Average skin-friction drag coefficients from tank tests of a parabolic body of revolution (NACA RM-10) Page: 4 of 10
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AVERAGE SKIN-FRICTION DRAG COEFFICIENTS FROM TANK TESTS OF A
PARABOLIC BODY OF REVOLUTION (NACA RM-10)1
By ELMO J. MOTTARD and J. DAN LOPOSER
Average skin-friction drag coefcients were obtained from
boundary-layer total-pressure measurements on a parabolic
body of revolution (NACA RM-1O, basic fineness ratio 15) in
water at Reynolds numbers from 4.4 X10 to 70X10". The
tests were made in the Langley tank no. 1 with the body sting-
mounted at a depth of two maximum body diameters. The
arithmetic mean of three drag measurements taken around the
body was in good agreement with flat-plate results, but, appar-
ently because of the slight surface wave caused by the body, the
distribution of the boundary layer around the body was not
uniform over part of the Reynolds number range.
Skin-friction-drag data obtained at high Reynolds numbers
in subsonic flow is, at the present time, confined mainly to
the results of tests of flat plates. Skin-friction data obtained
at high Reynolds numbers from tank tests of a body of
revolution would be useful both hydrodynamically and aero-
dynamically. Such data would make it possible in many
instances to estimate the error incurred by using flat-plate
data in calculating the skin-friction drag of curved surfaces,
such as ship hulls and submerged bodies. The data could
be obtained at Reynolds numbers ordinarily obtained in
air with supersonic flow and could therefore be used in
conjunction with the results of tests of missiles in the same
Reynolds number range in order to help evaluate the effect of
Mach number on the skin-friction coefficient.
Because of the need for slkin-friction coefficients for a
curved body at high Reynolds numbers in subsonic flow,
skin-friction coefficients were obtained on a parabolic body
of revolution (NACA RM-10, basic fineness ratio 15) in
water at Reynolds numbers from 4.4X 106 to 70 X 106 (4.9
fps to 78 fps). The skin-friction coefficients were obtained
from measurements of the total pressure through the
boundary layer by the use of the boundary-layer momentum
theorem. Measurements were made at the 69.4 percent sta-
tion (based on the length of the basic shape) at three radial
positions around the model. In the transition range of
Reynolds number (from 1.1X 106 to 8.9 X 106), a dye was
injected into the boundary layer and the flow was observed
on the upper surface of the model.
A skin area from nose to measuring station, sq ft
C, average skin-friction drag coefficient
a boundary-layer thickness, ft
Ap static pressure on body minus static pressure in
g acceleration due to gravity, 32.2 ft/sec2
h depth below water surface, ft
A absolute viscosity, slugs/ft-sec
p static pressure, lb/sq ft
pr total pressure inside boundary layer, lb/sq ft
pr5 total pressure just outside boundary layer, lb/sq ft
q free-stream dynamic pressure, lb/sq ft
R Reynolds number based on axial distance from nose
to measuring station
r radial distance from body axis, ft
r., radial distance from body axis to skin, ft
p density, slugs/cu ft
s distance along surface from nose, ft
t time, see
7t wall shearing stress, lb/sq ft
7ua, average wall shearing stress, lb/sq ft
u velocity inside boundary layer, fps
U velocity just outside boundary layer, fps
V free-steam velocity, fps
x axial distance from nose, ft
y distance normal to skin, ft
max maximum value
Average skin-friction drag coefficients were obtained from
rake surveys of the total pressure through the boundary
layer and calculated values of the pressure distribution.
The average skin-friction coefficient ahead of a measurement
7O Wav 2r J
= qA fo rr,~dx
Momentum theory is used to evaluate the integral f l 7r, dx
1 Supersedes NACA TN 2854, "Average Skin-Friction Drag Coefficients From Tank Tests of a Parabolic Body of Revolution (NACA RM-10)" by Elmo J. Mottard and J. Dan Loposer,
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Mottard, Elmo J. & Loposer, J. Dan. Average skin-friction drag coefficients from tank tests of a parabolic body of revolution (NACA RM-10), report, 1954; (digital.library.unt.edu/ark:/67531/metadc60535/m1/4/: accessed June 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.