Inclined shaft propeller performance characteristics

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U II1 U _{BEFORE COMPLETING.FORM}READ INSTRUCTIONS 1. REPORT NUMBER

4127

2. GOVT ACCCSSION NO. . . .

3. RECIPIENrsCATAL0G NUMBER

4. TITLE(d Subtitl.) .

-INCLINED-SHAFT PROPELLER PERFORMANCE CHARACTERISTICS

5. TYPE OF REPORT & PERIOD COVERED

- . .

6. PERFOMINO ORG. REPORT NUMBER

7. AuTIOR(a) . - . . . . .

James G. Peck and Donald H. Moore

S CONTRACTORORANTNuMBER(.)

9. PERFORMING ORGANIZATION NAME AND ADDRESS - - .

-Naval Ship Research and Development Center

Bethesda, Maryland 20034

10. PROGRAM ELEMENT PROJECT, TASK AREA & WORK UNIT NUMBERS

Project No. SF 35421-006 Task Area F 35-421.006 Work Unit h1520-100

I I. CONTROLLIN0 OFFICE ÑMEAÑD ADDRÏSS Naval Ship Systems Command Washington, D. C. 20360

12. REPORT DATE April 1974

13. NUMBER OF PAGES

14. MONITORING AGENCY NAME- & ADDRESS(Itdiff6r.nt from CositroliiÑ Office) IB. SECURITY CLASS. (of thi. ropotf)

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16. DISTRIBUTION STATEMENT (6f thu Report) - .

-APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED

17. DISTRIBUTION STATEMENT(of th. abatract .nt.r.d In Block 20, II dlfI.rent from R.port)

.

--IB. SUPPLEMENTARY NOTES

19. KEYWORDS(Càntiñúì än aid. if n.c.aamy aid id.ntiIy by block nomb.r) Propeller, CavitatiOn, Inclined-Shaft

20. ABSTRACT(Continu. on rvorae aid. If ary mid ideneiSTby bloCk iibòr)

Most small naval craft utilize commercially available propellers on inclined shafts as

thrusters. Information about the forces generated by inclined-shaft propellers is scarce.

To help the designer of small craft, an experimental program _{was undertaken to evaluate}

commercially available propeller performance when inclined to the oncoming flow. A series of four commercial propellers with pitch ratios of 0.8, 1 .0, 1 .2, and 1 .4 were

UNCLASSIFIED

..tC..URItY CLAUIPICATIOÑ OP THIS PAGI(P, D.fete. (Blöck. 20 coñtinùòd)

- characterized over á range of shaft angles, cavitation numbers and advanced coefficients.

Besides the usual shaftline thrust and torque, horizontal and vertical side forces were also meaSúred. The results of these experiments support the prévious assumption that a pro-peller on an inclined Shaft may produce. more forward thuSt than the same propro-peller on a. horizontal shaft This paper contams propeller characteristic curves and lift- and side-force data that are diréctly applicable in the design. of high-performance small craft.

UNCLASSIFIED.

TABLE OF CONTENTS ABSTRACT ADMÏNISTRATIVE INFORMATION INTRODUCTION . . ., . PROPELLER FORCES

..

. . PROPELLER SERIES

...

TEST FACILITIES AND PROCEDURE

REDUCTION AND ANALYSIS OF EXPERIMENTAL RESULTS ₄

CONCLUSIONS

APPENDIX A - PERFORMANCE CHARACTERISTICS OF PROPELLERS AT VARIOUS ANGLES OF SHAFT INCLINATION

APPENDIX B - REPRESENTATIVE PLOTS OF R:EDUCED DATA AND

SKETCHES OF CAVITATION .. 21

APPENDIX C USING SERIES DATA TO DESIGN A PROPELLER 43

LIST OF FIGURES

I - Force Diagram for Side-Force Measurements - 23

.2 _{Propeller Series Open-Water Charactefistics} . . 24

3 - Propeller Efficiencies versus KT/J2 for Various Pitch Ratios at

Zero Degree Shaft Inclination and à = 14.7 25

4 - Propeller Efficiencies versus KT/J2 for Various Pitch Ratios at

Zero Degree Shaft Inclination and _a

3.0 ...

. .25

5 - Propeller Efficiencies versus KT/J2 for Vanous Pitch Ratiosat

Zero Degree Shaft Inclination and a = 1.5 . . 26

6 - Propeller Efficiencies versus K1/J2 for Various Pitch-Ratios at

Zero Degree Shaft Inclination and a = 0.75, 0.5 ₂₇

7 -r Propeller Efficiencies versus KT/J2 for Various Pitch Ratios at

7.5 Degrees Shaft Inclination and _a 14.7 . 28

8 _{Propeller Efficiencies versus K1/J2 for Various Pitch Ratiosat}

7.5 Degrees Shaft Inclination arid _{a = 3.0 . 28}

Page I

iv

Page

9 - Propeller Efficiencies versus K1/J2 for Various Pitch Ratios at

7.5 Degrees Shaft Inclination and o 1.5 .. . 29

10 - Propeller Efficiencies versus KT/J2 fOr Various Pitch Ratios at.

7.5 Degrees Shaft Inclination and a = 0.75, 0.5 . . . 30

11 - Propeller Efficiencies versus K1/32 for Various Pitch Ratios at

15 Degrees Shaft Inclination and o = 14.7 . 30

1 2 - Propeller Efficiencies versus KT/J2 for Various Pitch Ratios at

15 Degrees Shaft Inclination and o = 3 0 31

13 - Propeller Efficiències versus KT/J2 for Various Pitch Ratios at

¡ 5 Degrees Shaft Inclination and o = I 5 31,

14 - Propeller Efficiencies versus KT/J2 for Various Pitch Ratios at

15 Degrees Shaft Inclination and o 0.75, 0.5 32

15 - Cavitation Characteristics of Propeller 4529 at Zero Degree

Shaft Inclination 33

16 - Cavitation Characteristics of Propeller 4529 at 7 5 Degrees

Shaft Inclination 34

17 - Cavitation Charácteristics of Propeller 4529 at 15 Degrees

Shaft Inclination 35

1 8 - The Effèct of Shaft Inclination on Cavitation Characteristics

of Propeller 4529 at o = 1.5 . 36

19 - The Effect of Shaft Incliñation on Cavitation Characteristics

of Propeller 4529 at o = 0 5 37

20 - Lift- and BearingForce Coefficients and Bearing-Force Angles

of Propeller 4529 at 7.5 Degrees Shaft Inclination . . . 38

21 Uft- and Bearing-Force Coefficients and Bearing-Force Angles

of Propeler 4529 at 1 5 Degrees Shaft Inclination . . . 39

22 - Cavitation Present on Propellers 4529 and 4530 at a 0.75

for Various Shaft Inciflatiörïs ... .

. . . 40

23 - Cavitation Present on Propellers at Zero Degree Shaft Inclination, a = 0.75,.

and TwO Thrust Loadings for Various Pitch Ratios ...

. 41

24 Cavitation Present on Propellers at 15. Degrees Shaft Inclination, o = 0.75,

and Two Thrust.Loadirìgs for VariöúsPitch Ratios

...42

LIST OF TABLES

- Experimental Progräín

2 - Pitch Range of Propeller Series

3 Performance Characteristics of Shaft Inclination . 4 Performance Characteristics of Shaft Inclination 5 - Performance Characteristics of Shaft Inclination 6 Performance Characteristics of Shaft Inclinatión . 7 Performance Characteristics of Shaft Inclination 8 - Petformance Characteristics of Shaft Incliñation . . 9 Performance Characteristics of Shaft Inclination 1 3 - PerfOrmance Characteristics of Shaft Inclination Propeller 4528 at 1 5 Degrees 10 Propeller 4529 at Zero Degree

11 Propéller 4329 at 7.5 Degrees . 12 Propeller 4529 'ät 15 Degrees ' . . _. 13 V Propeller 4531 at 7.5 Degrees 18 1 0 - Perförmance Characteristics of Propeller 4530 at 7.5 Degrees

Shaft Inclinatiòn 15

Il

Performance Characteristics of Propeller 4530 at 1 5 Degrees

Shaft Inclination 16

1 2 Prförmance Characteristics of Propeller 4531 at Zero,Degree

Shaft Inclination 17

14 Performance Chataëteristics of Propeller 4531 at 1 5 Degrees

Shaft Inclination . . . 19

Page

Propeller 4528, at Zero Degre Propeller 4528 at 7.5 Degrees

9

Propeller 4530 at Zero Degree

B Fang

NOTATION

Bearing force n.gle, measúred from the vertical

BFang arctan FH/FV [deg]'

Blade-section length at 0 7 radius [ft]

L

Propeller diameter [ft J :. .

Hrizontal force, measured perpendicular to the shaft [lb] "Verticäl" force, measured perpendicular to thé shaft [l]

Bearing fOrce FBF

v'F

+ _[lb]

J Advance ëoefficient J .= V/nD

KBF Bearing-force coefficient KBF ¡p n2 b"

KL.

Lift coeffiÏnt KL

Lip n2 D4

KQ

Torque cefficient'K'

.Q/pnD5

K.T Thrust coefficient KT = Tfpñ2D4

L ' Lift fOrce L 'T 'sin a + F cos a [lb]

n ..

Revölutii per ècond of unit time

P Ambient static pressure [lb/ft2 I

'Ambient vapor pressure [lb/ft2]

Q Torque [ft-lb j

T thrust in the horizontal plane T

t!

coS - F

Sjfl [lb]

T' Thrust measured on the shaft . [ib]

V . Speed of advance. [ft/sec]

a

Angle. of shaft inclination [degi

1? Efficiency = TVf2irQn

p Mass density of water [lb - sec2 /ft4 J

ppv

a CavitatiOn number a = 1/2 p V2 C07 D FH F FBF.

ABSTRACT

Most small naval craft utilize comtherciaily available propellers on inclined shafts as thrusters Information about the forces generated by inclined-shaft pro-pellers is scarce. To help the designer of small craft, an experimental program was undertaken to evaluate commercially available propeller performance when inclined to the oncoming flow. A series of four commercial propellers with pitch ratios of 0.8, 1 .0, 1.2, and 1 .4 were characterized over a range of shaft angles, cav-itation numbers and advanced coefficients. Besides the usual shaftline thrust and torque, horizontal and vertical side forces were also measured The results of these experiments support the. previous ãsumption that a propeller on an inclined shaft may produce more forward thrust than the same propeller on a horizontal shaft. This paper contains propeller characteristic curves and lift- and side-force data that are directly applicable in the design of high-performance small craft

ADMINISTRATIVE INFORMATION

This work was authorized and funded by the Naval Ship Systems Command Project SF 35-421-006, Task F 35-421-006,' Work Unit l-152OEl00.

INTRODUCTION

High-performance small craft are playing an increasing role in fulfilling Navy missions Histoncally, the small-craft designer has used commercially available propellers to absorb the power installed in the craft. -The majority of these craft use the inclined-shaft arrangement. Forces generated by 'the propeller in this arrangement have been accounted for only in an approximate way. As speed requirements increase for new craft designs, forces other than thrust and torque generated by the propeller become increasingly significant. The extent of cavitation on the propeller bladés at high speeds may also alter these forces as well as the

thrust and torque Detailed knowledge of the propeller-generated forces is essential for a

successful' high-speed craft dèsign.

Open-water characteristics of most commercial propellers follow closely the Troost-Series,1 which designers usually have used to choose a propeller. The 'effect of cavitation on the performance of a propeller was estimated from the Gawn-Burill2 series. However, data for both these series were obtaiñed at .a shaft inclination of zero degrees.

'Troost, L., "Open Water Test Series with Modern Propeller 'Forms," Presented' to the. North East Coast Institution of Engineers and Shipbúilders, Newc stie-upon-Tyne, Englaad (Dec 1950).

2Gawn, R. W. L. and L C. Bürril,"Effect of cavitation on the Performance of a Series of i6-lnch Model Propellers," Transactions of the Institute of Naval Architects (Mar 1957).

Because of the machinery arrangement on the new craft, the propellers operate on

shafts inclined at more than 5 degrees from the keel line. Although theoretical studies3 have

been made and some experimental work4 6 has been done concerning the effect of shaft inclination upon propeller forces, there are still three areas in which there is a lack of infor-mation about inclined shafts

1. Effect of shaft inclination on the thrust, torque, lift, and bearing forces generated

bya propeller.

2 Effect of cavitation on inclined-shaft propeller forces

3. Effectof pitch ratio on cavitation and on forces .generated by an inclined-shaft propeller. :

In addition, the lift generated by propellers on an inclined shaft can noticeably change the running trim of planing craft. It is also difficult to make a judgement as to what degree

of shaft inclination is required to produce a significant effect. Therefore, such information

is essential for a reliable design.

To assist the designer of small craft, an experimental program was started at the Center to develop usablé performance data for propellers operating on inclined shafts at cavitation conditions comparable to those of existing high-performance small craft.

Using a force measuring system similar to that in Reference 4, an .inclined-shaft pro-peller dynamometer has been built at the Center to facIlitate investigation of the forces

gen-erated on the propeller shaft. In the Navy small-craft building program, commercial

pro-pellers are used. Thus it.s decided that a limIted seiies of commercial ropellers would be

evaluated usmg the new facility This report presents the results of this investigation The

scope ofthe experimehtal program and the rangé of variable are shown in Table l

PROPELLER. FORCES

Due to shaft inclination, the flow will be ìlle to the propellers, and as a result,

vari-ations in thrust and torque forces will arise. A normal force and a yawing moment will bé

produced about an axis perpendicular to the propeller disk, i.e.,.about the propeller-shaft

3Gutschë, F., "Untersuchung vn Schiffsschrauben in Schrager Anstromung," Schiffbauforschuñg (Mar 1964). 4Hadller, J. B. and R. Hecker; "Performance of Partially Submerged Propellers," Office of Naval Reseaich Seventh Symposium on Naval Hydrodynamics, Rome, Italy ONR DR-i48 (1968).

5Hadier, J. B., "The Prediction of Power Perforinance on Planing Craft," Presented to the Society of Naval Architects and Marine Engineers, New York, N.Y. (Nov 1966).

...

.

6Taniguchi, K; et al., "Investigation into the Propeller Cavitàtion in Oblique Flow,' Mitsubithi Experimental Tank Re-port i 800 (May 1964); and NSRDC ReRe-port 2221 (May 1966).

TABLE I - EXPERIMENTAL PROGRAM

axis. Because of the uneven loading of the propeller as it rotates, a side force and pitching

moment develop about the horizontal axis through the propeller disk. These forces and

moments interact with the usúal thrust and torque forces as measured on the shaft.

PROPELLER SERIES

Four ten-inch diameter four-bladed bronze commercial propellers were purchased for the experiments. The propellers were entered into the Center's propeller numbering system. and their pitches were measured as a check on the nominal value of pitch provided commercially. The four propellers are listed in Table 2.

TABLE 2 - PITCH RANGE OF PROPELLER SERIES

The variation in pitch from blade to blade for any of the propellers was ± 0.2 in. The leading edges of the blades were smooth-rounded where necessary to eliminate flat spots.

3 NSRDC Propeller Number Nominal Pitch-Diameter Ratio Model Propeller Diameter in. Number of Blades 4528 0.8 10 4 4529 1.0 10 4 4530 1.2 10 4 4531 1.4 10 4

Advance Cavitation Shaft

Coefficient Number Inclination

deg. 4528 0.60-0.85 0.5-14.7 0-15.0 4529 0.65-1.00 0.5-14.7 0-15.0 4530 0.75-1.25 0.5-14.7 0-15.0 4531 0.90-1.40 0.5-14.7 0-15.0 NSRDC Propeller Number Nominal Pitch in. Averaged Measured Pitch in. 4528 4529 4530 4531 8 10 12 14 8.14 10.01 11.89 13.85

Except for this minor amount óf work, the propellers were left unaltered. It may be

ex-pected, therefore, that the perforniance characteristics of these propeflers will be somewhat

different from those manufactured to Center tolerances.

TEST FACILITIES AND PROCEDURE

Propeller open-water characteristics were öbtained in the deep-water towing basin using a propeller boat at zero-degree shaft inclination. Ail fbur propellers were characterized in òpen water over a range of advance coefficients J.

Cavitation characteristics of the propellers were obtained in the 36-inch variable pressure water tunnel using thé right-añgle shaft dynamomçter. The variable pressure water tunnel was used because a wIde range of ship speeds could be conveniently simulited by changing

pressures in the tunnel. This series of propellers was evaluated at five cavitatIon numbers a

representing small-craft speed from 7.5 to 40.3 knots. In addition to shaft thrust and torque, the right-angle ;.dynamometer measured forces perpendicular to the shaft in the vertical plane

and in the horizontal plane by means of a flexure system similar in design to the system

described in Reference 4..

For each set of experiments, the water speed and. static pressure in the test section were

held constant, while thrust, torque, and side forces were measured over a range of advance

coefficients J. The water speed was obtained by means of thrust Identity at zero shalt in-clination with open-water thrust. A water speed of 20 fps was used for all of the experi-ments except for cavitation number 0.5, for which the speed was increased to 25 fps. The shaft inclinatiOns studied were 0, 7.5, and ¡ 5 degrees for cavitation numbers ranging from

o.S to 14.1. .

REDUCTION AND ANALYSIS OF EXPERIMENTAL RESULTS

The openwater characteristics data of the propéllers were reduced to the usual non-dimensional thrust coefficient KT, torque coefficient KQ and efficiency i. These are

pre-sented as functions of the advance coefficient J inFigure 2. . (Reynolds number for the

pen-water tests ranged from 5.3 x

to 9.3 x l0.)

During the cavitation-characteristics experiments, forces perpendicular to the shaft were measured in addition to thé normal thrust and torque forces along the shaft. To present

the results in the usual coordinate system, the measured thrust and side forces were resolved

into horizontal and vertical components as shown in Figure 1 on page 23.

From the side forces, the1ift coefficient KL force coefficient KBF and bearing-force añgle.BFg wereca1cu1ated. Propeller efficiencies, loading coefficients KT/J2, and powering coefficients KQ/J3 were calculated from faired values of KT and K0. All the force coefficients are given in Appendix A, Tables 3 through 14. There are no lift or bear-ing force coefficients at zero shaft inclination since the side forces measured zero at this orientation;

Plots of the reduced data and sketches of cavitation are shown in Appendix B. Figures

3 through l4 show.propeller efficiency versus KTIJ2 for each pitch ratio PfD at constant cavitation nùmbers ánd at various shaft inclinations. These curves enable the propeller de-signer tochoose the most efficient pitch ratio within this propeller series for a given thrust and cavitation number.

Prop11er 4529; with a pitch ratio of 1 .0, has been chosen to illustrate the effect of the experimental conditions on propeller performance. It was selected because it has a medium pitch and the results are typical of the other propellers in this series. Figures 1 5, 16. and

17 present the cavitation characteristics of Propeller 4529 at the three shaft inclinations, 0, 7.5 and 15 degrees, respectively. Figure 1 8 shows the effect of shaft inclination on propeller

performance at a cavitation index of 1 .5, while Figure 1 9 shows the effect at a cavitation number of 0.5. These curves demonstrate that a propeller operating at 7.5-degree shaft inclination is more éfficientòver the entire range of advance coefficients than one operating

at zero degree. The curves also show that when heavily loaded, a propeller operating at

1 5-degtee shaft inclination is less efficient than one at either zero or 7.5 degrees. This is due primarily tó cavitation, which is about the same at zero or 7.5 degrees ort a heavily

loaded propeller, but at 1 5 degrees increases greatly when heavily loaded, thus reducing

efficiency. However, as the loâding decreases, the I 5-degree shaft inclination provides more efficient operation than the zerodegree inclination and when lightly loaded, the propeller at 15 degrees becomes môre efficient than at either zero or 7.5 degrees.

Figùres 20 and 21 show the lift and beariñg-force coefficients and the bearing-force angle of Propeller 4529 at shaft-inclination angles of 7.5 degrees and 15 degrees, respectively. As would be expected, both the lift and bearing forces increase as the shaft inclination in-creases. At a constant advance coefficient, both lift and bearing forces usually decrease with increasing blade cavitation. Although the bearing-force angle varies rather unpredictably over the range of cavitation numbers, at the same cavitation number, the trend of change of bearing-force angle with advance coefficient is similar for both shaft inclinations.

The "vertical" force F is proportional to the change of shaft angle. while the

lion-zontal force FH is relatively independent of it. Thus, as the shaft inclination increases. the

"vertical" force exerts a greater influence on the direction of the resultant bearing-force

angle. Since vertical was chosen as zero bearing-force angle, as the shaft inclination in-creased, the bearing-force angle deviated less from _{zero. Therefore, the range of values of} the bearing-force angle is wider at the 7.5-degree shaft inclination than at the i 5-degree. Shaft inclination.

Figure 22 presents sketches of the cavitation on Propellers. 4529 and 4530 for _{all three}

shaft inclinatiOns at a cavitation number of 0.75 and two different advance coefficients. At a constant advance coefficient, the cavitation increases as the shaft angle increases. Figúres

23 and 24 present sketches of cavitation on the propellers at zero and I 5-degree shaft inclination, respectively. The sketches are for various pitch ratios at two different thrust loadings and a cavitation number of 0.75. At zero shaft inclination (Figure 23), for the same loading coefficient K1/12 cavitation decreases as pitch ratio increases. In Figure 24 (15-degree shaft inclination), at a constant K/i2 value, minimum cavitation occurs at the mediUm pitch ratios.

To facilitate use of the information presented in this paper, _{a sample calculation is}

provided in Appendix C.

CONCLUSiONS

These experiments show that the lift and bearing forces generated by propellers on

inclined sháfts can be very significant in magnitude. Cavitation observations show that cavitation increases as the shaft angle increases. For 'this reason, the effect of cavitation on

propeller performance at 1 5 degrees is greater than might have been anticipated from cavi-tation data obtained at zero-degree shaft inclination.

The tables contained in this report provide data from which the small-craft designer should be able to select the type of propeller that will operate best on his craft. From the information contained herein, he will be able to predict the performance of a propeller on an inclined shaft as well 'as the lift and bearing forces which may affect the trim and handling of the craft.

APPENDIX A

PERFORMANCE CHARACTERISTICS OF PROPELLERS AT

VARIOUS ANGLES OF SHAFT INCLINATION

TABLE 3 - PERFORMANCE CHARACTERISTICS OF PROPELLER 4528 AT ZERO DEGREE SHAFT INCLINATION

INCLINATION ANGLE O

INCLINATION ANGLE - O PITCH RATIO - ¡800

PITCH RATtO .800 SIGP - 14.700

INCLINATION ANGLE O PITCH RATIO .800 SIGNA - 1.500,

INCLINATIO ANGLE O PITCH RATIO = .800.

8

SIGNA - 3.000

SIÔNA - .500

J KTOUT 1OP(QOUT EFIC tT/J K0/J3

.6500 .1149 .1921 .6189 .2719 .0699

.7000 .0937 .1702 .6135 .1913 .0496 .7500 .0706 .1482 .5685 .1255 .0351

.8000. .0471. .1220 .4915 .0736 .0238

.8500 .0289 .0937 .4177 .0400 .0152

J KTOLIT 10QOUT EFFIC KT/J2 KQ/J3

.6500 .1084 .1756 .6384 .2565 .0639 .7000 .0825 .1431 .6420 .1683 .0417 .7500 .0574 .1139 .6019 .1021 .0270 .8000 .0362 .0881. .5236 .0566 .0172 .8500 .0178 .0645 .3739 .0247 .0105

J .KTOIJT OkOOUT 'EFFIC KT/J2 ' kO/J3

.6500 .0941 .1568 .6208 .2228 .0571 .7000 .0760 .1346 .6286 .1550 .0393 .7500 .0530 .1126 .5625 .0943 .0267 .8000 .0306 .0916 .4252 .0478 .0179 .8500 .0117 .0686 .2310 .0162 .0112

j

ITOUT 1OKQOUT EFFIC KT/J2 KQ/J3

.6500 .0503 .1057 ¿4925 .1191 .0385

.7000 .0370 .0924 .4456 .0754 .0269

.7500 .0254 .0740 .4104 .0452 .0175 .8000 .0104 .0483 .2736 .0162 .0094

.8500 -.0307 .0061 .0425 .0010

J - KTOUT 1OKQOUT EFFIC KT/J2 KQ/J3

.6500 .0206 .0531 .4013 .0488 .0193 .7000 .010 .0475 .2416 .0210 .0138 .7500 .0050 .0283 .2109 .0089 .0067 .8000 .0000. .0068 .0000 .0000 .0009

.8500 -.0255 .0015 -,0353 .0002

TABLE 4 - PERFORMANCE CHARACTERISTICS OF PROPELLER 4528 AT 7.5 DEGREES SHAFT INCLINATION

INCLINATION ANGLE 2 7.500 PITCH RATIO = .800 SIGMA 2 .750

J (TOUT 1OKQOUT EFFIC KT/J2 KQ/J3 KL 8F 8F A W G

9 J .6000 .6500 .7000 .7500 .8uQ .850J J .6003 .6500 .7000 .7500 .8300 .650û INC4.INATION ANGLt KTCUT IOXOOUT .1293 .2195 .1107 .1833 .0884. .1578 .0652 .1335. .04.18 .1w59 .0162 .0?5C INCLINATION A.JSBL. KTOUT 1OKQOUT .1011 .188u .0903 .1550 .0731 .13D1 .054.6 .11'.1 03'.6 .0889 .0070 .05?o = = ?.5o0 t.FFIC .562? .6246 .6239 .5830 .502'. .2930 ?.,10 EFFIC .5745 .6026 .5981 .5716 .4954. .1635 PITCH RATIC KT/J2 .3592 .2620 180'. .iioi) .0653 .u2?5 PITCH RATIO KT/J2 .2808 .2137 .14.91 .0971 .054.0 .0096 = .803 KG/..J3 .1016 .0668 .0'.b0 .0317 .0207 .0122 z .800 kU/J3 .0778 .0565 .0397 .0270 .0174 .0094 SIGPA = KL .0274. .0258 .0V.'. .0231 .0216 .0193 SIGMA KL .0229 .0231 .0225 .0211 .0193 oj 3.000 K6F .0102 .0115 .0131 .0148 .0163 .0172 1.500 KBF .0090 .0113 .0131 .014.3 .0156 .018u BFANG -3.0071 -7.2345 -10.4.906 12.2904 -11.7831 -7.7528 FAbG 8.5882 -'..7199 -11.533? -15.9390 -1.082 -19.0998 .6000 .04.91 0986 .475'. .1363 .04.56 .0119 .0056 22.2 086 .6503 0'.bb .1002 .4.807 .1102 .0365 .0155 .0092 9.2811, .7000 0395 .0932 .4.718 .0805 .0272 .0177 .0126 -1. 7675 .7500 . 0266 .1779 .4066 .04.72 .0185 .0177 .014.7 -12.5 116 .8000 .0073 .054.8 .1705 .0114. .0107 .0159 .0162 -22. 177 3 .8503 -.0182 .0227 -1.0846 -.0251 .0037 .014.0 .010'. -27.6'.3e

INCLINATION ANGLE = ?.5u0 PITCH RATIO 2 .800 SIGMA 14.700

J i(TOUT IOKQOUT EFFIC KT/J2 K0/J3 KL ICUF BFANG .6J03 .1353 .225? .5725 .3758 .104.5 .0275 .0097 10.0120 .t5d0 .1135 .1961 .5985 .2636 .07i'. .0275 .0117 5.3392 .?OOJ .0918 .171.5 .5859 i873 .0509 .0250 .012? 1.683'. .750J .0705 .14.62 .5680 .125'. .0351 .0225 .0132 -.5775 .8J03 05U3 .1178 .544.0 .0786 .0230 .0205 .013E -1.9393 .8iOO .0319 .0964. .4470 .04.4.1 .0157 .0177 .ulJó -3.7713

J KTOUT 1OKQOUT EFFIC KT/J2 KQ/J3 KL KeF dFANG .6000 .0202 .0546 .3533 .u561 .0253 .0047 .0023 -28.0700 .6500 .0227 .0622 .3775 .0537 .0226 .0083 .0063 -31.7000 .700iJ .015'. _.0580. .2958 .031'. .0169 .0110 .0108 -33.6900 .7530 .0021 .-0503 .0498 .003? .3119 .012'. .014.. -33.6900 .8000 -.0133 .038S -.44.11 -.0237 .0075 .0117 .0158 -29.6561 8500 -.0266 .0119 -3.0308 -.068 .0019 .00?? .014.0 -17.8507 INCLINATION ANGLE = 7.5jO PITCH RATIO = .800 SIGMA = .500

TABLE 5 - PERFORMANCE CHARACTERISTICS OF PROPELLER 4528 AT

15. DEGREES SHAFT INCLINATION

INCLINATION ANGLE 150g0 PITCH RATIC = .800 SIGMA 14.700

INCLINATION ANGLE z 15o00' PITCH ¡ATIO = .800 SIGMA = 3.000

INCLINATION ANGLE 15.000. PITCH RATIO .800 SIGNA 1.500

INCLINATION ANGLE 15.000 PITCH RATIO z .800 SIGMA .750

J KTOUT. IOKQOUT EFFIC I(T/J2 Q/J3 KL KF

9FANG-.6000 .1367 .23?'?..' 549 , . 3797; i100 .. .0567 019 3.1765 650i] .111.5 .204g. .5793 .2710. .071.4 .051.5 .0230 .307? .7000 .0952 1881 .561.0 .191.4 .051.9 .0523 .0260 -1.8553 .7500 .071.5 .1681 .5289 .1321. .0396 .01.88 .0279 -..0347 .8000 .0533 .1397 ,1.861 _.0833 .0273 .01.1.6 .0291. '-6.2477 .8500 .0387 111.? .1.563' .0536 .0187 .01.29 .0318 -7.8065 J .6000 .6500 .7000, .7500 .8000 .8500 )(TOUT .0283 .0327 ' .0338 .0268' .0103 -.0142 IOKQOUT .0634: .0751 .0857-.0829 .0650 .0380. ' EFFIC .1.263 .4467 .4390 .3864 .2022 -.5046 ' KT/J2 .0786 .0773 .0689 . .0477 .0161 -.0196 KQ/J3 ' .0293 .0275 .0250 .0197 .0127 ' .0062 ' KL .0122 .0205 .0288 .0330. 0311 .0228 KBF .001.5 .0116 .0189 .0272: .0324 .0267 BFANG 11.8409 -4.294k -11.2613 -13.1.38'? -13.91.56 -14.6409

J KTOUT. 1OKQOUT: EFFIC kT/J2 KQ/J3 KL KBF BFANG

.6000 .1259 .2121 . .5671 .3498 .0982 .0530 .0187 8.6578 .6500 .1068 .1810 .6102 .2528 .0659 .01.98 .020 3.1.811 .7000 .081.6 .153? .b132 .1727 .01.48 .0452 ¿0217': -1.0822 .7500 .0637 .1272 .5977 .1132 .0301 .0390 .0212 -5.7278 .8000 .0431 .1018 .5393 .0671. .0199 .0338 .0217 -8.8011 .8500 .fl167 .0808 .2788 . .0231 .0132. . .0347 .0295 -6.2978

J KTOUT 10,KOOUT FFFIC ICT/J2 ICO/J3 _{KL KBF}

. BFANG .6000 .0972 .1668 .5562 .2699.0772 .042.1 .0161 17.3802. .6500 _.0931 .1630. .5911 .2208 .0594 .01.74 .0219 6.6592 .7000 .0779 .1491 . .5824 .1590 .01.35 .0476. .0258 .0016 .7500 .0603 .1284 .5802 .1071 .0304 01.60, . .02!9 -1..2116 .8000 .01.18 .1053 .5050. .0653 .0206 .01.46 .032k. -6.7092 .8500 .0169 .0850 .2695 .0234 _.0138 . .o43 .0379 -7.3302 J

lo.

TABLE 6 - PERFORMANCE CHARACTERISTICS OF PROPELLER 4529 AT

ZERO DEGREE SHAFT INCLINATION

O

II

ICLWT1C ANCLE - O PITCH PATIO - 1.000 SlOW. - 14.700

J KTOUT IOICQOUT EFFIC KT/J? K0/J3

.6500 .2212 409Q 5S81 .S?35 .1492 .7000 .1QQO 1660 .6058 .406? .1067 .7500 .1768 .3294 .6406 .1143 .0781 .8000 .1544 2957 .6647 .2412 .0577 .8500 .1316 .215 .6810 .1822 0426 .9000 .1084 .2247 .6910 .1338 .0308 .9500 0845 .1843 .6928 .0936 .0215 1.0000 .0595 .1405 .6744 .0595 .0141 1.0500 .0314 .0945 .5901 .0303 .0082 1.1000 .0056 .0488 .20?? .0047 .0037 J ANCLE -KTOUT PITCH RATIO - 1.000 1OICQOUT urIc KT/J2 SIGMA - 3.000 KO/j3 .6500 .2025 .3909 .5360 .4794 .1423 .7000 .1682 .3533 .5937 .3842 .1030 .7500 .1657 .3096 .6388 .2946 .0734 .8000 .1397 .2663 .6677 .2182 .0520 .8500 .1129 .2263 .6747 .1562 .0369 .9000 .0861 .1892 .65 19 .1063 .0259 .9500 .0580 .1510 .5813 .0643 .0 176 1.0000 .0255 .1045 .3887 .0255 .0105 1.0500 -.0167 .0392 -.7 106 -.0151 .0034 INCLWTION ANCLE -, J (TOUT PITCH RATIO - 1.000 1OKQOUT EFFIC KT/J2 SIGMA - .750 KQ/J3 .6500 .0715 .1518 .4873 .1692 0553 .7000 .0809 .1666 .5409 .1650 .0486 .7500 .0837 .175'. .5694 .1487 0416 .8000 .0856 1838 .592 8 133,7 .0359 .8500 0844 .1863 .6 128 1168 .0303 .9000 .0753 .1736 .6216 .0930 .0238 .9500 .0561 1393 .6 087 .0621 0162 1.0000 .0319 .0869 .5838 .0319 .0087 I1IcLINATIS ANCLE - O J KTOUT PITCH RATIO - 1.000 1OKQOUI EFFIC KT/J2 SIGMA - 1.500 KQ/J3 .6500 .1416 .2820 .5194 .3351 .1027 .7000 .1559 .2987 .5815 .3162 .0871 .7500 .1513 .2904 .6220 .2690 .0686 .8000 .1356 .2684 .6432 .2119 .0524 .8500 .1140 .2401 .6422 .1576 .0391 .9000 .0893 .2087 .6127 .1102 .0286 .9500 .0619 .1737 .5387 .0686 .0203 1.0000 .0296 .1301 .3618 .0296 .0 130 1.0500 -.0122 .0694 -.2929 -.0110 .0060 INCLIN&TION ANCLE - O J KTOUT PITCH PATIO. 1.000 1OKOOUT EFFIC KT/J2 SIGMA - .500 IÇQ,J3 .6500 .0310 .0813 .3939 .0733 .0296 .7000 .0374 .0952 .4375 .0763 .0278 .7500 .0442 .1064 .4955 .0785 .0252 .8000 .0500 .1166 .5460 .0781 .0228 .8500 .0521 .1226 .5743 .0721 .0200 .9000 .0462 .1169 .5659 .0570 .0 160 .9500 .0268 .0871 .4646 .0297 .0102 1.0000 -.0132 .0164 *.2864 -.0132 .0016

TABLE

7 -

PERFORMANCE CHARACTERISTICS OF PROPELLER 4529. AT

7.5 DEGREES SHAFT INCLINATION

PATIO i.00ó SIGMA 14.700 INCLINATION ANILF = 7.0fl PITCH =

12 J INCLINATION *NI.F (TOIIT 10'(QO(JT 7,5fl F:FFIC PITCH RATIO = 1.000 KT/J2 (Q/J3 SIGMA = 3.000 EL wqf HFAPU .6500 .7075, .3916 .5454 .4912 .1433 .0382 .0109 -7.231M .7000 .1940 .1575 .6045 1959 .1042 .0184 '11 26 -4.12)6 7500 .1708 .7111 .6506 .1036 ' .0743 0171 -R6206 .8000 .1441 .700 .6805 .7255 .0527 .0759 .0171 -14. 3140 .8500 .1181 .320 .6898 .1637 .0378 .0147 .020 1 -19 .57 .000 .0935 .1988 .6736 .1154 .0273 .0318 .0230 -22.5447 .9500 .0677 .1650 .6705 .0750 .0192 .0110. .0256 -71.1725 1.0000 .0361 .1208 .475? .0161. .0121 .0115 .0272 -13.1754 INCLINATION AWGLF 7.00 PITCH PATIO 1.000 SIGMA = 1.500

J KTOIIT IOKQOLJT EFFIC KT/J2 KQ/J3 KL KHF RFAMr,

.6500 .1415 .2794 .5238 .3349 .1018 .0762 .008? 23.4271 .7000 .151? .2912 .5862 .3127 .0849 .0127 .0177 2.1626 .7500 .1575 .?R43 .6402 .7711 .0674 .0156 .1)155 -3.7141 .N000 .1407 .2649 .676) .2198 .0517 0361 .0177 -3.977.7 .R500 .1198 .7370 .6815 .1658 .03R6 0158 .0200 -4.5775 .9000 .0976 .2011 .6571 .1143 .0279 .0346 .0225 -7.6172 .9500 .0625 .1641 .5756 .0693 .0142 .0334 .0254 -11.3803 10000 .0119 .1191 .4531 .0339 .01.19 .0323 .0781 -lfl.32q6

J KTfljT jOKQO(JT EFFIC KTtJP I(Q/J3 KL I'14F BFAPG

6500 .01Ml .09311 .4306 .0917 .0339 fl09 .0016 .1114 7000 .0575 .1162 .5031 ' .1071 .0339 .0051 -4.3825 .7500 0615 .1320 .559 .1093 .0313 .0211 .00Q? -9.7318 .8000 .0653 .L414 .5880 .1,020 .0276 .0211 .0118 -14.2174 $S0fl .0613 .1434 .5969 .0876 .0234 ,0'43 .0183 -16.9616 9000 .0546. .1355 .5767 .0673 .0186 .0778 .1)725 -.17.9776 .9500 .0380 .1134 .5067 .0421 .0132 .0712 .9260 -18.1199 1.0000 .0171 .0713 .2753 .0123 .0071 .0746 0M7 -19.1090

J KTOIIT IOKQOUT FFFTC ICT/J2 KO/J3 EL 11F AFAMe,

.6500 .?2?R .4160 .5542 .5274 .1515 .fl4? .fl12 7.1696 .7000 .1989 .3763 .5889 .4060 .1097 .0416 .0154 1.9614 .7500 .Ï767 13Q .6707 .1147 0M05 .0405 .0171 7.1949 .8000 .155? abS6 .6468 .426 .0597 .0188 .018? 2.2840 .8500 .1715 .72 66?0 .1R48 0444 .0169 .0191 1,64?? .9000 .1106 .2407 .6582 .1365 .0330 .0149 .020? -.3165 9500 .0854 .208? .6205 .fl947 .0243 .0111 .0718 -4.1785 1.0000 .0571 .1745 .5206 .0571 .0175 .0115 .0242 -10.5300 j .6500 .7000 .7500 .8000 .8500 .9000 .9500 1.0000 TNCLDIATTON ANr,1F = KTrUIT Lfl'0flUI .07fl .1650 0856 .1764 .0937 .1918 .0991 .2035 .0967 .2054 .0846 .1933 .067 .1646 0195 .1183 INClINATION AÑ(iI.,F = 75Q0 EFFIC .514? .5398 .5R34 .6200 .6366 .6269 .5872 .5Ì82 7.600 PITCH RATTO 1.000 KTIJ2 KQ/J3 EL .1941 0601 .0141 1.744 .0514 .0171 .1667 .0455 .0710 .1548 .0397 . .133R .0334 .0176 .1045 .0265

fl

341 .070P .0192 .0341 .0385 .0118 0117 PITCH PATIO = . 1.000 SIGMA 1)061 .0071 .0111 ,1c7 .0199 .0235 0765 )3QA SIGMA = .750 4M.7161 1?.719? 19.6548 8.3347 -1.7466 -10.4125 -16.8045 -19.3870 .500

TABLE 8 PERFORMANÇE CHARACTERISTICS OF PROPELLER 4529 AT 15 DEGREES SHAFT INCLINATION

INCLINATION ANGLF = .15.000 PUCk PTTÓ ' 1.000 SIGMA 'z 3.000

PTTCH PATTO = '1.000 SIGMA =

13

J KTOIPT IOVOO(IT FFFTC KT/J2 I(0/J3 _KL '(8F RFAir,

.6500 .2046 .1982 .5316 .4843 .1450 .0848 .0290 -.1826 .7000 .197' .168? .5817 .3921 .1073 .0857 .0331 -2.6610 .7500 .1719 .1286 .63!? .1091 .0779 .08Ç2 .0374 -1.0086 .8000 .15?R .7882, .6751 .7387 .0563 0839 '.0416 -1.3016 .8500 .1106 .2516 .7075 .1808 .0410 .08?? .0457 -1.6443 .9000 .1074 .7191 .70)7 .1126 .0301 .OAOI .1)497 -4.1591 .9500 .0816 .1878 .6575 .0905 .0219 .0772 .0536 -4.9885 1.0000 .0501 .1491 .534? .0501 .0149 07?8 .0577 -6.2950

INCLIPIATTON ANC.I.F = i.non PTTCH PATTO = 1.000 SIGMA z .500

J K'iT Ifl0Ù(IT FFFTC KT/J? KO/J3

.6600 .1150 .7787 .5011 .1195 .1015 .0520 .0165 76.5600 .7000 .1443 .2861 .5615 7945 .0835 .019 .0711 11.7100 .7500 .1417 .2810 .6101 .2554 .0666 .0690 .0297 6.1813 .AOOO .1141 .2659 .6431 .7098 .0519 fl777 .0355 1.5400 .Ásoo .117Q .2431. .6549 .1630 .0396 .071? .040? -1.8245 .9000 .0961 .7144 .6405 .1186 .0295 .0714 .044? -4.7000 .9500 .0716 .1815 .5965 .0794 .0212 .0687 .0481 -7.05)2 1.0000 .0471 .1434 .5227 .0471 .0143 .074 0534 -8.0200 J TPJCLINATTON APJIF KiflhlT IOKQOLJT.. = 15.fl')fl

EFFI.0 KT/J2 KO/J3 _KL 4F RFA!JG

.6500 .7000 .750( .0161 .0411 .0476 .0855' .0975 ,, .1081 ' . .4243'. .4721 .5241' .0830 .0641 0845 .0311 .0284 .0257 .0172 .0'19 .0281 .0076 .0106 .0152 8.3877 7.1410 6.6448 .8000 .0521 .11M3' .5611... ' .0815 .0231 .O1ÇR .0212 5.9016 .8500 .051? .1757' .5727, .0736 .0205 .0417 .0285 4.258 .9000 .0487 .1261,, ., .5525. .0601 .0173 .0506 .0363 1.4411 .950fl .0167 .l132' " .4838 - .0401 . .0132 .0547 .0435 _5fl94 1.0(100 .0114 .0781 .2734 .0134 .0078 .0516 .04l7 -7.1835 INCLINATIO# ANGLE = 15.300 PITCH PATIO z 1.000 SIGMA z .750

J KTOUT l3KQ0UT '. EFFIC KTFJ2 KQIJ3 EL K8F 8FANG

.6500 .1759 .1588 .4964 .1.797 .0578 .0271 .0fl73 22.7313 .7333 .377.1 .1698 .5060 .1.57'. .0495 .0'34 .01.36 14.773? .7500 .0797 .1808 .5264 .1617 _.0428 .0616 .0i9 10.0986 .8000 .0801 .1'70. .565? .1252 .0365 .o'.80 .0268 6.1596 .8500 .0761 .1858 .5%1 .1053 .0333 .0555 .0341 1.5916 .9000 .066'. .1764 .5396 .0820 .0242 .0607 .0418 -3.8493 .051? .1601 .4837 .0568 .016? .0644 .3499 -9.2506. 1.0000 .G12 .1632 .365 .0318 .0140 .0661 .0584 -12.5513 J INCLINATION ANGLF= KIOLIT IOKQOUT 15.000 EFFT,C PITC4 PATIO KT/J2 =. 1.000 KQ/J3 SIGMA EL z 14.7ó0 K'F .650(1 .22? .4703 .5465 .6255 .1530 .0856 .025? 3.5967 .7000 .1963 .1801 .5755 .4007 .1108 .0829 .0292 -.0439 .7500 .1756 .1441 .6092 .3127 _.0816 .0818 .0336 -3.2850 .8000 .1567 .3113 .6411 .449 .0608 .0814 .0383 -5.6368 .8500 .1174 .2804 .6627 .1901 .0457 .0810 .0430 -6.9533 .9000 .1158 .2499, .6640 .1430 .0343 .0798 .0474 -7.4317 .9500. .0912 .2178, .6332 .1010 .0254 .0770 .0517 -7.6129 1.0000 .0612 .1818 .5512 0A3 ¿0182 .0721 .0538 -8.3814

TABLE 9 - PERFORMANCE CHARACTERISTICS OF PROPELLER 4530 AT ZERO DEGREE SHAFT INCLINATION

IL1H&TIW £LI - O PITCH MITO - 1.200 SIC1 - 1.500

J KTOIJT l0c(if,UT ric T/J? K')/J3

14

J 'Titi1 Iu'cQOuT EI11C !T/J K'l/ J3

.750'V .2511 .54.43 .5510 .4500 .1300 .0000 .2391 .o131 .3739 .0970 .RS0fl .2144 .44Th .4604 30?S .0729 .9000 .1930 .3999 b4 7 2394 0549 .9500 .1676 3524 .7191 .1457 .0411 .A000 .1411 . 3(145 .1374 .1411 .0304 .0500 .1151 .2560 .7514 .1044 0221 .1000 .4,497 .?0 1'. .1515 .0742 .0 156 .1500 .0641 .7 363 .0485 .0105 .2000 .0369 .3137 .6197 .0256 .0 066 .7500 .0057 .0720 15t4'. 0037 .0037 .7500 1004 .2372 .5051 .1784 .0562 .0000 .1044 ..340 .1631 .0402 .0500 .1114 .250', ,M10 .1542 .0423 .0000 .1174 .269" .6239 .1450 0370 .9500 .119? 2731 .6597 .1320 .0318 1.0000 .1146 .2670 .6833 .1146 .0267 1.0500 .1070 .249? 6493 .0932 .0215 1. 1000 .0017 .2107 .6698 .0692 .0164 1. 1500 .054'. 17Sh .6090 .0442 .0115 1.7000 .029? .1210 '.609 0203 0070 1.2500 -.000R .0569 - .0292 -.0005 s 0029 L4TjCI AGL1 O J KTI)IIT PITCH ftATlO - 1.200 IOK(JOUT

lriC

_KT/J7 SIII - 14.700 14f1/J3 .7500 .26c2 .54 12 .5449 4714 .1243 .0000 2.11 .4951 .425? .3799 .0967 .500 .2213 .4514 .6633 .3063 .0 735 0000 .I'9A .4105 .6964 .2464 .0563 .S00 .1170 .3721 1219 .1970 .0434 1.0000 .1556 .3360 .7371 .1556 .0336 1.0500 .11M .1001 1199 .1205 .0259 1.1000

ifl?

0902 .0 197 1.1500 .044? .220 b994 .0637 .0 145 1.2000 .0576 .1701 .6466 .0400 0098 1.7500 .0249 I 04.1 324 .0 lbs .0055 .7500 .153 4!161 .447 _.3?.'. 0063 .0000 .201? .'.1W .6145 .3144 0 1'. .0500 .1979 40'e4

b22

.2740 .0658 .9000 .147k 311'e .b9S .2257 .0519 .0500 .1614 .345e .7070 .1789 .0403 1.0000 .1374 .3099 .7065 .1376 .0310 1.0500 .1134 .2140 .6913 .1024 .0237 1.1000 .0401 .?36I .6590 0737 .0178 1.1500 .061Ç

.19''

.5066 .0400 .0128 1.2000 .0314 14? .4480 .0232 .0082 1.2500 -.0062 .0703 -.1740 -.0040 .0036 EILTT J &L8 -0 KTOUT PITCH MIlO - 1.200

10f00UT FFIC IIT/J? K0/J3- .500

.7500 .0506 .1341 4500 .0099 .0318 .0000 .0631 .1595 .5038 .0986 .0312 .0500 .0711 1770 5431 0984 0288 .9000 .0 764 .1892 .5785 .0944 .0260 .9500 .0401 .1970 .6144 .0087 .0230 1.0000 .0417 .1996 .6513 .0817 .0200 1. 0500 .0798 .1944 b858 0724 0168 1.1000 .0717 .177? 7087 .0593 .0 133 1. 1500 .0537 .1419 .e922 0406 .0093 1.2000 .0206 .0409 .4869 .0143 0047 1.2500 -.0336 -.0 153 4.3.559 -.11215 -.0008

U!CLIMTICH ATÁ - O PITCH IATIO 1.200 SIGN - 3.000

flILI56TI0II *LI - O PITCH 11X10 1.2110 0IC - .750

'TABLE 10 - PERFORMANCE CHARACTERISTICS OF PROPELLER 4530 AT 7.5 DEGREES SHAFT INCLINATION

15

J - . KTOUT 10Q0UT EFFIC KT/J2 IC0/J3 EL KAF RF'ANG

.7500 .1C75 .2469. .5197 .1911 .0585 .0198 .0067 32.1856 .8000 - .1171 .2650 .5628 .1830 .0518 .0253 .0105 25.1801 .8500 .1733 .2801 .5956 .1707 .0456 .0326 .0168 ' 17.4922 .9000 -. .1251 '.2890 .6199 .1544 .0396 03QQ .0236 9.7621 .9500 .1216 .2890 .6363 .1348 .0337 .0458 .0299 ' 2.4956 1.0000 .1125 . 2784 .6434 .1125 .0278 .0498 .0350 3.9360 1.0500 .0976 .2560 .6369 .0885 .0221 .0515 -9.2956 1.1000 .0768 .2215 .6067 .0634 .0166 .0512 .0412 .13.4804 1.1500 1.2000 - 059 .0197 ' .17.55 .1189 .5265.3088 .0382 .0134 .0 115 .0069 .0497 .0485 .0436 .0474 -16.5222 -18.5871 1.2500 ' -.0161 .0538 -.5962 -.0103 0028 .0493 .0544 ' -19.9756

INCLINATION ANGLF á 7.500 PTTCH RATIO = 1.200 SIGMA z .500

J .7500 .8000 .8500 .9000 .9500 1.0000 1.0500 1.1000 1.1500 1.2000 1.2500 INCLINATION ANGtI z KTOUT 1OKOOUT .1851 .4155 .2013 .4347 .1982 .4227 .1837 .3931' .1634 .3563 .1414 .3190 .1198 .2844 .0989 .2523 .0772 .2191 .0512 .1775 .0159 .1169 INCLINATION ANGLF = 7.500 EFFIC .5318 .5895 .6345 .6692 .6934 .7055 .7039 .6861 .6445 .5511 .2704 7.500 PITCH RATIO z ' 1.2('0 KT/J2 XO/J3 .3291 .0985 .3145 . .0849 .2744' 0688 .2268 .0539 .1811 0416 .1414 .0319 .1087 .0246 .0817 .0190 .0583 .0144 .0356 . 0103 .0102 0060 PITCH RATTO = 1.700 SIGMA z EL .0509 .0537 .0548 .0550 .0547 .0545 .0547 .0554 .0566 .0580 .0594 SIGMA z 1.500 KIIF' .0264 .0269 .0283 ¡0304 .0329 .0357 .0387 .0420 .0460 .0509 .0573 .750 8FANG' -6.4482 -4.8842 -3.4891 2.4157 -1.7617 -1 .5700 -1.8283 -2.4693 -3.3709 -4.3558 -5.1918 J INCLINATION AÑGIF KTOUT 1OKOOUT 7.500 EFIC PITCH RATIO 1.200 KT/J2 K0/J3 SIGMA 14.700 EL KMF AFANG 7S00 .2624 .5464 .5733 .4666 .1295 .0542 .0198 -6.0625 '.8000 2412 .5033 .6103. .3769 0983 .0508 .0191 -7.6650 .8506 '.2226 .4594 .6555 .3081 .0748 ' .0505 0211 .8.0673 .9000 2044 .4175 7013 2524 .0573 .0517 .0246 -7.8317 .9500 .1852 3790 .7387 .2052 .0442 .0534 .028fi -7.3854 1.0000, 1641 .3442 .7589 .1641 .0344 .0549 .0332 -7.0206 1.0500 1411 .3120 .7559 .1280 .0269 .0561 .0375 -6.8946 1.1O00 1.1500 .1168 .0923 .2803 .2458 .7293 .6873 0965 .0698 .0211 .0162 .0571 .0585 .0418 .0465 -7.0296 -7.3127 1.2000. .0697 .2039 .6526 .0484 .0118 .0614 .0524 -7 .4963 1.2500 .0516 .1490 6884 .0330 .0076 .0672 .0605 -7.1975

J 'KTOUT 'LOKQOIJT EFFIC KT/J2 KQ/J3 EL KF AFANG

.7500 .oQ7 .1781 .4671' .1239 .0422 .0128. .0040 34.2000 .8000 .0716 .1826 .4976 .1115 .0357 .0163 .0078 27.1656 .8500 .0839 .2073 .5475 ' . 1161 .0338 .0233 .0129 20.7000 .9000 .2309 .5942 .1183 .0317 .0314 .0189 14.2544 .9500 .1000 .2405 .6287' .1108 .0281 .0387 .0254 ' 7.6000 1. 0000 .0939 .2315 6460 .0939 ' .0231 .0443 .0318 .8281 1. 0500 .95 . . .2074 .6406 .0721 .0179 .0480 .0376 -5.6500 1. 1000 .0630 ' . .1802 .6120 .0521 .0135 . .0503 .0424 -11.1031 1. 1500 .0552 .1700 .5943 0417 .0112 .0525 ,0456 -14.4800 J INCLINATION ANG1 z KTOIJT 10000UT 7.500 EFFIC PITCH PATIO z 1.700 KT/J2 KQ/J3 SIGMA z EL 3.000 AFANG .8500 .1968 .6443 .5992 .2724 .0723 .0520 .0258 -1.1900 .9000.. .1860 . .3997 .6665 .2296 .0548 .0522 .0274 -1 .7510 .9500 .1579 .3481' 6858 1750 .0406 .0510 .0299 -) .2900 1.0000 .1259 .3001 .6679 .1259 .0300 .0499 .0330 .. -.5334 1.0500 .0981 .2608 .6286 .0890 .0225 .0497 .0365 .000.0 1.1000. .0768 ' .2294 .5863 0635 .0172 .0506 .0402 -.0009 1.1500 .0591 .1995 .5422 .0447 .0 131 .0520 .0439 -.6400 1.2000 .0364 .1590 .4374 .0253 .0092 .0529 .0478 -1 .81.35 1.2500 -.0052 .0902 -.1147 - .0033 .0046 .0515 .0518 -3.2100

TABLE 11 PERFORMANCE CHARACTERISTICS OF PROPELLER 4530 AT 15 DEGREES SHAFT INCLINATION

16

J KTOIPT IOKOOLIT FFFT( KT/J2 KO/J3 EL ,cqF BFANG

7500 .2179 .5527 .5118 .4229 .1310 .1026 .0376 .9494 .0000 22?9 .5200 .5571 .3561 .1017 .1061 .0424 -.4922 .0500 .110 .4783 .604Q .2960 .0779 .1074 04R0 -1.8560 .9000 .1964 .4320 .651I .425 .0593 .1fl77 3.0720 .9500 .1762 3860 .68R9 .1953 .0451 .1074 .0594 -4 .0763 1.0000 .1517 .3453 .7006 .1537 .0345 .1071 .0645 -4.8198 1.0500 .1294 .3002 .70 14 .1173 .0266 .1060 .0692 -5.2637 1. 1000 1 034 .2738 6610 .0855 .0206 .1064 .0736 -5.3802 1.5o0 .0761 .2385 .5036 .0575 .0157 .1055 .0703 -5.1532 1.2000 .0475 .1966 4617 .0330 .0114 .1032 .0839 -'.5775 i .2500 .0 170 .1400 .2530 .0114 .0072 .0988 .0913 -3.6594 J INCLINATION ANGIF = KTOIJT 10'(QOUT 15.000 EFFIC PITCH RATIO = 1.700 KT/J2 KO/J3 SIGMA a IL 1.500 K8r AFAP1G .7500 2185 .5143 .507 1 .3084 .1219 .0921 .0327 1.0637 .8000 .2161 .4959 .5547 .3376 0969 .0994 .0392 -.8881: .0500 .2066 .4623 .6044 .2859 .0753 .1021 0444 -2.1485 .9000 1916 .4211 .65 18 .2366 .0578 .1018 .0489 -2.9454 .9500 .1726 .3770 .6900 .191? .0441 .0999 .0530 -3.4531 1.000A 15Ô5 .1358 .7135 .1505 .0336 .0976 .0571 -3.916 i.osoó .1261 2964 7109 .Ì144 0256 055 .0615 -4.0269 1.1000 .09R .2591 .6741 .0824 .0195 .0941 .0665 -4.1709 1.1500 .0715 .2209 .5929 .0541 .0145 0934 .0725 -4.1815 1.7000 .0412 .1769 .4450 .0286 .0 102 .0933 .0795 -3.9626 1.2500 .0002 .1202 .1362 .0053 .0062 .0931 .0879 -3.3637

INCLINATION ANGLE a 15.000 PITCH RATIO a 1.200 SIGMA a .750

J .7500 .0000 8500 .9000 9500 1.0000 1.0500 i.ióoO 1.1500 1.2000 1. 2500 IÇTOUT 1OKOOUT .1013 .2336 .1056 .2522 .1074 .2656 1067 .2738 .1037 .2767 .0978 .2736 .0885 .2636 .0748 .2451 .0554. .2164 .0288 .1754 -.0068 .1194 INCLINATION ANGLE = EFFIC .5176 .5332 .5469 - .5583 .5665 .5690 .5613 .5 344 .4689 .3142 -.1134 15.000 KT/J2 KQ/J3 .180 1 .0554 .1650 .0493 .1486 .0432 .1318 e 0376 .3149 .0323 .0978 .0274 .0803 .0228 .0618 .0184 .0419 .0142 0200 .0101 - .0044 0061 PTTCH.RATIO a 1.200 IL .0372 .0435 .0523 .0622 .0718 .0804 .0872 .0919 0943 .0945 .0931 SIGMA a KBF .0097 .0148 .0228 .0325 .0427 0528 0624 .0711 .0793 .0873 .0959 .500 OFANG 3.6134 6.4970 6.5829 4.s757 1 1441 -3.0784 -7.4941 -1 1.5411 -14.6929 -16.4588 -16.3834 J INCLINaTION ANGLF ICTOIJT 1OKOOIJT = 15.000 FFFIC PITCH RATIO a 1.200 KT/J2 K0/J3 SIGMA a IL 14.700 KOF RFAPW, 7500 .2690 .5729 .5604 .4782 .1358 .1106 .0373 2.891 1 .8000 _S°! .5348 .5999 .1908 .1037 .1007 .0405 -3.1564 .8500 .2780 .4092 .6328 .1167 .0797- .1004 .0458 -3.7744 .9000 .2067 .4500 .6580 .2552 .0617 .1008 .0520 -4.5092 9500 1049 .4142 .6748 .2048 .0483 .1094 .0503 -5 1811 I 0000 1630 .1010 .6829 .1638 .0382. .1090 .0641 -5.6667 1.0500 .1436 .1510 .6023 .1303 .0304 1fl9R .0694 -5.8909 1.1000 .1217 .1220 .6725 .1022 .0242 .1097 .0744 -5.8667 1.1500 .1029 .2893 .6509 .0778 .0190 .1096 .0797 -5.6156 1 .fl00 .0796 .2498 .6088 .0553 .0145 .110? .0862 -5.2470 i .2500 .0517 .1987 .5 190 .0331 .010 1 .1122 .0951 -4.9189

INCt.INATTON ANGLF 15.000 PTTCH PATTO a 1.200 SIGMA a 3.000

J KIOUT IOKOOUT EFFIC KT/J2 K0/J3- IL KAF BFANG

.7500 .0000 .osöo .9000 .9500 1,0000 1.0500 1.1000 1.1500 1 .000 1.7500 .0613 .06R8 .0746 .0795 0024 0020 .0770 .0660 .0476 .0205 -.0160 .1708 .1941 .?122 .2255 .2340 .2370 .2336 .2222 .2008 .1660 .1174 .4425 .4512 .4755 .5052 .5327 .5507 .5506 .5197 .4340 .2348 -.2851 .1126 .1075 .1032 .0982 .0913 .0020 .0698 .0545 .0360 .0 142 -.0108 .0405 .0379 .0346 .0309 .0273 .0237 .0202 .0167 .0132 .0097 0060 .0 184 .018I .0286 .0440 .0590 .0726 .0809 .0844 .0842 .0829 .0845 .0069 .0092 .0 184 .0303 .0418 .0510 .0574 .0616 .0655 .0723 .0866 24.2747 22.0929 IR.8366 14 8492 10.4468 S .9178 1.5232 -2.5036 -5.9566 - -8.6573 -10.4547

TABLE 12 PERFORMANCE CHARACTERISTICS OF PROPELLER 4531 AT ZERO DEGREE SHAFT INCLINATION

DLIN&TI0N ALE O PITCH RATIO 1.400 31GM - 14.700

flCLINATIOII 1IGLE - O PTCH RATIO - 1 400 31GM - 1 500

17

D!CLD4&TION â11Z. -O

j KTOUT

PITCH RATIO - 1.400

1OKOOUT EFFIC IT/J2

31GM. - 3.000 kQ/J3 .9000 .2926 .7004 5984 .3612 .0961 .9500 .2717 .286 .6535 .3010 .0733 i.0000 2467 .5680 .6913 .2467 .0568 1-.0500 .2198 .5151 .7129 .1993 .0445 1.1000 .1925 .4673 .7211 .1591 .0351 1.1500 .1659 .4219 .7196 .1254 .0277 1.2000 .1406 .3769 7123 .0976 .0218 1.2500 .1167 .3307 .7020 .0747 .0169 1.3000 .0938 .2820 .6879 .0555 .0128 1.3500 .9799 .2300 .6625 .0389 .0093 1.4000 .0467 .1743 .5974 .0238 .0064 1 4500 .0193 1148 3873 0092 0038 15000 .0139 .0520 -.6360 -.0062 .0015 ICLDATI j hHGLE O KTOUT PITCH RATIO - 1.400 loIcoOuT EFFIC KT/J2 SIGW. s .750 KQ/J3 .9000 .1300 .3475 .5358 .1605 .9477 .9500 .1344 .3606 .5634 .1489 .0421 1.0000 .1385 .3775 .5838 .1385 .0378 1.0500 .1412 .3908 .6038 .1281 .0338 1.1000 .1614 .3948 .6272 .1169 .0297 1.1500 .1380 .3859 .6544 .1043 .0254 i.2000 .1297 .3626 .6830 .0900 .0210 1.2500 .1153 .3252 .7052 .0738 .0167 1.3000 .0936 .2764 .7009 .0554 .0126 1.3500 .0634 .2204 .6182 .0348 .0090 1.4000 .0234 .1639 .3183 .0119 .0060

J KTOUT IOKOOUT EFFIC KT/J2 kO/J3

.9000 .2918 6746 .6195 3602 .0925 .9500 .2695 6250 .6520 .2986 .0729 1.0000 .2475 .5798 793 .2475 0580 i.Osoo .2256 .5376 .7012 2046 .0464 1.1000 .2037 .4970 .7177 .1684 .0373 1.1500 .1818 .4567 .7285 .1375 .0300 1.2000 .1596 .4158 _.7332 .1109 .0241 1.2500 .1371 .3734 .7302 .0877 .0191 .1.3000

.iis

.3287 .7164 .0673 .0150 1.3500 .0897 .2811 .6854 .0492 .0114 1.4000 .0644 .2303 .6226 .0328 .0084 1.4500 .0375 .1760 .4919 .0178 .0058 1.5000 .0088 .1180 .1781 .0039 .0035

J KTOUT 1OKOOUT EFFIC KT/J2 KO/J3

.9000 .2453 5e9 .5961 .3028 .8ø8 9500 2439 5675 .6499 2703 0662 i.000o .2294 .5313 .6871 .2294 .0531 1 0500 .2082 4890 7115 .1888 0422 1.1000 .1850 .4460 .7263 .1529 .0335 1.1500 .1627 .4052 .7347 .1230 .0266 1.2000 .1420 .3671 .7386 .0986 .0212 1.2500 .1220 .3295 .7366 .0781 .0169 .1.3000 .0998 .2876 .7181 .0591 .0131 1.3500 .0706 .2349 .6486 .0387 .0095 1.4000 .0277 .1589 .3889 .0142 .0058 DICLIN#TION AlElE - O J KTOUT PITCH RATIO - 1.400 10O0UT EFFIC KT/j2 SIGM& - .500 KQ/J3 i.O000 .0947 .2563 .5881 .0947 .0256 1.0500 .0946 .2567 .6158 .0858 .0222 1.1000 .0984 .2720 .6333 .0813 .0204 1.1500 ó1002 .2836 .6464 .0757 !0186 1.2000 .0961 .2798 .6560 .0667 .0162 1.2500 .0845 . .2555 .6579 .0541 .0131 1.3000 .0659 .2127 .6410 .0390 .0097 1.3500 .0429 .1600 .5766 0236 o0065 1.4000 .0204 .1128 .4030 .0104 .0041

TABLE 13 - PERFORMANCE CHARACTERISTICS OF PROPELLER 4531 AT 73 DEGREES SHAFT INCLINATION

INCLINATION ANGLE J KTOUT 1OKOOUT 7.500 PITCH RATIO a EFFIC KT/J2 1.400 IO/J3 SIGMA 14.700 K8F BTANG .9000 .2927 6848 .6122 .3613 .0352352 -6.8802-6.8802 .500 .2681 .6278 .6458 .2971 .0385.0385 -6.8017-6.8017 1.0000 .2455 5781 6760 .2455 .0418.0418 -6.6790-6.6790 1.0500 .2243 .5352 .7004 .2035 .0452.0452 -6.5299-6.5299 1.1000 .2041 .4982 .7172 .1687 04860486 -6.3720-6.3720 1.1500 .1844 .4653 .7252 .1394 .9521.9521 -6.2226-6.2226 1.2000 1647 .4343 1243 .1144 .0557.0557 -6.0980-6.0980 1.2500 .1448 .4024 .7157 .0926 .0594.0594 .6.0155.6.0155 1.3000 1240 .3658 .7012 .0736 .0633.0633 -5.9910-5.9910 1.3500 .1020 3205 .6837 ¡0560 .0672.0672 -6.0606-6.0606 1.4000 .0783 .2616 .6672 .0400 07120712 -6.1798-6.1798 INCLINATION ANGLE: à J KTOUT IOKOOUT 7.500 EFFIC PITCH RATIO a KT/J2 1.400 KO/J3 SIGMA a EL 3.000. KBF BFANGBFANG .9000 .2853 6861 .5957 .3523 .0422.0422 -13.3030-13.3030 .9500 .2702 .6248 .6538 .2994 .0458.0458 -7.1711-7.1711 1.0000 .2449 5641 .6910 .2449 .0496.0496 -10.2706-10.2706 1.0500 .2154 .5072 7096 .1954 05360536 -15.4433.-15.4433. 1.1000 .1857 .4558 .7134 a 1535 .0573.0573 -17.9289-17.9289 1.1500 1.2000 .1586,1353 .4101.3691 .7980.6999 .1200.0939 .0612 .0650 .0612 .0650 -IS. 3650-IS. 3650-7.7911-7.7911 1.2500 1.3000 1.3500 .11'52 .0965 .0755 .3302 .2893 .2408 .6941 .6899 .734 .0737 .0571 .0414 .0689 .0727 .0766 .0689 .0727 .0766 2.3592 10.2506 8.6495 2.3592 10.2506 8.6495 1.4000 .0472 .1778 .5910 .0241 .0805.0805 -12.0761-12.0761 J KTftIT tflW10UT F F 9000 .0600 1.0000 i . nc n n 1.1000 i.i5on

j

I .2500 I .lflflfl 1.3Çflfl I .4000 .1767 .177Q 1161 .1414 1479 .3461 I 166 .1 .0 OAf. .070F. .0462 130? .1351 1506 .1670 3770 4717 .3507 1270. ¿016 .2260 .If f6 .5497 .5770 .6141 AS 10 .6070 .7127 .7271 .7274 .7090 .6711 :. .61 75 .0155 .0454 0Ç4f, .0611 fl7ftR ,0 777 .0070 .0906 .0011 .0116 n204 .036M o )4511 .0534 .161 U .0702 .070?

i)54

.0913 .0116 n 204 .036M o )4511 .0534 .161 U .0702 .070?

i)54

.0913 4f.021 26.2671 13.1SQ5 4.5703 -1 40Q0 -6.43,60 11.0710 .16.4196 -71.2701 -20.0271 4f.021 26.2671 13.1SQ5 4.5703 -1 40Q0 -6.43,60 11.0710 .16.4196 -71.2701 -20.0271

1NCLINØTTO' aMr.IF = SIGNA a_- .500.500

EL MF A "'GMF A "'G .0207 .069 .0344 .0425 .0507 .osqi .0640 .0696 .0001 .0146 .0220 0301 0307 1)475 .0561 o 0639 .n7flI .0001 .0146 .0220 0301 0307 1)475 .0561 o 0639 .n7flI .0001 .0146 .0220 0301 0307 1)475 .0561 o 0639 .n7flI 17.8000 7.3491 2.6400 -1.5504 -5.3300 -0 6 109 -11. 1900 -12. 7004 1?.6A00 17.8000 7.3491 2.6400 -1.5504 -5.3300 -0 6 109 -11. 1900 -12. 7004 1?.6A00 .1 INCLINATION APIGLF a KTOIPT IOVOOIIT 7.500

EFFIC ICT/J2 ICO/J3

PITCH RATIO 1.400 SIGMA a .1.500

.0000 .5697 .5070 .7062 .0781 .0610 03110311 -1.9512-1.9512 .0500 1 .0000 I .flS0n 1.1!l0n I .1600 I.,000 I .?Sflfl hi000 I .1600 i .4000 .276? .5134 .70Ml .4964

Ji?

.4661 .1669 .4i6 .14cc .17Mg .I'57 .3417 ¡1044 .3010 .01RO ¡2507 .0410 .1016 .6366 .6749 .7011 .7205 .7311 7317 .-7177 .6606 .5020 2f. IA .2262 .1090 .1547 .1254 .1010 0004 .0618 .0420 .ñ209 .0654 .0533 .0429 0343 .0274 .0219 .0175' ¡0137 .010? .0066 .0660 .0'O 06g? in? .071? .0776 .0741 fl76I .0774 13775 .0146 .0100 34 16 11453 149? .0511 ocTh .. .067 072 .0146 .0100 34 16 11453 149? .0511 ocTh .. .067 072 -2.5101 -1.0040 -3.671M -4.3019 4QQ2? -S 7501 -7.5660

0

.626? -0.7000 -2.5101 -1.0040 -3.671M -4.3019 4QQ2? -S 7501 -7.5660 0 .626? -0.7000

TABLE 14 - PERFORMANCE CHARACTERISTICS OF PROPELLER 4531 AT 15 DEGREES SHAFT INCLINATION

19 9000 9500 1.0000 1.0500 1.1000 1.1500 1.2000 1.2500 1.3000 1.3500 1.4000 .2808 .7341 .2605 .6480 .215 .5960 .?174 .5514 .1942 .508" .1699 .4648 .1444 .1.175 .118 .3647 .0921 .3341 .0667 .2627 .0398 .?17 .%3i .6079 .6395 .6589 .6682 .6690 8615 .643 1 .6068 .5372 40$2 .3466 .2887 .2395 .1972 .1605 .1285 .1004 .0759 .0545 .0360 .0203 .0980 .0756 .0596 .0476 .0382 .0306 .0242 .0188 .0143 .O1Qt .0079 347M .1'9" .150' .1504 .150? .1498 .1494 .1495 .1503 .1525 .1563 .0705 .0785 .0845 .0895 .0944 .0997 .1058 .1131 .1216 .131? .1416 -7.1063 -7.201 -7.3185 -7.4229 -7.5031 -7.5366 -7.4969 -7.3534 -7.0715 -6.8126 -5.9137 !NCLINATIOPi ANGLF = 000 '1TC1 RATIO - 1.400 SIGMA a 1.500

KTOUT 101(0(JIIT EFFIC 1(T/J2 KQ/J3 KL 8F 8FANG .9000 .2199 .5752 .5476 .271.5 .0789 .1079 .0481 2.4841 .9500 .5623 .5976 .2463 .0656 .1227 .0672 _-?.5924 1.0000 .2167 5472 .6304 .2167 .0547 .1323 .0729 -5.1904 1.0500 1.1000 1.1500 .2051 .5273 .1ÑQQ .5011 .1A93 .4677 .8503 .6600 .6624 .1561 .1280 .0456 .0376 .030 .1385 .1427 .1461 .0817 .0699 .0978 -6.2103 -6.3691 6.1997 1.2000 .1471 .4273 .6574 .3021 .0247 .i4W3 .1061 -6.0509 1.2500 .1229 .3807 .6424 .0787 0195 .1524 .1155 6.0873 1. 3000 .097 1 .1298 .6089 .0574 .0150 .I5 _.125? -6.2896 1 .3500 .0694. .2770 .S380 .0381 .0113 .1585 .1353 -6.4543 1.4000 .0395 .??Sq s 3896 _{.0202 .0082} .1597 .1451 -6.1941

INCLINATION ANGLE = 15.000 P11CM iaT)fl = 1.400 SIGMA a .750

J K TOuT I OKOOujT EFFIC KT/J2 KQ/J3 _KL KRF

.9000 .9500 1.0000 1.0500 1. 1000 1. 1500 1.000 1.2500 1.1000 1.3500 1.4000 .12% .3373 .1338 .352U .1 36 .3549 .1282 . 3S0l .1219 .343? .114? o 131II .104g .1279 .098 loicA .2949 a05 16 .2567 .0157 .1911 .5506 .5732 .5945 .6116 .6217 .8224 .611) .5640 .5321 .4298 .1.632 .1600 .1482 .1326 .1162 .1007 .0864 . .0729 .0594 04 .0282 . .0080 .0462 .0412 .0355 .0303 .0258 .0221 .0190 .0162 .0134 .0104 .0070 .0569 .0656 .0757 .0870 .0993 .1121 .1245 .1356 .143w .1479 .1457 .021A .0291 .0399 .058 .0668 .0811 .094e .1075 .1188 .1297 .1172 11.2887 9.1578 7.5287 5.9936 4.3065 2.3638 .13S -1.9461 -3.7667 -4.7503 -4.2487

INCLINATION ANGIF 15.000 PITCH RATIO J KTOUT 1OKOOUT EFFIC 1(7/Je

1.400 1(Q/J3 SIGMA 14.700 8FANG .9000 .2870 .6978 .5891 .3543 .0957 .1378 .0591 -6.1541 .9500 .2703 .6664 .6132 .2995 .0777 .1401 .0663 -6.3555 1.0000 .2499 .6325 .6289 .2499 .0632 .1625 .0735 -6.7094 1.0500 .2278 .5960 6387 .2066 .0515 .1441 .0609 -7.1142 1.1000 .20cl .5570 .6447 .1695 .0419 .145? .0679 -7.49J3 1.100 .1827 .5158 .6484 .1382 .0339 .1460 .0946 -7.7841 1.2000 .1609 .47?S .4503 .1117 .0273 .1466 .1009 -7.9587 1.2500 .1395 .4276 .6490 .08*3 .0219 .1473 .1072 -8.0039 1.3000 .1179 .3815 .6392 0697 .0174 .1485 .1141 -7.9306 1.3500 .0948 .3349 .6085 .0520 .0136 .1S0 .1222 -7.7726 1.4000 .0688. .2884 .316 .0351 .0105 .1546 .1327 -7.5859

INCLINATION ANGLE 15.000 I1TCN 8T!O 1.400 SIGM8 3.000

J KTOtJT 10'CUOUT. EFFIC KT/J2 $CQ/J3 _{EL KNF}

RFANG

TNC.INATION . ANGL = 15.000 a'ITC's9AT3Q = 1.400 SIGMA z .500

J 1.0000 '(T')IIT _l0'"()tJI .O.Ic .?5Ñ7 EF F ¡C I'T/J2 .',t,29 .úqlS 1(Q/J3 .0759 EL .0462 .0210 . 8FAMC, 11.sloo 1.0500 .n89' .2499 .5566 .0233 .0573 .031.1 8.7423 1.1000 .0867 ?'7s .,72 .0717 .0?Q1 .0666 .0421 7.2700 1.1S00 0$12. .?41 .5766 .0629 .0174 .0768 .0541 5. 9204 1.000 .0797 ?644 .5757 .0553 .0153 .0889 .067? :3.8000 1.2500 .07cc .2662 .5644 .0483 .0136 .1029 .0Ml? .b547 1.1000 .0691 _.,?601 .5497 .0409 .0118 .1176 .0959 -3.1300 1.1500 .0579 .294 .5422 .0318 .0093 .1309 .1110 -6.5296 1.4000 .0384 .150.3 .5700 .0196 .0055 .1395 .1240 -7.M#uO

APPENDIX B

REPRESENTATIVE PLOTS OF REDUCED DATA AND SKETCHES OF CAVITATION

"VERTICAL FORCE" _(Fv) SHAFT AXIS AFT IFWD LIFT (L) "VERTICAL FORCE" (F SHAFT ANGLE ()

TH'RUST ALONG SHAFT IT')

AESULÏANT THRUST (t)

Figure la - Side View

PORT I STBD

BEARING FORCE ANGLE

BEang

+

Figure lb - End View

Figure 1 Force Diagram fOr Side-Force Measuréments

23

dEARING FORCE

.1

-

u

.,_ U2A

_rnurarivA

_IfEáfA

_

-- wi

ri

rA

II

w4gvay,iri

0.8 0.7

»0.6

Q

z

w 0.5 U. U. w w .4 -J -J w 0.3 0.2 0.1 KT/J2

Figure 3 - Propeller Efficiencies versus K1/J2 for Various Pitch Ratios at Zero Degree Shaft Inclination and a = 14.7

0.8 0.7 0.6 Q

z

w 0.5 U. u. w w -J -J w o-o 0. 0.2 0.1 KT/J2

Figure 4 - Propeller Efficiencies versus K1¡J2 for Various Pitch Ratios at Zero Degree

Shaft Inclination and a = 3.0

25

,

-P/D I = 1.2I P/D=1.4 -= 0.8 ) 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 P/b = 1.4 PfD = 1 0

-/D = 1.2

= 0.8

,rPP/D

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

0.8 0.7 0.6 >-0.5 ci

z

w ci u-wO.4 w -j -J Ui 0.3 0.2 0.1 O KTIJ2

Figure 5 - Propeller Efficiencies versus KT ¡J2 for Various Pitch Ratios at Zero Degree Shaft Inclination and o = 1.5

26 i PfD = 1.4

-D1.0

PfD = 0.8 n ûû 0.10 0.15 0.20 0.25 0.30

0.8 0.7 0.6

>..

0:5

o..

z. LU C-) u-, u-., LU LU -J w

0.3 0.2 0.1

P/D = 1.2.

a = 0.5

Figure6 - PrOpeller Efficiencies versus KT/J2 for 'Various 'Pitch Ratiós at Zero Degree

Shaft Inclination and o

'O75.,O.5 -u-' 1.4 0.05 0.10 0.15

20

0. 0.05 0.10 0.15 T'

0.8 0.7 .0.3 0.8. 0.7 C.,

Z.

LU

o

u. -u. w 0.5 w -j -j w Q.

o

Q. 0.3 0.2 o = 1.0 = 08 1.2 P/D=o.8 28 0.05 0.10 0.15 0.20 0.25 0.30 0.35 040 0.45 0.50 KT/J2

Figure 8 - Propeller Efficiencies versus K1/J2 for Various Pitch Ratios at 7.5 Degrees Shaft

Inclination änd o 3.0

0.2

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 045 0.50

KT/J2

Figure 7 - Propeller Efficiencies versus KT ¡J2 for Various Pitch Ratios at 7.5 Degrees Shaft

Inclination and a = 14.7

0.8 0.7 0.6 0.2 0.1 O PfD 1.4

j

A:

PfD = 0.8 PID = 1.0 PID = 1.2 29 o 0.05 0.10 0.15 0.20 0.25 0.30 0.35 .KT/J2

Figure 9 Ptopeller Efficiencies versus K1/J2 for VariOus Pitch .Ratios at 7.5 Degrees Shaft Inclination and a = 1.5

o o >. C.)O

z

w Q

u-u-O

w w -j -I w a-o a. O 0.7 C., O.6 ç, u-

u

-wO.5

w -J -J

wO.4

_a. o a. 0.3 0.2 0.05 0.10 - 0.15 0.20 O 0.05 0.10 0.15 KT/J21 KT/J2

Figure 10 - Propeller Effiiencies versus KT/J2 for Various Pitch Ratios at 7.5 Degrees Shaft Inclination and o = 075, 0.5

0.8

30

KT/J2

Figure 11 - Propeller Efficiencies versus K1/J2 for Various Pitch Ratios at 15 Degrees Shaft Inclination and a = 14.7 .0 .7. .6 .5 .4 I a=0.75I a-0.5 V Z P/D=1.4 P/D = 1.2 PIO = 1.2

V

P'

P/D=1.4V

j

P/D=1.0 V. .

vi

3V

V .2 PID=0.8 V V -P/0=0.8 '.1 V

f

V P/D =1.4 V 08 . n nnc niA fl1 020 02 030 035 040 045 050

0.7 0.6 >..

o

_Z0.5

Ui

o

U. U. LU _0.4 W -J -J W. o Q-0.2 0.1 0.7 0.6 >.

00.3

Q-0.2 0.1 P/D = 1.4 Pl Pl = 1.2 D = 0.8 P/D D = 1.0 I PI P/D = D = 1.2 1.0 31 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 040 0.45 KTIJ2

Figure 13 - Propeller Efficiencies versus KT ¡J2 for Various Pitch Ratios at 1 5 Degrees Shaft Inclination and a = 1.5

0.

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Figure 12 - Propeller Efficiencies versus KT/J2 for Various Pitch Ratios at 15 Degrees Shaft Inclination and a = 3.0

l'ID = 0.8 o 0.75. o = 0.5 0.20 0.15 0.05 0.10 0.15 O2O O

05

0.10 KT/J2 K../J2

Figure 14 - Propeller Efficiencies versus KT

¡J2

for Various Pitch Ratios at 1.5 Degrees Shaft

Ò.5 0.6 0 7 0 8 0 9 1.0 1.1 1.2 ADVANCE COEFFICIENT (J)

Figure .15. -, Cavitation Charaçteristics of Propeller 4529 at Zero Degree Shaft Incliflation

0.8 a.

o

I-z

w Q u. u. w o Q 0.6 o

g

û

z

<0.5

)-Q

z

w 0.4 U. u-LU

I-i

0.3

z

Ui Q 1*. u-W O Q I-u,

I

I-. 0. 34 t

/4s

,_

0- 14.7 a-ao 10Ko p o =0.75 o =1.5

:::;

0=0.5

-0.5 0.6 0.7 0.8 0.9 ADVANCE COEFFICIENT (J)

Figure 16 - Cavitation Characteristics of Propeller 4529 at 7.5 Degrees Shaft Inclination

0.8 o.. o

I.

_0.7

Q.

w o Q 0.6 D

C.

o

I,

O 0.5 >-z. w .0.4

u-I,

.0.3

z

w Q u-w o

Q..

I.

cd, D X 0.1 a= 1.5 C=14.7 U=0.75

:1IjI

U= 1.5 Û 0.5 O Ò.75: Û0.5 a= 3.0 n 35 0.5 . 0.6' 07 08 0.9 _{1..0 1.1 1.2} ADVAÑCE COEFFICIENT (J)

Figure 17 Cavitation Charactêri.stics of Propèller 4529 at 15 Degrees

0.8

o

o

z

w 0.7 Q u. u-w

o

C-) w

o

o

o

z

¶0.5

o

z

w 0.4 u-IL w .1-z 0.3 w o u-w

o

o Cl) X

I-I

0.1 10K0 750 750 15.00 36 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 ADVANCE COEFFICIENT (J)

Figuré 18 - Effect of Shaft IìÍdlination on Cavitation Characteristics of Propeller 4529 at a =1.5

08 o o 0:7 O 0.6 w o O

I-z

>-O

z

w 0.4 O u. U. w 0.3

I-z

w O u. 0.1 O --0.5 06 0.7 08 09 ADVANCE COEFFICIENT (J)

Figure 19 - Effect of Shaft Inclinatiôn on Cavitation Characteristics of Propeller 4529 at o = 0.5

37

IL. I-0.06 0.05 0.04 O.03 20.02 L _0.01 O

z

w -J w

z

LU

o

o

U. w

z

W 50 40 30 20 10 O

10

20

30 0.60 0.65 0.70 0.75 0.80 0.85 0.90 ADVANCE COEFFICIENT (J)

Figure 20 - Lift- and Bearing-Force Coefficients and Bearing-Force Angles of Propeller 4529 at 7.5 Degrees Shaft Inclination

38 KL 0 14.7

KBL0147.

0-0.75 ,KBF 0 0.75 -«7= 1.5

u

-'s_

O 14.7 a =0.5 0.95 1.00 1.05

- 0.10 u. 0.09 I-0.08 0.07 0.06 0.05 WO g . 0.04 w

-

0.03 -j W 0.01 W -i 30 Q 20 W

o

_lo O u-Q O z

10

20

39

-t4 2=__

G= 14.7

-- 1.5 =O.5

i

L"<

=1.5 c = O.75....

il1

U

-K P/D=1.O__

'"U=O.5

KBF

--a cy=a5 c=o.:75 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1 05 ADVANCE COEFFICIENT (J)

Figure 21 _{- Lift- and Bearing-Force Coefficients and Bearing-Force Angles of Propeller 4529}

7 50 FACE J 1.0 BACK J=0.8 PROPELLER 4529 FACEJ 1.25. BACK J = 085 PROPELLER 430 40 150

Figure 22 - Cavitation Present on Propellers 4529 and 4530 at a = 0.75 for Various Shaft Inclinations

PfD 0.8 1.0 FACE 1.2 1.4 41 P/D 0.8 1.0 BACK 1.2 1.4 KT/J2 = 0.016 PfD 0.8 1.0 FACE 12 14 P/D 0.8 1.0 BACK 1.2 1.4 KT/J2 = 0.119

Figure 23 - Cavitation Present on Propellers at Zero Degree Shaft Inclination. a = 0.75. and Two Thrust Loadings for Various Pitch Ratios

1.0 FACE 1.2

1.2 BACK

tÇtfJ2 =0.119

Figure 24 - Cavitation Present on Propellers at 15 Degrees Shalt Incimation, o = 0 75,

and Two Thrust Loadings for various Pitch Ratios 42 1.4 1.4 0.8 1.0 BACK 1.2 1.4 KT/J2 = 0.016 P/D 1.0 1.2 FACE 1.4 PfD 1.0 PfD 0.8

APPENDIX C.

USING SERIES DATA Tb DESIGN A PROPELLER

The tables in Appendix A and the curves in Appendix B may be used as a guide in choosing

the dimensions of a propeller for a particular application as follows:

Given:

Horsepower per shaft,.hp 330

Maximum propeller revolutions, N = 1,900 rpm èsigii spèed of craft, V 7 knOts

Wake fraction, 1 - w 0.93

Thrust-déduction fraction, 1- t = 0.95 Cavitation number, a = 1 .15

Weight of craft, W = 26,000 lb

Resistance of craft at 27 knots, R = 5,200 lb Two shafts

Shaft inclination, 7.5 deg

The design problem is to select a propeller withsUitablediameter and pitch to produce the design thrust at design power and rpm.

Procedure for propeller selection

Four or flve diameters are chosen, and values of loading coefficient

KT _R.

j2

_{p(Ï - t)(1 w)2 V2 ¡}

are calculated for each diameter.

Curves (similar to Figures 3 through 14) of K1/J2 versusare plotted for a range

of pitch ratio at the apropriate cavitation number. From these curves the propeller effici-ency for each diameter änd pitch ratio này be obtained.

43

D 1.5' 1.75' 2.0' 2.25'

Curves of versus J are plotted using the experimental data at the pertinent a and shaft angle. The J for each pitch ratio and diameter is determined by the r of that curve.

From the i's given, the operating N and power delivered are calculated by

means of

V(l_w)

ND and

V(l -w)T

44 D 2.0' 2.25' KT/J2 0.165 0.131 PfD 1.0 1.2 1.4 1.0 1.2 1.4 n 0.68 0.70 0.72 0.68 0.71 0.73 J 0.82 0.99 1.10 0.81 1.02 1.15 N 1550 1284 1156 1395 1108 982 310 301 292 312 397 289

The results are tabulated as follows:

D 1.5'

= 550(1 -t)

1.75' K1/J2 0.294 0.2 16 P/D 1.0 1.2 1.0 1.2 1.4 n 0.62 0.62 0.67 0.67 0.68 J 0.73 0.84 0.78 0.91 0.99 N 2322 2030 1851 1597 1460 340 340 315 315 315 PfD 1.0 1.2 1.0 1.2 1.4 1.0 1.2 1.4 1.0 1.2 1.4 n 0.62 0.62

0.67 0.67 0.67

0.68 0.70 0.72

0.675 0.71 0.73 0 D 1.5' 1.75' 2.0' 2.25' KT 0.294 0.2 16 0.165 0.131

From this table the choice ofa tôpeIlet would be .75 ft and P/D = 1 .0. This

propeller most nearly meets the requitements of absorbing 30 hp at 1900 rpm.

5. One may now determine the lift and bearing, forces on the craft transmitted through the shaft. From the tables at the proper P/D, a, shaft angle, and J, it is fòund that

KL 0.031. BFang = +2 deg, and KBF. = 0.0164. From these we may calculate lift and

bearing force

L= KLpn2D4 = 551 lb

BF KBFpn2D4 = 291 lb

BFang = 2 deg inboard

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