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National Advisory Committee for Aeronautics, Technical Notes - Sphere Drag Tests in the Variable Density Wind Tunnel

The air forces on a twenty—centimeter sphere were measured
in the Variable Density Wind Tunnel during February, 1929, af—
ter it had been rebuilt as an open—throat type. The results
from tests made at widely different densities and air speeds
and also on a smaller sphere, chosen to give the same range of
the Reynolds Number, are given. The results are compared with
those obtained in the old Variable Density Tunnel and in other
tunnels in order that an estimate of the conditions of turbu—
lence existing in the new tunnel may be formed.

The conclusions are that approximately the same drag coef—
ficient‘is obtained at a given Value of the Reynolds Number ir—
respective of what oombination of the Variables is used to obe
tainlthat value of the Reynolds Number and that the turbulence
of the air stream at the test section, as measured by the crit—
ical Reynolds Number of a sphere, is less for the new tunnel
than for the old one.

The sphere, because of its simplicity, is one of the ob—
jects Whose characteristics have been most Widely studied in
hydrodynamic research: It has hydrodynamic characteristics,
first discovered by Eiffel, which cause it to be of particular
interest in the present connection. These are} a large scale
effect occurrinngithin a range of the Reynolds Number conven—
iently reached in most wind tunnels and a susceptibility to
chang;s_in its aerodynamic characteristics with changes in the
turbulence of the air stream in which it is tested. Because of
these characteristics there has been a striking lack of agree—
ment between the drag measurements made on spheres in various
wind tunnels.

In spite of the lack of quantitative agreement between the
different investigations, all agree qualitatively as to the var—
iationaof the drag with dynamic scale. At low values of the
Reynolds Number the drag coefficient is high and falls off
rather abruptly as the Reynolds number is increased, approach—
ing a value known as the critical Reynolds Number for a sphere.
In this report the range of Values of the Reynolds Number
throughout which the drag coefficient changes rapidly will be
spoken of as the critical Reynolds Number. As the Reynolds
Number is further increased the drag coefficient reaches a min—
imum and then increases slowly. The more or less abrupt drop
in the drag coefficient, as explained by Prandtl (Reference74),
accompanies a change in the flow about the sphere from the lami~
nar to the turbulent type. The reduction of drag is caused
by the accompanying backward shift of the separation line of
the flow on the surface of the sphere to a position aft of the
equator,.thus reducing the size of the wake and, consequently,
the drag