Drag of Cylinders of Simple Shapes Page: 2 of 8
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REPORT NO. 619--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The models tested were (a) circular, (b) semitubular,
(c) elliptical, (d) square, and (e) triangular (isosceles)
cylinders. The shapes and the dimensions of the cross
sections are shown in figure 1. Because of the small size
of the models and the relatively large forces involved,
the models were constructed of steel. The surfaces were
highly polished, and the edges of the semitubular, the
square, and the triangular cylinders were sharp.Wind direction
for c =0-/32'" 1/6"' /78"
o 0 Q
2emitubular
r = 50*
R= t/8"
ooD
a
8:/
1/" 1/4" face14" diameter
DCircular
oE//f s ic/
Major axis.92"
Squareaa a
30'
Triangular
(i osce/es)60" 90' IBO"apex angle
1/4" boseFIGURE 1.--Cross sections of cylinders.
The models were so mounted that they extended
across the tunnel and passed through holes in the tunnel
wall. These holes were covered with circular end plates
of thin brass, which fitted into recesses in the tunnel
wall and maintained the contour of the walls. Holes
of the same shape but slightly larger than the model
were cut in the end plates and provided a small clear-
ance so that the end plates and the model did not
touch. Previous investigations indicated that the
results so obtained approximate infinite-aspect-ratio
data.
The tests were conducted over a speed range from 5
percent of the speed of sound to a value above the speed
at which the compressibility burble occurred.
The dynamic pressure, % p2n, and the ratio of the
velocity at the test section to the speed of sound at
the test section, V/V , were determined from pressures
measured at calibrated static-pressure orifices.
The areas used in computing the coefficients were
taken as the product of a transverse dimension and the
"effective span." The effective span, 10.93 inches, was
determined from an impact-pressure survey across the
tunnel. The computed coefficients are based on frontal
area unless otherwise specified on the figures.
The angles of attack were measured from an arbi-
trarily chosen initial reference position (a =00), shown
in figure 1 for each of the models.PRECISION
The various factors affecting the accuracy of these
data may, in general, be divided into two classes: (a)
accidental errors, and (b) systematic errors.
The accidental errors, indicated by the scatter of the
test points on the curves, arose from slight changes in
the calibrations of the balances and of the static-
pressure orifices, from very small variations in the
direction of the air flow, and from similar sources. The
magnitude of these errors was estimated to be t2
percent from an examination of the point scatter.
The systematic errors, arising from tunnel-wall
effects and end interference, were impossible to evaluate
without a special series of tests but, because the models
were small in relation to the tunnel and tests of several
sizes of circular cylinders indicated that the correction
for the data presented is small, a correction was con-
sidered unnecessary.
PRESENTATION OF DATA
The results are presented in the standard nondimen-
sional coefficient form; that is, the force divided by the
product of pTV2 and the area. The area used in com-
puting the coefficients is the frontal area, except as
shown on the figures. The coefficients are plotted
against the speed ratio V/V, and against Reynolds
Number. Cross plots and summary plots of the data
are included to facilitate analysis and for purposes of
comparison.
The Reynolds Numbers for the data presented are
based on the length of the model parallel to the wind
direction, except for the semitubular cylinder for which
the characteristic length, like that for the circular
cylinder, is taken as the outside diameter.
DISCUSSION
The resistance, or drag, coefficients of the various
bodies depend on both Reynolds Number and compres-
sibility. Because the turbulence of the tunnel air
stream is small, the Reynolds Number almost entirely
determines the flow pattern around the model at low
speeds; whereas, at high speeds the compressibility
effects become important and, ultimately, as the speed
increases, become relatively so large that the Reynolds
Number effects may, to a first approximation, be dis-
regarded. Accordingly, throughout the discussion,
Reynolds Number effects are considered as those
changes in the coefficient that occur at low speeds and
compressibility effects as those that occur at high
speeds. Furthermore, the speed at which the flow
breakdown occurs due to compressibility phenomenon
is referred to as the "critical speed." Previous tests
(reference 6) have demonstrated the critical speed to
be that value of the translational velocity for which the170
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Lindsey, W. F. Drag of Cylinders of Simple Shapes, report, October 27, 1937; (https://digital.library.unt.edu/ark:/67531/metadc66277/m1/2/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.