naca-rm-a52b13-the effect of bluntness on the drag of spherical-tipped truncated cones of fineness...
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RM A52B13
COPYRESEARCHMEMORANDUM
THE EFFECT OF BLUNTNESS ON THE DRAG OF SPHERICAL-TIPPED
,'l TRUNCATED CONES OF FINENESS RATIO 3 AT
" MACH NUMBERS 1.2 TO 7.4
By Simon C. Sommer and James A. Stark
Ames Aeronautical LaboratoryMoffettField, Calif.
NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS
WASHI NGTON
i April 25, 1952
IS NACA RM A52BI3
_ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
RESEARCH MEMORANDUM
THE EFFECT OF BLUNTNESS ON THE DRAG OF SPHERICAL-TIPPED
TRUNCATED CONES OF FINENESS RATIO 3 AT
MACH NUMBERS 1.2 TO 7.4
By Simon C. Sommer and James A. Stark
SUMMARY
The drag of spherically blunted conical models of fineness ratio 3
was investigated at Mach numbers from 1.2 to 7.4 in the Reynolds number
range from 1.0 × 10 6 to 7.5 x 106. Results of the tests showed thatslightly blunted models had less drag than cones of the same fineness
ratio throughout the Mach number range. At Mach numbers less than 1.5,
drag penalties due to large bluntnesses were moderate but these becamesevere with increasing Mach number.
Wave drag obtained by the method of Munk and Crown, in which the
wave drag is determined by integrating the momentum loss through the head
shock wave, showed that the wave drag and total drag followed the sametrends with increasing bluntness. Wave drag was also estimated by com-
bining the experimental wave drag of a hemisphere with the theoretical
wave drag of a conical afterbody, and this estimate of wave drag is
believed to be adequate for many engineering purposes.
INTRODUCTION
Blunt noses are being considered for some supersonic vehicles for
the purpose of housing guidance equipment. In some cases a high degree
of bluntness is required, and the drag penalty due to this bluntness may
be significant. On the other hand, work done by others indicated that
slightly blunt noses will have less drag than pointed noses of the samefineness ratio. For these two reasons the drag of blunt-nose shapes is
of current interest and therefore an investigation was made in the Ames
supersonic free-flight wind tunnel to determine the influence of blunt-
ness on drag at Mach numbers from 1.2 to 7.4. The models tested weretruncated cones with spherical noses having bluntness ratios of nose
2 NACA RM A52BI3
diameter to base diameter from O to 0.50. All models had a fineness
ratio of length to base diameter of 3-
SYMBOLS
A frontal area of model, square feet
/total dragCD total drag coefficient _ , qA
Z_CD total drag penalty compared to the cone (CDmodel- CDcone_
CDb base drag coefficient _base dra_k qA _2
CDf skin-friction drag coefficient _skin-friction drag_k qA
CDv total drag coefficient based on volume to the two-thirds power
total drag'
qv2---/_)
/wave dra_CD_T wave drag coefficient _ qA
d diameter of the base, feet
dn diameter of the nose, feet
M free-stream Mach number
q free-stream dynamic pressure_ pounds per square foot
R free-stream Reynolds number, based on axial length of model
V volume of model, cubic feet
MODELS
The models tested were truncated circular cones with tangentially
connected spherical nose segments_ as shown in figure l(a). All models
had a fineness ratio of 3, with base diameters and lengths of 0.45 and
1.35 inches, respectively. The models had holes bored in their bases for
aerodynamic stabS. Five different shapes were test_--with nose diam-eZers of__2 percent, 15 percent, 30 percent_ and 50 percent of thebase diameter.
NACA RM A52-BI3 3
The models were constructed of 75-ST aluminum alloy. The maximum
measured dimensional deviations were as follows: nose diameter,
±0.0005 inch; base diameter, ±0.0015 inch; length, ±0.020 inch; and the
half-angle of the conical section, ±0.05 °• For the majority of the
models tested, the deviations were less than half of those given. The
machined and polished surfaces had average peak to trough roughnessesof 20 microinches. In no case was there any correlation between the
scatter of the test results and the dimensional deviations of the models.
TESTS AND EQUIPMENT
These tests were conducted in the Ames supersonic free-flight wind
tunnel (reference l) where models are fired from guns into still air or
upstream into a supersonic air stream. The models were launched from a
smooth-bore 20 mm gun, and were supported in the gun by plastic sabots
(fig. l(b)). Separation of the model from sabot was achieved by amuzzle constriction which retarded the sabot and allowed the model to
proceed in free flight through the test section of the wind tunnel.
Drag coefficient was obtained by recording the time-distance history of
the flight of the model with the aid of a chronograph and four shadow-graph stations at 5-foot intervals along the test section. From these
data, deceleration was computed and converted to drag coefficient.
With no air flow through the wind tunnel, Mach numbers varied from
1.2 to 4.2 depending on the model launching velocity. This condition isreferred to as "air off." Reynolds number varied linearly with Mach
number from 1.0 X 106 to 3.3 × 106, as shown in figure 2. With air flow
established in the wind tunnel, referred to as "air on," the combined
velocities of the model and Mach number 2 air stream, with the reduced
speed of sound in the test section, provided test Math numbersfrom 3.8 to 7.4. In this region of testing, Reynolds number was held
approximately at 4 x 106 by controlling test-section static pressure.
In addition, some models were tested at approximate Reynolds numbersof 3 X 106 and 7-5 X l0s at Mach number 6.
The purpose of this investigation was to obtain drag data near
0° angle of attack. This report includes only the data from models
which had maximum observed angles of attack of less than 3° since larger
angles measurably increased the drag.
Since there are no known systematic errors, the accuracy of the
results is indicated by the repeatability of the data. Examination of
these data shows that repeat firings of similar models under almost
identical conditions of Reynolds number and Mach number yielded results
for which the average deviation from the faired curve was 1 percent and
the maximum deviation was 4 percent.
4 NACA P_ ASP_BI3
RESULTS AND DISCUSSION
Total Drag
Variation of the total drag coefficient with Mach number for each
of the models tested is presented in figure 3- No attempt was made to
join the air-off and air-on data due to differences in Reynolds number,
recovery temperature, and stream turbulence. Variation of drag coeffi-
cient with Mach number for all models is similar 3 in that the drag
coefficient continually decreased with increasing Mach number. There is3however 3 a tendency for the blunter models to show less decrease in drag
coefficient withincreasing Mach number.
These data have been cross-plotted in figure 4 to show the effect
of bluntness on tolal drag coefficient for various Mach numbers. The
nose bluntness for minimum drag shown by each curve decreases with
increasing Mach number. This is shown by the dashed curve. At Mach
number 1.2 the bluntness with minimum drag is 28 percent as compared to
ll percent at Mach number 7- At Mach numbers less than 1.53 drag penal-
ties for models with bluntnesses approaching 50 percent are moderate but
grow large with increasing Mach number. As Mach number becomes greater
than 4.5, the drag penalties for large bluntnesses do not increase meas-urablybut nevertheless are severe.
Drag in terms of volume may be important in some design consider-ations. In order to indicate the relative merit of the models in terms
of drag for equal volume s the data of figure 4 have been replotted in
figure 53 where drag coefficient is referred to volume to the two-thlrdspower. These curves show that moderate and even large bluntnesses (the
degree of bluntness depending on Mach number) may be used to decrease thedrag for equal volume.
Wave Drag
The variation of the total drag with model bluntness is believed to
result primarily from the variation of the wave drag of the models and to
be essentially independent of the base drag and skin-friction drag.
In order to show this, the wave drag of the blunt models was estimatedfrom the experiment by assuming the combined base drag and skin-friction
drag independent of bluntness and these results were compared to wave
drag determined by the method of Munk and Crown (reference 2). In the
estimation of the wave drag, the base drag and skin-friction drag used
were those of the cone, and were obtained by subtracting the theoreticalwave drag of the cone (reference3) from the experimental total drag of
the cone at each Mach number. These values of combined base drag and
NACA RM A52B13 5
skin-friction drag were then subtracted from the total drag of the blunt
models to obtain the wave drag of each model. The results are shown by
the solid curves in figure 6, where wave drag is plotted as a functionof model bluntness.
In the method of Munk and Crown, the wave drag is computed by summing
up the momentum change through the head shock wave. Since part of the
wave shape is unaccounted for because of the limited field of view in
the shadowgraphs, an approximation suggested by Nucci (reference 4) wasused to estimate the wave drag omitted. This approximation gives the
upper and lower limits of the wave drag omitted. The mean value of theselimits was used in all cases. These results are indicated by the points
in figure 6. The mean disagreement between the results of this methodand the results obtained by assuming base drag and skin-friction drag
independent of bluntness is 7 percent.
Another method of estimating wave drag of the blunt models isby the
addition of the wave drag of a hemisphere to that of a conical afterbody.
Collected data showing the manner in which the wave drag of a hemispherevaries with Mach number is shown in figure 7.1 The wave drag of the hemi-
spherical tip was obtained directly from this figure, and the wave drag
of the conical afterbody was obtained from the tables of reference 3.
The results of this method are presented as the dashed curves in figure 6.
A comparison of the results of this method with the results of the first
two methods shows that although the method of estimating wave drag by
the addition of the wave drag of a hemisphere to that of a conical after-
body appears to overestimate wave drag of the blunt models, it may
nevertheless be adequate for many engineering purposes.
Viscous Effects
The effect of Reynolds number on total drag coefficient was investi-
gated at Mach number 6. In figure 3, data for three Reynolds numbers,
,,,,,, , , ,
iWave drag of a hemisphere at Mach numbers from 1.O_ to 1.40 was esti-
mated from the data of reference _ by calculating the wave drag of the
pointed body and assuming that the drag due to the afterbody and fins
was not a function of nose shape. At Mach numbers of lo_, 2.0, 3.0,
and 3.8, wave drag of a hemisphere was obtained from unpublished pres-sure distributions from the Ames l- by 3-foot supersonic wind tunnel.
Wave drag of a hemisphere at Mach numbers of 3.0, 4._, 6.0, and 8.0 were
estimated from total drag measurements of spheres (reference 6) by sub-
tracting ?0 percent of the maximum possible base drag and neglecting
skin-friction drag. The possible error introduced by estimating the
wave drag of the pointed body of reference _ and the base drag of the
s_here is believed to be no greater than ±4 percent.
6 NACA RM A52BI3
3 X i06, 4 X i06, and 7-5 X i06 are included for cones and 50-percentblunt models. For the cones, the drag coefficient increased approximately
l0 percent with increasing Reynolds number. For the 50-percent bluntmodels little or no change in drag coefficient was measured. The vari-
ation in drag coefficient for the cones was undoubtedly due to changes in
the boundary-layer flow on the models at varying Reynolds numbers, as
shown by the shshowgraphs in figure 8(a). At a Reynolds number of
3 × lO s the clearly defined wake (as indicated by the arrow in the
figure) is associated with laminar flow. At high Reynolds numbers, thediffused wake indicates turbulent flow. Referring to figure 8(b), the
boundary-layer wakes of the 50-percent blunt models appear diffused andturbulent at all Reynolds numbers. Since the wake of the 50-percent
blunt model at Reynolds number of 3 x l0s appears turbulent compared to
the laminar wake of the cone at this condition, it is concluded that
boundary-layer transition occurred at lower Reynolds numbers on the
50-percent blunt model than on the cone.
An interesting flaw phenomenon is illustrated in figure 9 by
shadowgraphs of two cones at Mach number 3.7- The shadowgraph in
figure 9(a) shows a smooth flow condition in contrast to a nonsteadydisturbed flow condition shown in figure 9(b). The disturbed flow seems
to consist of regions of turbulent air moving aft on the model surface,
with pressure waves attached to the leading edges of these regions.Flow disturbance of this nature was observed occasionally on cones at
small angles of attack at Reynolds numbers of 2.5 x lOe and greater.Cones with angles of attack in the order of 3° to 6° consistently haddisturbed flow. This flow condition occurred less often on blunt models
than on cones; and when present on blunt models, was always of slight
intensity. Data for models that exhibited this flow condition were not
included in this paper. The effect of flow disturbance on cones with
angles of attack of less than 3° was to raise the drag about 8 percent.This increase in drag is attributed to increases in base drag as well as
wave drag.
CONCLUSIONS
From this investigation, the following conclusions were drawn for
spherically blunted conical models of fineness ratio 3:
1. Small amounts of spherical bluntness (nose diameters in the
order of 15 percent of base diameter) have been found to be beneficial
for reducing drag.
2. For large spherical bluntnesses (nose diameters in the order of
50 percent of base diameter) drag penalties were moderate at Mach numbers
of less than 1.5, but became severe with increasing Mach number.
NACA RM A52BI3 7
3. Estimation of wave drag by combining experimental values of
wave drag of a hemisphere with wave drag of the conical surfaces is
believed to predict wave drag adequately for many engineering purposes.
Ames Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Moffett Field, Calif.
REFERENCES
i. Seiff, Alvin, James, Carlton S., Canning, Thomas N., and Boissevain,Alfred G.: The Ames Supersonic Free-Flight Wind Tunnel.
NACARMA52A24, 1952.
2. Munk, Max M., and Crown, J. Conrad: The Head Shock Wave. Naval
Ordnance Lab. Memo 9773, 1948.
3. Staff of the Computing Section, Center of Analysis, under the direc-
tion of Zdenek Kopal: Tables of Supersonic Flow Around Cones.
M.I.T. Tech. Rep. No. i, Cambridge, 1947.
4. Nucci, Louis M.: The External-Shock-Drag of Supersonic Inlets HavingSubsonic Entrance Flow. NACARML5OGI4a, 1950.
5- Hart, Roger G.: Flight Investlgation of the Drag of Round-NosedBodies of Revolution at Mach Numbers from 0.6 to 1.5 Using Rocket-
Propelled Test Vehicles. NACARM LSIE25, 1951.
6. Hodges, A. J.: The Drag Coefficient of Very High Velocity Spheres.New Mexico School of Mines, Research and Devel. Div., Socorro,
New Mexico, Oct. 1949.
2S NACA _ A52BI3 9
d =.45 inches
3d o
2_ Cone, Olg blunt
8"87°
0.075 d dio. . __ 7J Z blunt
__825°
015 d die. _j/__ l 15 _ blunt
6.98=
0.30 d die. c_-----_--I I 30 blunt
50 d dio. _ _ _l- I 50 _ blunt0
v _- . " "'J <"
(a) Mode/ geometry.
Figure L- Models tested.
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Moch number, M
Figure 2.- Ronge of Moch numbers ond Reynolds numbers of test.
12 NACARMA52BI3
.5o 0,.°...,o,°,°,
.40 501 _ _'_ o_.s,,o_°,, o.[] R.4 x lO_ olr onZ_ R.Z6x 106, olr on
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Mach number, M
Figure 3.- Variation of total drag coefficient with Mach number..
NACA RMA52BI3 13
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M=L2
__ R..'I.OxlO 6 .+. + ++ +........%
.4 _ I_ i/// _" /
!
7.O
I
0 I0 I0 20 30 40 5 0 _o
Percent bluntness, dn/d xlO0
F/gure 4.-The effect of bluntness on totaldrag coefficient.
14 NACARMA52BI3
.5
@ _ _ R.v.o,,ioe
"•/ _ _ ..._-4..---_[ 1\\
Z'_ 4 x lO b. ___LQ
1
0 I0 I0 20 30 40 50
Percent bluntness, dn/d x I00
Figure 5.-The effect of bluntness on fofol drog coefficient
bosed on volume to the two-thirds power.
From experiment, ossumlng (CDb'bGDf) independentof bluntness
Extropoloted to hemisphereo From experiment, method of references 2 and 4
Estimated by method of this report
to i i•B -- M=2 -- M=3 // i
i J/
.6 ,. /
.4 !/ f
._ 0
_ Lo II IJ - M-a /
.8- M=4.5 / // /
•6 tf ¢*
/
4 I f ;'J
2 ..-._' "2" , I
O0 20 40 60 80 I00 0 20 40 60 80 I00
Percent bluntness, dn/d x I00
Figure 6.-Van'otion of wave drag coefficient with bluntness.
LO,
,, (_,,, <
_ .4
<3 60_ blunt modeb,Unpublished pressure dolei
.2 E] Hemisphere ._ supersonic wind runnel
A Estlmofed from reference L_
Es¢imofed from reference 6
00 I 2 3 4 $ 6 T 8
Moch number, M
Figure T.-Voriofion of wove drog coef'ficienf with Moch number for o hemisphere.
3SNACARMA52BI3 17
ii!iI._ __._ .
R= 3x i0 e
<
]
R= 4 x 106
[. :/
" #
R = 7.5 X I0 e <_A-16704
(a) Cones. (b) The 50--percent blunt models.
7 i!
Figure 8.-- Shadowgraphs of cones and 50-percent blunt models atMach number 6.
/
NACA RM A52BI318
(a) Smooth flow.
(b) Disturbed flow.
Figure 9._ Shadowgraphscomparing smooth fl0w with disturbe_ flow
on cones at Mach nlnnber 3.7, Reynolds number of 3 x 106.
NACA-Langley - 2-14-55 - 75