Department of the Navy Bureau of Ships

Contract ~ o n r -220( 12)

W a t e r T u n n e l T e s t s o f

T H E N A C A 6 6 1 - 0 1 2 H Y D R O F O I L I N

N O N C A V I T A T I N G A N D C A V I T A T I N G F L O W S

by

Robert W. Kermeen

Th i s r e s e a r c h was c a r r i e d out under the Bureau of Ships Fundamental Hydromechanics Resea rch P r o g r a m Pro j ec t NS 7 15- 102, David Taylor Model Basin

Reproduction in whole o r in pa r t i s permit ted for any purpose of the United States Government

Hydrodynamics Laboratory California Institute of Technology

Pasadena, California

Repor t No. 4 7 - 7 Februa ry , 1956

Approved: M.S. P l e s se t

ABSTRACT

The resu l t s of force tes t s on the NACA bbl -0 12 hydrofoil in non-

cavitating and cavitating two-dimensional flow a r e presented. The

r e su l t s of wind tunnel tes t s on this profile a r e included for comparison

with the resu l t s of the noncavitating water tunnel experiments. The non-

cavitating experiments were made a t Reynolds numbers f rom 0.89 to 6 1.65 x 10 and the cavitation experiments a t Reynolds numbers of 0.89

6 and 1.18 x 10 .

INTRODUCTION

Two-dimensional hydrodynamic data a r e now available for a

number of hydrofoil shapes. The force coefficients in noncavitating and

cavitating flow have been obtained on simple geometrical shapes such a s

wedges, f lat plates and c i rcu lar a r c hydrofoils, a s well a s conventional

cambered airfoi l shapes. Symmetr ical hydrofoil shapes, such a s those

descr ibed in this report , a r e important both for lifting surfaces and for

nonlifting support s t ru t s and fairings. The requirements for support

s t ru ts , such a s low drag, low cr i t ical cavitation number, and high

strength a r e much the same as for lifting hydrofoils.

The NACA 661-012 hydrofoil was selected a s a representative ex-

ample of a c l a s s of a irfoi l shapes which would be suitable for symmetr i -

c a l hydrofoil design applications where sl.-ength is important. The

NACA 6bl -012 hydrofoil has a thickness to chord rat io of 0. 12 with a

c r i t ica l cavitation .index of approximately 0. 35 a t a n angle of attack of

zero degree, F o r applications where cavitation resis tance is a more

important consideration, a thinner hydrofoil section would be selected.

In addition, this hydrofoil shape was selected to be tested in the

High Speed Water Tunnel a t the Hydrodynamics Laboratory and in the

water tunnel a t the Iowa Institute of Hydraulic Resea rch in o r d e r that

the r e su l t s obtained in the two facil i t ies could be compared.

APPARATUS AND TESTS

Hydrofoil

The hydrofoil model has a 3,30-in. chord and a 2.90-in. span.

The model was made of s ta inless steel. The NACA 661 -0 12 hydrofoil

i s a symmet r i ca l profile with a maximum thickness of 12 percent of the

chord. Ordinates of the hydrofoil a r e given in Table I and a photograph

of the model in Fig. 1.

Water Tunnel and T e s t Procedure

The hydrofoil model was tes ted in the two-dimensional working

sect ion of the High Speed Water Tunnel. The model was mounted on a

5. 0 -in, d i ame te r c i r cu l a r disk a t tached to the force balance spindle and

s e t flush in the working section wall. The re was a na r row gap of ap -

proximately 0.002 in. between the f r e e end of the model and the working

sect ion wall. Detai ls of the tes t setup, fo rce balance, tes t procedure ,

and data reduction methods a r e given in Refs. 1 and 2.

T e s t s

The section lift, d rag , and quar te r -chord pitching moment were

m e a s u r e d for noncavitating flow a t wate r velocit ies of 3 0 , 40, 50 and 60 6

fps , which gave Reynolds numbers f r o m 0.89 x lo6 to 1.65 x 10 . Lift,

drag, and qua r t e r - cho rd pitching moment were measu red for cavitating

flow a t a velocity of 40 fps for hydrofoil a t tack angles f r o m ze ro to 7

deg rees and a t 30 fps for angles of at tack g rea t e r than 7 degrees . Be-

cause the hydrofoil i s symmetr ica l , the cavitating force runs were made

o r ~ l y a t positive a t tack angles. In each cavitation force run the angle of

a t tack of the model and the velocity were held constant and the cavitation

number var ied f r o m noncavitating flow to full cavity flow. Photographs

were taken of the cavitat ing hydrofoil a t each tes t point.

Fig. 1 - The NACA 661 -0 12 hydrofoil.

TABLE I

ORDINATES OF THE NACA 66 -0 12 HYDROFOIL

Ordinate Ordinate (Upper and (upper and

Station Lower Surface) Station Lower Surface) 70 Chord % Chord 310 Chord 70 Chord

Leading Edge Radius: 0 . 9 5 2 % Chord

Data Reduction

The test data were reduced to dimensionless coefficients a s

follows:

Lift coefficient, CL = I Lift

p/2 V'A

7 Drag coefficient, C,, - Drag

p/2 V'A

Quarter-chord pitching moment, Pitching Moment

P -P Cavitation number, K = 0 v

1

v c Reynolds number, Re = - v

where:

V = velocity of undisturbed flow, ft/sec

p = density of water a t the temperature of the run , slugs/ft 3

A = plan a r e a of the hydrofoil (chord X span), ft 2

c = chord of hydrofoil, ft

P = pressure of undisturbed flow, lb/ft 2

0

PV = vapor p res su re of f r e sh water a t the temperature of the

run, 1b/ft 2

v = kinematic viscosity of f resh water at the temperature of

the run, ftL/sec.

A number of correct ions were applied to the measured data. The

ta re forces on the spindle disk were measured by mounting the hydro-

foil f rom the opposite wall with a small gap between the end of the

hydrofoil and the spindle disk. The force runs were repeated with this

setup and the fo rces measured on the mounting disk alone. The lift and

pitching moment disk ta re correct ions were negligible, hence only the

d r a g cor rec t ion was applied to the data. The data for fully wetted flow

were co r r ec t ed for tunnel interference effects. The methods of data

cor rec t ion a r e descr ibed in deta i l in Ref. 1.

RESULTS

Curves of lift and quart .er-chord pitching moment coefficients a s

functions of angle of at tack for noncavitating flow a r e shown in Fig. 2.

F igu re 3 i s a polar d iagram giving lift and drag coefficients for non-

cavitating flow. The r e su l t s of wind tunnel t e s t s of thi s profile made

with the Langley two -dimensional, low- turbulence wind tunnel a r e shown

in F igs . 2 and 3 for comparison.3 The wind tunnel data shown a r e for a 6

Reynolds number of 3 .0 x 10 . Figure 4 shows lift coefficient a s a func - tion of angle of a t tack for s eve ra l cavitation numbers f r o m fully wetted

to full cavity flow. The cavitation diagram, Fig. 5, shows the extent

of the cavitation on the hydrofoil a s a function of angle of at tack and

cavitation number. F igu re 7 shows lift coefficient data a s a function

of cavitation number a t constant angles of at tack. Drag coefficient i s

shown a s a function of cavitation number a t constant angles of at tack in

F ig . 8. F igure 9 i s a cavitation polar d iagram showing lift and d r a g

coefficients for a range of cavitation numbers . F igure 10 shows the

pitching moment coefficient about the qua r t e r - cho rd point a s a function

of angle of a t tack and cavitation number . ~ i f t / d r a ~ ra t io i s shown in

Fig. 1 1 a s a function of cavitation number and angle of at tack.

DISCUSSION OF RESULTS

Noncavitating Flow

Lift coefficient a s a fu.nction of angle of a t tack for noncavitating

flow i s shown in Fig. 2. The r e su l t s of wind tunnel t es t s of the s a m e

profi le3 a r e shown for comparison. The presen t t e s t s we re made a t 6

Reynolds numbers f r o m 0.89 to 1. 65 x 10 . The wind tunnel data a r e 6

for a Reynolds number of 3.0 x 10 . There a r e considerable

differences in Fig . 2 between the water tunnel and the wind tunnel r e - su l t s both in the slope of the lift coefficient curve and in the maximum

lift coefficient. The lift coefficient, however, can easi ly change by

this amount over a range of Reynolds numbers f r o m one to three million.

Data were not available for the NACA 661 -0 12 profile for Reynolds num- 6

b e r s l e s s than 3.0 x 10 ; however, t es t s of a s imi l a r symmet r i ca l 4 NACA 641 -0 12 a i r foi l made a t Reynolds numbers f r o m 0 . 7 to

9 .0 x lo6 show changes in lift coefficient with Reynolds number of the

s a m e magnitude a s the differences between the water tunnel and wind

tunnel r e s u l t s of Fig . 2. The NACA 641-012 ai r foi l has a thickness of

12 percen t of the chord and a profile very s imi l a r to that of the NACA

661 -01 2 profile except that the maximum thickness o c c u r s a t approxi-

mate ly the 40 percent chord point on the f o r m e r and a t the 45 percent

chord point on the la t t e r . The min imum p r e s s u r e coefficient o c c u r s at

the 40 percent chord point on the NACA 64 -0 12 and a t the 60 percent

chord point on the NACA 66 -0 12 profile. The slope of the lift coeffi-

c ient curve for the NACA 64 -0 12 profile i nc rea sed f r o m 0.099 per 6

degree a t a Reynolds number of I . 0 x 10 to 0. 110 per degree a t a b

Reynolds number of 3.0 x 10 . In Fig. 2 the slope s f the lift coefficient

for the wate r tunnel data i s 0.084 per degree a t a Reynolds number of 4

1. 18 x 10 and 0. 105 per degree for the wind tunnel data a t a Reynolds 6

number of 3.0 x k O . The maximum lift coefficient fo r the NACA

641 -0 12 ai r foi l i nc rea sed f r o m 0.887 a t a Reynolds number of 1.0 x 10 6

6 to 1.430 a t a Reynolds number of 3.0 x 10 o r a change of 0.543. The

maximum lift coefficient fo r the NACA 661 -0 12 profile was 0. 747 a t a 6

Reynolds number of I . 18 x 10 for the water tunnel t e s t s and. 1.222 a t 6

a Reynolds number of 3.0 x 10 for the wind tunnel t e s t s , o r a n i nc rease

of 0.475.

The qua r t e r -chord pitching moment coefficients a r e a l so shown i n

F ig . 2. The pitching moment coefficient does not change appreciably

with Reynolds number . The curve of pitching moment coefficient f r o m 3 the wind tunnel t e s t s is quite different f r o m that obtained in the wate r

tunnel exper iments . Since the hydrofoil is symmetr ica l , i t s e e m s

reasonable that the fo rce and moment coefficient cu rves should be s y m -

m e t r i c a l about z e r o degree a t tack angle. The pitching moment

coefficients about the quarter - chord point obtained in the water tunnel

tes t s a r e symmetr ical about zero degree and very nearly zero for

angles of attack up to stall.

Figure 3 i s a polar diagram showing lift and drag coefficients for

noncavitating flow. At large attack angles the drag coefficient f rom the

water tunnel tests increases rapidly due to the s tal l occurr ing a t

smal le r attack angles than for the higher Reynolds number wind tunnel

tests. In the low drag range, for lift coefficients less than t 0. 3

corresponding to angle of attack of l e s s than f 3 degrees, the water

tunnel resu l t s , though somewhat higher due to smal le r Reynolds num-

be r s , a r e in good agreement with the wind tunnel resul ts .

The water tunnel resul ts show a slight increase in drag coeffi-

cient with increasing Reynolds number, indicating that a laminar boundary

layer may have existed over a considerable portion of the hydrofoil. The

NACA 66 -012 profile has i ts minimum pressure coefficient occurr ing 1 a t the 60 percent chord point a t zero degree attack angle. At smal l

attack angles the large region of decreasing pressure over the forward

par t of the profile would tend to delay laminar turbulent boundary layer

transition and would cause an increase in d rag coefficient with Reynolds

number due to the laminar turbulent boundary layer transition point

moving forward on the profile a s the velocity is increased.

Cavitating Flow

Lift, drag, and quarter - chord pitching moment were measured for

the NACA 661 - 0 12 hydrofoil for a range of cavitation numbers f rom

fully wetted to full cavity flow a t angles of attack of 0 to 10 degrees.

The tes t s were made a t a tunnel velocity of 40 fps for angles of attack

up to 7 degrees and a t 30 fps for attack angles grea ter than 7 degrees.

Because the hydrofoil i s symmetrical, the data a r e presented only for

positive attack angles. No tunnel interference correct ions have been

applied to the data f rom the cavitation force runs. The cavitation num-

ber in all figures i s based on the vapor pressure of water.

Figure 4 shows curves of lift coefficient a s a function of angle of

attack a t constant cavitation numbers. The curve marked K > 3 . 0 i s

ANGLE OF ATTACK I N DEGREES, a CAVITATION NUMBER, K

Fig . 4 - Lift coefficient as a function of angle of a t tack and cavitat ion number for the NACA 661-0 12 hydrofoil, These c u r v e s a r e c r o s s plots of the da ta curves , Fig . 7.

F ig . 5 - Cavitation d i ag ram f o r the NACA 66 1-0 12 hydrofoil.

fo r noncavitating flow. F o r angles of attack grea ter than 3 degrees

there i s an increase in lift smal l amounts of cavitation on the hydrofoil.

The cavitation diagram, Fig. 5, shows the extent of cavitation on the

hydrofoil a s a function of angle of attack and cavitation number. At

angles of attack up to 3 degrees, the cavitation first appears a t approxi-

mately the 65 percent chord point, as shown by the lower, broken line.

At angles of attack grea ter than 3 degrees, cavitation began near the

leading edge of the hydrofoil. In the region between three and four

degrees attack angle, the position of the cavitation on the hydrofoil

became unstable and incipient cavitation might occur either at the

leading edge o r a t the 60 percent chord point, After cavitation had been

established on the hydrofoil a t these attack angles, i t would often

fluctuate between the leading edge and the 60 percent chord point o r

the cavitation would separate into long thin individual cavities attached

a t the leading edge. F igure 6 shows examples of the three patterns of

cavitation on the NACA 6 b l -0 12 hydrofoil a t a n angle of attack of 3

degrees. In Fig. 6a there is a continuous cavity attached a t the lead-

ing edge of the hydrofoil. As the cavitation number is reduced, Figs .

6b and 6c, the cavity spl i ts into a number of long individual cavities

separated by portions of fully wetted flow. At s t i l l lower cavitation

numbers the cavitation disappears f rom the leading edge and begins

on the after portion of the hydrofoil, Fig. 6d, e , and f . At the attack

angles where the position of the cavitation on the hydrofoil is not

stable, the presence of the tunnel walls causes the cavitation to remain

attached near the leading edge of the hydrofoil a t the walls.

The dashed lines in Fig. 5, noted a s X1 = 0.25 c to 1.00 c show

the extent of the cavitation on the upper surface of the hydrofoil. At

X I = 1.00 c the downstream end, o r closure, of the cavity just extends

to the trail ing edge of the model. The region to the left of the

X I = 1.00 c line gives the cavitation number for which the hydrofoil i s

in full cavity flow with the cavity extending downstream f r o m the hydro-

foil.

Cavitation occurred on the lower, p res su re surface of the hydro-

foils for angles of attack up to 8 degrees. The cavitation number a t

which the cavitation begins on the lower surface i s indicated in Fig. 5.

At angles of attack grea ter than 3 degrees, cavitation did not being on

the lower surface until a long, full cavity covered the entire upper s u r -

face.

Figure 7 shows lift coefficient a s a function of cavitation number

a t constant angle of attack. Each curve in Fig. 7 represents the resul ts

of one test run, and the data points a r e the measured values of the lift

coefficient. Figure 4 is a c ross plot of Fig. 7. The dashed line in Fig.

7 shows the cavitation number for incipient cavitation on the upper sur-

face. As noted in Fig. 4, there i s an increase in lift coefficient a t

constant angle of attack when cavitation f i r s t begins near the leading edge

of the hydrofoil. F o r small angles of attack where the cavitation begins

nearly a t the mid-chord point, the lift coefficient decreases a s soon a s

the hydrofoil begins to cavitate.

Figure 8 shows drag coefficient a s a function of cavitation number

a t constant angle of attack. Each curve in Fig. 8 i s for the same test

run a s the data for the corresponding angle of attack in Fig. 7. The drag

coefficient increases a s soon a s cavitation begins on the hydrofoil,

reaches a maximum when the cavitation extends approximately to the

trailing edge and then decreases a s the cavitation number is reduced

fur the r . Lift and drag coefficients a t constant cavitation numbers a r e s h o w

in the cavitation polar diagram, Fig. 9. The dashed lines in Fig. 9 a r e

lines of constant angle of attack. Figure 9, like Fig. 4, was compiled

f rom many test runs in which the velocity and angle of attack were held

constant and the cavitation number varied from noncavitating to fully

cavitating flow. The drag coefficient has been plotted to a scale ten

times that of the lift coefficient in Fig. 9.

Figure 10 shows curves of quarter-chord pitching moment as a

function of angle of attack a t constant cavitation number. It should be

noted that the moment coefficient in Fig. 10 has been plotted to a much

expanded scale compared with that for noncavitating flow, Fig. 2, in

order to show the changes more clearly. F o r noncavitating flow with

K* 3.0 the pitching moment i s slightly positive, o r nose up. When

Fig. 8 - Drag coefficient as a function of cavitation number at constant angle of attack for the NACA 661 -0 12 hydrofoil. Each angle of attack represents one test run.

DRAG COEFFICIENT, CD

Fig. 9 - Polar diagram for cavitating and noncavitating flow for the NACA 661 -012 hydrofoil. These curves are cross plots of the data curves, Fig. 8.

NACA 66[ - 0 12

ANGLE OF ATTACK I N DEGREES, a

Fig. 10 - Quarter-chord moment coefficient as a function of angle of attack and cavitation number for the NACA 661 -012 hydrofoil.

cavitation begins a t higher attack angles the pitching moment becomes

negative, then increases toward the noncavitating value a s the cavita-

tion number i s decreased, and finally becomes more positive a t

cavitation numSer s l e s s than 0. 3, The pitching moment i s zero for

attack angles l e s s than two degrees for a l l cavitation numbers.

Figure 11 shows the lift/drag ratio a s a function of cavitation

number. Each curve in this figure i s for a constant angle of attack. The

horizontal portions of the curves in Fig. 1 1 a r e regions of zero cavita-

tion. When cavitation begins there i s a rapid decrease in lift/drag rat io

even though Figs. 4 and 7 show an increase in lift with sma l l amounts of

cavitation a t angles of attack grea ter than 3 degrees. As cavitation be-

gins, the increase in drag i s proportionately grea ter than the increase

in lift. As the cavitation number i s reduced to give a large cavity on

the hydrofoil, the drag coefficient reaches a maximum and then de-

c reases . The lift coefficient, however, decreases rapidly with cavita-

tion number and the reduction in drag coefficient mere ly causes a reduc-

tion in the slope of the lift/drag ratio curves.

REFERENCES

1. Kermeen, Robert W . , "Water Tunnel T e s t s of NACA 4412 and Walchne r Profile 7 Hydrofoils in Noncavitating and Cavi - tating Flows", California Institute of Technology, Hydro- dynamics Laboratory Report No. 47-5, January 1956.

2. Hotz, G. M. and McGraw, J. T. , "The High Speed Water Tunnel Three -Component Force Balance If, California Institute of Technology, Hydrodyriamics Laboratory Report No. 47- 1, January 1955.

3 . Abbot, I . H . , von Doerihoff, A . E . , and Stivers, L.S. J r . , ' 'Summary of Airfoil Data", NACA Report No. 824, 1945.

4. Lof tin, L. K. and Smith, H. A. , '*Aerodynamic Character is t ics of 15 NACA Airfoil Section a t Seven Reynolds Numbers f rom 0.7 x l o 6 to 9 . 0 x log", NACA Technical Note 1945, October 1949.

APPEND] X

DATA TABLES

I. Section Characteristics of the NACA 601 -012 tfvdrofoil In Non- cavitating Flow (lift and drag corrected for tunnel interference effects).

1 V = I I . O f p s Re = 0.893 x lo6 Y = 41.2 Ips R e = 1 . 185 x lo6 I V = 49.5 fps Re = 1 . 4 2 5 ~ 10 6

V = 57.4 fps

0 a C L

0 -0,007 1 .090 2 . I85 3 .247 4 .338 5 ,434

650 x lo6

CF.4 . oou -0,001 -0.002

,004 '004 .004

11. F o r c e Character is t ics of the NACA 6bl-012 Hydrofoil in Cavitating Flow (datn not cor rec ted for tunnel interference effects; cavitation number baeed on vapor pressure).

V = 40 fps a = - l o V = 40 fps V = 40 fps

K

2.984 2.081 1.615 1.106 0.844

.580

.336

.220 . 174

. I 3 9 ,115 .LO2 .089 ,092 ,089 ,387

1. 119 2.984

11. (cont . ) Force Ctlaracteristics of the N.4CA 661-OlZ HydrofoiI in Cavitating Flow (data not corrected for tunnel interference effects; cavitation number based on vapor pressure).

2.984 . 193 .DO98 -0.002 2.955 .437 . Dl48 . 0 0 5 5 .198 .674 . 0 2 I 8 .010

i . 2 0 2 . 4 1 6 , 0 1 6 0 , 0 0 5 1 .122 .448 , 0 1 7 6 . 0 0 5 0 5 0 3 , 0 1 1 1 . 0 0 8 .451 . 01 80 , 0 0 5 . 0'597 - 0 1 2

. 0457 . 0 12. . 05,tL . 008 .0179 . 0 3 0 . 534 . 252 . 104 .047 . a 1 7 4 . 0 3 0

. 0 9 8 . 0 4 8 .0171 .032 . 6 1 2 . 4 3 2 .0738 - 0 . 0 4 7

. 0 8 3 , 0 4 4 .0186 .(I36 . 0 4 0 . 0 3 8 I , 0 1 6 .086 .0500 . 024

. l l Z .046 . D l 9 7 .03! 1 . 160 . 183 , 0 1 0 3 .OZO . 142 .039 .O284 .016 . 189 . a 1 0 3 .007 , 0 4 3 1 -0 .003 . 1055 -0 .073

. O l 7 3 . 0 0 5

. 0 1 37 . 0 0 4

2 .973 . 2 6 7 . D l 0 2 . 0 0 3 2.955 . 531 . 0 1 4 9 .006 5 . 323 . 756 . (1522 . 010 2 , 0 4 8 . 522 . 0 1 6 b . O O i 3.680 .750 .051R .009 1 . 739 . 520 .0112 . 0 0 6 3.614 .768 . 0 4 3 1 .Of16 1 . 6 1 7 . 5 2 0 .OZO2 .OO6 3 . 195 . 3 5 5 . 0448 . 009

, 2 6 3 .0108 .004 .266 .0109 . 0 0 3 . 2 9 5 .0111 -0.001

. 384 . Z l b .0267 -0.015

. 3 4 0 . 176 .0232 -0 .009

. 2 3 8 . 135 . 0 2 0 0 .004 . 191 . 103 . 0 2 0 2 .016

. I 4 7 .084 .0194 .016

. 123 .077 . 0 1 8 5 . 0 1 5 1 1 0 . 0 6 7 . 0 1 8 6 . 0 1 5 . 104 . 0 7 2 . 0 1 8 5 .(I16 . 6 1 7 . 2 4 6 , 0 1 0 4 . 0 0 7

1.092 .257 .0097 . 0 0 5 2 .925 . 2 5 8 . 0 1 0 l .(I05

V = 4 0 Ips a 1 4 O

K <3 1) (; M

3. 049 . 353 .0111 . 0 0 5 2.080 .347 . 0 1 0 5 . 0 0 5 1 .662 .3i?. .004 1 . 131 . 349 . 0 0 9 9 .004 0 . 846 . 358 .OI 1 3 , 0 0 5

. 8 1 6 .358 .0111 .DO5 - 8 1 9 . 36'1 .0117 . 0 0 5 . 8 5 9 . 3 7 4 . 0 1 2 1 .004 . 758 . 389 . 0124 . 0 0 3 . 70 3 . 397 . 0 1 2 9 .001 . 6 5 6 .410 , 0 1 9 0 -0 .009 . 5 3 9 . 2 7 9 . 0 4 0 2 - 0 . 0 3 5 . 4 3 5 . 231 .0371 -0 .019 . 1314 . 1 5 i .0329 - 0 . 0 0 3 . 2 1 9 . 0 6 7 . 0 2 8 2 .GI3 . 133 . 0 4 7 . 0 2 1 6 . 0 1 5 . 132 . 0 4 6 . 0 2 1 5 .014 . I22 . 0 6 1 .0204 . 0 1 5 . I 0 7 .080 .0171 . O l i .011 . 3 9 3 . 0 3 6 0 -0.021

I. i 0 5 .341 . 0 l 6 L .004 2. 996 . 344 .0101 .004

. 5 6 0 .0261 . 0 0 7 . 562 . 0281 .005 0 .950 .600 . 040.1 --0.007

, 6 7 5 , 5 1 3 0 7 1 4 -0 .056 . 5 7 5 , 3 3 5 . 0662 -0. 012 :138 . 2 6 9 . 0 5 9 7 - 0 . 0 1 8 . 6 . 104 . 0 4 5 5 . 0 1 1 . 2fr 1 . 0 ? 6 .O-10.1 , 0 1 6 . 2 3 2 .066 . 0 3 7 1 . 0 I B . 1113 .052 . 0 3 3 6 . O I L . I70 . 0 5 0 .07!8 .Ol6 . If14 .050 .0314 . O I / J . 162 . 0 .I 'I .0311 . @ I f > . 152 . 0.19 . 0 3 0 5 . O l 7 . 6 . OH4 .0427 .GI6

1 . 129 , 5 5 8 . 0 2 7 5 .C05 2 .968 . 522 . 11144 . 0 0 5

V = 1 0 fps a - 7O

K (; 1 . c; 1) C: M

2 .930 . 6 0 9 .0171 .007 2.353 .6ui3 . OZL? .006 2. I80 .611 .OZ48 , 0 0 7 1 .991 .615 .02711 . 0 0 8 1.61 I . 6 1 6 .029'1 .009 I . 684 . 6 l S . 030'1 . O!l9 1 . 4 5 3 . b28 . 0 3 4 8 .f?09 I . 336 . 6 35 . 0 3 7 0 . @ O H 1 . 227 . 6 37 . 0 3 9 3 .OOb 1 . 100 .678 . 0509 -0. 009 0. 762 . 564 . 0874 -0 .067

. 563 . 391 . 0 7 8 I -0 .042 , 4 1 0 .232 . 0 6 4 6 - 0 , 0 1 2 . 332 . 120 0 5 i 7 . 0 1 5 . 2 8 2 . 0 7 6 . 0469 . 022 . 2 3 5 . 0 69 , 0.i32 . 0 2 0 . 185 , 0 6 0 . 0 3 8 5 .017 . 184 ' 0 5 7 . 0386 . 017 . 180 . 0 5 8 ,05611 .017 . I80 .I156 . 0 3 6 3 . 0 1 7 , 340 . :44 . 0 5 3 7 .011

I I . 6 8 7 . 0 5 3 9 0.00'1 I . 675 . 6 1 7 . 0301 .DO? 2 .955 .60L . 017i . 0 0 7

2 .465 .764 . 0567 . 010 .759 .0543 .010

Z.Oi3 . 758 .0574 .010 1 .808 . 770 , 0 6 3 4 .008 1 . 6 9 9 . 770 .0651 .OOh I . 605 . 783 .0700 .002 1.499 .785 , 0 7 5 4 -0 .003 1 .427 , 7 9 0 . 0 5 1 6 - 0 . 0 1 0 1 . 285 . 7 8 5 . 0991 -0 .025 1 . 105 . 7 4 7 . 12.12 -0.1173 0 .870 .57Y . 1286 -0.080

. 7 1 0 .517 . I I75 -0.060 . 56'7 , 3 7 0 .0992 -0.0'50 . 27 3 . OM , 0 5 1 7. . O Z 5 , 2 0 2 . 0 5 0 . 0 4 2 3 , 1127 . 8 l O . 587 . 1241 -0 .Oih

2. 72.7 . I 4 8 . 04'78 . 010 5 . 287 .740 . 0509 . 01 1

\: - 7 l fps a : lo0

r( 0 I c; 1.) c: M

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DISTRIBUTION LIST FOR TECHNICAL REPORTS ISSUED UNDER

CONTRACT NONR -220( 12)

I t e m A d d r e s s - No. Cop ie s

1 Commanding Officer and Di rec to r , David Tay lo r Model Bas in , Washington 7, D. C. , Attn: Code 580 54

2 Chief of Naval R e s e a r c h , Office of Naval R e s e a r c h , Depa r tmen t of the Navy, Washington 25, D. C, , Attn: Mechanics Branch (Code 438)

3 Commanding Off icer , Branch Office, Office of Naval R e s e a r c h , 495 S u m m e r St. , Boston 10, M a s s ,

4 Commanding Officer , Branch Office, Office of Naval R e s e a r c h , 346 Broadway, New York 13, N, Y.

5 Commanding Off icer , Branch Office, Office of Naval R e s e a r c h , T h e John C r e r a r L i b r a r y Bldg . , 10th F l o o r , 86 E. Randolph St . , Chicago 1, Ill,

6 Commanding Off icer , B r a n c h Office, Office of Naval R e s e a r c h , 1000 G e a r y St. , San F r a n c i s c o 9, Calif.

7 Commanding Off icer , Branch Office, Office of Naval R e s e a r c h , 1030 E. G r e e n S t r ee t , Pasadena 1, Calif.

8 Asst . Naval Attache f o r Resea rch , Office of Naval R e s e a r c h , A m e r i c a n Embassy , London, England, Navy 100, F, P.O. New York , N. Y.

9 D i r e c t o r , Naval Re s e a r c h Labora to ry , Office of Naval R e s e a r c h , Washington 25, D. C , Attn: L i b r a r i a n

10 Bureau of Aeronaut ics , Dept. of the Navy, Washington 25, D. C. , Attn: A e r o a n d Hydro Branch (Code AD3)

11 Bureau of Ordnance , Dept, of the Navy, Washington 25, D. C . , Attn: Code Re9

Code Re6 Code Re3

12 Commander , U. S . Naval Ordnance Labora tory , U . S. Navy Bureau of Ordnance, White Oak, S i lve r Spr ing 19, Maryland 2

13 Underwater Ordnance Dept . , Naval Ordnance T e s t Station, 3202 E. Footh i l l Blvd. , Pasadena , Calif. Attn: Pasadena Annex L i b r a r y (Code P 5507) 3

14 Chief , Bureau of Ships, Dept. of the Navy, Washington 25, D. C . Attn: Techn ica l L i b r a r y (Code 312) f o r addi t ional d i s t r ibu t ion to: 10

Dis t r ibu t ion I.,ist (continued)

I t e m A d d r e s s - (Bureau of Ships dis t r ibut ion) R e s e a r c h a n d D e v e l o p ~ n ~ t ~ t (Code 300) Ship D e s i g n (Code 410) P r e l i m i n a r y Design (Code 420) Hull. Design (Code 440) Hull Scientific (Cocle 442) P r o p e l l e r Design (Code 554)

Mr. R. II, Kent, Ballistic R e s e a r c h Labora to r i e s , Dept. of the A r m y , Aberdeen P r o v i ~ ~ g Ground, Maryland 1

Di rec to r of R e s e a r c h , National Advisory Comtni t tee for Aeronaut ics , 1512 H S t r ee t , N. W. , Washington 25, D. C. 1

Direc to r , Langley Aeronaut ica l Lab., National Advisory Commi t t ee fo r Aeronaut ics , Langley F ie ld , Virginia 1

Commander , Naval Ordnance T e s t Station, Inyokern, China Lake, Calif., Attn: L i b r a r y (Code 5507) 1

Dr. K. S , M. Davidson, Expe r imen ta l Towing Tank, Stevens Inst i tute of Technology, Hoboken, N. J. 1

D r . J. H. McMillen, National Science Foundation, 1520 H S t r ee t , N. W., Washington 25, D. C. 1

Dr. A. Mil l e r , Bureau of Ordnance (Code Re3d) Navy Dept. Washington 25, D.C. I

Dr . H. Rouse , Iowa Inst i tute of Hydraul ic R e s e a r c h , State Univers i ty of Iowa, Iowa City, Iowa 1

Dr . R.G. F o l s o m , Di rec to r , Engineering R e s e a r c h Institute, Univers i ty of Michigan, E a s t Engineering Bldg. Ann Arbor , Michigan 1

Dr . V.L. S t r e e t e r , Engineering Dept., Universi ty of Michigan, Ann Arbor , Michigan 1

Dr . G.F. Wisl icenus, Pennsylvania State Universi ty , Ordnance R e s e a r c h Labora tory , Univers i ty Park, Pa. I

Dr. A. T, Ippen, Dept. of Civi l and San i t a ry Engineering, Massachuse t t s Inst i tute of Technology, Cambr idge 39, Mass . 1

Dr . L. G. Straub , St. Anthony F a l l s Hydraul ic Labora tory , Univers i ty of Minnesota , Minneapolis 14, Minn. 1

Prof . K. E. Schoenherr , Universi ty of Notre Dame, College of Engineering, Notre Dame, Indiana 1

D i r e c t o r , Ordnance R e s e a r c h Labora tory , Pennsylvania State Universi ty , Univers i ty P a r k , Pa. 1

Dis t r ibu t ion L i s t (continued)

Item A d d r c s s - Societ,y of Naval Arch i t ec t s and Mar ine Eng inee r s 74 Tr in i ty P lace , New York 6, N. Y.

P ro f . J. K. Vennard, St,anford Universi ty , Dept. of Civ i l Engineering, Stanford, Cal i fornia 1

Prof , 3. L. Hooper, Worces te r Polytechnic Inst i tute , Alden f iydraul ic Labora to ry , Worces t e r 6, Mass . 1

Prof . J. M. Robertson, Dept. of Theore t i ca l and Applied Mechanics , Universi ty of Il l inois, Urbana, Ill. 1

Dr. A.B. Kinzel, P re s iden t , Union Carb ide and Carbon R e s e a r c h Lab. , Inc., 30 E. 42nd St., New York, N. Y, 1

Goodyear A i r c r a f t Gorp., Akron 15, Ohio, Attn: Secur i ty Off icer

Prof . H.R. Henry, Hydraul ics Labora tory , Michigan State College, E a s t Lansing, Michigan 1

B r i t i s h Jo in t S e r v i c e s Mission, Navy Staff, Via: David Tay lo r Model Bas in , Code 580, Navy Depar tment , Washington 7, D. C. 9

Commander , Submar ine Development Group TWO, Box 70, U. S. Naval Submar ine Base , New London, Conn. 1

Commanding Officer and Di rec to r , U. S. Navy Engineer ing Expe r imen t Station, Annapolis, Maryland 1

L i b r a r y of Congres s , Washington 25, D. C, , Attn: ASTSA 1

Dr. P. R. Garabedian, Stanford Universi ty , Applied Mathemat i c s a n d Sta t i s t i c s Labora tory , Stanford, Cal i forn ia 1

A r m e d S e r v i c e s Techrlical Information Agency, Knott Building, Dayton, Ohio

M r . J . G. Bake r , Baker Manufacturing Company, Evansvi l le , Wiscons in

M r . T . M . Buerman , Gibbs a n d Cox, Inc., 21 Wes t S t . , New York 6, New York 1

Dynamic Developments , Inc. , St. Mark ' s Lane, Is l ip , Long Is land, New York, Attn: Mr . W. P. C a r l , Jr. 1

Hydrodynamics R e s e a r c h Labora to ry , Consolidated- Vultee A i r c r a f t Corpora t ion , San Diego 12, Cal i fornia 1

Distribution L i s t (continued)

I tem Address No. Copies

47 Mr . R. K. Johnston, Miami Shipbuilding Corporation, 615 S. W. Second Avenue, Miami 36, Florida 1

48 Mr . J. D. P i e r son, The Glenn L. Martin Company, Balt imore 3 , Maryland 1

49 Mr . W. R . Ryan, Edo Corporation, College Point 56, Long Island, New York 1

50 Dr. Robert C. Seamans, Radio Corporation of America , Waltham, Massachusetts 1

5 1 Dr . A. G. Strandhagen, Department of Engineering Mechanics, University of Notre Dame, Notre Dame, fnd. 1

52 Dr. H. W, E. Lerbs , Hamburgische Schiffbau-Versuchsanstalt Hamburg 33, Bramfe lders t rasse 164 1

53 Commander, Air Research and Development Command, P. 0, Box 1395, Balt imore, Maryland. Attn: RDTDED 1

54 Avco Manufacturing Gorp. , ~ d v a h c e d Development Div. , 2385 Revere Beach Parkway, Everet t 49, Mass. Atten: Technical Librar ian 1

55 Dr. L. Landweber, Iowa Inst, of Hydraulic Research, State University of Iowa, Iowa City, Ia. 1