Drag of Cylinders of Simple Shapes Page: 4 of 8
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REPORT NO. 619-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
the region where the drag coefficient is approximately
constant.
Semitubular cylinder.--The data from the tests of
the semitubular cylinder (figs. 4 and 5) indicate that
the drag coefficient, when the concave surface is to
the wind (a= 180), is approximately twice as large as
when the convex surface is to the wind (a=00). A
large increase in drag would be expected from elemen-
tary considerations.FIGURE 6.--Variation in Ca, with V/V, for the elliptical cylinders.
t'.
v
U
0.
u
a-
'35
K
0
ci *Reynolds Number"
FIGURE 7.-Variation in C.o with Reynolds Number for the elliptical cylinders.
Elliptical cylinder.-A study of the compressibility
effects on elliptical cylinders (figs. 6 and 7) shows a
marked decrease in critical speed with decrease in
fineness ratio. This result is to be expected from
previous investigations since experiments have indi-
cated (reference 6) that the compressibility burble
occurs when the velocity at any point in the field of
flow around the model exceeds a value corresponding
to the local speed of sound, and investigations of the
pressure distribution around elliptical cylinders (refer-
ence 7) show that the induced velocities decrease with
increasing fineness ratio.Relations between the fineness ratio and the critical
speed can be obtained quantitatively from theoretical
considerations. From the potential-flow theory, the
induced pressure over the elliptical cylinder can be
obtained from the equation
4p1 (a+b)y2
- -- +(a'-b)y2 (reference 8, equation (14))
where a is the semimajor axis.
b, the semiminor axis.
Ap, the difference between the undisturbed stream
pressure and p, the pressure at the surface
of the model.
y, the ordinate from the major axis to the point
of pressure, p.
For the maximum negative value of Ap/q, y is equal to b.
The equation easily reduces to the form (P =
-t(2+t) where t is the thickness-chord ratio. The
relation between the maximum induced pressure (-)
(from low-speed tests or as calculated from the poten-
tial-flow theory for incompressible fluids) and the
critical speed is developed and presented graphically
in reference 9. The results from references 8 and 9
may be combined to give the relation between the
critical speed and the thickness-chord ratio presented
in figure 8. A comparison of the theoretical with the
experimental results, also shown in figure 8, indicates0 .2 .4 .6 .8 10 /.2
Thickness
Chord
FIGURE 8.-Variation in critical speed with thickness-chord ratio for the elliptical
cylinders.
that the theory gives a fair approximation of the critical
speed for elliptical cylinders. The predicted values
are somewhat high. Even higher values are obtained
if, instead of the theoretically derived values, low-speed
measurements of are used in computing the
q mar
critical speeds.
As regards Reynolds Number effects, the results of
tests of the model (fig. 7) having the highest fineness
ratio (8:1) indicate no pronounced change in drag
coefficient with Reynolds Number. With decrease in172
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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/m1/4/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.