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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j _" ......,......:!iiiiii!ili_i

00 / 2 3 4 5 6 7 8

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

I

! _ a ""

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o.io.2o _ _TI_

o.io _I

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Mach number, M

Figure 3.- Variation of total drag coefficient with Mach number..

NACA RMA52BI3 13

.5

M=L2

__ R..'I.OxlO 6 .+. + ++ +........%

.4 _ I_ i/// _" /

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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