Comparison of the experimental and theoretical distributions of lift on a slender inclined body of revolution at M = 2

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Title:
Comparison of the experimental and theoretical distributions of lift on a slender inclined body of revolution at M = 2
Series Title:
NACA RM
Physical Description:
39 p. : ill. ; 28 cm.
Language:
English
Creator:
Perkins, Edward W
Kuehn, Donald M
Ames Research Center
United States -- National Advisory Committee for Aeronautics
Publisher:
NACA
Place of Publication:
Washington, D.C
Publication Date:

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Subjects / Keywords:
Heat -- Transmission   ( lcsh )
Laminar boundary layer -- Research   ( lcsh )
Aerodynamics -- Research   ( lcsh )
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federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
Abstract: An investigation of the pressure distribution for a body of revolution, consisting of a 33-1/3-caliber (5.75 fineness ratio) tangent ogival nose and a cylindrical afterbody, has been made for an angle-of-attack range of 0° to 35.5° at a Mach number of 1.98 and a Reynolds number of approximately 0.5 x 10⁶m based on body diameter. Comparisons of the theoretical and experimental pressure distributions are made to show the nature of the effects of both viscosity and cross-flow compressibility. The experimental load distributions are compared with those predicted by the method suggested in NACA RM A9I26 which includes an approximate method for taking into account the effects of viscosity on the lift distribution.
Bibliography:
Includes bibliographic references (p. 15-17).
Statement of Responsibility:
by Edward W. Perkins and Donald M. Kuehn.
General Note:
"Report date August 25, 1953."
General Note:
"SECURITY INFORMATION and CONFIDENTIAL"--stamped on front and back covers
General Note:
"Copy 411."--stamped on front cover
General Note:
"Classification changed to unclassified Authority: Mr. J.W. Crowley Date: Aug. 17, 1955 Change #3067 E.L.B."--stamped on front cover

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Source Institution:
University of Florida
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003854796
oclc - 156210140
sobekcm - AA00006173_00001
System ID:
AA00006173:00001

Full Text

SI- Copy 4.

RM A53EOI


RESEARCH MEMORANDUM




COMPARISON OF THE EXPERIMENTAL AND THEORETICAL


DISTRIBUTIONS OF LIFT ON A SLENDER INCLINED

BODY OF REVOLUTION AT M = 2

By Edward W. Perkins and Donald M. Kuehn


Ames Aeronautical Laboratory
Moffett Field, Calif.
CIA SSIPICA TION CHQIM TO
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AUTlfxfTy MR J, WR. (RaLFT
CH&zGE # 3o6v


'ATE AUG., 1.7 1955


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NATIONAL ADVISORY COMMITTEE

:. FOR AERONAUTICS
i. WASHINGTON
August 25, 1953


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NACA RM A53E01


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


RESEARCH MEICRAIJTII.


COMPARISON OF THE EXPERIMENTAL AND THEORETICAL

DIST'rIBiJTIUiS OF LIFT ON A SLENDER INCLINED

BODY OF REVOLUTION AT M = 2

By Edward W. Perkins and Donald M. Kuehn


SUMMARY


Pressure distributions and force characteristics have been deter-
mined for a body of revolution consisting of a fineness ratio 5.75,
circular-arc, ogival nose tangent to a cylindrical afterbody for an
angle-of-attack range of 00 to 35.50. T.he free-stream Mach number was
1.98 and the free-stream Reynolds number was approximately 0.5 x 106,
based on body diameter.

Comparison of the theoretical and experimental pressure distributions
shows that for zero lift, either slender-body theory or higher-order
theories yield results which are in good agreement with experiment. For
the lifting case, good agreement with theory is found only for low angles
of attack and for the region in which the body cross-sectional area is
increasing in the downstream direction. Because of the effects of cross-
flow separation and the effects of cominirescibility due to the high cross-
flow Mach numbers at large angles of attack, the experimental pressure
distributions differ fr-m those predicted by potential theory.

Although the flow about the inclined body was, in general, similar
to that assumed as the basis for Allen's method of estimating the forces
resulting from viscous effects (NACA RM A9126), the distribution of the
forces was significantly different from that assumed. Nevertheless, the
lift and pitching-moment characteristics were in fair agreement with the
estimated values.


I!iTRODUCTION


The need for accurate knowledge of the flow about bodies of revolution
has become increasingly important for the design of high-speed missiles
and airplanes. For these aircraft the body contribution to the aerodynamic


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NACA RM A53E01


characteristics of the complete vehicle has assumed greater importance
than heretofore. Not only is there need for more accurate knowledge of
the flow for the customary low angles of attack but, because of maneu-
verability requirements, the flow characteristics must be known for a
much larger angle-of-attack range.

Since the effects of viscosity play a predominant role in determining
the flow over inclined bodies even at moderate angles of attack, the
results of potential-flow theories are valid only for small angles of
attack. An additional limitation on the range of applicability of certain
theories results from the assumption of incompressible cross flow.
In reference 1, for instance, it is indicated that the method developed
should be applicable as long as the Mach number normal to the inclined
axis of the body is not large compared with the critical Mach number for
a circular cylinder. However, for supersonic speeds, the Mach number
normal to the inclined axis may become so large, even at relatively small
angles of attack, that the effects of compressibility on the cross flow
can no longer be neglected. One of the purposes of the present investi-
gation is, therefore, to indicate the nature of the effects of both
viscosity and cross-flow compressibility and to show wherein the pressure
distribution for a slender inclined body of revolution in a supersonic
air stream differs from that predicted by available theory.

Although there is no simple theoretical method available for pre-
dicting either the viscous or the cross-flow compressibility effects on
the pressure distributions, an approximate method to account for these
effects on the over-all aerodynamic characteristics was proposed in
reference 2. It has been shown (ref. 3) that this method provides an
improvement over the prediction of potential theory alone for both the
lift and the drag rise. However, it was found that the centers of pres-
sure for the bodies considered were aft of the positions predicted by
the approximate theory. Because of this discrepancy, the present experi-
mental investigation of the loading of an inclined body has been under-
taken to assess the validity of certain of the assumptions made in the
approximate method of reference 2. In particular, the purpose of the
present investigation is to determine wherein the magnitude and distri-
bution of the cross forces resulting from viscous effects differ from
those assumed in the approximate method. The results of a similar study
of the pressure distributions and force characteristics of a parabolic-
arc body of revolution (NACA RM-10) are available in reference 4.



SYMBOLS

d2
A reference area, li-
4
Cdc section drag coefficient of a circular cylinder based on
body diameter
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Cder experimental local cross-flow drag coefficient based on body
diameter
L
CL lift coefficient, -
L oA

C, pitching-moment coefficient about the nose of the model,
I 1 0C x dx
qoAd 1 o n

Cn local normal-force coefficient per unit length,
2r V cos 0 dO
A o qo

CN total normal-force c-> ficient, f Cndx

d maximum body diameter

L lift force

z body length

In length of ogival nose

M pitching moment

Mo free-stream Mach number

Mc cross-flow Mach number, Mo sin a

p local static pressure on the model surface

P0 free-stream static pressure
P P0
Cp pressure coefficient,
qo

ACp lifting pressure coefficient, Cp CPa=0

q free-stream dynamic pressure

Reo free-stream Reynolds number per inch

Rec cross-flow ,E-ynT:.lds number based on body diameter

x,r,@ model cylindrical coordinates, origin at the apex (0 = 00
in the vertical plane of symmetry on the windward side)

a angle of attack


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APPARATUS AND TESTS

Tunnel


This investigation was conducted in the Ames 1- by 3-foot supersonic
wind tunnel No. 1. It is a closed-circuit variable-pressure tunnel in
which the Reynolds number is changed by varying the total pressure within
the approximate limits of one-fifth of an atmosphere to three atmos-
pheres. Adjustment of the flexible steel plates, which form the upper
and lower walls of the nozzle, provides a Mach number range of 1.2 to 2.2.


Models


Two ogive-cylinder models were tested with geometrically similar
noses, but with different maximum diameters and different fineness-ratio
cylindrical afterbodies. Both models had a 33-1/3-caliber tangent ogive
nose (fineness ratio 5.75). All pertinent model dimensions and orifice
locations are shown in figure 1.


Tests


The pressure-distribution data for both models were obtained for
a Mach number of 1.98 and a free-stream Reynolds number of 0.5 x 106
per inch. Model 1, for which pressure-distribution data were obtained
on the cylindrical afterbody only, was tested through the angle-of-attack
range of 0 to 35.50. Because the errors due to the irregularities in
the air stream were large compared to the measured pressures for low
angles of attack, all the data for angles of attack of less than 100 were
discarded. Subsequently, model 2, for which pressure-distribution data
were obtained for the nose as well as the cylindrical afterbody, was
tested in an improved air stream through the angle-of-attack range of
00 to 150. Since the models were instrumented with longitudinal rows
of orifices, circumferential pressure distributions were obtained by
rotating the models through the desired range of circumferential angle
(0) in increments of 150. All pressures were photographically recorded
from a multiple-tube manometer system.


FEiLE'CTION OF DATA


The data were initially reduced to the form of an uncorrected
pressure coefficient based upon free-stream conditions at the nose of
the model. With the assumption of a two-dimensional stream, the data


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were then corrected for nonuniformities of the free-stream pressure by
a simple linear superposition of these pressure nonuniformities and the
measured body pressures. All corrected pressure coefficients for models
1 and 2 are shown in tables I and II, respectively.

The corrected pressure coefficients have been integrated around
the body at 23 axial stations on model 1 and at 29 axial stations on
model 2 for each angle of attack to obtain the section normal-force
-oefficients. These force coefficients have been corrected for the
effects of local stream angle and stream curvature by the method
described in reference 5. For model 2, the loadirn was known over the
complete body length; therefore, total force and moment coefficients
were obtained from graphical integration of the corrected cross-force
distribution.


PRECISIONI OF MEASUREMENT


The uncertainty of the experimental data has been determined by
consideration of the possible errors of the individual quantities
(including corrections) used in the calculation of the final data.
These individual errors were combined by the root mean square to give
the total uncertainty which is shown in the following tabulation for
each parameter:

Cp (in plane of symmetry) 0.004
Cp (other than in plane of symmetry) .006
Cn .003
CL .008
Cm .056
a .lo

The values of the possible uncertainty in Cp appear quite large relative
to the scatter of the pressure-distribution data (figs. 5 and 7). However,
the possible uncertainty consists, for the most part, of errors which
would introduce a constant shift in the entire distribution at a given
station or errors which would result in a small gradient. Hence, although
these possible errors contribute to the total uncertainty, they are not
reflected in the scatter of the data.


RESULTS AND DISCUSSION

Vapor-Screen Studies


Before discussing the results of the pres-ure measurements, it is
appropriate to consider the characteristics of the flow around an inclined


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body of the type used in this investigation. Limited results describing
certain characteristics of the flow as determined with the vapor-screen
technique have been given in reference 3. A more detailed consideration
is presented in the following discussion.

VapDr-screen studies have shown the existence of vortices in the
flow field adjacent to the lee side of an inclined body. These studies
have shown that for a given body, the configuration and behavior of the
vortices, in addition to depending on the free-stream Reynolds number and
Mach number, are strong functions of the angle of attack. The behavior
of the vortices with regard to angle-of-attack effects may be roughly
divided into three regimes based upon observations of the steadiness and
disposition of the vortices at the base of the model: the low angle-of-
attack regime in which a steady symmetric pair is formed, the intermediate
range in which a steady asymmetric configuration of two vortices exists,
and the high angle range in which an periodically unsteady asymmetric
configuration of two or more vortices appears. Although adequate for
dividing the flow into steady and unsteady regimes, these simple classi-
fications are not always indicative of the vortex configuration over the
entire l-n th of the body since the configuration varies with distance
downstream from the nose of the model.

For angles of attack less than approximately 220, a symmetric pair
of steady oppositely rotating vortices is formed on the upper side of the
body. These vortices, which were first detected near the base of the
model, were not found with the vapor-screen technique for angles of attack
less than 60. However, it is known from the pressure distributions to be
discussed later that cross-flow separation with presumed formation of the
vortices occurred at even smaller angles of attack. As the angle of
attack is increased above 60, the vortices appear to increase in strength
and may be traced progressively farther forward on the body so that at
aFpr-::.imately 150, they extend over the entire length of the body.

The angle-of-attack range in which a steady asymmetric configuration
of two vortices appears is from approximately 220 to 260. The asymmetry
is first detected near the base of the model so that while the vortex
pattern is asymmetric near the base, it may be symmetric over the forward
part of the model. With increase in angle of attack within this range,
the asymmetry becomes more pronounced and, at approximately 260, the flow
becomes unsteady.

For all angles of attack from approximately 260 to 360, the maximum
angle of attack of the tests, the periodically unsteady configuration of
two or more vortices appears. The vortex configuration is similar to that
shown by the vapor screen and schlieren pictures of figure 2 in which the
pattern of vortices near the base, figure 2(c), resembles the familiar
Karman vortex street. Two different unsteady configurations are found in
this angle-of-attack range. One is associated with the appearance of an
additional vortex in the flow field and the other with a simple shifting


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of the asymmetry of the vortex pattern. In either case these changes
occur periodically with no apparent change in either the angle of attack
or the free-stream flow conditions and are accompanied by a shuddering of
the model, indicating a sudden change in force distribution.

It has been pointed out previously (ref. 3) that there is an analogy
between the development of the cross-flow vortex system with distance
along an inclined body and the development with time of the flow about a
circular cylinder set in motion impulsively from rest in a direction nor-
mal to the axis of revolution. In both flows a pair of symmetric vor-
tices is developed initially. These vortices grow in size and are
elongated in the cross-flow direction with distance along the body for
the inclined body and with time elapsed for the circular cylinder.
Eventually, this flow pattern becomes unstable and a periodic discharge
of vortices results. For the inclined body, the periodic vortex discharge
appears when the development of the flow is viewed in a plane which moves
with the fluid; whereas for the circular cylinder, the periodicity appears
when the flow is viewed in a plane which is fixed with respect to the
cylinder.


Pressure Distributions


Zero lift.- The theoretical pressure distribution at zero angle of
attack has been calculated by several different methods for comparison
with the experimental data presented in figure 3. Since the slope of the
surface of the body is everywhere small relative to the free-stream Mach
angle, there is little difference between the results obtained by the use
of the linear theory (ref. 6) and the more exact methods of the second-
order theory or the method of characteristics, references 7 and 8,
respectively. The principal difference in the theoretical results is in
the pressure coefficient at the nose of the model. For this Mach number
and nose angle, the second-order theory yields results which agree with
the exact Taylor-Maccoll value; whereas the linear theory yields a some-
what lower value. The method of characteristics solution for the pressure
distribution over the nose of this model was computed from the analytic
expression given in reference 8. The expression results from the corre-
lation of a number of characteristics solutions, and is expressed in terms
of the hypersonic similarity parameter. Since it was necessary to extra-
polate the results presented therein for the present application, the
accuracy has undoubtedly suffered to some extent. !l-.-ertheless, the
agreement of this result with experiment may be considered adequate in
view of the extreme simplicity of computation achieved by use of the
simple equation. The corresponding distribution over the cylindrical
afterbody was determined by cross-plotting values obtained from the
appropriate figures of reference 8. The distributions calculated with
linear theory and second-order theory coincide over most of the body
length. These distributions were calculated only to a point approximately

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two body diameters aft of the point of tangency of the nose with the
afterbody since the trend of the curves was clearly established, and
the large amount of calculation necessary to obtain the distribution
for the full body length was not considered justified.

The waviness of the experimental pressure distribution over the
nose section has been attributed directly to irregularities of slope of
the model surface. As determined by a contour projector, the magnitude
of slope deviation from the theoretical was approximately 0.250 at
x = 2.7d and approximately 0.12 at x = 1.4d. The apparently low
values of the pressure coefficients for x/d smaller nose angle on the model than was assumed for the theoretical
calculations.

Angle of attack.- Although there are a number of theoretical methods
for calculating the pressure distributions for inclined bodies of
revolution refss. 1 and 9 to 16, for example), the angles of attack and
body shapes for which these methods might be expected to yield accurate
results are limited. These limitations result from both the failure to
consider the effects of viscosity and the assumption of small disturb-
ances in the development of the theory.

Since the viscous effects are associated with separation of the
cross flow and since separation would be expected only if the pressure
gradient in the flow direction were adverse, a study of the theoretical
inviscid pressure distributions should give some indication of the con-
ditions for which cross-flow separation might be anticipated. In this
regard, it is of interest to consider the variation with angle of attack
of the position of the minimum pressure line as determined from the
pressure distribution predicted by the following expression refss. 1,
9, or 10):

Cp = 2 dr cos e sin 2a + sin2a (1-4 sin2G)


As shown in figure 4, for all angles of attack other than zero, the
theoretical minimum pressure line on the cylindrical afterbody is at
0 = 900. On the nose section of the body, as the angle of attack is
increased from 0 to 900, the minimnum-pressure line moves progressively
from 0 = 1800 to 0 = 900. Although the cross-flow separation line
would not be expected to coincide with the minimum-pressure line, it
might be expected to follow the same trends. Hence, based upon the
results shown in figure 4, cross-flow separation should occur initially
on the cylindrical afterbody and should move forward with increasing
angle of attack. That this expected trend is actually realized is
illustrated by the typical pressure-distribution data in figure 5. The
circumferential pressure distributions are shown for four argles of
attack. The data for the station 11.33 diameters from the bow of the
model indicate that at this station, the cross flow has separated at an


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angle of attack as low as 10. With increasing angle of attack, the
position along the body aft of which the cross flow has separated moves
forward. Plots of the data appearing in table I show that at approx-
imately 150, the cross flow has separated over the entire body length.
The position along the body at which cross-flow separation first occurs
is plotted as a function of angle of attack in figure 6.

It is within this separated-flow region that the vortices which
were observed with the aid of the vapor-screen technique are formed.
The secondary flow of these vortices has pronounced effects on the local
distribution of pressure within the separated-flow region. These effects
are predominant in the lower angle-of-attack range where the vortices
are close to the surface of the body. The low pressure region near
0 = 1500 (figs. 5(c) and 5(d), for example) is associated with the loca-
tion of a vortex core. The higher pressure which occurs in the plane of
symmetry on the lee side (0 = 1800) results from the combined effects
of the two symmetrically situated vortices which rotate in opposite
directions and tend to produce a quasi-stagnation line along the body
surface. The variation with distance along the body of the effect of
the vortex pair on the local pressure distribution is illustrated by the
data shown in figure 5(d). The magnitude of the expected pressure rise
at 0 = 1800 is proportional to the strength of the vortices and
inversely proportional to their distance from the body surface. Over
the nose where the vortices were weak, but still close to the body, a
small pressure rise is shown. At station 6.67d the combination of vortex
strength and location was such that the largest pressure rise occurred
at this station. At stations farther downstream the effect of the vor-
tices was less, and at station x = 11.33d the pressure was nearly
constant because the vortices were so far from the Ibdy that in spite of
their increased strength, they had little local influence on the body
pressure.

Although it is apparent from the foregoing that viscous effects are
important even at low angles of attack, it is evident that the region of
influence of these viscous effects is confined principally to the lee
side of the body. Hence, the pressure distribution for the remainder of
the body might be adequately predicted by potential theory. For compar-
ison with the experimental results, the pressure distributions predicted
by slender-body theory (ref. 1) have been plotted in figure 5 for several
stations along the body. These particular stations were chosen for the
comparisons since they are representative of the three different flow
regions of the body. The first station is on the e:qanding portion, the
second and third stations are within the region of lift carry-over on the
cylindrical afterbody, and the fourth station is sufficiently far along
the cylindrical portion of the body so that it should be influenced very
little by the lift carry-over from the nose. At the lowest angle of
attack the magnitude of the lifting pressure coefficients is so small
relative to the uncertainty in the measurements that comparisons with the
theoretical distributions have little significance. For low angles of


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attack where the effects of cross-flow separation are not evidenced, the
experimental pressure distributions for the station on the nose of the
body are in good agreement with the theory on both the windward and
leeward sides. For the balance of the stations the agreement is gener-
ally poor for angles of attack of 0.90 and 4.00. However, for 80, fair
agreement over most of the windward side of the model is found.

For angles of attack greater than 100 the Mach number normal to the
inclined axis of the body exceeds the well-known critical cross-flow Mach
number for a circular cylinder. Hence, it might be anticipated that for
this and larger angles of attack, compressibility effects would contrib-
ute to the lack of agreement of the experimental pressure distributions
with those predicted by the theory. The pressure-distribution data show
that this compressibility effect results in larger pressures than pre-
dicted over the windward side of the model. At 150 angle of attack this
compressibility effect is not constant along the body length; instead,
the difference between the experiment and theory on the windward side
diminishes with distance along the body, and at x = 11.33d the experi-
mental distribution is in good agreement with the incompressible theory.
However, as the angle of attack is increased above 150, the circumferen-
tial distributions over the cylindrical portion of the body become less
dependent upon axial position. The variation with angle of attack at
stations along the cylindrical afterbody in this high angle-of-attack
range is shown in figure 7. At approximately 29.50 angle of attack, or
a cross Mach number of 1.0, the circumferential pressure distributions
are almost identical over the entire cylindrical afterbody and thus
depend only on the cross-stream characteristics. As shown by the data
in figure 7, at high angles of attack the pressure distribution over the
windward side of the body approaches that predicted by classical Newtonian
theory (ref. 14), although, as would be expected, the pressures are all
somewhat lower than the Newtonian values. The level of the pressure in
the wake (fig. 7) decreases with increasing angle of attack. At
a = 35.50, the pressure over most of the lee side of the body is constant
and the pressure coefficient is equal to approximately 0.7 of that cor-
rezponding, to a vacuum. It is interesting to note that the pressure
level is very close to the minimum pressure on the lee side of a cylinder
in two-dimensional flow at the same free-stream Mach number (ref. 17).
Hence, it appears that the lee-side pressure for the inclined body may
have already reached a lower limit at the maximum angle of attack of
these tests and would therefore not decrease with further increases in
incidence.


Lift Distribution


Theory.- In the analysis of reference 2, it was assumed that the
viscous cross flow about an inclined body of revolution is similar to
that about a circular cylinder normal to an air stream of velocity


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Vo sin a. Thus, the local cross force resulting from the effects of
viscosity could be computed from a knowledge of the drag characteristics
of circular cylinders. It was further assumed that this so-called
viscous cross force could be added directly to the local cross force
resulting from the potential flow. Based upon these assumptions, expres-
sions for the lift, drag rise, and moment were developed as functions of
the angle of attack. It is the purpose of the following section to
examine the experimental lift distribution and center-of-pressure loca-
tion in light of this theory.

Comparison of theory and experiment.- The experimental longitudinal
distribution of local normal-force coefficient for model 2 is compared
with theoretical distributions in figure 8 for several angles of attack.
Munk's slender-body theory (ref. 18) and Tsien's linearized theory
(ref. 13) have each been combined with the so-called viscous cross force
calculated in accordance with reference 2 to yield two different theoret-
ical distributions. The theoretical viscous cross-flow contribution has
also been shown separately. Insofar as the absolute magnitude of the
local cross-force coefficients at angles of attack of 10 and 20 is con-
cerned, the small difference between the two theoretical results is
somewhat overshadowed by the uncertainty in the experimental data, thus
precluding a selection of the better theory on this basis alone. However,
in this low angle range the linearized theory does predict the general
trends of the experimental data better than the slender-body theory. In
particular, the negative lift region on the cylindrical afterbody is
indicated, although neither the exact location nor magnitude of the max-
imum negative lift is correctly predicted. For the highest angle-of-
attack data of figure 8, there is little semblance between theory and
experiment except over the first three or four body diameters.

The local normal-force data for model 1 presented in figure 9 afford
an opportunity to assess the validity of two of the assumptions of the
approximate method of reference 2. These two assumptions were: First,
that the cross-flow drag coefficient used for calculating the local
cross force on each element of an inclined body was constant along the
length of the body; and second, that the appropriate magnitude of the
cross-flow drag coefficient should be the two-dimensional value reduced
by a factor to account for the finite length of the body.1 Thus, in the
approximate method, the cross force on each element of the body was

IThis suggestion was made since it was known that the drag coefficient of
a circular cylinder of finite length was less than the drag coefficient
of a circular cylinder of infinite length. Although it was recognized
that the largest portion of the drag reduction due to finite length
should occur near the ends of the body, it was expedient to consider
the drag reduction to be equal for each element along the length of
the body.


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reduced by the factor T which is the ratio of the drag of a circular
cylinder of finite length to that of a circular cylinder of infinite
length. Since, for the angle-of-attack range of the data of figure 9,
the major contribution to the local normal force over the cylindrical
afterbody results from the cross-flow separation forces, the validity
of these assumptions can be assessed. As to the assumed constancy of
the cross-flow drag coefficient, only at the highest angle of attack is
the cross force constant over the afterbody length. For the angle-of-
attack range between 100 and 200 the normal force decreases continuously
with distance downstream from the beginning of the cylindrical afterbody.
Although the cross force does vary with distance along the body, the
nature of the distributions indicates that for each angle of attack, the
cross force is approaching a constant value far downstream. However,
this asymptotic value is not reached on the body for angles of attack
less than about 200. For angles of attack of 24.5 and greater, the
cross force is constant over a portion of the afterbody. It appears,
therefore, that for all but the largest angles of attack the cross-
force distribution on the cylindrical afterbody is influenced by the
presence of the nose of the body and that the length of afterbody influ-
enced by this end effect decreases as the angle of attack increases.
Hence, the assumption of reference 2 that the cross-flow drag coefficient
is constant along the length of the afterbody is most appropriate for
very large angles of attack.

The second assumption of reference 2 that may be examined is that
of the appropriate magnitude of the cross-flow drag coefficient. The
dashed lines shown in figure 9 represent the magnitude of the local
normal-force coefficient calculated with the section drag coefficient
for infinitely long circular cylinders (n = 1) for the appropriate cross
Mach numbers and cross Reynolds numbers. These values, rather than the
reduced values suggested in reference 2 (W 0.76), are shown since the
reduced values yielded results which were, in general, too low over most
of the length of the cylindrical afterbody. From these comparisons it is
apparent that neither the reduced values nor the values represented by
the dashed lines in figure 9 are appropriate for the complete angle-of-
attack range. It was conjectured in reference 2 that the value of
for cross Mach numbers other than that for which data were available
(M->0) could be estimated by considering the effective length-to-diameter
ratio as proportional to the true length-to-diameter ratio multiplied by
the ratio of the drag coefficient, 1.2, to the section drag coefficient
at the Mach number under consideration. Thus, as the cross Mach number
increased in the subsonic rang-, the value of q would decrease. However,
it appears from the data of figure 9 that it would be more appropriate to
consider that T approaches unity as the normal Mach number approaches
unity. This is further supported by the results presented in references
17 and 19 wherein it was shown that r is effectively unity for superEonic
cross Mach numbers.


CONFIDENTIAL


CONFIDENTIAL







NACA RM A53EO1


An effect of Reynolds number.- An effect of Reynolds number on the
local cross force is indicated by the comparison in figure 8(e) of the
local cross-force distribution on the cylindrical afterbodies of models
1 and 2 for an angle of attack of 15.10. These data show that the local
cross force over the aft portion of the afterbody of model 2 is much
less than that for model 1.2 Although the two sets of experimental data
were obtained for identical free-stream conditions, the difference in
size of the two models results in a difference in the Reynolds number
based on model dimensions. This loss in cross force for model 2 appears
to be similar in nature to the reduction in cross force or drag of a
circular cylinder which occurs when the critical Reynolds number is
exceeded. For this latter case, the reduction in drag results from
transition of the boundary layer on the cylinder which alters the sepa-
ration point and effects an increase in the pressure recovery on the lee
side of the body. Comparison of the circumferential pressure distribu-
tions at x = 14d for models 1 and 2 with typical pressure distributions
for the subcritical and supercritical Reynolds number flow around a
circular cylinder (fig. 10) shows that the differences between the dis-
tributions for models 1 and 2 are similar to the differences between the
distributions for the circular cylinder.3 An increase of Reynolds number
results in a larger pressure recovery on the leeward side of the body
and a lower minimum pressure which occurs nearer 8 = 90.

Two significant facts concerning the values of the cross-flow Mach
number and the Reynolds number at which this effect was found should be
noted. The cross-flow Mach number was approximately 0.5 which is greater
than the critical Mach number for a circular cylinder. Thus, it is
apparent that contrary to expectations, the critical cross-flow Mach
number for a circular cylinder (M = 0.4) is not the maximum cross Mach
number for which Reynolds number effects can be important. However, this
result does not imply that the Reynolds number will have important effects
for all cross Mach numbers since it is obvious that if the cross-flow
separation characteristics are primarily dependent on shock-wave boundary-
layer interaction, as they must be for large cross Mach numbers, the
Reynolds number should have little effect. The second significant result
is that the cross-flow Reynolds number, based upon the velocity normal
to the inclined axis and the afterbody diameter of model 2, was less
than the familiar critical cross-flow Reynolds number for a circular
cylinder. This result is in agreement with the results of reference 19
which show that the critical Reynolds number for the flow about a circu-
lar cylinder inclined to the air stream is less than the critical Reynolds

2To provide a direct comparison of the local normal-force distribution
of models 1 and 2, the experimental data for model 1, as plotted in
figure 8, have been referred to the dimensions of model 2 since, by
definition (see list of symbols), the local normal-force coefficient
has the dimensions r-1.
3The reference q used for this plot is the q normal to the axis of
revolution (qosin2a).

C .lfF T EIjTIAL


CONFIDENTIAL







NACA RM A53E01


number based upon the local diameter of the body, and the velocity normal
to the axis of the body. Thus, the cross-flow Reynolds number may not be
the proper parameter for correlating transition effects on the cross force
for inclined bodies. In this regard, it should be noted that for model 2
of the present investigation, the Reynolds number, based upon the free-
stream velocity and the distance from the nose of the model to the axial
position at which the transition effects on the cross flow were first
detected, was near the value for which transition of the longitudinal
boundary layer would be expected for the test conditions and within this
particular wind tunnel. Thus, transition of the longitudinal boundary
layer may have contributed to the apparently low value of the critical
cross-flow Reynolds number.


Lift and Moment Characteristics


Tht pressure-distribution data for model 2 have been integrated to
determine lift and moment characteristics. To provide a direct compar-
ison with force data obtained from previous tests of a model with an
identical ogival nose but of over-all fineness ratio of 13.1, the inte-
grations were terminated at x = 13.1d. The comparison of these results
is shown in figures 11 and 12. Also included in the figures are the
characteristics predicted with potential theory alone and with both
slender-body theory and Tsien's linearized theory in combination with
estimates of the viscous effects. The viscous contribution has been
estimated by both the method suggested in reference 2 in which the
reduced value of the cross-flow drag coefficient is used (n = 0.72) and
by assuming the full value of the cross-flow drag coefficient to be
effective (j = 1.0). The use of Tsien's linearized theory in place of
slender-body theory has little effect on moment and center of pressure.
Some slight improvement in the prediction of the lift and pitching
moment at the higher angles of attack results from use of the full value
of the cross-flow drag coefficient, but this is accompanied by a loss in
agreement in the low angle-of-attack range.


CONCLUDING REMARKS


The pressure distribution and force characteristics of a slender
body of revolution consisting of a fineness ratio 5.75, circular-arc,
ogival nose tangent to a cylindrical afterbody have been measured for
an angle-of-attack range of 00 to approximately 360. The free-stream
Reynolds number and Mach number were 0.5 x 106 per inch and 1.98,
respectively. Comparisons of the results with theory show that the
pressure distribution over the nose of the body is adequately predicted
for low angles of attack. Viscous effects which result in separation of
the cross flow caused considerable disagreement over the aft leeward side
of the cylindrical afterbody even at very low angles of attack. The


CONFIDENTIAL


CONFIDENTIAL







NACA RM A53E01


cross-flow-separation point (the position on the body aft of which the
cross flow is separated) moved forward with increasing angle of attack,
with the result that the cross flow is separated for the entire length
of the body at an angle of attack of 15.10.

The results of the study of the cross-force distribution have shown
that even though the total cross force or lift is in fair agreement with
that predicted by the approximate method proposed by Allen (NACA RM A9126),
the distribution of loading differs appreciably from that assumed in the
analysis. It is not possible to determine from the present tests if the
differences between the experimental results and the various theories
may be attributed to failure of the potential-flow theory or to viscous
effects which have not been taken into account. However, because of the
nature of these differences, it appears that they result largely from
the viscous effects. Additional theoretical and experimental work is
needed to explore the possible relationship between the time dependency
of the viscous forces for the circular cylinder impulsively set in
motion from rest and the axial distribution of the viscous forces for
the inclined body, which is suggested by the analogy between the devel-
opment with time of the flow about the circular cylinder and the devel-
opment with distance of the flow along the inclined body.

An effect of Reynolds number on the cross flow about the inclined
body was found. The effect was similar to that which occurs for the
two-dimensional flow around a circular cylinder when the Reynolds number
exceeds the well-known critical value. Two significant facts about this
effect should be noted. The cross-flow Reynolds number at which the
reduction in cross force occurred was less than the familiar critical
value for a circular cylinder normal to the air stream. The cross Mach
number was greater than the critical Mach number for a circular cylinder.
Thus, it appears that the critical cross-flow Reynolds number for the
flow around the inclined body is less than that of a circular cylinder
normal to the air stream, and that Reynolds number effects are important
even at cross Mach numbers greater than the critical Mach number for a
circular cylinder.


Ames Aeronautical Laboratory
National Advisory Committee for Aeronautics
Moffett Field, Calif.


REFERENCES


1. Allen, H. Julian: Pressure Distribution and some Effects of Viscosity
on Slender Inclined Bodies of Revolution. NACA TN 2044, 1950.


CONFIDENTIAL


CONFIDENTIAL







NACA RM A53E01


2. Alien, H. Julian: Estimation of the Forces and Moments Acting on
Inclined Bodies of Revolution of High Fineness Ratio.
NACA RM A9126, 1949.

3. Allen, H. Julian, and Perkins, Edward W.: Characteristics of Flow
Over Inclined Bodies of Revolution. NACA RM A50L07, 1951.

4. Cooper, Morton, Gapcynski, John P., and Hasel, Lowell E.: A
Pressure-Distribution Investigation of a Fineness-Ratio-12.2
Parabolic Body of Revolution (NACA RM-10) at M = 1.59 and
Angles of Attack up to 360. NACA RM L52G14a, 1952.

5. Nielsen, Jack N., Katzen, Elliott D., and Tang, Kenneth K.: Lift and
Pitching-Moment Interference Between a Pointed Cylindrical Body and
Triangular Wings of Various Aspect Ratios at Mach Numbers of 1.50
and 2.02. NACA RM A50F06, 1950.

6. von Karman, Theodor, and Moore, Norton B.: Resistance of Slender
Bodies Moving with Supersonic Velocities with Special Reference
to Projectiles. Trans. ASME, vol. 54, no. 23, Dec. 15, 1932,
pp. 303-310.

7. Van Dyke, Milton D.: A Study of Second-Order Supersonic-Flow Theory.
NACA Rep. 1081, 1952. (Formerly NACA TN 2200)

8. Ehret, Dorris M., Rossow, Vernon J., and Stevens, Victor I., Jr.:
An Analysis of the Applicability of the Hypersonic Similarity Law
to the Study of Flow about Bodies of Revolution at Zero Angle of
Attack. NACA TN 2250, 1950.

9. Luidens, Roger W., and Simon, Paul C.: Aerodynamic Characteristics
of IHACA RM-10 Missile in the 8- by 6-Foot Supersonic Wind Tunnel
at Mach liJumb-rs from 1.49 to 1.98. I Presentation and Analysis
of Pressure Measurements (Stabilizing Fins Removed).
NACA RM E50D1O, 1950.

10. Lighthill, M. J.: Supersonic Flow Past Slender Pointed Bodies of
Revolution at Yaw. Quart. Jour. Mech. and Appl. Math., vol. 1,
pt. 1, March 1948, pp. 76-89.

11. Laitone, E. V.: The Linearized Subsonic and Supersonic Flow About
Inclined Slender Bodies of Revolution. Jour. Aero. Sci., vol. 14,
no. 11, Nov. 1947, pp. 631-642.

12. Ward, G. N.: Supersonic Flow Past Slender Pointed Bodies. Quart.
Jour. Mech. and Appl. Math., vol. 2, pt. 1, March 1949, pp. 75-97.


ClAF IDEE[TIAL


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NACA RM A53E01


13. Tsien, Hsue-Shen: Supersonic Flow Over an Inclined Body of Revo-
lution. Jour. Aero. Sci., vol. 5, no. 12, Oct. 19 pp. 4)1-483.

14. Grimminger, G., Williams, E. P., and Young, G. B. W.: Lift on
Inclined Bodies of Revolution in Hypersonic Flow. Jour. Aero.
Sci., vol. 17, no. 11, Nov. 1950, pp. 675-690.

15. Kaplan, Carl: Potential Flow about Elongated Bodies of Revolution.
NACA Rep. 516, 1935.

16. Ferri, Antonio: The Method of Characteristics for the Determination
of Supersonic Flow over Bodies of Revolution at Small Angles of
Attack. NACA Rep. 1044, 1951. (Formerly NACA TN 1309)

17. Gowen, Forrest E., and Perkins, Edward W.: Drag of Circular Cylin-
ders for a Wide Ra..- of Reynolds Numbers and Mach Numbers.
NACA TN 2960, 1953. (Formerly NACA RM A52C20)

18. Munk, Max M.: T'he Aerodynamic Forces on Airship Hulls.
i;ACA\ Rep. 184, 1924.

19. Bursnall, William J., and Loftin, Laurence K., Jr.: Experimental
Investigation of the Pressure Distribution about a Yawed Circular
Cylinder in the Critical Reynolds Number Range. NACA TN 2463, 1951.


CONFIDENTIAL


CONFIDENTIAL










CONFIDENTIAL


NACA RM A5 .E'O:


TABLE I.- EXPERIMENTAL PRESSURE COEFFICIENTS FOR A 33-1/3-CALIEER OGIVE-

CYLIFEF: 10DLEL AT VARIOUS ANGLES OF ATTACK. Mo = 1.98,

Reo = 0.5 x 106/INCH, MODEL 1

(a) a = 10.50


o """ + o I 1 1 I h T 0 'oTi I5 i' [ i' 1i5l Iw 5 5 I 2'25 2051 5 82""" 0 5 55I55I" i '33

5 I I 11 5 0. 505 '- \- 1-I -0,085.53 0.00
I ... I -.>7 -.ot ,o

.1 0 7 .0 .c .u .05 .8200,m
i. 5i .- -. 1 0 -. *O3 T I 6 -.1 o1






(b) GL = 14.5o
4T 1 ... ... .. i.
".f .>iI)dO? 0.0?-0 00?0 5<.0c -0 008*i11 -.' 0
105 70 ... ...











000. .- .* -."i(i -,0j' -,0j 1 iI -.B -o -




















9,- b ,it* ,I>; ,?'^ .i/ 101 i J -.1? 1 -,.:=ti -,;t6 -.iSZ'i .r-ja


,2.7'. i-7 .13 i i 0$1 -- .7 -. iX.' i .i:,n | I --.ij f -- W
... .... --... 0 0 0 1 1 ..o. .. 1. 2. -- .00 -.7 20 -.01,6 -0
(b) a 19.5






























50-_ 5 ,.41,. .
5.5- 0'. I 051 .00" 0.s 0 o IP502. 00 000~i 0155 0 ~1 0



























05GH 0l5 -~j -,w -. ll '* .01 9 -.ji *-10 -.W -10.0 --5 07061
10 '.1 ll( r00/r.l- 1 ra .7 M ,0. '. '.0 05 0iiu j ~ 5 .05 5- 51 10~


14i Iih Ioi 47C -U6 -.i~ '7
___________________________________________________ .5~1 '-n 552.00S





20700155 15.00 INX "'I > 15






40,'.- 0 1000 17'.
127 .517 70 5 5 20 0 I1
15 711002 07 0' 50.)L "
0.il-.0i I .11-0iI-i~i-~1-(n o-.l -C8 00*i.S
5 5- -. iS '.2 I 00 '2
050T b~ 5OL 01i ~ -0~2 '0 .0 I -(Y I .09 iI 0.oB 0'*Y 5s~p -


(d) a 16950


S ~ ~ ~ ~ Rbn 7 4'.0 0 2' '0 ". 1 -o1


551 0 15 ('.1 00Y iP. I i 1,0 0017 141 i' : '.15" 551 ~oo n"iXY 1" )~' .
O ~ ~~ ~ ~ ~ '. '0 0. 1 0 1

5 l I 07'. 01 00, 7i: .i
011020 '.I 0 00 20 1' 1 0 1 .02 ,5


'.5020 014100 'nLi. 0' -UO-10' iQ 0 -( 01 -. 7 '1.ii 5 0
.55 isi .7( 01 .00 9: ,; '. ..i ii. .i
,na~~~~~ MACA.t ~ ~ .i


CONFIDENTIAL










NACA RM A53E01


CONFIDENTIAL


TABLE I.- EXPERIMENTAL PRESSURE C)JFFFI,:IEJlT3 FOR A 33-1/3-CALIBER OGIVE-

CYLINDER MODEL AT VARIOUS ANGLES OF ATTACK. Mo = 1.98,

Reo = 0.5 x IO6/INCH, MODEL 1 Continued

(e) a. = 22.5


0- 3e 1 31 600o 1 i 0.56 eLIOzo 6 I.1. 3 3_5_ 0113 '_ ,05 ii++



I | -. j.1 -.I 9 .., 19 1-. .w -82 -.1 .1 -. 1'0 1.1
.21 19.124 -.11-.i2 -.12 -.1 -.0 0 11 19 5 -. 179 5.3-0 .04 .11
1 .2 1 122 ... ..... 5 .115 0 ...... ..
10-5 -2 197 16 .-. 1 -" i .12 1 .. 76 .. .. 0301 5 -126
.,,, 212 .13 6 10 03| 11.3 .. 3 -3 .1 63 .1 2.0 126
S12.75j + I -7 .1 0. .9 1. 1....11... ..1.... ...... 5 1.++ .123... ....161 .6 6 ... .... 12.1


Sl8 6. 1-1 -- 7 33 1 19 7 .-i l 30 1 2 -.2i -65 -_3 3 1
-8 i .06 170 1. 0 1.. 135 .. .127 -13. .19 9 .1 1 .072.0. 301..

S. .0 -16 3-.07- -.2 i -.160. I 107 12 133 -130i -.0711 7 037 .31 6
.1 .9 .003170.109017-17--336 .1-13 -136 1-601-7 .30
S .201 ..1.2 .02 -.O 1. 0 .. .135 -.... I .6.1 -. ..2. -.157 .17 -76 .027 .l11


(f) a = 24.5




.I ... .


1 a .163 -1 -l 3 1 -.6 16 l' -i3
S12 -129 -.361 36 -.15 .. .. I
11.41 2 .3099 9 i.019 --030 -.161 -.l'.9| -160 -13: .1 -5 -- I-0 -115 37 1. 1
.12.0. .211 ii .. 7 02 3 17 1 130 3 2-.. .

12-75 .212 .8"10 .04q -. 18 .. 10 7 .165 ---1 -* -1069 .0 37 .715
2 59 .. .5 .13 ..15. | .14 0 0 51. 11
S* i I |1 .--1. .0 1 I -- 2 7




-6I a = 26.50
-231.07 1 I- I .051 .15. r -- -5.13 .7.9 I9.3 72 3ll 1 9.i 2 *1 6





a 26.50


3l1.l9l i0991, 9 I





.. ..


06- '. 3 l -3o6 4.L 6 0 6 ..j1 -. -

3.a 3 -7 -i
.1 .0 .0.. -" '16 *1 1 07 T7-6
. 09 1 7I .03 -.0291 .... 1 9 .1.1 .. .. 6
-. .. ..0 9 15 3 01
0. .17 15 ..9 -199 .7,1 -- ....6

' 1 .L .I3 -.. ... I 10.1.1 2 ...1. 1 7..-- 17 3 .o-
,, .7? .196 .o0,* -.ff + .. 8- -.: -1.IiS -.+1 9 -. SO-.,^a8 o71 .1.7

f t +I s I 16 T66 1, 991. .. 7 167



(h) a= 29.50

rt I kBu.lle, .


S... .. .. ... .

I -

-753 36. -a0 ," 1 .. .
I I zu I
.- .. .13 -.1 .0 2 17 .. | .1 F .-.N. A- 2.. .3 1.06 .
-' ,. *362 .01.3 .303 -.2'36 -+64 3 -. 6.02 *-. .a -3.2101 130-0.1. 0 .|- O ,0
6... i. 1* .129, 6 .9-- 0 -.2S 32 ... 9-. ,I2 ..3. 6-+ |.... 0.1 .. 01.2
1.75 I I 1 .I 92 3 .21 3 I- 21. -233 .22 .3 --.3 I.099 .. ... i .31 5.
* 102 93. 0 2 0-3 -.20 -.013 .210 232 -220 9293 .0 -.230 1.2 -.-03 209 -2
.7 *... -.26 .I2;6 .20 -205 217 .1 .3 0I.02 2
6B.06 .382 -. 22 -. -- 217 10 .31 1 2
13" .. .. 1 7.2u. -.262 2 3 217 210 132 25
> *W9 0 *. *3 *.217 .1 .0.201 3.9 12 .25
a 1, I' .2757 .132 06 -.. -.220 -.217 -.219 -.2.1 .. .. l ,..S .. .2 .11 -- .. -- --
SI O ID ENI006 -219L -.V 9 -i -- 59 -.222 5 ri -.216 -.20 ..2S1 -167|-.05I .110 .Z-9










CONFIDENTIAL


NACA RM A53E01


TABLE I.- EXPERIMENTAL PRESSURE COEFFICIENTS FOR A 33-1/3-CALIBER OGIVE-

CYLINDER MODEL AT VARIOUS ANGLES OF ATTACK. Mo = 1.98,

Reo = 0.5 x 106/INCH, MODEL 1 Concluded

(i) a = 32.50


Radial angle, 8

00 15 30 145 60 90 1050 120 135 1500 180 195 2100 2250 2400 2700 285 3000 315 3300

6.0 0.16 4 0.4o4 0.364 0.212 j0.04 -0.lo -U.23 -0.224!-0.21 -0.243 -0.239 -0.25 25 252 -0. 239 -0.232 -0.195 -0.079 0.063 0.224 0.369
6.74 .498 .459 .36 .213 .044 -.201 -.213 -.211 -.212 -.214 -.241 -.25 -.253 -.225 -.216 -.204 -.095 .045 .208 .356
7.41 .507 2 .359 .25 .040 -.o20 -.1'i -.20 -.251 -.243 -.242 -..22 -.252 -.214 -.207 -.214 -.100 .038 .200 .340
9.08 .49) .412 .351 .20 .030 -.205 -.1)> -.2 0 -.253 -.242 -. 40 -.268 -.249 -.213 -.204 -.213 -.103 .035 .196 .339
'.75 .484 .44 .3 .00 .034 -.20b -.21 -.216 -.41 -.231 -.247 -.261 -.241 -.225 -.212 -.211 -.102 .036 .193 .344
.41 .49 .442 .34j .117 .02 -.0: -.2) -.25 -.221 -.23 -.24 -.243 -.225 -.240 -.226 -.211 -.104 .028 .185 .332
10.0 .400 .42 .335 .6 .0 -.203 -.274 -.2 -.211 -.211 -.230 -.224 -.213 -.253 -.240 -.210 -.105 .023 .182 .324
10.75 .4>i4 .4j0 .337 .1'0 .03 -.19 -.2o -.2I1 -.203 -. 25 -.235 -.27 -.215 -.252 -.244 -.211 -.111 .024 .175 .320
11.41 73 .437 .33 -- .045' -.20 -.24 -.2 --- -.241 -.241 -.241 -.236 -.230 -.216 -.105 .027 ---.317
12.08 .461 .429 .3 --- .4b -.2 -.22 -.220 --- -.224 -.237 -.245 -.248 --- -.249 -- -- ---
12.75 .46 .5 .322 --- .01'7 -.U -.1 -.10 --- -.215 -.232 -.243 -.250 --- -.256 -.216 -.112 .023 ---.306
1 .41 .515 .4 .349 .1 .0 -.21 -.23 .-.25| -.244| -.249 -.241 -.250 -.241 -.235 -.234 -.220 -.110 .033 .202 .307
14.08 .49b .,4 .34 1 .049 -.21u -.24 -. 3 -.231 -.37 -.237 -.2 -.235 -.241 -.240 -.219 -.108 -.033 .201 .332
14.75 .- .44 .344 .1 9 4 -. -.2241 -.0 -.33 -.229 -.243 -.2o -.214 -.10b .034 .200 .340
15.41 .41 .339 .19 .049 -.20u -.258 -.235 -.2 -. 2 -.233 -.230 -.225 -.23 -.2.241 -.215 -.108 .031 .192 .326
10.08 .475 .4 1 .333 .194 nu -.205 -.241 -.2 -.225 -.22 -.22 -.21 -.22 -.228 -.230 -.215 -.110 .028 .187 .319
16.75 .471 .4 3 33 .195 51 -.201 -.223 -.217 -.2?5 -.225 -.22 -.234 -.22Y -.223 -.222 -.2 -.21 -.111 .023 .181 .313
17.'41 .53 .405 .354 .201 .052 -.211 -.243 -.. 3 -.23 -. :' -. -229 -.237 -233 -.3 3 219 -.105 .037 .204 .325
18.08 .493 .4' .31 .201 2 -.208 -.24 -.31 -.2 -.229 -. -23 -1 -4-.21 .231 -.235 -.220 -.104 .036 .204 .32
197 .75 .4 .449 i 19 .0 1 -.207 -.247 -.231 -.34 -.329 -.235 -.237 -.230 -.229 -.23 -.213 -.099 .037 .201 .341
19.41 .480 .446 .>4j .197 .0 -.203 -.24) -.2 ) -.22) -230 -.235 -.35 -.22 -.2Jo -.223 -.214 -.103 .033 .193 .329
20.08 .469 .436 .37) .190 .03 -.203 -.37 -.2.2 -.226 -.230 -.231 -.33 -.225 -.226 -.226
20.75 .4. 4 .3 .336 .19'. .054i -.200 -.230 -.21) -.221 -.223 -.231 -.233 -.228 -.228 -.225 -.215 -.108 .025 .183 .315


(j) a = 35.50


I Radal angle, 9


90' 105' 120 13i

-0.1 -0.26. -.21 -0.229

-.1,7 -.211 -.-71 -.2 80
-19 -.210 -.- 2 -.2'0
-.201 -.209 -.280 -.;3

-.1 -.267 -.2 -.32 -.231
-.197 -.206 -.220 -.230
-.1i1 -.260 -.222 -.230>

-.201 -.2b | -.22 -.2 4
-.1-.1 1o -.225t -.24;
-.187 -.240, -.23 -.244

-.202 -. 231 -.30
-.201 -.231 -.225 -.233
-.21 -.2>1 -. '5 -.230)
-.13 -.2 -.235 -. 31


-.197 -.'23 -.239 -.237
-.20 -.23 -.223 -.233
-.17 31 -.29 -. 37


150> 1680 190 2100

-0. -22` tb -0.28 .'4 -0.271
-.2 1. -.-250
-.209 -. -.o1 -.229
-.27[ -.24 -.2bo -.227
S-. -.267 -.2
-.24 -.24 -.252 -.
-.231 -.248 -.240 -.266
-.224 -.242 -.240 -.259
-.255 -.2451 -.240 -.240
-.2o0 -.241 -.238 -.23e
-.247 -.237 -.237 -.237
-.254 -.243 -.24 -.229
-.245 -.242 -.240 -.238
-.232 -.241 -.235 -.247
-.229 -239 -.236 -.244
-.234 -.238 -.240 -.238
-.234 -. 36 -.240 -.230
-.225 -.236 -.232 -.235
-.226 -.242 -.233 -.235
-.22 -.240 -.234 -.235
-.226 -.241 -.231 -.238
-.22 -.240 -.231 -.239
-23 -.239 -.229 -.237


225 240

-0.278 -0.274
-.245 -.245
-.22 -.213
-.226 -.205
-.50 -.222
-.270 -.252
-.27 -.274
-.259 -.264
-.240 -.243
-.229 -.239
-.233 -.230
-.250 -.224
-.248 -.2341
-.238 -.246
-.230 -.249
-.231 -.240
-.234 -.22
-.233 -.221
-.240o -.225
-.237) -.225
-.235 -.220
-.233 -.226
-.231 -.223


2700

-0.188
-.189
-.200
-.201
-.200
-.203


-.198

-.201
-.206
-.204
-.2o4
-.203
-.205
-.200
-.207
-.208
-.208
-.204
-.208
-. 04
-.212
-.214


285 300' 315 3300

-0.056 0.102 0.284 0.447
-.074 .083 .266 .432
-.085 .071 .249 .400
-.084 .087 .215 .409
-.082 .074 .254 .422
-.085 .068 .246 .412
-.088 .062 .242 .405
-.091 .059 .237 .400
-.083 .069 .244 .398

-.088 .059 .233 .387
-.086 .064 .250 .365
-.084 .069 .250 .396
-.082 .072 .259 .416
-.08i .067 .254 .408
-.088 .063 .250 .401
-. 09 .061 .243
-.04 .060 .234 .
-.083 .004 .240 .399
-.083 .067 .245 .418
-.091 .059 .233 .411
-.093 .054 .229 .406
-.093 .049 .225 .398

,NACA


CONFIDENTIAL


q.604 0.567
.5'9 .54'
.571 .534
.5%77 1 .5)1

.5 '7 .'11
. 571 .533

,4 0;,c
.0~ .>4<

.!02 .923
,55 .532
.586 .510
.05 2 .:.1)
.575 -28
.54 512

.'XI2 .%11
.'45 .507
.541 .50.)


I








NACA RM A53E01


CONFIDENTIAL


TABLE II.- EXPERIMENTAL PRESSURE COEFFICIENTS FOR A 33-1/3-CALIBER OGIVE-
CYLINDER MODEL AT VARIOUS ANGLES OF ATTACK. Mo = 1.98,
Reo = 0.5 x 106/INCH, MODEL 2
(a) a = 00


Radial angle, 0


(b) a = 0.90



Radial angle, a

d 00 150 300 450 600 75o 90 105 120 1350 1 150 18o00 1. 210 2250 210 2700

0.44 I I
.89 .081 .082 .081 .079 .077 .074 .072 .071 .070 .008 .067 .006 .065 .0 .06o .0 .070 .071 .073
1.33 .074 .074 .-.73 .071 .068 .065 .063 .061 .060 .0 59 8 .0558 .08 .06o 0o .l .O2 .062 .060
1.78 .058 .058 .:' .055 .043 050 .048 .046 o466 .045 .o-4 .044 .043 .o4 .o03 .044 .04 .o5 .048
2.22 .041 .042 .0O2 .041 .040 .039 .037 .036 .035 .032 .028 .027 .0 .29 .030 .031 032 035
2.67 .028 .030 .030 .029 .027 .025 .024 .022 .021 .020 017 .016 .01 .10 .017 .017 .018 .121
3.11 .023 .024 .024 .023 .021 .019 .018 .016 .016 .015 .014 .010 .013 .014 .01 .012 .013 .013 .015
3.56 .014 .014 .015 .014 .012 .011 .010 .009 .009 .007 .006 .00o .005 .0 .00 .o 005 .005 .005 .007
4.00 .'1 7 .-* .003 .001 0 -.001 -.002 -. ...........- -.00o -.00 -.000 -. 006 -.06 -005
4.44 .* -.009 -.009 -.010 -.011 -.013 -.i.i. -.-.015 -.016 -.016 .017 -.015
4.89 -.017 -.015 -.015 -.015 -.016 -.017 -.018 -.018 -.018 -.019 -.021 -.021 -.023 2-.1 -.022 -.21 -.022 -.022 -.021
5.33 -."? "-.^1 -.021 -.020 -.020 -.019 011- -1 -.022 -.020 -.027 -.028 -.027 -.27-.02 .-.029 -.29 -.028
5.78 -.- -. '3 -.021 -.023 -.024 -.025 .- .-.024 -.2 -.0 -.29 -.0 -.02 -.029 -.29 -.025 -.023
6.22 -.-.02 -.025 25 -5 -.024 -.021 -.019 -.1- -.. I- -.027 -.09 -.023 -.028 -.026 -. -.27 -.31 -.031 -.028
6.67 -.025 -.022 -.021 -22 -.021 -.019 -. 1 1 -.019 -.019 -.02 -.025 -.022 -.022 19 -.-.-19 .019 -.016
7.11 -.* : -.i- .017 -.016 -.0 17.017 -.017 -.017 -.017 -.018 -.019 -.017 -.010 -.014 -.14 -.016 -.016
7.55 -- 1"- :' -.- -.013 -14.014 -.01 -.01 .01015 01 5 -.14 -.012 -.01414.01 -.013 -.010 -.009 -.008 -.006
8.00 -.014 -.013 -.13 -.014 -.-.013 14-.0 13-.014 -.014 -.014 -.o4 -.o13 -.01 -.010 -.008 -.006 -.015 -.007 -.008-.008
8.44 -.012 -.012 -.013 -.011 -.011 -.012 -.013 -.013 -011-.011 -.009 -.007 -.004 -.001 -.003 -.003 -.004-.005-.005
8.89 -.010 -.010 -.011 -.011 -.012 -.013 -.012 -.012 1 -.009 -.009-008 -.007 -.006 -.002 -.ooh -.005 -.00o -.o08 -.008
9.33 .001 .001.001 0 -.002 -003.0003 3 -001 -.0-.00.002 0 .001 .003 .002 0 -.001 -.001 0
9.78 .002 .003 .005 .002 -.-.001 002 -.004 -.004 -.003 -.002 -.001 0 -.001 .001 .002 .003 .002 .001 .001
10.22 .009 .010 .008 .004 .001 0 -.001 -.002 -.001 -.001 0 .001 .003 .007 .006 .005 .004 .003 .004
10.67 .003 .003 .002 -.002 -.005 -.006 -. ^- I ..c.- -.oo, -.002 -.001 .002 .002 .001 -.001 -.003 -.002
11.33 .002 .002 0 -.003 -.000 -.008 -. -.:.:. -.00 -.004 -.o4 -.002 -.002 -.001 -.002 -.003 -.002
12.00 .005 .004 .002 0 -.004 -.006 .r. -.'-..0. .. .. .005 -.003 -.001 .002 .002 .002 0 -.001 .001
12.67 -.004 -.003 -.004 -.007 -.009 -.011 -.012 -.012 -.010 -.008 -.005 -.004 -.00 -.003 -.003 -.004 -.005-.006-.004
13.33 -.003 -.005 --.00 7 -.007007 -007 -.007 -.006 -.005 -.005 -.005 -.004 -.004 -.002 -.002 -.003 -.003 -.002
14.00 0 .001 .001 .001 0 .001 0 0 0 0 0 .001 0 .0.001 0 0 -.001 0 .002


CONFIDENTIAL









CONFIDENTIAL


NACA RM A53E01


TABLE II.- EXPERIMENTAL PRESSURE COEFFICIENTS FOR A 33-1/3-CALIBER OGIVE-
CYLINDER MODEL AT VARIOUS ANGLES OF ATTACK. Mo = 1.98,
Reo = 0.5 x 106/INCH, MODEL 2 Continued
(c) a = 2.00



Radial angle, 0
x
d 00 150 300 450o )0 75 90 105 120 135 1500 105 1800 1950 2100 2250 2400 2550 2700

0.44 0.103 0.102 0.099 0.095 0.091 0.086 0.081 0.076 0.073 0.00 0.008 0.0o7 0.067 0.067 0.068 0.070 0.073 0.077 0.081
.89 .094 .093 .090 .086 .084 .079 .074 .009 .0o .063 .Ool .06o .060 .059 .000 .062 .065 .069 .072
1.33 .084 .083 .080 .076 .073 .068 .064 .060 .057 054 .053 .052 .052 .052 .053 .054 .057 .060 .063
1.78 .066 .060 .062 .058 ..05 .051 .047 .043 .042 .039 .038 .038 .039 .037 038 .039 .041 .043 .045
2.22 .052 .050 .048 .044 .042 .039 .035 .031 .028 .025 .023 .022 .023 .022 .0 .02 .024 .020 .029 .031
2.0, .038 .038 .037 .034 .031 .02 .022 .019 .017 .014 .012 .012 .011 .010 .010 .010 .012 .015 .018
3.11 .033 .032 .030 .027 .029 .021 .017 .01 .01 1 .010 .008 .008 .007 .008 .008 .010 .010 .012
3.'o .022 .021 .019 .017 .016 .013 .009 .00 .004 .003 .001 0 0 0 0 .001 .002 .004
4.00 .008 .007 .005 .004 .004 .001 -.002 -. ..005 -.O 008 -.008 --.09 -.011 -.0Ol -.011 -.011 -.009 -.008 -.006
4.44 -.005 -.005 -0-.007 8 -.009 -.011 -.014 -.O16 -.017 -.019 -.021 -.21 -.020 -.020 -.02121 -.022 -.021 -.020 -.018
4.89 -.011 -.012 -.014 -.013 -.014 -.017 -.020 -.022 -.022 -024 -.02 -.024 -.022 -.024 -.025 -.026 -.024 -.024 -.024
5.33 -.020 -.020 -.021 -.018 -.010 -.019 -.021 -.023 -.023 -.02 -.030 -030 -.029 -029 -.030 -.031 -.030 -.031 -.031
5.78 -.02 -.022 -.020 -019 -.021 -.024 -.027 -.029 -.27-.027 -.02 -.027-.027 -.03 -.031 -.032 -.032 -.033 -.032
.22 -.022 -.023 -.024 -.2 -.021 -. -.22 -.023 -.023 -.029 -.029 -.027-.026 -.027 -.029 -.028 -.028 -.031 -.032
0.67 -.020 -.01o -.014 -.016 -.017 -.019 -.021 -.022 -.021 -.021 -.021 -.021 -.021 -.020 -.019 -.021 -.021 -.022 -.022
7.11 -.017 -.017 -.01 -.017 -.016 -.018 -.020 -.021 -.020 -.020 -.019 -.10 -.014 -.015 -.016 -.016 -.01 -.017 -.019
7. -.012 -.013 -.013 -.014 -.014 -.018 -.0o 2 -.021 -.019 -.017 -.014 -.012 -.009 -.009 -.010 -.012 -.010 -.010 -.010
8.00 -.011 -.011 -.013 -.014 -.01o -.018 -.019 -.019 -.017 -.015 -.013 -.10 -.08 -.007 -.006 -.007 -.009 -.010 -.011
8.44 -.000 -.009 -.011 -.013 -.014 -.01O -.01 -.016 -.013 -.010 -.006 -.00o -.002 -.003 -.003 -.005 -.006 -.008 -.009
8.98 -.005 -.007 -.012 -.014 -.013 -.04 -.014 -.014 -.011 -.010 -.0o' -.007 -.005 -.000 -.006 -.007 -.007 -.008 -.010
.J33 .002 .001 -.004 -.005 -003 -.o004 -.5 -.006 -.004 -.004 -.004 -.003 -.02 -.003 -00 00 004 005 -.004
9.78 -.001 -.001 -.003 -.0-. -.5 -. 00 -.7 -.005 -.005 -.004 -.004 -.003 -.00oo4 -.4 .003 0 o -.001
10.22 .006 .003 0 -.003 -.003 -. o0 -.00o -.006 -,005 -.004 -.004 -.002 -.001 .001 .001 0 .001 -.001 -.001
10.0 .004 .002 -.002 -.006 -.008 -.010 -.011 -.011 -.00 -.00 -00-.7 -.000 -.004 -.003 -.003-.003-.003 -.005 -.005
11.33 .003 -.003 -.006 -. 12.0 .008 .004 0 -.005 -.007 -,010 -.010 -.009 -00 -.005-. 4- 0 -.004 -O -001 -.002 -.001 -.002 -.002
12.07 .002 -.004 -.009 -.010 -.013 -.014 -.013 -.010-.00 -.0 004 -.003 03-.o03 -.o4 -.00 -.oo00 -.007 -.008
13.33 -.002 0 -.4-.00 -.o7 -.o -. 00 -. 00) -. .00 -00 003 -.002 -.003 -.003 -.00 -.005 -.007 -.007
14.00 .O1' .004 .001 -.01 0 -.002 -.003 -.003 -.001 -.<01 -.0010 .001 0 -.002 -.003 -.003 -.004 -.005



(d) a= 4.00




Radial angle, &

d 0 15 3 00 ,5 o 75 90 105 0 120 135' 1500 l105 180 195 210 225 2400 2550 270

0.44 0.129 0.127 0.11' 0.110 0.099 0.087 0.07 0.0&7 0.059 0.054 0.052 0.0o5 01049 0.051 51 0.051 3 0.o58 0.004 0.074
.8 .12) .120 .113 .105 .0 4 .0'2 .071 .061 .053 .048 .0,5 .044 .048 .047 .043 .045 .049 .054 .003
1.33 .108 .1' .100 .o92 .o81 .070 .054 .052 .044 .039 .038 .o4u .039 .040 .037 .037 .041 .047 .054
1.78 .08 .0= .07 .0 .0'40 .033 .027 .02 .022 .022 .022 ..2 .002 .024 .020 .030 .037
2.22 .08 .007 .062 .050 .048 39 .031 .024 .018 .015 .014 .012 .011 .011 .012 .012 .014 .018 .025
2.67 .5 .053 .047 .041 .032 .04 .015 008 .4 .02 .03 .00 .. 002 .002 .002 0 .001 .004 .008
3.11 .5 .044 .038 .0 32 .025 .017 .011 .005 .000 .005 .003 .001 .002 .002 .003 -.003 .001 .001 .005
3.50 .033 .03 .02 .024 .017 10 .0,4 0 -.004 -.,00 -.o00. -.00f -.00 -.0007-. -. -.007 -.00 -.004
4.00 .023 .022 .017 .011 .004 -.003 -.07 -.012 -.015 --.016 -.01 -.01 -.015 -.01 -.7 -.018 -.1 -.017 -.015
4.44 .010 .009 .000 -.08 -. 14 -.01) -.024 -.02 -.026 -.025 -.025 -.024 -.024 -.025 -.027 -.028 -.028 -.025
".8 .02 ..002 002 -.009 -.015 -.'i -.024 -.02-.-029 -.029 -.027 -.026 -.025 -.026 -.028 -.030 -.033 -.035 -.032
.33 -.010 -.010 -.012 -.010 -.01t -,022 -.02, -.033 -.031 -.030 -.0.9 -.029 -.029 -.C30 -.032 -.03 -.037 -.040 -.038
.8 -.4 -.012 -.013 -. 20 -.01 -.27 -.13 -.033 -.033 -032 -.03 -.0 -.02 -.029 -032 -.035 -.038 -.040 -.041
.2 -.,01 -.014 -.016 -.024 -.028 -.01 -.031 -.033 -.031 -.030 -.27 -.02' -.024 -.024 -.027 -.031 -.037 -.042 -.043
.67 -.o14 -.014 -.01-.1 -.02 -. 2 -.028 -.02 -.020 2 1.022-.o01 -. O -.o01 -.0 -.019 -.019 -.021 -.027 -.030
7.11 -.o9 -.00o9 -.012 -.018 -.022 -.0 7 -.029 -.028 -.024 -.020 -.01o -.014 -.011 -.009 -.011 -.014 -.019 -.024 -.027
7.55 -.00o -.006 -..00 -.016-. .01 -.24-. 3 0.20 -.010 -.013 -.010 -.00 -.012 -.014 -.017 -.020 -.022
.0 .0 -.0 -.012 -. -.2-. -.02 -.022 -.019 -.0o -.013 -.010 -.00 -.8 -.o -.012 -.017 -.020
8.44 -.o04 -.05 -.008 -.012 -.017 .0 -.01 -.O) -.011-. 01-.012 -.010 -.007 -.003 -.009 -.011 -.012 -.015 -.017
8-.9 05 00 -.-05 -.010 -.014 -.017 20 -.0 -.019 -.01 -.014 -.012 -.011 -.009 -.010 -.011 -.011 -.012 -.015 -.0O1
.3 .001 .00 -.00. -.05 -.001 -.013 -.ol) -.014 -.011 -.10 -008 -.07 -.03 -.00 -.007 -.08 -.0 -.011 -.012
9. .002 -.001 -.004 -.007 -.011 -.01 -.015 -.014 -.O1l -.009 -.00 -.00 -.003 -.004 -.OO -.007 -.011 -.013
.2 .0 .0 -.04 -.8 -.( -.12 -.011 -.009 -. -.000 -.004 .001 -.001 -.003 -.4 -.0 -.006 -.007
10. .3 -.002 -.00I -.009 -.013 -.15 -.-.013.013 -.Oll -.010 -.008 -.008 -.003 -.003 -.004 -.004 -..005 -.008 -.009
11. 3 .002 -.0)1 -.004 -. .01 -.017 -.015 -.011 -.00-.0.007 -.007 -.003 -.003 -.004 -.005 -.000 -.010 -.011

l.6 .00 .00)' l-.001 -.'07 i-.02 -.i I4 -.01 -.01 -.008 -.007 -.o00 -.00 -.2 002 -.00 5 -. 0 0 I I 3
11.)i .08' -0' -.001 -.o00" -.11 -.11-5 .1 .0 1-.004 -. -.001 -.003 -.005 -.007 -.009 -.014 -.016
14.C .1 11 0 .C1 -..4 -. 7-.10.8 -.00 -.003 -.oOl 0 0 .004 0 -.003 -.005-.008 -.013 -.015
NACA-


CONFIDENTIAL









NACA RM A53E01


CONFIDENTIAL


TABLE II.- EXPERIMENTAL PRESSURE COEFFICIENTS FOR A 33-1/3-CALIBER OGIVE-
CYLINDER MODEL AT VARIOUS ANGLES OF ATTACK. Mo = 1.98,

Reo = 0.5 x 106/INCH, MODEL 2 Continued

(e) a.= 5.7


Radial angle, v

05 120 135


Ij
13 .1 __
o" 1952io 225


I .021
.1?

)- -..ol -.015 -.010

O -.02 -.20 -.010
03 *. O-.l3


l0 -.3: -.o15 -.oi1


17 -.005 -.021 -.0311
'2 1 -."01 -.013

0,/-.132j -.o3
o2 -.o291-.03][-.O3S
-.0 1.- i-. o
01 -.o2 -. -, 2
00-. 1-.l-

a I. 01]-- '
10 -.

-.154-.el .
1. -. 10-.11


127 .0
.019 .0
.000 .0

.00a -.0
.0C8 -.0
.022 -.0
.02i t0


-. 4 -.
-.o3 -.032 -
-.07} -. 0 -.,




-.o15-.05 -.
-.021 -.02 -.
-.021 -. -.
-.022i -,0-.


-.1 -.1

-.o1i|-.oi -.
-.01- ..


(f) a = 8.00


CONFIDENTIAL


Radial angle, 3

d 0o 15 30 45 6C0 75 90 1050 135 150 1 iS 210 22 40 2 270

0.41 0.17 0.175 0.160 0.13 0.104 0.071 0.047 0.028 0.02 0.019 0.021 9.02 0.026 0.00 0.022 0.0~ 0.022 0.032 .05
.59 .17. .1l1 .1' .13 .10 3 .044 .23 .015 .01 .020 .01 .015 .01 .00 .037
1.33 .161 .154 .137 .112 .05 .053 .030 .012 .00' .006 .008 .014 .o01 .013 11 .007 .005 .012 .02
1.78 .3 .130 .1141 0 00 .061 .033 .12 -.00 -.11-.10 -.007 03 .1.5 0 -. 03 -.006 -.00 -.003 .012
2.22 .116 .108 .092 .070 .0-5 ..011 -.C7I* -.02 -.OO -.008 -.-01 -.022 -.017 -.004
2.67 .098 .093 .050 .05 .033 .004-. -. 0 0 -.015 -.010 -.00 -.01 -.017 -.023 -.031 -.032 -.020
3.11 .093 .0 7 .071 .048 .023 -.00 -.024 -.032 -.033 -.6 -. -.012 -.01 -.027 .03 -.037 -.02
3.56 -- .073 .059 .037 .013 -.014 -.031 -.1LO -. -41 33 -.0231 -. -. -.01 -.23 -.033 -.043 -.041 -.037
4.oo .053 .01*0 .020 -.003 -.028 -.0 44 -.052 -. 01-.1 -.02-..033 -.025 -.023 -.025 -.031 -.0o0 o -. .
4.44 .04 .035 .022 .002 -.019 -.043 -.0 -.065-.O1 -.O51 -. .1 33-.03 -.033 -.033 -.04 -.
4.99 .029 .024 .011 -.o.0 -. 27 -.0 -.063 -.071 -.064 -.1 -.o2 -.33 -.030 -.03 .. -.072 -.069
5.33 .017 .014 0 -.019 -.037 -.055 -.066 -.072-..062 -.048 -.03 -.37 -033 -.037 .078 -.079
5.78 .009 .006 -.003 -.020 -.039 -.02 -.074 -.06 -.7 .-. 7 -.00 .-.03 -.028 -.035 -.040 -.048 -.062 -.079 -.0E
6.22 .006 .004 -.010 -.032 -.054 -.074 -.077 -.072 -.07 .041 -.033 -.025 -.032 -.03 -.0 -.0 -.076 -.
6.67 .005 -.002 -.013 -.025 -.046 -.008 -.7 .0-51 -.03- -.3 -.o -.016 -.025-.03 -.033-.03 -.063 -.078
7.11 .003 .004 -.010 -.030 -.050 -.009 -030 -.032 -.02 -.010 -.020 -.026 -.02 -.3 -.05 -.071
7.55 .0070 -.013 -.030 -.049 -.067 -.033 -.032 -.023 -.00 -.o18 -. 02 -.024 -.029 -
8.00 .006 .003 -.010 -.031 -.051 -.006 .065 35 -.3 -.030 -.024 0 -.014 -.022 -.22 -.02
8.44 .004 -.002 -.013 -.032 -.050 -.00 -.1 31 -.02- -.02- -.023 .001 -.017 -. -.021 -.0211-
8.89 .003 -.001 -.016 -.034 -.051 -.0,3 -.057 -.042 -.027 -.025 -.029 -.02 -.002 -.021 -. -.020 -. ..,- -I-
9.33 .007 .001 -.013 -.028 -.044 -.054 -.017 -.032 -.022 -.021 -.024 -.018 .009 -.015 -.02 -.020-.
9.78 .009 .004 -.009 -.025 -.038 .048 -.04 -.032 -.022 -.019 -.024 -.021 .002 -.020 -.020 -.15 -.017-.025 -.39
10.22 .018 .013 -.001 -.- : .043 -.030 -.022 -.020 -.023 -.021 .007 -.011 -.01-.014 -.018 -. .039
10.67 .023 .016 -. .0" -. -.035 -.024 -.021 -.023 .-.02 -.002 -.019 -.1 -.01 -.018 .04
11.33 .024 .018 .003 -.016 -.035 -.051 -.0 -.035 -.025 -.021 -.023 -.028 -.009 -.023 -.018 -.01 -.01 -.029 -.044
12.00 .027 .020 .002 -.017 -.035 -.051 -.051 -.037 -.029 -.024 -.024 -.021 -.005 -.017 -.017 -.017 -.022 -.030 -.041
12.67 .020 .013 -.004 -.021 -.038 -.053 -.049 -.032 -.0 -.022 -.022 -.022 -.012 -.022 -.19 -.020 -.023-.03 -.044
13.33 .017 .010 -.006 -.023 -.039 -.050 -.042 018 26 -.021 -.021 -.021 -.023 -.012 -.019 -.016 -.017 -.018 -.027 -.0
14.00 .023 .016 -.004 -.021 -.033 -.039 -.030 -.018 -.017 -.016 -.017 -.012 -.002 -.013 -.016 -.016 -.018 -.023-.038


15 30C








CONFIDENTIAL


NACA RM A53E01


TABLE II.- EXPERIMENTAL PRESSURE COEFFICIENTS FOR A 33-1/3-CALIBER OGIVE-
CYLINDER MODEL AT VARIOUS ANGLES OF ATTACK. Mo = 1.98,
Reo = 0.5 x lO/INCH, MODEL 2 Concluded
(g) a = 15.10



Radial angle, 9

S0 15 300 45" 60 75 90 120 135 1 10 1650 I 210 225 240 255 270

0.34 0332 0.2o7 0.192 0.100 0.02-.044.0.074.o 0.052 .0550.04-.021-01.0540.049-0.052-0.07 0.068 0.017
S.335 .323 .265 .130 .111 .027 -.047 -.09 -.07 -.64 -.003 -.060 -.011 -.054 -.060 -.064 -.088 -.088 -.056
1.33 .319 .300 .23 1 .13 .01 -.O -.072 -.0 -.073 --073 -.077 -.045 -.014 -.073 -.071 -.073 -.096 -.096 -.062
1.7 .256 .271 .211 .1.4 .000 -.021 -. 09 -.110 -.S0 -.078 -.087 -.058 -.023 -.081 -.088 -.084 -.108 -.108 -.082
S.265 .249 .1)0 .10 .041 .031 -.lo -.134 -.10 -.075 -.03 -.059 -.030 -.088 -.089 -.071 -.13 -131 -.094
.20 .223 .171 .101 .027 -.051 -.11 -.15 -.12i -.075 -.083 -.072 -.039 -.08 -.086 -.077 -.157 -.155 -.113
3.11 .22 .211 .153 .085 .009 -.06 -.133 -.177 -.129 -.073 -.063 -.6 -.0-45 -.066 -.067 -.032 -.17 -.172 -.122
3-. 0 .200 .10 .132 .o0 -.0o4 -.077 -.144 1 1 -.1 -.14 77 -.0o -.065 -.052 -.060 -.067 -.033 -.19C -.188 -.138
,.CO .170 .154 .111 .050 -.021 -.09j -.15 -.208 -.14 -. 0 -.071 -.068 -.059 -.062 -.071 -. 34 -.208 -.205 -.154
.151 .131 .00 31 1 -.O38 -.10 -.171 -.21 -.144 -.091 -.079 -.074 -.063 -.068 -.078 -.095 -.223 -.220 -.170
S.133 .114 .074 .01 o -.01 -.11i -.182 -.210 -.13 -.104 -.084 -.075 -.061 -.071 -.083 -.110 -.222 -.222 -.181
.3 .115 .0 .057 0 -. -.132 -.193 -.204 -.132 -.11 -.09 -.084 -.063 -.076 -.093 -.128 -.208 -.210 -.195
S .102 .084 .04o -.010 -.074 -.133 -.200 -.189 -.129 -.125 -.110 -.092 -.060 -.082 -.105 -.131 -.187 -.188 -.204
6.22 .092 .075 .042 -.015 -.O 3 -.152 -.212 -.169 -.127 -.138 -.12o -.105 -.051 -.087 -.122 -.133 -.166 -.172 -.207
o. .090 .074 .032 -.010 -.093 -.15 -.206 -.151 -.-- -.134 -.14, -.123 -.039 -.096 -.139 -.132 -.134 -.137 -.201
7.11 .08 0 .029 -.027 -.03 -.15 -.18o -.116 -.10 -.147 -.134 -.041 -.107 -.150 -.116 -.115 -.118 -.183
7.5 .0 .068 .020 -.033 -.a09 -.lo3 -.168 -. -. 97 -.107 -.152 -.130 -.034 -.103 -.150 -.095 -.092 -.093 -.162
8.00 .084 .061 .020 -.037 -.102 -.168 -.155 -.092 -.089 -110 -.153 -.136 -.033 -.099 -.132 -.097 -.077 -.078 -.154
.44 .086 .005 .023 -.037 -.107 -.16 -.137 -.08 -.086 -.111 -.138 -131 -.036 -.101 -.130 -.103 -.071 -.073 -.119
8.89 .081 .061 .019 -.040 -.108 -.lo -.109 -.077 -.082 -.107 -.132 -.117 -.049 -.105 -. i -.094 -.071 -.071 -.087
9.33 .092 .00o .024 -.033 -.103 -.163 -.080 -.006 -.070 -.095 -.11 -.110 -.046 -.094 -.*.; : -.080 -.063 -.063 -.075
9.75 .082 .059 .01 -.01 -1-.110 -.159 -.076 -.067 -.070 -.086 -.094 -.111 -.056 -.086 -.077 -.072 -.064 -.064 -.071
10.22 .088 .0o4 .020 -.041 -.11 -.150 -.072 -.006 -.068 -.075 -.076 -.090 -.050 -.074 -.059 -.060 -.067 -.068 -.076
10.o7 .082 .061 .018 -.043 -.113 -.156 -.085 -.072 -.072 -.069 -.070 -.086 -.046 -.062 -.052 -.057 -.068 -.068 -.087
11.33 .072 .054 .012 -.048 -.110 -.152 -.110 -.071 -.066 -.0o2 -.062 -.073 -.046 -.052 -.048 -.054 -.064 -.065 -.116
12.(O .078 .054 .010 -.051 -.119 -.142 -.13 -.0o -.058 -.057 -.062 -.062 -.038 .04 2 1-.0 -.046 -.060 -.062 -.135
12.07 .081 .049 .005 -.055 -.100 -.158 -.143 -.058 -.051 -.050 -.057 -.061 -.038 -.037 -.039 -.043 -.01 -.064 -.157
13.33 .0o0 .053 .012 -.038 -.100 -.lo0 -.146 -.o05 -.048 -.043 -.o8 -:- -.041 -.037 -.038 -.042 -.059 -.062 -.164
14.00 .0)1 .065 .023 -.037 -.100 -.16 -.131 -.051 45 -.0 -.054 -. 4. -.033 -.030 -.036 -.040 -.068 -.069 -.164


CONFIDENTIAL






NACA RM A53E01


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CONFIDENTIAL







NACA RM A53E01


A


(a) Side view schlieren photograph.


(b) Vapor-screen photograph
forward station.


(c) Vapor-screen photograph
rearward station.


Firnre 2.- Schlieren and vapor-screen photographs showing vortex
configuration for an inclined body of revolution. a ^ 300,
Mo = 2.0.
A-17693A
A-17693


CONFIDENTIAL


CONFIDENTIAL






NACA RM A53E01


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- -- -Slender-body theory (ref /8) + viscous theory (ref 2)
- Tsien's potential theory (ref /3) + viscous theory (ref 2)
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---o- Experiment, Me L98, Re = 0.5x /0 per inch

Model 2






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Figure 8 Comparison of theoretical and experimental normal-force distri-
bution at various angles of attack.


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NACA RM A53E01 CONFIDENTIAL
Slender-body theory (ref 18) + viscous theory (ref 2)
Tsien's potential theory (ref /3) + viscous theory (ref 2)
----- Viscous theory (ref 2)
Experiment, Mo. =98, Re = 0.5x 06 per inch


Model 2


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Distance from bow of model in diameters, x/d
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Figure 8.-Concluded
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UNIVERSITY OF FLORIDA


3 1262 08106 594 7





UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE UBRARY
P.O. BOX 117011
GAINESVILLE, FL 32611-7011 USA































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