical form for submarines is frequently abandoned in regard to surface run; for instance the stern with the screw-propeller is pressed down in order to make the water flow more easily toward the screw, or the ~row is lifted to keep the deck from being flooded.

For dimensioning the control elements it is important to know the influence of such cambers of the center line of a round body on the longitudinal stability, thus the ratio between the moment coefficients for cambered round bodies and the body of revolution.

This problem caused the investigation of the moments and the position of the force centers in a series of round bodies derived from a torpedo-like body of revolution. The length-width ratio of all bodies is 6:1; all show the same circular cross sections as the body of rota­tion and consequently, all have the same longitudinal volume distribution (fig. 1). They differ solely by the form of the axis of gravity of their cross sections, that is, the line connecting the centers of the Circles, thus their center line.

In case of the body of rotation A this center line is the axis going through the main -bulkhead plane.

For the four round bodies derived from it the center line is for body

B - cambered in front •

C - cambered toward the rear

D - cambered in the same sense on both sides

E - cambered in the opposite sense on both sides

The extent of these two-dimensional cambers is determined by the circular cross sections being shifted in each case until they touch a plane parallel to the center axis and tangent to the main bulkhead.

* 'Momente von gekrlimmten Rundkorpern. II Ludwig Prandtl zum 70. Geburtstag, Schriften der Deutschen Akademie der Luftfahrtforschung, pp. 139-151. (To Ludwig Prandtl upon his 70th birthday, Publications of the German Academy for Aviation Research), Berlin 1945.

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Figure 2 represents the five round bodies thus originated. Their length is Bo.8 centimeters, their maximum diameter 13.9 centimeters.

The tor~ues about two axes normal to the plane of the cambered center line were measured by moving the body along in the water toward both sides for various angles of attack from 00 to 400, the center line being immersed below the water surface to a depth of 2.65-times the diameter of the body. At this depth the influence of the surface waves is already sufficiently eliminated. After a sufficient constancy of the moment coefficient at small angles of attack had been determined for speeds of 1 to 2.5 meters per second, the tests were, for reasons of measuring accuracy, performed at a constant speed of 1 meter per second corresponding to a Reynolds number of RI = 6.7 X 105 or

6 5 1 Rd* = 1.1 X 10 ..

The measurement was made as follows (fig. 3):

A traction exerted by a weight was applied at a horizontal disc placed on the vertical axis of rotation. The body rotated during the measurement at constant water speed up to the angle corresponding to the prescribed weight moment which was then read off. The measurement was made about two axes of rotation at a distance a from each other. If x is the distance of the point of attack of the force P from the axis of rotation of the moment Ml, there follows from the two moments Ml = Px and ~ = p(x + a) for the same position of angles by elimination of P:

In the presentation of the moment coefficients Cm = M/~FI body, and the force centers are respect to the body. F is the body.

results in figures 4, 5, 6, 7, and 8 the are referred to the leading edge of the

represented in their position with main-bulkhead area, I, the length of the

*Reviewer's note: Rd signifies, according to Forschungsbericht Nr.1982 by Albring,the Reynolds number referred to the maximum diameter of the body.

lAccording to Albring's investigations in Forschungsbericht Nr.1982 the results can be transferred to higher Reynolds numbers only from Rd sin ~ = 3 X 105 onward, that is, in the present case for angles of attack below 220. This is indicated also by the fluctuations in measurement observed in case of larger angles. For the present pur­pose the transferability for angles of attack smaller than 220 is sufficient. An investigation for higher Reynolds numbers would have re~uired a considerably more complicated test-apparatus.

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I ,t is seen that all five bodies have a considerable unstable region, referred to the leading edge; this extends for instance for the body of rotation up to ± 170 toward both sides whereas it is more or less unilaterally shifted for the other bodies, according to their asymmetry; on the whole, however, it covers about the same angular range from 300 to 350

•

The moment coefficients of the five round bodies are plotted referred to the leading edge in figure 9 and referred to the center of gravi ty of the body in figure 10.

The essential difference in ' the stability properties of these round bodies compared to a cylinder of the same profile as it is given, for instance, by the Gottingen profiles 409, 410, and 411, is striking; whereas the latter are stable, referred to their leading edge, the round bodies are, to a great extent, unstable.

Thus arises the problem of what effect, fins on the rear part have on the longitudinal stability of the round body. In order to solve this problem, four fins of different size were investigated for the body of revolution as to their stabilizing effect. The form and magnitude of these fins is represented in figure 11. The fins I, II, and IV lie within the circumference of the round body given by the main bulkhead. The magnitude is

for I 1/20

for II 1/10

of the horizontal section

of the horizontal section

for IV 1/6.66 of the horizontal section

Fin III is of the same magnitude as IV, but the area attached to fin II outside of the circumference is in case of IV attached ahead of the fin II within the circumference.

Moreover, for fin II the effect of a "stagnation wedge" attached to its trailing edge was investigated.

The results of these measurements are plotted together in figure 12.

The curves show that the tail finS, in order to ensure sufficient stability, must have a magnitude of at least approximately one-eighth of the horizontal ,section.

The investigation will be completed by determination of the Ca and Cw values for the five round bodies.

Translated by Mary L. Mahler National Advisory Comnittee for Aeronautics.

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