Section moduli and incipient cavitation diagrams for a number of NACA sections

ARCHIE.

iiagMWIM HYDROMEC AERODYNAMICS

SIM

MECHAM MATHEMAll

by

A. B. Milani and

W. B. Mcirgan

-

Delft-sEctIoN MODULI AND.INCIPIENT

CAVITATION

'DIAGRAMS. FOR A-NUMBER OF NACA

RESEARCH AND DEVELOPMENT.REPORT>

HydrOmechanics Laboratory:

by

A .34 Mi lam - and W

October

1957

SECTION MODULI AND ./NCIPIENT CAVITATION DIAGRAMS.FOR A NUMBER OF NAC A SECTIONS

Morgan:

TABLE OF CONTENTS'

REFERENCES 10.

APPENDIX At Geometric Coefficients for 12

TMB EPH,. NACA 16, 65A

and-66-TNB

Modified Sections

Incipient Cavitation Curves 17 for .NACA 16, 65A,

0000-1.10 40/1.575.

and 66 TMB Modified Sections . ii Page ABSTRACT INTRODUCTION 1 GEOMETRIC COEFFICIENTS _2. INCIPIENT:CAVITATION DIAGRAMS 6

coicosIoNs

₉

Table 1 Table 2

-Table.

3

-LIST OF TABLES

Half-ordinates for Various Geometric Coefficients for Section

Geometric Coefficientsfor Section

Table 4 - Geometric Coefficients for 65A Section

Table

5 -

Geometric Coefficients for

66

(TMB Modified) Section

LIST OF FIGURES

Figure 1 - Coordinate System for a Section

Figure 2 - Pressure 'Distribution on NACA 16-512 Section

Figure

3 -

Incipient Cavitation Curves for NACA 16 Thickness Form with a = 0.8 Mean Line

Figure 4 - Incipient Cavitation Curves for NACA 16 Thickness Form with a = 1.0 Mean Line .

Figure

5 -

Incipient Cavitation Curves for NACA'65A Thickness Form with a = 0.8 Mean Line

Figure 6 - Incipient Cavitation Curves for NACA 65A Thickness Form with a = 1.0 Mean Line

Figure 7 - Incipient Cavitation Curves for a Thickness Form with NACA 66 Nose and Parabolic Tail and with a = 0.8 Mean Line iii Sections TMB EPH 13 NACA 16 14 Page

18

19

20 21 22 NACA 15 NACA 16

LIST OF FIGURES (Con'

Figure 8 - Incipient CatritatiPTIClittei.

WA :0000-1.10 1f0/1.7

Thick-ness, Form 40iith0.--== 0.8 jlettn,'

_,

.

Line

Figure

9 -

Incipient.,CatitatiOn.Nrv0.6.

for NACX,0000-1410;404475

ThicknesFormyith,a_-=

V.

6V

va

A Area of section

CL Lift coefficient

Maximum camber of section

Total head (p0

+ q0).

Moment of inertia about the x0-axii

IYo Moment of inertia about the 70-axis

)e

Section length

Bending moment about x0-axis

xo

My0 Bending moment about y0-axis

Pv Vapor pressure of the fluid

.130 _Static pressure in free stream

p1 Static pressure at a point on the body go Dynamic pressure (1/2

rV2)

Pressure coefficient

scrit Pressure coefficient at inception of cavitation

NOTATION

Maximum thickness of section

Free stream velocity

Perturbation velocity resulting thickness distribution

Perturbation velocity resulting mean, line distribution .

Perturbation velocity resulting angle of attack

from the

from the

NOTATIONS Cont'd.)

Abscissa measured from the leading edge parallel to the.nose-tail line.

Abscissa measured from the centroid parallel

° tb the nose-tail line

Abscissa

of nosewith reference to

axis

'through the centroid

Abscissa

of tail with reference to axis

through the bentroid

Abscissa of point of-maximum thickness with reference to axis: through the

centrad..

Yo Ordinate measured from the centroid

,Y1 .Ordinate of nose with reference tO:axis

through the centrOid

Ordinate of back with reference to

axis

through the centroid.

y3

Ordinate of point of. maximum thickness with reference to axis through the

centroid

p

Density of the fluid

Cr Cavitation number of the section

ABSTRACT

The section moduli for the TIC EPH, NACA

16,

65A and

66

TNB modified sections are given In this report along with incipient cavitation curves for

the NACA

16, 65A, 0000-1.10 40/1.575

sections with a = 1.0 and 0.8 mean lines and the NACA

66 TNB

modified section with an 4 = 0.8 mean line.

INTRODUCTION

In obtaining the maximum stress In a propeller blade or a hydrofoil it is necessary to know the

section modulus. The geometric properties usually

calculated in determining the section modulus are

(1) the area of the section, (2) the Position of the center of gravity and

(3)

the moments of

inertia. In this report these properties have

been combined into coefficients for a number of

sections which have different camber ratios and thickness ratios.

The cavitation number at which cavitation first

begins on the section is known as the incipient

cavitation number. This value is derived theoret-ically by assuming that cavitation begins at the point of minimum pressure on the section. Incipient

cavitation diagrams have la.een prepared for a'

number of.NACASActions operating at shock free entry.; From these diagrams it is possible to

determine the section chord length which i

necessary to prevent cavitation.

GEOMETRIC COEFFICIENTS

The geometric properties were programmed

and computed on the Burroughs E-102 electronic

computer for the TMB EPH, BACA 161 NACA 65A and

NACA 66 TMB modified sections. Table 1 gives the half-ordinates for the sections investigated when

the camber is zero and the thickness ratio is 0.10. The basic equations involved in calculating

the geometric coefficients for a coordinate system

as shown in Figure 1 gives:

for the area. A =

to the nose-tail line

I =

10

dy dx

o o,

for the moment of inertia about an axis .(x0) parallel to ..the note-tail line and through the centrOid

I = _{S S}

y:%y

dx

lcco

o o o

/-and for the moment

of

inertia about the vertical axis .(Y0),through the centroid and perpendicular

S S

x ?dy dx

x

(per cent

Table. 1

..,. 5,70 '2:325....

,.2091

-..7!..,5 2..:834. .

2. 527

...10.0

3.186..:

2 .881-.

. . '

20.0

4.204

3.,887

0.0

)+ ,:,750- ' 4.'- 5i4 . . . .... 4o-,:p

;983:

4.879..-1I-.997

50.0

':4494,

5.000,

-60.0.

..

4.64'..:

4.862 -.

70.0 :

44085

-.4.391'.

80.0[ 3..260,"

3 A99,

90.0

.. .

. . 2

2.170

.098 .'

1 ,.. , . . :9 5 ..,.P. 1

1..480 :

,

''10179.

. _

-100.0

-1 0.000

.

0-.190

-.9-20

5..000

45.§62

4.653

3.110

:

1.877

b3r3'

Is the abscissa --measured from the

tiintrbidr -Parallel to the nose-tall line

Is the ordinate measured from the

: centrbid

.

tion and for the NICA 16 and 65.k sections may be

=

found In Reference 1.

For the IACA 66 TlikB modified

..;section, the equations:, ,solved May be found in

(-1 - 7

Reference 2.

. .

The equations for finding the -streSSeS a

different points on the section

are1*

e:Sre.b).7Ce:qi/La,tiOni.Thave_.bee*,sizaplified:'::tisr

.

numerical'integration and it,is this simplified

'form Which was used in the computations for this

report'.

The 'equations. solved for the Ti413. EP R Sec.

. ,

StreSs at leading edge

Stress at trailing edge'.

-Stress..onTbaOlc,at point of. MaxiMUM.thickriess

Y M

3 :xo

3 yo

xo.

Yo-*References are listed on page 10

Iyo

As shown in Figure 1, the abscissas xl, x2, and x3 and the ordinates yi, 72, and y3 are used

to denote the abscissas and ordinates of the leading edge, trailing edge, and point of maximum back

or-dinate, respectively, when the center of the

coordi-nate system is at the.centroid of the section. The momentslco and My0 are bending moments abaft -the

xo and yo axis.

Also,

it should be noted that in the above,e'quations.a positive stress denotes ten-sion ana a negative str4ss:denotes compresten-sion.

The numerical values for the geometric

proper-ties for the four sections were computed for values

of the camber ratio (f/2) from 0 to 0.05 and for

the thickness ratio (ti,e) from 0.02 to 0.20 where

is the section chord. The results were combined to form non-dimensional coefficients in the form of

Yo _and

_3c0'1

_{3 and are tabulated in Appendix A.}

xo 170

The section area (A) is also tabulated in Appendix A. It should be noted that these values are practically

independent of the shape of the camber line and depend only on the magnitude of the camber ratio. For the range of camber ratios investigated the

results hold for a circular arc, NACA a = 1.0 or

With these coefficients it is a rather easy

operation to.compute an approximate value for the

stresses in a section by using Equations (1) to

₍₃₎₀

It must be noted that the geometric coefficients

must be divided by23 and the units of the stress

will depend upon the unit of

.iand

the bending moments.

INCIPIENT CAVITATION DIAGRAMS

The incipient cavitation number is Used to

determine when a hydrofoil section should be free

from cavitation. This value is theoretically

derived by assuming that cavitation begins at the

point of minimum pressure on the section. Diagrams have been prepared using resultsderived from NACA data3'4'5'.for the NACA 16, 65A and four digit

series -1.10 40/1.575 witha =1,0 and 0.8 mean lines and the NACA 66 TMB modified section with an

a =

0a8.

mean line,all operating at shoCk7free entry. With these diagrams it is possible to obtain the

maximum thickness ratio that the section can have

and still be free from cavitation. These diagrams also include theeffect of the camber ratio (f/Ae ).

The cavitation number can be expressed in terms

of the pressure coefficient on the body. Reference

(3)

describes the pressure coefficient S) at any point

on the body as

Ho Po - 131 4.

CIO (110

where

Ho is the total head (P0 go)

po is the static pressure in the free stream

p1 is the static pressure at a point on. the body

clo is the dynamic pressure. (1/2/0V2)

V is the velocity of the free stream

(2 is the density of the fluid

The cavitation, number at which the section is operating is given by

P P

= ° v

1/2/0V2

where p., the vapor pressure of the fluid.

If it is assumed that cavitation occurs at any

point on a body when P1

_{=p.then S.=}

Scrit

and

the cavitation number i

cr = s

_crit

From Reference

3,

S has been derived 1n terms of increments of velocity ratios

s

I.

eva ) V .

-7-(5)

(6) (7)

where

X

is the local velocity ratio resulting V

from the thickness distribution

AZ

is the change in velocityratio resulting V

from the mean line distribution

va

is the Change

in

velocity ratio resulting from the angle of attack

Figure 2 shows a pressure distribution (1 - S)

on the NACA 16-512 section as calculated from

Equation (7). From this plot it can be seen that

cavitation will first occur at 0.55 of the section

length and at 1 - Scrit = - 0.6.

The incipient cavitation charts were derived

by using the critical cavitation number of the

various sections. To facilitate the plotting and the use of the diagrams the results were plotted in

CLZ

terms of the coefficient . These charts are for shock free entry in which case

gvas

zero. The

V

angle of attack may be taken into consideration using

the method shown in Reference 30

Calculations were performed for the NACA 16, 65A and 0000-1.10 40/1.575 sections with NACA a ra

100

and

008 mean lines and the NACA 66 TMB modified

section, with an a = 008 mean line and the results are plotted In Figures 3 to 9 and given in Appendix B.

CONCLUSIONS

This repott gives the geometric coefficients

which are necessary to calculate the stresses in a

propeller blade or hydrofoil. These have been

- computed and compiled in table form for the THB

EPH NACA 161 65A

and

66

TMB modified sections. By .

substituting these values in Equations (1) to (3), stresses in a section may be .found with a minimum of work.

The cavitation number of a section must be determined to give the best cavitation

characteris-tics for the design. This report gives the

theoretically derived Incipient cavitation charts

for the

NACA 16, 65A1 0000-1.10 40/1.575

and

66

REFERENCES

Morgan, IC B., "An Approximate Method of Obtaining Stress in a Propeller Blade,"

DT} B Report No.

919,

October

1954.

Eckhardt, M. K. and Morgan, W. g., "A Propeller Design Method," Transactions of The Society of Naval Architects and Marine Engineers,

1955.

30 Abbott, I. H., et. al., "Summary of

Airfoil Data," NAGA Report No, 824, 1945.

4. Loftin, Lawrence, K., Jr., "Theoretical and Experimental Data for a Number of NACA óA-Series Airfoil Sections," NACA Report No. 903, 1948.

Berggren, Robert E. and Graham, Donald J., "Effects of Leading-Edge Radius and Maximum Thickness-Chord Ratio on the Variation with Mach Number of the Aerodynamic Characteristics of Several Thin NACA Airfoil Sections,"

NACA Technical Note 3172, 1954.

-10-1 - S

1.0 -70 CG '----Nose -Toil Line yo

Figure 1 - Coordinate System for a Section

-1.0

rT

Suction Side Pressure Side

02.

0.4 o e '

08

1.0 ly/

APPENDIX

A-- .

Geometric Coefficianta for TNB EPH,

- tri/ 40)/3

t//

t2 Area and

- (7k/ 40)13

Table 2 - Geometric Coefficients for TMB EH Section

1 MN

.80 2.3 342,0 17 69 10 29 65.1 43.7 3 0.8 225 2 333 BO 4551,1 1496.1 657.8 344.3 201.8. 1282 86.5 61.1 44.7 2 202 89 55867 2016.9 92 40 494.1 293.2 187.6 127.1 904 66.1 193361 5938.7 23514 11313 621.3 374.4 241,7 1648 11%4 86.5 1 679 2.9 5888.5 25390 1279.6 72 16 443.8 289.6 1990 1446 10 5.4

-13-(y0)13 VI .. 0 2 785 a 696 4 309 5 1741 111 4 773 (li",0)13 535.9 267.9 178.6 133.9 107.1 89,3 (x2//io)/3 596.5 298.2 198.8 149.1 119.3 99.4 (./I) L3 4207 21.03 14.02 10.51 8.41 7.01 568 76.5 85.2 601 435 669 74,5 525 343 595 66.2 4.67 278 53.5 59.6 420 f/L . 0.01 _ 2714.a 536.2. 597.5 41.94 723 268.1 298.7 2092 320 9 178.7 199.1 1394 179 5 134.0 1495 10.46 114 4 107.2 119,5 8.36 791 89.3 99.5 497 579 76.9 85.3 5,97 442 67.0 74.6 5.2 3 349 59.5 66.3 4.64 282 516 59,7 4,18 f/1- 0.02 2 037 5 681 2 316 7 179 8 1719528 537.9 26 89 179.3 134.4 10 7,5 89.6 599.9 2999 199.9 1499 1199 999 41,75 2027 1 110,1943 8.3 5 695 585 748 85.7 5.96 446 67,2 749 591 352 59,7 662 4.63 284 537 59,9 4,17 fil .. 0.0S 1 459 8 601 9 54 0.7 270.3 6500312:7 417 9 24,8 9 300 4 (1:15.1 111802035 2012 150.9 13.93 10.44 11775149580455 90.1 118200061.7 8.35 496 77.2 5.97 447 67.5 754 5,22 352 60.1) 67,8 424 285 54.0 60,3 4.17 fit -.0.04 1 078 0 51 53 277 0 167 7 0 17118 57 a 544.9 27 2.5 181.5 13 41 10 a9 90.7 7 72 630084,37 120522..91 18216.9,7 41,96 20.9 8 13,9 8 10,4 9 8.3 9 49 9 599 443 351 69060.58.0 1706/67..:24 4 4.66 284 54.4 602 4.19 fit - 0.05 83Ô2 436 8 250 8 54 9.4 274.7 183.1 1 6 301743 204.9 4292 21,11 14.07 157 7 157,3 10 9 .8 3.6 22.9 145 5 8.4 4 1762067 567 437 91.5 78.4 68.6 187.8 11756.802 .4

73

603 52 7 347 610 683 429 281 54,0 61,4 492 0.02 . 014 9 0.04 .0298 0.06 .044 7 0.08 .0596 0.10 .074 6 0.12 .0895 0.14 .104 4 0.16 .1193 0.18 .134 2 0.20

1492

0.02 .0.149 0.04 .0298 0.06 .044 7 0.08 .0596 0.10 .0746 0.12 .0895 0.14 .1044 0.16 .1193 0.18 .1342 0.20 .1492 0.02 .0149 0.04 .0298 0.06 .0447 0.08 .0597 0.10 .074.6 0.12 .0895 0.14 .1045 0.16 1194 0.18 .1343 0.20 .1493 0.02 .0 14 9 0.04 .0 298 0.04 .0448 0.08 .0597 0.10 .0747 0.12 .0896 0.14 .104 6 0.16 .1195 0.18 .1345 0.20

j494

0.02 .0149 0.04 .0299 0.06 .0449 0.08 O599 0.10 .0749 0.12 .0898 0.H .1048 0.N .1198 0.18 .1.34 8 0.20 .149 8 0.02 .01.50 0.04 _.0300 0.06 0450 0.88 .0601 0.10 .0751 0.12 .0901 0.14 .1051 0.16 .1202 0.18 .1352 0.20 .1502

ngae 3- Geometric Coefficients for NACA 16 Section / 0.02 0.04 0.06 0.08 0.10 0'12 ta A-a 0i47 .0294 .0443. .0588 .Q735 .0382 -(Y1/120) 15 end - (72/120)13 tag OM 6.0 0.0, 0,0 (73ii3O)13 f/i - 0 2806& 70 17 31 18 17 54 11 22 779 (11/1y0)13 579.1 2893 1930 1 447 1 158 965 - (121170) 61%9 308.9 205.9 1544 1215 102.9 !(23/1y0) 13 -19.39 - 9.69 - 6.46

- 484

- 367*

- 323

0.14 1029 0.0 572 82.7 862

- 277

036 0.18 0.20 .1176' .1324 .147 1 0.0 00 0.0 458 346 280, 72.3 64.3 57.9 77.2 68.6 61.7 - 2.42 - 21 5 - 1.93 fit - 0.01 0.02 0.66 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 .0147. .0294 ,0441 .0586 ,O735 :0882 .1029 .1177 .1324 .1471 180013 . 2618.2 800.1. 3420 176.4 102.6 f 42. 43.6 30.7 22.5 27905 73 68 32 57 1819 11 58 800 586 447 352 285 579.5 289.7 193.1 144.8 1 159 965 82.7 7244 643 57.9 618.9 309.4 206.3 154.7 123.7 103.1 88.4, 77.3 68.7 616'. j9.72 - 9.86 - 6.57 - 4.9 3 - 3.94

- 328

- 2.81 - 2.4 6 . - 2.19 - 1.97 2/1 - 0.02 0.02 0.04 0.06 0.08 0.10 0.12 0.14 .0147 .0294 J0441 .0588 .0736 .0883 .1030 2 327 6.3 '4539.1 1492.2 656.1 343.4 201.3 127.9 212 42 70-03 32 37 1832 11 71 811 593 581.3 290.6 193.7 1453 1 162 9613 83.0 621.5 310.7 207.1 155.3 124.3 103.5 68.7 -20.11 -10.05 - 6.70

-

502 - 402 - 3.35 - 2.87 0.16 0.18 0.20 .1177 .1325 .1472 86.2 609 44.6. 452 356 288 723 64.5 581 77.6 69.0 62.1

- Z51

- 223

-

2131 f/t - 0.03 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 .0147 .0294 .0442 40589 .0736 .0$84 303 1 .1179 .1326 .1473. 21970.7 5573.9 2011.6. 921.6 492.8 292.4 187.1 126.8 898 660 153 82 6235 30 89 17 96 11 63 810 594 454 358 289 5b4.3 292.1. 1 942 1 460 1 163 97.3 83.4 730 649 58.4 625.4 3122-208.4 156.3 125.0 104.2 89.3 78.1 69.4 623 -20.54 -1027

- 664

- 5.13 - 4.10

- 3.42

- 293

- 2.56

- 228

- 205

f/t - 0.04 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 .0147 .0295 .0443 .0590 .0738. 10886 .1033 .1181 .1329 .1477 i 928 60 5923.1 23492. 112 83 619.7 373.4 2414 164.4 IA 71-₈₆₂ 114 52 53 73 2862 17 24 11 37 800 589 452 357 289 5 886 294.3 1 962 147.1 1 172 984 840 733 654 583 630.6 3153 2102 157.6 1264 105.1 90.0 78.8 70.0 63.0 -21P1 -10.543

- 700

- 5.2 5

- 420

- 3.50 - 3.00

-

2.62 - 233 - 2.10 f/1 - 0.05 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 .0:148 .0296 .0:444 .0592 .0740 .0889 .1037 418 5 .1333 4481. 1 674 8.6 58729 25323. 127 63 721.7 44 26 2886 198.5 14 22 .105.1 8878 4580 2604 16 27 10 97 781 580 446 354 287 593-2 2962 1 979 1 484 118.7 989 849 742 659 593 636.8 318.4 2122 159,2 127.3 106.1 90.9 79.6 70.7 63.6 -2133 -10.76 - 7.17

- 538

-

4.30 - 3.58

- 307

-

2.69 - 2.39

-

2.15

t/ 21.2 Area

Table 4 - Geometric Coefficients for NACA 65-A Section

- (Wirt))/3 and - (121I10)/3 21101.5 3069.1 .937.9 400.9 206.8 120.3 76.1 51.1 3 6.0 26.3 2 728 50 532 0.8 174 9.1 769.1 402.5 2340. 149.9 101.1 71.4 52.3 2 575 46 6531.5 235 20 1080.3 577.7 342.6 219.3 148.6 10 53 773 2 260 63 694 3.1 2753.7 132 26 726.4 437.7 282.6 192.7 137.2 101.1 1 963 10 688 43 29663 14940 846.0 518.9 33 8.6 232.6 166.7 123.2 (yeIzo)/3 f/i -0

(.1/I,0)13 - (z2gy0)13 (x5/I70)/3

322 43 6 411. 794.1 67.03 80 60 320.5 397.0 3351 3582 213.7 264.7 223 4 20 15 1602.' 198.5 16.75 12 89 128.2 158.8 134 0 895 106.8 132.3 11.17 65e 915 113.4 9.57 503 801 992 8.37 398 712 88.2 7.44 322 643. 79.4 6.70 VI .. 0.01 305 77 641.5 795.4 66.77 82 49 320.7 397.7 333 8 36 76 2 158 265.1 222 5 20 62 1 603 198.8 16.69 13 16 128.3 159.0 13.35 911 106.9 132.5 111 2. 668 91.6 113.6 953 510 801 99.4 834, 402 71.2 88.3 7.4 1' 32! 64.1 79.5 6.67' 2/1 0.02 224 91 643.4 798.7 66.75 76 73 321.7 399.3 33.37 3596 214.4 266.2 2225' 20 51 1 608 .199.6 16.68' 13 18 128.6 159.7 1335' 915 107.2 133.1 1 1.1 2 671 91.9 114.1 9.53 513 80.4 99.8 834. 404 71.4 88.7 7.4 1. 327. 64.3 79.8 6.6 7 1/1 - 0.03 158 66 646.7 , 803.6 6694 6706 323.3 401,8 33.47 3384' 2 155 267.8 223 1 19 89 161.6 200.9 16.73 12 96 129.3 160.7 133 8 907 107.7 133.9 11.3.5 667 923 114.8 9.56 511 808 100.4 8.36 404 71.8 89.2 7.43 327 646 80.3 6.69 f/1. 0.04 11572 651.4 810.3 67.35 5687 325.7 405.1 3367. 30 96 217.1 270.1 22.45 1888 162.8 202.5 16.83 12 56 1 302 162.0 13.47' 888 1 085 135.0 112 2 658 930 115,7 9.62 506 81.4 1012 8.41' 400 723 90.0 748 325 651 81.0 6.73 fit -. 0.05 8824 657.1 818.2 67.94 47 81 328.5 409.1 33.97 27 84 219.0 272.7 22.64 1765.

i64

204.5 16.98 12 02 131,4 163,6 1158 861. 109.5 136.3 11,52 643 93.8 116.8 9.70 496 82,1 102.2 849 395 730 90.9 734 321 617 81.8 6.79 0.02 0.06 0.06 .d13 4 .026 9 A404 0.00 .0538 0.10 .0673 0.12 .0808 0.14 p.943 0.16 .1077 0.18 .1212 0.20 .1347 0.02 .013 0.04 .0269 0.06 .0404 0.00 .0538 0.10 .0673 0.12 DSOS 0.14 p943 0.16 .1077 0.10 .1212 0.20 .134 0.02 D134 0.04 .0.269 0.06 .0404 0.08 .0 53 9 0.10 .0 67 4 0.12 PS09 0.14 p943 0,16 .107 0.18 .1213 0.20 .1348 0.02 .0134. 0.04 .0269 0.06 .0404 0.08 .0539 0.10 .0674. 0.12 AS09 0.14 _.0944 0.16 .1079 0.18 .121 4 0.20 .134 9 0.02 .013 5 0.04 .0 27 0 0.06 .0405 0.08 .0541 0.10 .0676 0.12 .0811 0.14 .0946 0.16 .3082 0.18 .1217. 0.20 .1352 0.02 .o135 0.04 .0 27 1 0.06 .0 40 7 0.08 P 54 2 0.10 067.8 0.12 .0814 0.14 $394 9 0.16 .1085 0.10 .1221 0.20 .1357

Table 5 - Geometric Coefficients for NACA 66 (TMB Modified) Section

-16-t/i

Is Area 1 (ri/Ixo)t3 and - (70110)18 (Y3/1)13, fil 0 (x1/I7o)t3 - (x2/170)0 (I1070)13 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 #1 43 .0287 .01431 0574 .0:718 p862 .1005 .1149 .1293 .1456 OD OD OD OD OD OD OD OD OD OD 294 79 73 69 3275, 1842 11 79 818 601 460 363 294 5860 293,0 195.3 146.3 117.2 97.6 83.7 73.2 65,1 58.6 652.9 326.4 217,6 163,2 130.5 108,8 93,2 81,6 72.5 65.2 28.49 142 4 9.49 7.12 5.69 4.74 4.07 3.56 3.1. 6 2,84 f/I m 0.01 0;02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.10 0.20 .0143 .0287 .0431 .0.574 .0718 .0862 .1005 .114 9 .1293 .1436 1 934 1.0 2813.0 859,7 367.4 189.6 11 03 69,7 46.9 33.0 24,1 28631 7640 3391' 18 98 1209. 837 613. 468 369 298 580.4 2 932 1 9 54 1 466 1 172 977 83.7 733 651 586 654.0 327.0 21E10 163.5 130.8 109.0 93.4 81.7 72.6 65.4 28.23 14.13 9.43 7.08 5.67. 4.73 4,05 3.55 3.16 285' fil 0.02 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 .0143 .0287 .0431 p575 .0718 p 862 .1006 .1150 .129 4 .1437 2 500 E16 4876.8 1603.2 704,9 '368.9 216.3 132.4 92.6 65.4 47,9 214 36 71 85 33 44 18 99 12 17 844 618 472 372 301 5882 294.1 196.0 147.0 117.6 98,0 84,0 73.5 65,3 58,8 656.7 328.3 218.9 1641 131.3 109.4 93,8 82,0 72.9 65.6 28,04 14,05 938 7,05 5.65 4,72 4,05 3.55 3,16' 2.135 VI .. 0.03 0.02 0.04 0.06 0.00 0.10 0.12 0.14 0.16 0'.18 0.20 .0143 p287 p431 p575 0719 p865 .1007 .1151 .1295 .1439 2 360 a9 5986.5 2161.3 990.1 529.5 314.2' 20W '136.2 96.5' 70.9' 153 30 63 39 31 68 18 52 12 04 840 617 472 372 .301 5912 2 956 197.0 147.8 118.2 985 84,4 739 656 59,1 660.8 330.4 220.2 165.2 1321 110.1 94.4 82,6 73.4 66.0 27.91 j4,00 9,36 7,04 5,65 4,72 4,06 3.56 3,18 287 fil 0.04 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 3144 .0288 D432 .0577 .0721 p865 .1009. 1154 .1298 1442 20720.3 6363.8 25219 1212.3' 665.8 401.2 259.0. 176.6 125.8 Q 235 113 04 54 21 29 18 17 69 11 72 826 610 468 370 300 595.5 297.7 198.5 148.8 119.1 992 85,0 744 661 59.5 666.3 333.1 222.1 166.5 133.2 111.0 95,1* 832' 74,0 66.6 27.83 13.97 93.5. 704' 5,66 4.73' 4,07 3.58 320' 2.89 fil - 0.03 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 p144 p 28 9 p434 p.578 .0723 p.868 .1013 .11.57 .1302' .1447 1 799 41 6309.9 2720.7 1371.2 775,4 47'5.5 31 03 2132 152A 1150 8695 4590 26 40 16 62 11 26 804 598, 461 366 297 boa/ 3 003 200.2 150.1 120.1 100.1 85,8 75.0 607 60,0 672,8 336,4 224.2 1682' 134,5 112.1 961 84,1 74.7 67,2 27.79 13.97 9.36 7.06' 5.68 4.75 4,10 3.60 322 2.91

.A.PPiNt4X B

. .

Incipient '.Cavitation ,CurveS.,for NACA 161

65A, 0000-1010 1i.0/1575 and 66::

Tie

INCIPIENT CAVITATION CURVES FOR

NACA le THICKNESS FORM WITH a - 0.8 MEAN LINE

'CI. Coefficient of Lift a Cavitation Number

t/i

Thickness Ratio

f/I

-Camber Ratio

0. 1

0.5

0.4

0-0.5

0-G

-1.9-INCIPIENT CAVITATION CURVES FOR

NACA 16 THICKNESS FORM WITH a = 1.0 MEAN LINE

CL

Coefficient of. Lift

a. Cavitation Number tit Thickness Ratio fit Camber Ratio

0.7

Figure

0.6

INCIPIENT CAVITATION CURVES FOR

NACA 66A THICKNESS FORM WITH a = 0.8 (modified) MEAN LINE

CL

Coefficient of Lift Cavitation Number

t/1

Thickness Ratio

/VI

3 0

2 5

2 0

CL

1 5

10

5

INCIPIENT CAVITATION CURVES FOR

NAGA OSA THICKNESS FORM WITH a = i.0 WEAN LINE

CL

Coefficient of Lift Cavitation Number Thickness Ratio camber Ratio

0.1 0.2

03

04

CT"

Q5

0.6

-21-0.7 Figure - 0 0.8

20

15 10

5

... - .. ...

...

.

.. ... .... . .

INCIPIENT CAVITATION CURVES FOR

NACA 0000-1.10. 40/1.175 THICKNESS FORM WITH a =0.8 MEAN LINE

Coefficient of Lift Cavitation Number Thickness Ratio Camber Ratio

:1:: .. . . ... ... _ .... ... ... ... . "." 0.1

0.2

0.5

0.4

0.5

0.G

-23--0.7

Figure - 8

0 6

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