The 2-, 3-, and 4- bladed supercavitating Propeller series

ARCHEF

HYDROMECHANICS

o

AERODYNAMICS

o

STRUC11JRAI MECHANICS

o

APPLIED MATHEMA1IGS PRNC-THB-68 (Rev. 3-58)

L

I L,i_4"e

'1 . e.

Tedmche Hoschóo1

Dell

t!...-.-.-.-.-...-TMB 2-, 3-, AND 4-BLADED

SUPERCAVIT.ATING PROPELTFR SERIES

by

E. B. Caster

HYDROMECILANIcS LABORATORY

RESEARCH AND DEVELOPMENT REPORT

'FMB 2-, 3-, AND 4-BLADED SUPERCAVITATING PROP SERIES by E. B. Caster January 1963 Report 1637 S-R009 01 01

METhOD OF APPROACH PRESENTATION OF DIAGRAMS USE OF DIAGRAMS CONCLUSION ACKNOWLEDGMENT REIERENCES TABLE OF CONTENTS Page ABSTRACT - 1 INTRODUCTION : - -- 1

APPENDIX A - CTJ DIAGRAMS F)R TMB SC PROPB1LER SERIES

APPENDIX B - C-J DIAGRA S FOR TMB SC PROPELLER SERIES 23

APPENDIX C BLADE THICKNESS FRACTIONS FOR TMB SC PROPELLER

SRES

33

APPENDIX D - PITCH CORRECTION COEFFICIENTS FOR TMB SC

PRO-PEllER SERIES 43

APPENDIX E MxtM14 FACE ORDINATES AT 0.3, 0.5, 0.7, AND

0.9 RADIUS 'OR TMB SC PROPELLER SERIES 54

APPENDIX F MAXI}WM THICKNESS ORDINATES AT 0.2, 0.5, 0.7,

AND 0.9 RADIUS FOR TMB SC PROPELLER SERIES . 91

LIST OF TABLES

Page

Table 1 - RadiaJ. DistributiOn of Blade Chord for

Super-cavitating Propellers -

-4

Table 2 - CoefficientS for Obtaining Radial Distribution 9

of Pitch

Table 3 - Coefficients for Obtaining Face and Thickness

Distribution along Chord 10

2 3 7 11 11 12 13

BTF

cP

Blade thickness fraction

Power coefficient

Thrust coefficient

NOTATION

C Pitch correctiOn coefficient

D Propeller diameter

E A R cpanded area ratio

g Acceleration due to gravity

H Atmospheric pressure plus the submergence pressure at

0.7 section mTus the cavity pressure

J Speed coefficient

(_V

1 Chord length

10.7 Chord length at 0.7 radius

n Revolutions per unit time

Shaft horsepower

P/B Pitch ratio along the radius for finite cavitation numbers

R Maximum propeller radius

550 P8 U

D2V3)

8 a

(

(p

_{- D2V}

a iii

Re

_{Re)moids number07}

vv

+

o.7TTflD2)

(7

Xh Nondimensional radius at the hub

Kinematic viscosity

P Density of fluid

O.7

Cavitation nuiiber at 0.7 radius

iv

1)

r Radius of any prOpeller blade section

S0 Maximum compressive stress

T Thrust

t Section thickness

t Maximum section thickness along the radius

x

Va Speed of advance

0.7 Inflow velocity to section at 0.7 radius

x

Nondimensional radius - r

x1 Fractional distance along the chord measured from the

leading edge

y PresSure face ordinate

Maximum pressure face ordinate along the radius

x

Z Number of blades

(P/D) Pitch correction coefficient

fl PropeUr efficiency

2gH 2gHJ2

r 0.7

ABSTRACT

This report presents theoretically derived series Of 2-bladed supercavitating propellers with expanded area ratios of 0.3, 0.4, and 0.5; 3-bladed propellers with expanded area ratios of 0.4, 0.5, and 0.6; and 4-bladéd propellers with expanded area ratios of 0.5, 0.6, and 0.7. These propellers have a specified radial distri-bution of' 'the section chord and a hub radius of 0.2 of

the propefler radius. _{The series data are plotted in}

the form of nondimensional coefficients so that the performance of the propellers can be easily predicted and a complete design obtained if desired.

INTRODUCTION

Supercavitating (Sc) propellers, which have fully developed cavitation on the suction side (back) of their blades, are of interest to naval architects since conventional propellers experience an un-predictable performance breakdown, because of cavitation, when _operated

at very high speeds.

This report presents series data which can be used to predict

the performance of SC propellers. _{Since an experimental series is} /

costly and time-consuming, a theoretical series is of great value, if

only in a qualitative way. _{The series presented can be compared with}

experimental resuits1'2' _{of propellers designed using this method. It}

is apparent that there is some deviation from the _{experimental values,} but this difference is not unreasonable compared to propellers design from experimentally derived subcavitating series.

A 3-bladed supercavitating propeller series with an expanded area ratio of 0.5 has already been derived at the Taylor Model Basin.4 Since the ultimate aim of a designer is to obtain the best propeller for a given craft, there is need for a method of predicting the performance of SC propellers due to variations in number of blades and expanded

ratio. The choice, of the number of blades and expanded area ratio is

important in designing propellers since the propeller stress is

d.ependent on these parameters. Because the propeller stress is directly

related to the loading of SC propellers, which have sectiOns that are usually thin and highly stressed, the choice of these parameters is invaluable.

In addition to stress considerations, the choice of number of blades and expanded area ratio is also important since it has been determined that any type of SC section operating at a given angle of attack has an optimum point, i.e , a minimum drag-lift ratio, which occurs at a specific lift coefficient.5 Thismeans that the blade chord becomes importaiit in deriving the most efficient propeller.

This report presents a series of 2-, 3-,, and 4-bladed SC propellers having various expanded area ratios. The results are plotted in a series of diagrams in the form of nondimensional

co-efficients which can be used to predict the performance and character-istics of SC propellers.

METHOD OF APPROACH

The series charts preSented here were derived by first designing

a ntniber of 2-, 3-, and 4-bladed sc propellers for zero cavitation

numbet operating in uniform flow. Each propeller had a hub radius of

0.2 of the propeller radius. The Reynolds numbers used for calculating

the section diag varied from 7.2 x io6 to

x

1O7 which corresponds to

propellers having a diameter of 3 feet and operating at a speed of

ad-vance of 60 knots. It should be noted that these propellers were designed

for the same dIameter, speed of advance, speed coefficients, and non-viscous thrust coefficients as those propellers designed to derive the series presented in Reference 3, i.e., the speed coefficients covered a range from 0.3142 to 1.5708 and the nonviscous thrust coefficients covered a range from 0.15 to 4.0,

Like the series derived in Reference 4, the nonviscous thrust

and power coefficients, ideal efficiency, and hydrodynaxnic pitch

distribution for each of the series of 2-, 3-., and 4-bladed SC propellers were computed using Lerbs' mOderately loaded propeller theory.6 This

propeller theory has been programmed for the high-speed conuters at the

.7

Model Basin.

Once the above calculations were obtained, the next step was to determine the viscous corrections that must be applied to these nonviscous calculations, using the method given in Reference 1. In order to make these calculations, it was necessary to know the values of the section drag-lift ratio, which is dependent mainly on the section lift coefficient

and angle of attack. Table 1 gives the radial distribution of the section

chord for each series. From these values, the viscous thrust and power

coefficients and propeller efficiency were calculated for each propeller. The next step was to calculate the propeller pitch distribution for nonzero as well as zero cavitation numbers, using the method given

in Reference 1. Since the amount of cavitation changes the thrust and

power of a propeller, this effect must be compenated for by a corresponding

change in the propeller pitch. This was obtained by calculating the

pitch of each propeller at cavitation nthiibers ranging from 0 to 0.205 and comparing the results with the pitch calculated for zero cavitation number.

The section. ordinates of the "TMB Modified Tulin Section," used on these propellers, were calculated next. The camber line of this type section is the pressure side (face) of the foil, and the thickness is applied between the camber line and the free-stream line. The camber and thickness ordinates were calculated using the method presented in

Reference 1. The blade thicknesS fraction (BTF) was also calculated for

each propeller in order to compute the nominal stress at the blade root of these propellers by a siilified method derived from Reference 8.

PRESENTATION OF DIAGRAMS

Most of the diagrams presented here are designated by a number

and letter. The number indicates the propeller parameter and the letter

indicates the number of blades and the eanded area ratio (EAR) of the

propeller. The letters a, b, and c represent 2-bladed propellers having

expanded area ratios of 0.3, 0.4,. and 0.5, respectively; the letters d, e, and f represent 3-bladed propellers having expanded area ratios of

TABLE 1

Radial Distribution of Blade Chord for

Supercavitating Propellers 2-Biaded Series 3-Bladed Series 4-Bladed Series x

EAR0.3

1/fl

EAR0.4

1/I) EAR=0.5 1/fl

EAR0.4

1./I)

EAR0.5

lID

EARO.6

1/fl

EARO.5

1/fl

EPRO.6

1/fl

EARO.7

1/fl 0.2 0.3438 0.4584 0.5730 0.3056 0.3820 0.4584 0.2865 0.3438 0.4011 0.3 0.3438 0.4584 0.5730 0.3056 0.3820 0.4584 0.2865 0.3438 0.4011 0.4 0.3438 0.4584 0.5730 0.3056 0.3820 0.4584 Q.28b5 0.3438 0.401.1 0.5 0.3429 0.4572 0.5715 0.3048 0.3810 0f4572 0.2858 0.3429 0.4001 0.6 0.3357 0.4476 0.5595 0.2984 0.3730 0.4476 0.2798 0.3357 0.3917 0.7 0.3159 0.4212 0.5265 0.2808 0.3510 0.421:2 0.2633 0.3159 0.3686 0.8 0.2754 0.3672 0.4590 0.2448 0.3060 0.3672 0.2295 0.2754 0.3213. 0.9 0.2070 0.27:60 0.3450 0á184O 0.2300 0'.2760 0.1725 0.2070 0.2415 0.95 0.1503 0.2004 0.2505 0.13,36 0.1670 0.2004 0.1253 0.].503 0.1754 1.0 0 0 0 0 0 0 0 0

0.4, 0.5, and 0.6, respectively; and the letters g, h, and i represent 4-bladed propellers having expanded _{area ratios of 0.5, 0.6, and 0.7,}

respectively. _{it should be noted that the 3-bladed}

series diagrams presented in Reference 4 are also _{presented here.}

The propeller efficiency _{contours and the pitch ratio}

calculated at 0.7 radius for _{zero cavitation number P/fl}

are presented in Appendix A, Figures la through ii, as a function of the thrust

co-efficient /and the speed coco-efficient J _{and in Appendix B, Figures}

2a

through 21, as _{a function of the power coefficient /çand J. The}

solid efficiency contours in these diagrams indicate the region _where the section-lift coefficient is between 0.0548 and 0.2 and the _section

angle of attack is 2 degrees. _{The dashed portion below the solid}

efficiency Contours represents the region where the section-lift co-efficient is less than 0.0548, resulting in flat-face sections having

angles of attack less than 2 degrees. _{This area should be avoided because}

face cavitation is likely to occur on SC sections operating _{at these small}

angles. _{The dashed portion above the solid efficient contours}

re-presents the approximate _{area where the section-lift coefficient is} greater than 0.2 and the angle of attack _{greater than 2 degrees. In} this region, the cavities become thick _{and section loading high, and the.}

theoretical results may be in.question. _{Also included in these diagrams}

are maximum efficiency curves for obtaining the optimum rpm or diameter _D.

The thrust coefficient _{CT, power coefficient C, speed}

co-efficient J and propeller efficiency _{presented in Figures la through}

2i were calculated using the _{following equations:}

yT=

J T P ₂ D 8 a 550P S V a nD 5 [1]

where T is the propeller thrust, is the Shaft horsepower,

p is the density of the fluid,

D is the propeller diameter,

Va is the speed of advance, and

n is the revolutions per unit time.

CT cp

2gHJ2

0.7

v (J2± 484)

and where H is the atmospheric pressure plus the submergence pressure at

0.7 section minus the cavity pressure, and is the acceleration due to

gravity. The other parameter 4 (PIP) derived for these propellers is also

presented in Appendix D, Figures 4a through 41, as a function of and J.

[4]

The propeller blade thic1iess fractions (BTF) derived for these propellers are presented next in Appendix C, Figtires 3a through 3i., as a

function of arid J so the propeller stress can be calculated. An

approximate method for calculating the maximum compressive stress at the blade root derived from Reference 8 is

l.95PC

_Ta

V 2

[5;]

z (BTF)2

ihere BTF is the blade thicithess fraction given In Appendix C..

As mentioned above, Appendices A and B give the pitch ratjo calculated at 0.7 radius for zero cavitation number P/Pd Since there is a change in thrust an power of a propeller due to cavitation, a corre-sponding change in this pitch must be iade to offset the variation in

thrust Or power. This change in P/P0 due to zero cavitation numbers

(A(P/D)C0) is presented in Appendix D, Figures 4 through 4i. The

paiwneter C is plotted in Figure 4 as a functicfriof the section cavitation number at the 0.7 radius (o7) Only, where

The final pitch ratio at .0.7 radius for propeflers operating at various cavitation numbers (P/D)07 can be obtained from the equation

(P/B)07 = P/B0

-[7]

where C is the pitch correction coefficient from _{Figure .4 of Appendix .D}

and _{P/B is the pitch correction coefficient from Figures 4a through 41}

of Appendix B. _{The radial distribution of (P/D)07 is presented in Table}

2.

The section ordinates at various radii for the propellers are

presented in Appendices E and F. _{The maximum face ordinates are presented}

in Appendix E, Figures 5a through 8i, _{and the maximum thickness ordinates}

are presented in Appendix F, Figures 9a through 121, _{as a function o'}

/çandJ.

A replot of the maximum efficiency curves given in Appendix A is

presented in Figiires 13 through 20 to show the.reiationship _{of number of}

blades and expanded area ratio to optimum _{rpm and diameter. The}

incon-.sistency in. these diagrams is undoubtedly due _{to the method of fairing}

used as the curves were not cross-faired on the basis of number of blades

nor expanded area ratio. _{They do indicate, however, the trend with}

varying number of blades and expanded area ratio.

USE OF DIAGRAMS

For a design based on thrust T, the propeller efficiency and

the Q.,7 radius pitch for _{zero cavitation number P/B}

can be obtained from Appendix A, Figures la through li, depending on the number of blades and

expanded area ratio, once the thrust cOefficient _{and speed coefficient}

J are obtained. _{Similarily, for a design based on shaft horsepower P5}

values of and P/Il _{can be obtained from Appendix B, Figures 2a through}

2i, once the power coefficient _{and J are obtained. Equations [1],}

[2], and [3] can be used to calculate iç / _{and J, respectively.}

Figures presented in Appendices A and B can also be used to obtain the optimum rpm or diameter D for a given thrust or power. The

optimum rpm for a given diameter is obtained by _{plotting iç or /?5 on}

the maximuni efficiency line for a given CT or C,

in.

these figures. This

point represents the J that gives the optimum _{rpm fOr a given diameter,}

and using this J value, the optimum rpm can be calculated using Equation [3]. The optimum diameter D for a given rpm is obtained by assuming a

diameter and plotting the calculated J and or iç on the figures

presented

in

Appendices A and B. The J obtained at the intersection of

a straight line drawn from the origin of the diagram through this point and the line of maximum efficiency for a given CT/J2 or C,/J2 represents the J that gives the optimum diameter for a given rpm. Using this J, the optimum diameter D can be calculated using Equation [3].

It should be noted at this point that. if the design being considered is based on shaft horsepower, the corresponding CT must be calculated since the remaining design diagrams are presented as a

function of

/5

an4 J. .This value of CT can be calculated using Equation

[4] once and C are obtained from Appendix B for the propeller based

on power.

The approximate maximum compressive stress of the propeller can be calcUlated using Equation [5] where the blade thickness fraction

(BTF) is obtained from Appendix C, Figures 3a through 3' The final

pitch ratio for the propeller at the 0.7 radius for any cavitation number (P/D)07 is calculated using Equation [7] where P/B0 is obtained from

Appendix A or B. C(y is given

in

Appendix B, Figure 4, as a function of

O.7 which is calculated Using Equation [6]; 'and (P/D) is given

in

ppendix B, Figures 4a through 4i. The radial pitch distribution for th.is propeller is then obtained froi Table 2.

The section shape for these propellers can be obtained from

Appendix E which gives the maximum face ordinates (y/i and Appendix F

which gives the maximum thickness Ordinates (til)max atvarious radii. Once these ordinates are obtained, faired curves are then drawn to obtain

values for and (t/i)max at other radii where from, theory,

(y/)

is zero at the hub and tip. Table 1 gives the section chord

lengths i chosen for these propellers. Thus, once y and t. are

max max

obtained, the chordwise distribution of the ordinates. y and t can be

obtained using the distribution given in Table 3. The method of

completing the, design of a SC propeller, using this series, is identical to the method presented in the Appendix of Reference 3.

TABLE 2

Coefficients for Obtaining Radial Distribution _{of Pitch}

9 x (P/D)07 0.2 0.974 0.3 0.979 0.4 0.984 0.5 0.990 0.6 _0.995 0.7 1.0 0.8 _1.006 O.9 _1.011 0.95 1.011 1.0 _1.010

TABLE

3

Coefficients for Obtaining Face and Thickness Distribution along Chord

Y When i

t

When

t

When _____ t max t max max max

0.051

O.05l<(-)

0.0753

0.O753(--)

max max max O O 0 0 0 0.0075 0.0189 0.0476 0.0343 0.0297 0.0125 0.0324 0.0705 0.0501 0.0429 0.05 0.1419 0.2053 O;.1326 0.1068 0.10 0.2915 0.3532 0.2124 0.1626 0.20 0.5669 0.5951 0.3421 0.2513 0.30 0.7846 0.7659 0.4453 0.3311 0.40 0.9319 0.8663 0.5285 0.4082 0.50 1.0000 0.9305 i 0.6075 0.4925 0.60 0.9834 0.9725 0.68.79 0.5866 0.70 0.8780

1.0100

0.7787 0.6963 0.80 0.6806 1..0215 0.8645

0,8064

0.90 0.3886 1.0236 0.9401 H

0,9104

0.95 0.2065 1.0141 0.9719 0.9570

1.00

1.0

1.0

1.0

CONCLUSION

Theoretical results have been presented for 2-bladed SC

propellers having expanded area ratios of 0.3, 0.4, and O.5; for 3-bladed SC propellers having expanded: area ratios of 0.4, 0.5, and 0.6, and for 4-bladed SC propellers having expanded _{area ratios of 0.5, 0.6, and 0.7.} This theoretical series should be of great value, if only in a qualitative way, in predicting the performance of SC propellers due to variations in number of blades and expanded area ratio.

Caution must be exercised in using these results in any but a

qualitative way. _{This is especially true for designs which deviate too}

much from the optimum efficiency curves. _{Experimental results indicate}

that, as would be expected, there is more of a variation from the theoretical

results than for subcavitating propellers. _{The theory used is the best}

available for such propellers, but questions arise _{as to the validity of}

the lifting surface corrections used _{as well as the lift and drag}

characteristics available for SC sections. These questionable areas

should not detract from the usefulness of the series presented since the relative characteristics of different propellers would be _expected to change little.

AC KNOWLEDGMENT

The author wishes tç thank Max. H. Morris, Inc. for their help in preparing the data for publication.

REFERENCES

1. Tachmindji, A. J. and Morgan, W. B., "The Design and Estimated Performance of a Series of Supercavitating Propellers," Presented at the Second Symposiwn on Naval Hydrodynamics (Aug 1958).

2, yenning, E. Jr. and Haberman, W. L., "Supercavitating Propeller Performance," Presented at the 1962 Annual Meeting of the Society of Naval Architects and Marine Engineers.

--/

3. Hecker, R., "Experimental Performance of TMB SC Propellers,"

David Taylor Model Basin Report 1432 (in preparation).

Caster, E. B., "TMB 3-Bladed supercavitating Propeller Series," Dadd Taylor Model Basin Report 1245 (Aug 1959).

Morgan, W. B., "Optimum Supercavitating Sections," David Taylor Model Basin Report C-856 (Aug 1957).

Lerbs, H. W., "Moderately Loaded Propellers with a Finite Number of Blades and an Arbitrary DistributiOn of Circulation," Trans-actions, Society of Naval Architects and Marine Engineers (1952).

Hecker, R., "Manual for Preparing and Interpreting Data of Propeller Problems Which Are Programmed for High-Speed Computers at the David Taylor Model Basin," David Taylor Model Basin Report 1244 (Aug 1959).

MOrgan, W. B., "Centroid and Moment of Inertia of a

Supercavitating Section," David Taylor Model BasIn Report 1193 (Aug 1957).

APPENDIX A

Cri DIAGR AMS FOR TMB Sc PROPELLER SERIES

Maximum Efficiency for a given C1,ij2

-Maximum Efficiency for a given CT.

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C "-I

60

01

61 81 10 0 °0/d °Ok 'p60 :0 °0/d O/d UAI9 0 A3Ue!3i3 WflW!XOJ I I /13 UM9 0 i0 43uaI3Ifl] WflWIXDAJ N 9.' °O/d

Ia'

oco cso 090 c90 OLO LO PLO 9L0

ill

9I c

-uui

LO

U....

,

--.

81 90

____

j70

ki1&TUI1U

Q 0. °O/d c:0 90 90 LO

80 i51

-II

60 0I LI 91

90 = UV 'eue aeIiedod

pepjj-j UPL aoj W8J!Q

- qi eanJ

P 1.LNJI?Idd3OD OJJdS LI 91 91 I LI l

II

.01 60 80.

[0

90 90 VO £0 O

1.6 1.5

02

01

Maximum Efficiency for a given C,ij2 I I

Maximum Efficiency for a given C1

\

'-0.6

-10

\

-EIHHI

0

010.20.30,4

0.5

0.60.7 0.80.9

10 U 1.2 13 1.4 1.5 1.6 17 Speed Coefficient J

Figure ii

_{- CT-J}

Diagram for TMB 4-Bladed SC Propeller Series, EAR = 0.7

%1.9.8°:i

II

I

I

0

II'I

I

04.*Ipii

1.8

I

urnitir';

I

I__1III'IN. :°

_ti

I__

iiiiir.

Q70

IUO.5

:74

076 Efflciency 18 19

ao

1.4 13 1.2 I.' 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3

APPENDIX B

Cp.i DIAGRAMS FOR 1MB SC PROPELLER SERIES

Mazurnum Efficiency for Constant C,/J°

...i...-.. MozumumEtfic'uency for Constant Cp I

L WD_{04.05 06O7}

II iii

5"

11111

IkA

I1II'.

I

;

_P/Do

uuurniiiu'

U....

UUUUUUUUUUU 06

0.76

UUUUUIUUU.

07

-09 to

1111111111

_1.3 4 P/Do 2.5 20 0,I 0.2 0.3 04 0.5 Ô6 0.7 08 09 Speed Coefficient J

Figure 2a - C-J Diagram for TMB 2-Bladed SC Propeller Series, EAR =

0.3

1.0 I.' 20 1.9 I.e I? 1.6 '.5 14 13 1.2 9 9 0.7 0.6 0.5 0.4 0.2 0.I

1.6 '.5

"I'll"

_{...__}

uguuiohiz

0.9 .1

III

1.-I I I I I i... ..;.... ,. , 2 1.2 1.4 1.6 !

I

r

I'

18. P/DO

uIIuIiI I!1

IHIIILI

1.2 1.4 -2.0 .8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Speed. Coefficient J

Figure 2b - C-J Diagram for TMB 2-Bladed SC Propeller Series, EAR = 0.4

t

.25 Efficien cy

-- _- 72

P/D0 2.2 2.1 2.0 1.9 1.8 1.7 I.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3. 0.2 0.1

, Maximum Efficiencyfora iven -A Q4 u6 0

,.

p,r

uirUwii

'

IIUh1I11ro

iflhiIIlIHhllIflhIIIIHhIIHI

EuuIrnsiI

IIIMtWiii&1II1IIIUIIIIIIIIUIflhIIB

..III1fluhIUlLI.

-'.

UlUNIU1iLS

UUUliU*1111L1IUi MU

U....

LII

UUUUU

UUUUUUII1I1W1

Efficlenc

uu

..UU.UUU&i&1Ui

Ui... *UUU

_a65

lU

0.72

U...

0.6 20 0.7 Q

...U..UUUI

- . 16

Maximum Efficiency for a given C/J21

I -1

0 0.1

02 03 04 Q5 06

0.7

Q8 ü9

1.0 1.1 12

131.4

15 16 1.7 1.8 l 2.0

Speed

Coefficient J

Figure 2c - C-J Diagram for TMB 2'Bladed SC Propeller Serios, EAR = 0.5

26 2.0 '.9 18 17 1.6 '.5 '.4 '.3 .2 I.' I.0 09 0.8 0.7 0.6 0.5 0.4 0.3 02

2.3 2.2 2.1 2.0 1.9 1.8 '.7 1.6 1.5 1.4 1.3 12 Ia. LU LI l.0 0.9 0.8 0.7 0.6 0.4 0.3 02 27

Moximurn Efficiency for a given Cp,'1j2

Maximum Efficlenc for a Iven

C

-iu

-II1i1i:uIHIHhIH

1

I&iIiSflU ____________

!IiIUL1I1!iiIIUIIIH____________

-I11IUi9hIIHI

U

IIHII1%1

411

nu!LIii!!r

SUUEff

0.55 0.60 0.65 0 0.1

02 0.3

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 13 1.4 15 1.6 1.7 18 1.9 2.Ô Speed coefficnt J

Figure 2d

- C,-J Diagram for TMB 3-Bladed SC Propeller Series, EAR = O4

0.1

UIIIIIHH1llN1Iil

1.9 -

1.4

0.4

0.3 0.2

,MoiimUm Efficiency for o given

Moilmum Efficiency for 0 given Cp

Op/p/ .___

lIWIl

i.o0 'I '

IiiiT ::

L

Ufll!flW

I*I__

__

2.5

I__

UURNRUII

0.9 1.0 0.1

Figure 2e C,-J Diagram for TMB 3-Bladed SC Propeller Series, EAR = 0.5

28 - os os 0.7 0.0 09 1.0 .2 Speed Coefficient J 2.0 1.9 i.e I.? I.e I.e 1.4 '.5 0.9 0.8 0.7 0.8 0.5

0.9 0.8 0.7 0.6 0.5 0.4 0.3

02

0.I P/E

V

Effic y for a given

C1j2

1 1 1

4

0

Max urn Efficiency for a given Cp

1 III

I2 14

...

'.8

1

'.9

'!

--.

1.0 1.6

0

0.1

02 0.3

0.4

05 0.6

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Speed Coefficient J

Figure 2f - C,-J Diagram for TMB 3-Bladed SC Propeller Series, EAR = 0.6

1i

I. \

"

p,,

11It1

Eff

1:iII

0.60 0.65 0.70 0.72 0.74 0.76 29 1.2 1.4 2.1 2.0 1.9 1.8 1.7 1.6 15 1.4 13

2.3 2.2 2J 2.0 1.9 1.8 1.7 1.6 IS 1.4 1.3 1.2 I.' 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ' I

Maximum Efficienc for a iven Cp,ijt

UNUU.U.UUUUlUU

IlHPI!i1hiiIIiIHHHIHHIH1HH

uii..

'D0 0.9

...U...UUUUUNUUNU

iUIEiUi

LO

iiiiUI1!IIIIH1HhIHIIIIIIHIHhIII

....iiiiii,iri1iii.uuuUl.U.UUUUUUUUU

UUtIIIHh1UIUI L4

U1IUII1iIII11 UR....UUUUUUUUmU

_{NUUNiI1i1itSIUU r,}

_{U..U..UUUUUUUUU}

D0 ...u...a.

::::%iHflHIuI1flhIIHHH

Efficiency '.50 a70 0.55

UU

0.60 0.65

0.70 UUU

8

..

U

urn....

°

0.8

uuuuuu

111111

I.g 0 0.1

0.2 03 04 05 0.6

0.7 0.8 0.9 1.0 1.1 12 13 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Speed Coefficieni J I I I T. I .I I L

Figure 2g - C-J Diagram fr TMB 4-Bladed SC

Propeller Series, EAR = 0.5

22 ai 20 '9 1.8 '.7 l.6 1.5 14 1.3 12 I0 a9 Q8 0.7 0.6 05 04 03 02 0.1 I I

Ill

I

Maximum Efficiency far a Given C,/J2

II

III

Maximum Efficiency far a Given C

H

p/Do

i.0liii

1 0.9

i p,r,0.8

. DO

AI

P/Dna

I'hIflU

04

Ii'

iiii

.iiiini1iI1!I

I

I.

-.,' ----2

2.0

mr.uu

EffIciency

...

i=_ 8:

[2 _1.4 050 16

31

0 0.1 0.2 0.3 4 0.5 0.6 0.7 02 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 I.? 1.8 1.9 2.0 SPEED COEFFICIENT, J

Maximum Efficiency for a given CpjZ

Maximum Efficiency for a given Cp

I,

0Q

0:c1. 4UUii

'A1I1tl

__Ofl

t1III!iflU

rnviiiii'

__InhIiIw0p

_2.51

____I1L1iii!1!tIiL

____

in

ui

_I

____-

_{___}

-uuuu

_{uuuluUUUI__}

-09

-u

I1.2

14 1.6 0 0.1 0.2

0.3 04 0.5

0.6 0.7 0.8

0.9 1.0 1.1 1.2 13 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Speed Coefficient J

Figure 2i - C-J Diagram for TMB 4-Bladed SC Propeller Series, EAR = 0.7

32

i

-Ef

-0.60

-070

0.76

IILllliIiki 'IRkII*k'!

____

IIRIWiI

'/D

0..

0.6

1nSV

2.2 2.1

ao

19 1.8 1.7 1.6 1.5 .4 .3 1.2 1.0 0.9. 0.8 0.7 0.6 0.5 0.4 0.3

02

0.I

APPENDIX C

BLADE THICKNESS FRACTIONS FOR TMB SC PROPELLER SERIES

0.09

0.08

0.07

0.06

0.05

LI-0.04

0.03

0.02

0.01

JI 5

m1.2

__

_

H

I_

I

IqiAwAr4riu

Pd

ri

i, yr

0.20

0.40

0.60

0.80

1.00 1.20

I40

160

0.07

0.06

0.05

0.04

Li

I-0.03

0.02

0.01

J

I.

ii.o

I/

0.8

4

06

05

FIV1A1

)7

4

0.3

0.20

040

0.60

0.80

L00

1.20

140

1.60

007

006.

0.05

0.04

IL

I-0.03

0.02

0.01

8

.7.

AVA9. 0.6

0.5

I.0

J=I.5

0.20

0.40

0.60

0.80

1.00

1.20 1.40 I .60 'YCT

0.07

0.06

0.05

0.04

Li

I-0.03

0.02

0.01

4M

;3

- rrrr

I.'

1.0

0.9

J=I.5

1.4

8

_0.7

0.6

0.5

04

0.3

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

Figure 3d

0.07

0.06

0.05

0.04

003

0O2

!.ol

0

I.

AAAA

-± !hVFIKAVA

A

1.0 0.9 0.8

or

0.6

0.5

:0.4

0.3

0.20

0.40

060

0.80

1.00

.20

1.40

1.60

Figure 3e - Blade Thickness Fraction for TMB

3-Bladed SC Propeller Series:, EAR

0.07

0.06

0.05

0.04

LL

I-

a)

0.03

0.02

0.01

KA

08

Ii

0

II

_0.5

04

__AVAI

-_______I

I

Figure 3f - Blade Thickness Fraction for TMB 3-Bladed SC Propeller Series, EAR

= 0.6

0.20

0.40

0.60

0.80

1.00 1.20 1.40 1.60

0.07

0.06

0.05

0.04

0

0.02

0.01

JI.5

.4-

1.3

A

05

0.4

i:ii

½'

_0.20

0.40

0.60

0.80

I.00

1.20 1.40

160

Figure 3g - Blade Thickness Fraction for TMB 4-Bladed SC

0.07 0.06

0.05

0.04

0.03

002

Q.0I

/

0 4

JI.5

1.4 2

44'.'

AVArV

V VO7

,03

r

r

r

0.3 0.20 0.40

0.60

080

1.29

140

I.60

0.07

0.06

0.05

0.02

0.01

J:15

I.

0.7

0.6

0.5

0

3

0.20

0.40

0.60

080

100

1.20

140

1.60

Figure3i - Blade Thickness Fraction for TMB 4-Bladed SC Propeller Series, EAR = 0.7

0:04

APPENDIX D

PITCH CORRECTOON COEFFICIENTS FOR TMB Sc PROPELLER SERIES

20

1.8

1.6

1.4

12

10

08

0.6

0.4

0.2

44

002

004

006

008

010

012

014

016

018

0'0

0.22

a07

Figure 4 - Pitch Correótion Coefficient (C

for Finite Cavitation.Numbers for

0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09

a

ooe (10? 0.06 0.05 004 003 0.0i

J.

1.5 1.4 '.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6

/

0.5 0.4 0.3

45

Figure 4a - Pitch Correction Coefficient A(P/D) for Finite Cavitation Numbers for TMB

2-Bladed SC Propeller Series, EAR = 0.3

0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 a 0.08 0.07 0.06 005 0.04 0.03 0.02 0.01 0 0.1. 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 I.0 1.2 1.3 1.4 1.5 1.5 ''.3 1.2 1.0 0.9 0.8 0.7

/

JIlL

06

"IA'-0.5 0.4

Figure 4b - Pitch Correction Coefficient

(P/D) for Finite Cavitation Numbers for TMB

2-Bladed SC Propeller Series, EAR = 0.4

46

0.10 0.09 a 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 l.0 0.9 0.5 0.6 0.4 0.3

47,

0.16 015 0.14 G13 0.12 Oil J: 1.6

/

1.5 1.4 '3 2 I.' 0 aI 02 03 4 0.5 08 07 08 09 10 I.' _'2 1.3 14

Figure 4c

Pitch Correction Coefficient A(P/D) for Finite Cavitation Numbers for TMB

2-Bladed SC Propeller Series, EAR = 0 5

/

0.8

0.15 0.14 0.13 0.10 0.09 a 008 0.07 0.06 0.05 0.04 1.6 1.5 1.4 1.3 12 0.9 0.8 07 0.6 0.5 0.4 0.3 0 01 02 _{0.4 0.6 0.7} 08 1.0 II 12 1.3 1.4 L5

0.16 0.15

0(4

0.13 0.12 0.11 0.10

0.09

0

0.01

0.06

0.05

0.04

0.03

0.02

0.01

0.8

uiuu

0.6

0l

0.2. 0.3 0.4

0.5

_0.6

0.7

0.8

0.9

1. 1.1 u.

i.

1.4 5

Figure 4e - Pitch Correction Coefficient i (P4)) for Finite Cavitation Numbers for TMB

3-Bladed SC Propeller Series, EAR

0.5

cU6 0.15 0.14. 0.13 0.12 OH 0.10 0.09 0.06 0.05 0.04 003 002 0.01

I

_I

_H!JPJ:t

/

I41ii1iiL1

0.7

/

_0.6 0.5 0.4 0.3 50 oP 0.2 03 0.4 0.5 0.6 0.7 08 09 10 12 13 14 1.5

Figure 4f - Pith Correction Coefficient A(P/D) for Finite Cavitation Numbers for TMB

3-Bladed SC Propeller Series, EAR = 0.6

0 0.15 0.14 0.13. 0.12 0.11 0.10 009 Q _0.08 0.07 0.06 0.05 1104 0.03 i 1.4 .3 1.2

I

jI.0 0.9 0.8 .0.7

/

0.5 0.4 0.6 0.3 0.2 0.3 04 0.5 0.6 07 08 09 0 0I 1.0 1.2 1.3 .4 .5

016 0.15 0.14 0.13 0.12 0.11 aI0-O.09 0.08

I

0.07 0.06 0.05 0.04 0.03 002 0.Q 52 0 a' 0.2 03 04 Q5 0.6 07 08 09 10 1.2 13 14 (.5

Figure 4h - Pitch Co'rectionCoefficient A(P/D) for Finite Cavitation Numbers for TMB

4-Bladed SC Propeller Series,

AR = O6

1! 1.6 1.5 1.2 I.' 1.0 0.9 08 0.4

V

.4

0.3

crrrpPv

pr

0.16 J. 1.5 0.15 '.4 a" I.0 010 0.9 0.14 1.3 0.13 .1.2 0.12 I.' 0 0.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 13 1.4 15

Figure 41 - Pitch Correction Coefficient A (P/D) for Finite. Cavitatjon

_{Numbers for TMB}

4-Bladed SC Propeller Series, EAR

_{= O.7}

53

/

0.8 07 0.07

___M1VAW1iA

0.6 0.5

Iffff4d

ill

I 0.09 0.08 0.06 005 0.04 0.03 00l ,0.4 0.3

APPENDIXE

MAXIMUM FACE ORDINATES AT O.3 O5O.7, AND 0.9 RADIUS FOR

TMB .SC PROPELLER SERIES

0.10 0.09 0.08 0.07 0.04 003 0.02 00I

A.

!

riiiiiiirnuiiuwm

iiiiiiuir

uI,iii,AiHiI

UViVAiPrUW4Nl__ A

iiuui___

AiiiiU

04 D 1.5. 11.4 1.3 1.2 0.5 0.3 0.1 0.2 0.3 0.4 0 5 0:6 0.7 0.8 0:9

I0

1:1 1:2

'3

'4

Figure5a

Maximum Face Ordinate at .0 3 Radius for TMB 2-Bladed SC Propeller Series, EAR

= 0.3 1.1. I.0. 0.9 0.8 0.06 max 0.05

vu

= j'y

'8OUe .IeIIedOJcl

pepI- fflj,

J snpj rO

eUpJ eoj

wnwLxp

-qQ Oãfl!jj 131% ci i Fl 01 60

80'LO

90 co o £0 I0 P.O

illløØpV/

I

41111/

90 10

pr,'

80. 60 I.' ci

ucr

100 z0.0 £0.0

t00

80.0 600 °lrO 0 coo In .xow 1/i 90.0

0.10 0.09 0.08 0.07 0.06

Y/.tmax

0.05 0L04 0.03 0.02 0.01

Iiviur_1__A__w_It

It,i,AVAVIr4ii,AIIr__I

va,iriIriIr1Iprd

,r

pPP -'0.3 1.5 1.4 1.3 1.2. 1

H

Ii

ill

if 11U4.

01 02 03 04 05 06 07 08

Figure 5c

- Maximum Face Ordinate at .0.3 Radius fr TMB 2-Bladed SC Propeller Series, EAR = 0.5

09 10 II 12 13 14 15

0.10 0 09 008 0.07 0.06 1mox 06 0.5 J I 5 1.4 .1.3 1.2

Ii

lo

0.4 0.3

1

AiAAA

A

,iuiusii

Figure 5d - Maximum Face Ordinate at

.3 Radius for TMB 3-Bladed SC Propeller Series, EAR

= 0.4 13 0.05 0.04 0.02

,0l

0 0.03

0I

02 0.3

I0

04 05 06 07 08 09

OiIV '°ØS JOHOdOJd3S P°PIfl-2 WL JOJ SflIPll

OUUipJ0e3,J WflWIXU

-91

1

21

1

ri.

oi

60

80L0

90

90

O

20

O

ro

4iIUiU

Jl1iu1liLiLii44/4d1uuuII

Iiuu!ii!IHhIHH

IiHHfl1PIIIUIIHIH

iiiuiini:iiiiiuiuiiiuu

l'J!flJJ

1111111111

UII

4

A

1

£1 bi 9il

I00

oo

200

U)

900

900

£00

600

010

0J 0 0.09 0.08 0.07 0.06

o

0.05: 0.04 0.03 0.02 0.0l A

V

_A

j

1.4 1.3: 1:2,

//

H4

14

0.9

/

0.8 0.7 0.6 0.5 .3 0 0.I 0.2 0.3 0.4 0.5 0.6 07 0.8 0.9 l.0 1.2 13 14 '.5

0.10 o.oe 0O7 006 005 0.04 0.03 0.02 0.01

HIIIiUIH III

_______IIIIMII!iiiI__06

uuirirwirijiuriur

_______I1tVAVM1UUI4 r

_______r1,Aur4uruuruw

_______M7IUUr

-0.3 0.5 0.4 0 01 02 03 04 05 06 07 08 09 10 II 12

'3

'4

15

Figure 5g

0.10 0.09 0.08 0.07 0.06 y/A max 0.05; 0.04 0.03 0.02 0.01 J L4 1.3 1.0 I

JAA

A

III Iiiiiiii!I

H

IIiiiNiiiiiflI

li&VAUJiUiNiU__

AiUiIUI

0.9 0.6 0 0.1 02 0.3 0.4 0.5 08 07 0.8 0.9 I 0 ! 1.2 3

'4

15

Figure 5h - Maximum Face Ordinate at 0.8 Radius for TMB 4-Bladed SC Propeller Series, EAR

(.J 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 I.'

I

0.9 08

/

0.6 0.4 0.5 Jn 1.5 1.4 1.3 1.2 0.(0 0.9 1.0 1.2 1.3 0 0.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Figure 5i - Maximum Face Ordinate at

0.3 Radius for TMB 4-Bladed SC Propeller Series, EAR = 0.7

1.4

0.06 0.0 I 1.51. 1.3 1.2 i. 10 9

11111 II! uIiii!1iiIII1II

04

.aaa.aI,IAw1F1,iill.r4IlUIUlI

0.31

lIlWWIIlilIIU1lIIUl

II V

141 II .l.Uill U

I

2

Figure 6a - Maximum Face Ordinate at 0.5 Radius

f

TMB 2-Bladed SC Propeller Series, EAR = 0.3

0.8

02

0 10 009 0'08 007 006 max c 0.05 th 0.04 0.03 0.02 0.01

IIuhiiIjIqIuuI

0.?

II1IIiiiIiiHhIi1

I',wj,iiiu'uiuI

IDDuPJHUUIHt

0.5 04 0.3 0 01 0.2 03 0.4

05

06 0.7 0.9

09

1.0 I.' 1 2 13 I A Figure Ob

- Maximum Face Ordinate at 0.5 Radius for TMB 2-Bladed SC Propeller Series, EAR

aio 0.09 008 0.07 0.06 0.05 0.04 0.03' 0.02 0.01

,

i1ii!

0.7

0.6

Ir1i1NVjVAiiVUr

I1MII1UUU411

1qv4riru!iuPJ-

ffiFAUUU

lip

0.4 03 01 02 03 04 05 06 '07 08 09 I0 'I F 12 3 I 4 I5

Figure 6c - Maximum Face Ordinate at 0.5 Radius for TMB 2-Bladed SC Propeller Series, EAR

OLIO 0.09 0.08 0.07 0.06 max

-0.05 0.04 03 0.02 0.01

Aii

d

MPJIII11___

NUViiIW1iiUi___

iiL!JUPUUP

WPIilP2U_

r

iuuu

J I. 1.4 1.3 r.2 1.1 0. 0.7 .8 1.0 0.6 0

0I

02 0.3 04 05 06 07 08 0.9 10 12

'3

14

'5

Figure 6d - Maximum Face Ordinate at 0.5 Radius for TMB 3-B laded SC Propeller Series, EAR

0.01

J:I.5 1.4

1.3 1.2

I 1UP

-I

0.9 0.8

P1!

0.7 0.6

/IJA&A14i

0.5 0.4 0.3 0.1

0.2

0.3 0.4 0.5 0.6 0.7

08

0.9 1.0

I.'

1.2 1.3

Figure 6e

- Maximum Face Ordinate at 0.5 Radius for TMB 3-Bladed SC Propeller Series, EAR

= 0.5

0.10 _{0.09 0.08}

₀₀₇

_0.06

±

0.04

0.03 0.02

1.4

0.10 0.09 0.08 0.07 0.04 0.03 0.02 0.01

0.3

IIi iiI1IiiiiIi

II!AIIIHHHIH___

UFiii AU VAUuUi__

rir1rir4iIUU

/AUiUIPNUUUP'

1.5 1.4 1.3 0.6 0.5 0 0.1 0.2 0.3 04 0.5 0.6 0.7 0.8 09 1.0 I 2 3

Figure of - Maximum Face Ordinate at

0.5 Radius for TMB 3-Bladed SC Propeller Series, EAR = 0.0

14

'5

0.10 0.06 0.04

03

0.02 0.0I

JI.5

1.4 1.3 I.0

44

0.9

IIIIIIIIIHAIUI

4,i.I.PIUI.

0.8 0.7 0.6 0.5 3 0 01 0.2 03 04 05 06 07 08 09 I0 12

Figure 6g - Maximum Face Ordinate at 0.5

adius for TMB 4-1laded SC Propeller Series, 1AR

= 0.5 0.09 0.08 0.07 0.3 IS 0.4 14

0.7

____

J5 1.4

1.3 I2

14111

0.6

UV1V1!1iiMVAUUVAi______

I VAM

U VIUUU V

VA!IVAVAVUIIrdUUPA

--.

i,AUUPi___

AU44UUIU_____0.'

JUUU-

_JiUUUiU

-0.9 -1 0 12

'3

0.10 0.09 0.09 0.07 0.06. 0.05 0.04 003 002 0.01 '0 0J 02 0.3 0.4 0.5 ,0 6. 07 0.8

Figure 6h

- Maximum Face Ordinate at0.5r-Radius for TMB 4-Bladed SC Propeller Series, EA

0.6

14

0.10 0.09 0.08 0.07 0.04 0.03

A______

urnrM1i!1VAi__

IiiIWU!1VAUVAU

I WA VA

WA__

iriiurirwiirnu

/IIu"

0.5 0.6 _0.4 J -1.5 1.4 .3 1.2 l.1 1.0 0.9 .8 0.7

Figure Gi - Maximum Face Ordinate at 0.5 Radius fcr TMB 4-B laded SC Propeller Series, EAR = a7

0.02 0.0I 0 0.1

02

03

04

05 06 0.7 08 09

I0

2 13 '.4 '.5

0.10 0.09 0.08 0.07 0.06 y6 .'mox 0.05 0.04 0.03 0.02 0.01

I

A1HIii____

____WVAiPiilI

.4

____

__

AIdUIUI

0.3 J .15 1.4 13 1.2 1.1 1.0 0 0.8 0.7 0.6 0.5 0 0 I 0.2 0.3 0.4 0.5 0 6

0 7%/S 0 8

09

I0

12 13

Figure 7a - Maximum Face Ordinate at 0.7 Radius for TMB 2-Bladed SC Propeller Series, EAR = 0.3

14

0.09 0.08 0.071 0.06 y mox 0.05 0.04 0.03 0.02 0.0I

4Ll1

"A'

_JV1W

VU V

w

441(411

rr.,p-pp

1.0 0.5

1

0.3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

,- 0.8

0.9 1.0 1.1 1.2 1.3

i/c,

Figure 7b - Maximum Face Ordinate at 0.7 Radius for TMB 2-Bladed SC Propeller Series, EAR = 0.4

/

0.4 1.4 I.5 0.I0 J,.I. I4 1.3 12 LI:

/

/ /

0.9

as

0.7 1 0.6

0.10 0.09 0.08 0.07 04 0.03 0.02 0.01 0

I__l.5

1.4

__U1UIIEU.I III

ilIøltWUVlo.9 N...

I__i11IAiiII1I!UU

I ItII1I1 VAN WINI

0.6

I IJiiAiiHhIiii_

IV1NAAIVIIVAN!4___

.r1'vA,iv....iiw

Y!ANIPIdIII___

0.4

0.3

0.5

Figure Ic - Maximum Face Ordinate at 0.7 Radius for TMB 2-Bladed SC Propeller Series, EAR = 0.5

2 13 14 15 0I 02 03 q.4 05 06 07 08 09 10 a06 Y/Im G05

0.10 0.O9 .

I.

0.9 08

.111111141

0:5 0.4 0.3 J 1.5 4 1.3 1.2 1.1 0.6

/

Figure Td - Maximum Face Ordinate at 0.7 Radius for TMB 3-Bladed SC Propeller Series,, EAR

ü4

0.06 mo 0.05 0.04 0.03 0.02, 00II 0

0I

02 03 0.4 05 06 08 09 I 0 I 2 1.3 14 5 0.08 0.07

0.10

_0.04

0.03

0.02

0.01

I

J.l5 1.4

1.3

I.2_I.I

41

A

444

.0

a5

0.4 .3

c.

Figure 7e - Maximum Face Ordinate at 0.7 Radius for TMB 3-Bladed SC Prc?eller Series, EAR = 0.5

0.9

1.0 1.1 1.2 I. 3 14 1.5 0. I 0.2 0.3

0.4

0.5

0.6 0.7.

0.8

0.9 8 0.7

0.09

0.08

0.07 0.06 x 0 E

0.10 0.09 0o8 0.07, 0.04 Q03 _0.02 0.01 0 0.4 1.0 0.9 0.8

ItV1VAVAIIVAUVAUIW

rnr'ivAwi'.rA..r

,,i,,.T1r4Ii.

0.6 0.5 J 1.5 1.4 1.3 l2 0.1 0.2 0.3 04 05 0.6 07 0.8 0.9 10 I. I 12 13

Figure 7f

- Maximum Face Ordinate at 0.7 Radius for TMB 3-B laded SC Propeller Series, EAR = 0.6

1.4

1.5

0.06

Yb 'mox.

0.10 0.09 0.08 0.07 0. .3 0.05 002

___liliiiT1VAlA.

Al__

___lVAVi1AVAliiWAU_

___IIiDIiAWAlVlt

___ 11 VA

VA

VA

__IL

___IVMJVAIVA

VA___

___iiiAVAiUVAl

__

-.

__-I/aAlr1ur4l

__/ffFiUl___

iii

0.5 0.4j _0:3 1.5 .1.4 .13 1.2. 1.1; 09 0.8 0.7' 0.6 0.04 0:03 0.01 0.1 02 03 04 05 . 06

07

08

09 I0 12 13 14 15

CE

0

0.10 0.09, 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 .5 1.4 .3 12 1.0 I.'

/

0.9

/

o.e 0.7 0.6 0.5 0.4 1.4 1.3 1.2 0.9 1.0 I.' 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Figure 7h - Maximum Face Ordinate at 0.7 Radius for TMB 4-Bladed Sc

0.10 0.09 0.08 0.07 006 0.05 0.04 0.03 0.02 0.01 a.?

I Vi IA VA VAWA I!1Ii _____V

____4l

J 1.5 1.4 1.3 1:2 I'.G 0.4 0.5 0 0.1 02 03 04 05 0.6

.07 _08

09 F 0 I F 12 13 14

Figure 7i

Maximum Face Ordinate at 07 Radius for TMB 4-Bladed SC Propeller Series, EAR

0.10 0.09 0.08, 007 0.06, 0.o O.04 0.03 0.02 0.01

11111111

I1iiii11F Iflhllilil

P*IPIIFIIIIIII

0.3 0I 02 0.3 04 0.5 0.6 0.7 0.8 O9 1.0

II

I2 13 1.4 1.5

0.3

J.I.5

1.4 0.7

I

!

1.0 0.9 0.8 A

4111

iiA__

__wirnmvirauruu__

ih11V11W1VAill

I1F1i4iWillU

0102

03 0.4 0 06

0.7 ,- 08

v'T

Figure 8b

- Maximum Face Ordinate at 0.9 Radius for TMB 2-Bladed SC

Propeller Series, EAR

= 0.4 0.6 09 I.0

II

1.2 13 1.3 1.2 14 15

0.10 J 14 i.3 1.2 1.I 1.0 0.9 o.e 0.3

/

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 12 1.3 14 15

Figure 8c - Maximum Face Ordinate at 0.9 Radius for TMB 2-Bladed SC Propeller Series, EAR = 0.5

0.7

/

0.6 0.5 0.4 0.09 0.08 0.07 0.06 y,Ina* 0.05 a) 0.04 0.03 0.02 0.01 0

0.10 0.09 0.08 0.07 0.04 0.03 0.02 0.01 J 1.5 1.4 .3 1.2 1.1 1.0

4M1iiiii1

_1IuiiiPAFl!

0.5

I/IA

0.7 0.6 0 01 02 03 04 0.5 06 07 08 09 10

II

1.2 3

Figure 8d - Maximum Face Ordinate at 0.9 Radius for TMB 3-Bladed SC Propeller Series, EAR = 0.4

4

15

0.06

max

0.10

009

0.08 0.07

0.06

0.04

003

0.02 0.01

I

I111'41I

IIOIllhiIAUhiUi!iIiHh1!

uuuuuuurnr1rurAui u.uuuau

urn

lIIlIiVMMAV

uaiiruuiuuu

UI

IHIHIUJIPPHPI!,i

PVØl

ill

ill

l.0

0.1 0.2

a3

0.4 0.5

06

0.7 0.8

0.9

.0

LI

1.2 1.3 1.4 1.5

Figure 8e - Maximum Face Ordinate at 0.9. Radius for TMB 3-Bladed SC Propeller Series, EAR

0.5 J=I.5 '.4 .3 1.2

0.9

0.8

0.10 0:09 0.08 0.07 0.06 y1'Q "max. cri 0.05 0.04' 0.03 0.02 o:oi 0 1.5 1.4 1.3 1.2

7.

I.' I.0 '.9

Aiii141___

0.5

iiviwiuririir

NM1Y1VAW1iUPJi________

IrA

0.7 0.6 09 I0 12 13 0.1 0.2 03 04 05 06 0.7 0.8

Figure 8f - Maximum Face Ordinate at 0.9 Radius for TMB 3-Bladed SC Propeller Series, EAR = 0.6

14

y'o

0.10 0.09 0.08 0.07 0.06 P0.05 0.04 0.03 0.o2 0 0.4 1.5. 1.4 1.3 1.2

A

06

iiiiviwiuw__

I1AVAVAIIUV

1iW1I!1V4UiN_______

4

IA VI VNAi!1UUUU

V

rwluurlur4ird_______

-.

p

0.1

.'

02 0 04 05

06

07 08 09 10 12

'3

Figure 8g

Maximum Face Ordinate at 0.9 Radius for TMB 4-Bladed SC Propeller Series,

EAR = 0.5

'4

0I0 0.09 0.0e 0.07 0.06 0.05 0.04 0.03 0.02 0.01 5

H

II IIIII1H1

I

V1IUUL____

____VA1Ji!iViWUWAl

____IAliV1UUiWA

____W?VMM1VAIiW1UUV

-,Ai,.iw1.--A

0.7 0.6 0 01 02 0.3 0.4 05 0.6 07 08 0.9 1.0 I., 1.2 3

Figure 8h - Maximum Face Ordinate at 0.9 Radius for TMB 4..Bladed

SC Propeller Series, EAR

= 0.6

14

0.10 0.0 0.07 0.0

o

0.05 0.04 0.0 002 0.0I

IIiIiUVA .0111.

lriM1rnlVAUo. I

raiiirnuawuu

NI1W1W1IVUI

WW1NAIIMIAIW1__

ra-A,A-r1-.iIw

0.7 0 I 0 2 0.3 0 4 0 5 0.6 07 08

Figure Si - Maximum Face Ordinate at 0.9 Radius for TMB

4-Bladed SC Propeller Series, EAR = 0.7

0.6 oA ₄ Is 0.9

I0

12 13

APPENDIX F

MAXIMUM THICKNESS ORDINATES AT 0.2, 0.5, 0.7, AND 0.9 RADIUS FOR TMB SC PROPELLER SERIES

014

0.12

O.iO 0.081

0.06

0.O4

0.02

0.5

I.0/

0.9

0;8

0.7

-j

IiMA I

_IMIJ4áAV

_1IhiiiAVMd

V

_V1I4d

/1 V'

0.6

0.4

0.3

0

0.20

040

0.60

0.80

1.00

1.20

1.40 I .60

1.80

2.00

Figure 9a - Maximum Thickness at 0.2 Radius for TMB 2-Bladed SC Propeller Series, EAR = 0.3

1.4 1.2

0.02

1110.8110.6

.IV4UUI

05

Figure 9b - Maximum Thickness at 0.2 Radius for TMB 2-Bladed SC Propeller Series, EAR = 0.4

02 04 06 08 1.0 12 14 16 I.e 2.0 2.2 2.4 2:6 2.8 30 0.20 0.18 0.16 0.14 0.12 max 0.10 0.08 0.06 0.04

.0.20 0.I8 0I6. 0.14 0.08 006 J 1.5 1.4 1.3 12 1.1 1.0. 0.9

AA4.4

d1dIIId1dIIId.

H H :0.8 0.3 0.5 0.4 37 Z 2 x 0.2 EAR. 0.5 I8 20 22 24 02 04 06 08 10 12

4 ,-

16

Figure 9c - Maximum Thickness at 0.2 Radius

for TMB 2-Bladed SC Propeller Series, EAR = 0.5

2.6 0.12

L

0.10 0.04 0.02 2.8. 30

0.20 0.18 0.16 0.14 0.08 0.06 0.04 0.02

iinniuii

HhIiIiIiIo.7____

.vji,.r____

4MiIiiiII

iiiiiui

0.6 0.5 0.4 0.3 () _{02 0.4 0.6}

₀₈

_{1.0 12 1.4} 16

Figure 9d - Maximum Thickness at 0.2 Radius for TMB 3-Bladed SC Propeller Series, EAR = 0.4

8 2.0 2.2

22

26

28

3.0

0.12

Zmox

0.12

.0.I0

0.08 0 E i:30.O6 0.04 0.02

JI.5

1.3 .1.1

I.00.9

08

0.7 0.6 0 5

FIWJW1UU4N

4

-IIFAPA

1

WilA

1A

wi4

-0.3

04

0.20 0.40 0.60

0.80

1.00 1.20 1.40

Figure 9e

Maximum Thickness at. 0.2 Radius for TMB 3B1aded SC Propeller Series., F

htR = 0.5 I .60

0.20 0.8 0.16 0.14 0.12 max 0.10 0.06 0.06 0.04 0.02

U...

IU .H

1111111.8

IIIrFjr,

0

0.4 05 0.3 0.7 06 1.8 20 2.2 2.4 26 28 30 0 02 0.4 06 08 1.0 12 16

0.20 0.18' 016 0I4 0.12 0.08 0.06 0.04 0.02 0 0 2 0 4 06 0.8 1.0 1.2 I 4 I 6 I 8 20 2 2 2 4 26 28 30

Figure 9g - Maximum Thickness at 0.2 Radius for TMB 4-Bladed SC Propeller Series:, EAR = 0.5

J 1.5 1.4 1.3 1.2 II I.' 0.9 0.8 0.7 0.6 0.5

0.4

0.3

0.20 0.18 0.16 0.14 0.08 0.06 0.04 0.02 0 7 J .4l.3 1.2 1 0.6 0.5 0.4 0.3 0.2 0.4 0.6 08 1.0 1.2 1.4 1.6

Figure 9h - Maximum Thickness at 0.2 Radius for TMB 4-Bladed SC Propeller Series, EAR = 0.6

0.18 0.I6 014 0.12 0.08 0.06 0.04 0.02 020 0.6 H H

AidliLi

/

H

,/f

0.4 0.3

Figure 9i - Maximum Thickness at 0.2 Radius for TMB 4-Bladed SC Propeller Series, EAR = 0.7

max 0.10 0.09 0.08 0.07 0.06 0.05 I 0.04 003 0.02 0.01

!!IPV

AM4ilil

, irliflhl

0.3 0

0l

02 0.3 0.4 0.5 0.6 0.7 0.8 o9 l.0 12 13 14 1 5

Figure lOa - Maximum Thickness at 0.5 Radius for

_{TMB 2-Bladed SC Propeller Series, EAR}

_{= 0.3}

t/D m 0.10 0.09 0.08 007 0.06 H 0.05: 0.04 0.03 0.02 0.01

1A

i

A

.

UUIWWAJUV

uriwiraiirair

iiiidt!iuIi

0.3 0 0:1 02

03

_0.4

05

06

_{07 0.8} 0L9

I0

12 13

'4

1.5

Figure lOb - Maximum Thickness at 0.5 Radius for TMB 2-Bladed SC Propeller Series,

.'tR 0.4

0I0 0.09 0.08 0.07 0.06 ti61011 0.05 (J 0.04 0.03 0.02 0.01

iuwririiirir__________

IIIF!NIV1NWA

IU1ii11JJiVAlV_______

UIWffVAVAW

6'rir4r4iiIr_______

,1iiiiUiAiV

huM'

_'

r

r

/tIIIIAAA

A

A

4

1/II17ArA.pP

rr,,

U 1.5 1,4 3 12 1.1 1.0 0.9 0.8 0.7 0.5 0.4 0.3 01 02 03 05 06 07 0.8

Figure lOc - Maximum Thiàkness at 0.5 Radius for TMB 2-Bladèd SC Propeller Series, EAR = 0.5

0.10 J-I 41.3 1.2 iI L.. 0 0.8 0.7 0.6 0.5 0.09 0.08 0.07 0.06 0.05

0

0.04 0.03 a02 0.0I 0

UP7MAV

,r

li9ppii

i4liliiii

0.4 0.3 09 10

I!

12 13 14 15 0.1 0.2 03 04 05 06 07 08

0

U' 0.10 0.09 0.08 0.07 0.06 a E 0.05

±

0.04 0.03 0.02 0.01

/

0.6 0.5

A

0.4.

/r

0.3 1.3 1.4 1.5

0

0.1

02

0.3 0.4 0.5 0.6 0.7

0.8

0.9

1.0 1.2

Figure lOe - Maximum Thickness at 0.5 Radius for TMB 3Bladed SC Propeller Series, EAR

0.5

I I

0.10 0.09 0.08 0.07 0.06 ti3O 4mox 0.05 0.04 0.03 0.02 0.01

.JI.5I.

1.3 1.21.1 1.0 09 0.8 0.7 O.b 0.0

uiiuum

ill..i

IW4UU4lU1UPgU aiii

v

Oi 02 0.3 04 05 0.6 0.7 08 09 10

II

12 1.3 4 1.5

0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

uu:rjjririipju_________

iiuurniiiiwirii__

iiu!fviriiirivapuv

.IvrffA,.pi.rn____

II. rI1rrir4ui_________

II

PA

1UI________

riiirniu

iiuuiuiu

U2_I.I

10 0.9 08 0.7

06

₀₅

0.4 0.3

0I

02 03 04 05

06

07

08

Figure lOg - Maximum Thickness at 0.5 Radius for TMB 4-Bladed SC Propeller Series, EAR = 0.5

a

90 = LV

'S9!JOS °I1°'°d 3S pepj-f ffltL °J 'Pl

0 BBOU)tOL4j. UIflUIiX

- 401 OflI

±2t

tO tO 01

ri

31 SI L0 9O G0 O O 30 IO 0

.i.i..Iii

UI...

Hi

!j

jp1pJiJJIJiJpp/iI'iiiH

::H

1.1 7.1 Li i c;i - p

u--I''

P00 100

0l0

L0

6'

600 co

Imoii 0.10 009 0.08. 0.07: 0.06 H 0.05

0

0.04 0.03. 0.02 0.0I J .5 1.4:13 12 1.1 1.0 0.9 . 0.8

uuiiiiu

I1J1WiiiiHPJH___

iIIII VIA

IIFIIII1IIIIIOI

0.7 0.6 0.3 0:4

/

05

Figure lOi - Maximum Thickness at 0.5 ?.ad.ius for TMB .4-Bladed SC Propeller Series, EAR

0.7

Z.4

0.5 E.A R 0.7

0.10 0 09 008! 0.07 0.06' max 005

0

004 0.03 0.02 0.01 0

IIIflIILiI______

i:iiiiEiR1ii_

IIU1HiRI1

IRRRdl

_RWiiP

Iuiip

p;pr

iir

0.3

Figure ha - Maximum Thickness at 0.7 Radius for TMB 2-Bladed SC Propeller Series, EAR = 0.3

0.10 009 0.08 0.07 0.06 max. _i 0.05 0.04 0.03 0.02 0.01 J .5 I 1.3 1.2 1.1 1.0 08 0.7 0.: 0.5

IUIlJJ1TiUi4W1W1UI1UUU II

111111

_{..U.,rI.r4UI.uUUIr4IUIIU}

4i'JXII!i1ii!iiiiili

.INI

IIIIPIUIUUIIUUI

!,PI1!PIPV

0 F 02 0.3 04 0.5 06 07 0.8 09 1.0

II

I 2 13 14 IS

0.10 0.09. 0.08 007 0.05 0.04 0.03 0.02 00 I 0

UUiU

i:. Ii 1.0

U

08

:uuin v i-i

0.4

I____________

//ilM4WAiUIlIUU

liIUPIII

1rlHiiIIIIIII

IUIUIIIIUUIU

7N$DIVAWAIIIIU__

___AAU

UI

1.11

Ii

I__

01 0.2 03 04 05 0.6 07 0.8 09

Figure lic - Maximum Thickness at 0.7 Radius for TMB 2-Bladed

10 2 13

SC Propeller Series, E.R

= 0.5

0.5

mo 0.10 0.09 0.08 0.07 0.06 005 0.04 0.03 0.02 0.01 0

uuiiiiiiuiumi'__H

Ill

VA VA VA VAU

uivivivwiariuuv

/AWAiHiIiiIiIl.

6 0.4 05 O3 0I

02

03 04 05 06 07 08 09 I0 12 I 3

Figure lid - Maximum Thickness at 0.7 Radius for TMB 3-Bladed SC Propeller Series, EAR

0.4

0.10 J=I.5 1,4 1.3 1.2' 1.1 1.0 0.9 0.8, 0.7 0.6, . . 0.5 0.09

0.08.

0.04

0.03'

--

--a - - - - I

VAllrdlll!iIIIIII

&

iiVUi Al Al All

I Ill

0.07

PiHh!IF 11111

0.06

A1diHhi!iI

PU!

IIIpriAflUiHiiflhiiiIIIII

002

llFdJIHdIHuIIIHIH11111I

.0 r 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.8

0.9 1.0 1.1 12 1.3 1.4 1.5

0.10 0.09 0.08 0.07 0.06 0.05 0.04 O3 0.02 0.01 J 1.5 1.4 1.3 1.2

Ii

LO 0.9 0.8 0.7 0.6

RiiihAiUiIIUiiiIIUUii

uuuuauuuuii

_p

_{v vr'p}

0.1 0.2 0.3 04 0.5 06 0.7 0 8 09 1.0 12 1.3

Figure hf - Maximum Thickness at 0.7 Radius for TMB 3-Bladed SC Propeller Series, EAR = 0.6

0J0 0.09 0.08 0.07 0.06 0.06 0.04 0.03 002 0.0I 0 0.9 0.8 0.7 0.6 05 0.4 0.3 0.1 0.2 0.3 0.4 05 0.6 0.7 0.8

Figure hg

_{- Maxiniuni Thickness at 0.7 Radius for TMB 4-fliadéd SC Propeller Series,}

E.&R = 0.5