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DRAG .FOR A HEMISPHERICAL NOSE AT MACH
: : NUMBERS 2.05, 2.54, AND 3.04
:.'. .. a HE IPEIA.N S TM C
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i. By Leo T. Chauvin
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iiLangley Aeronautical Laboratory
i...:Langley Field, Va.
: ;:UN RS3YOF FLORIDA
i~~~~, 20 MARSTON SCIENCE UBEIA
RO. R 0X 117011
'GAIN: A S FL. 32811-7011 US
Si IONAL ADVISORY COh
S i'; FOR AERONAUTICS
: December 31, 1952
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NACA RM L52K06
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
PRESSURE DISTRIBUTION AND PRESSURE
DRAG FOR A HEMISPHERICAL NOSE AT MACH
NUMBERS 2.05, 2.54, AND 3.04
By Leo T. Chauvin
An experimental investigation of the pressure distributions on a
hemispherical nose 3.98 inches in diameter, mounted on a cylindrical
support, has been made at Mach numbers of 2.05, 2.54, and 3.04 and for
Reynolds numbers of 4.44 x 106, 4.57 x 106, and 4.16 x 106, respectively.
The Reynolds number was based on body diameter and free-stream conditions.
Pressure-drag coefficients were calculated and good agreement was obtained
between these tests and other investigations.
From the standpoint of minimum drag, high fineness ratios and nearly
pointed noses are desirable in the design of supersonic missiles and air-
planes. However, it is necessary for some supersonic vehicles to have a
hemispherical nose to house guidance equipment. Since use of this nose
shape may result in severe drag penalties, with corresponding reduction
in speed and range, the National Advisory Committee for Aeronautics has
made tests in the preflight jet and in free flight to determine the pres-
sure drag, pressure distribution, and aerodynamic heating of hemispher-
ical nose bodies. The tests were made at the Langley Pilotless Aircraft
Research Station at Wallops Island, Va. Flight tests to determine the
drag of several round-nosed bodies at supersonic speeds have been reported
in reference 1. The present paper presents the data obtained from pres-
sure measurements at Mach numbers of 2.05, 2.54, and 3.04 and for Reynolds
numbers of 4.44 x 106, 4.57 x 106, and 4.16 x 106, respectively. The
Reynolds number was based on body diameter and free-stream condition.
NACA RM L52K06
M Mach number
Cp pressure coefficient,
p static pressure on body, lb/sq in. abs
pO free-stream static pressure, lb/sq in. abs
V0 free-stream velocity, ft/sec
CDW pressure-drag coefficient
HO stagnation pressure, Ib/sq in. abs
pO free-stream density, slugs/cu ft
R Reynolds number, based on body diameter
x coordinate in free-stream direction
r radius of hemispherical nose
The tests were made in the 8-inch auxiliary jet of the preflight
jet of the Langley Pilotless Aircraft Research Station at Wallops
Island, Va. Air for the operation of the preflight jet was stored in
two spheres at 220 pounds per square inch absolute. A hydraulically
controlled valve regulated the air from the sphere. The air then passed
through a heat exchanger where it was heated sufficiently to compensate
for the adiabatic temperature drop through the supersonic nozzle. The
air next passed through a three-dimensional nozzle and exhausted to the
atmosphere. Different test Mach numbers were provided by interchange-
able nozzles. A shadowgraph system was provided for flow observations.
Further information concerning the preflight jet can be found in
NACA BM L52K06
The model was a hemispherical nose 3.98 inches in diameter, mounted
on a cylindrical support, alined with the center line of the jet. Four-
teen pressure orifices were located on the nose and spiraled rearward of
the stagnation point to 0.6 inch on the cylindrical portion of the body.
The ratio of model diameter to jet diameter was 0.498 for the M = 2.05
and M = 2.54 tests and 0.532 for the M = 3.04 test. Figure 1 shows
the general arrangement of the nose mounted in the 8-inch auxiliary jet.
The test nose was made from spun K-Monel 0.05 inch thick, with a
smooth and highly polished surface.
Measurements of the free-stream total pressure, free-stream stagna-
tion temperature, and pressures on the body were obtained by a six-cell
recording manometer, thermocouples, and electrical pressure pickups,
respectively. These data were recorded by using two recording galva-
nometers and one optical recorder. The three recorders were synchronized
with a timer of 10 cycles per second. The instruments used were accurate
to 1 percent of their full scale.
The orifices on the model were 0.04-inch inside diameter, and the
data presented were taken when the pressures on the body had reached a
The Reynolds numbers for the Mach numbers 2.05, 2.54, and 3.04 were
4.44 X 106, 4.57 x 10 and 4.16 x 10 respectively. The relatively
constant Reynolds number of the tests was due to the variation of static
pressure and temperature. The test at M = 2.05 was for a sea-level
condition. The conditions for the tests at M = 2.54 and M = 3.04
represented a static pressure corresponding to altitudes of 12,000 and
28,000 feet, respectively.
The test results for Mach numbers 2.05, 2.54, and 3.04 are shown in
figure 2 plotted as pressure coefficient as a function of the nondimen-
sional parameter x/r, where x is the distance in the stream direction
from the stagnation point on the nose to the measurement station and r
is the radius of the hemisphere. Figure 2(a) shows the results for two
tests made at M = 2.05 and at approximately the same free-stream total
pressure. This figure shows that the pressure measurements can be
repeated with good accuracy and that no duplication of the tests is needed.
mACA RM L52K06
Figure 3 shows a shadowgram taken for each test. Shocks eminating
from the edge of the nozzle intersect the bow wave and influence the
flow somewhere on the body. If the intersection was between the stagna-
tion point of the body and the sonic point of the body, the pressure
over the entire nose would be affected. For each Mach number tested the
sonic point was estimated, and, in each case, the nozzle shock was found
to lie well outside the subsonic region. For the M = 2.05 and
M = 2.54 tests, the disturbance from the intersection does not affect
the flow over the hemisphere. For the M = 3.04 case, however, the
disturbance from intersection was stronger and caused a standing shock
to occur on the hemisphere at a value of x/r of approximately 0.71
(see fig. 3(c)). Rearward of this point the measured pressures were
affected by this disturbance and no data were presented for a value of
x/r greater than 0.66. For the purpose of calculating the pressure
drag for M = 3.04, the data were extrapolated to x = 1.0, as shown in
Figure 4 shows the faired curves through the points of pressure
coefficients plotted as a function of x/r for M = 2.05 of this
series of tests. Also shown are the results from references 3 and 4
taken at M = 1.90 and M = 1.62 and at Reynolds numbers of approxi-
mately 0.44 x 10 and 0.811 X 10 respectively. The data from refer-
ence 3 were obtained with a hemispherical nose attached to a cylindrical
body, and the data from reference 4 were calculated from interferometer
observations on a sting-supported sphere.
The pressure-drag coefficient, plotted as a function of Mach number
(fig. 5), was calculated by integrating the pressures from the present
tests and from references 3 and 4. Pressure-drag coefficients obtained
from reference 5 are shown in figure 5 for Mach numbers of 1.5, 1.98,
and 3.02. The data from the references 3 to 5 correlate well with the
faired curve through the points calculated from these tests.
Pressure distributions were measured on a hemispherical nose
3.98 inches in diameter at Mach numbers of 2.05, 2.54, and 3.04 and for
Reynolds numbers of 4.44 x 106, 4.57 X 106, and 4.16 X 106, respectively.
The Reynolds number for these tests was based on body diameter and free-
stream conditions. The pressure-drag coefficients obtained from previous
NASA RK L52K06
investigations are in agreement with a faired curve through the points
of pressure-drag coefficient calculated from these tests.
Langley Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Va.
1. Hart, Roger G.: Flight Investigation of the Drag of Round-Nosed
Bodies of Revolution at Mach Numbers From 0.6 to 1.5 Using Rocket-
Propelled Test Vehicles. NACA RM L51E25, 1951.
2. Faget, Maxime A., Watson, Raymond S., and Bartlett, Walter A., Jr.:
Free-Jet Tests of a 6.5-Inch-Diameter Ram-Jet Engine at Mach
Numbers of 1.81 and 2.00. NACA RM L50L06, 1951.
3. Moeckel, W. E.: Experimental Investigation of Supersonic Flow With
Detached Shock Waves for Mach Numbers Between 1.8 and 2.9.
NACA RM E50D05, 1950.
4. Wood, George P., and Gooderum, Paul B.: Method of Determining
Initial Tangents of Contours of Flow Variables Behind a Curved,
Axially Symmetrical Shock Wave. NACA TN 2411, 1951.
5. Sommer, Simon C., and Stark, James A.: The Effect of Bluntness on
the Drag of Spherical-Tipped Truncated Cones of Fineness Ratio 3
at Mach Numbers 1.2 to 7.4. NACA RM A52B13, 1952.
6 NACA RM L52KOr6
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UNIVERSITY OF FLORIDA
3126208106 6184 .
UNNERSITY OF FLORA
DOCUMENTS DEPARTMENT ."
120 MARSTON SCIENCE LIBRARY
P.O. BOX 117011
GAINESVILLE, FL 32611-7011 USAl