Curvas Kt Kq de B Series Wageningen

K.r, ~ and Efficiency Curves for

the Wageningen B-Series Propellers

by 0'1 ~. " . M.M."Bern~tsas

D. Ray

P. Kinley

Department of Naval Architecture and Marine Engineering College of Engineering

The University of Michigan Ann Arbor, Michigan 48109

j j j j j j j j j j j j j j j j j j j j

J

j j j j j j j j j j

j j j j j

j j j

j

j j j j

ABSTRACT

The B-series propellers were designed and tested at the Netherlands Ship Model Basin in Wageningen. The open-water characteristics of 120 propeller models of the B-series were tested at N.S.M.B. and analyzed with multiple polynomial regression analysis [1]. The derived polynomials express the thrust and torque coefficients in terms of the number of blades, the blade area ratio, the pitch-diameter ratio and the advance coefficient. The Rey-nolds number effect and the effect of variation of blade thickness on the B-series propeller characteristics have also been evaluated at N.S.M.B. In this report the polynomials derived in [1] are used to plot the open water propel-ler characteristics for Reynolds number 2.0x10 6 and for the ranges of number of blades, blade area ratio and pitch-diameter ratio recommended by N.S.M.B. The extent of applicability of the regression polynomials is also discussed.

-iii-

ACKNOWLEDGEMENTS

This report was prepared in fulfillment of the requirements for the de-sign project in the graduate computer-aided design course, NA 574, of the Dp.-partment of Naval Architecture and Marine Engineering of the University of Michigan. Computer funds were provided by the department. Thanks are due to Professor R.F. Beck for his constructive comments and Mrs. Paula Bousley for the excellent typing and editing of this report.

-v-

TABLE OF CONTENTS

ABSTRACT .......................................................... ..

ACKN'OWLEDGEMENTS

LIST OF FIGURES

NOMENCLATURE

INTRODUCTION

~, ~ POLYNOMIALS AND REYNOLDS NUMBER CORRECTIONS LIMITATIONS OF APPLICABILITY OF THE REGRESSION POLYNOMIALS REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FIGU'RES ............................................................. .

-vii-

Page

iii

v

ix xii

3

6

6

7

LIST OF FIGURES

Figure No. Page

1. Propeller with 2 blades and AE/Ao = 0.30..................... 7 2. Propeller with 2 blades and AE/Ao = 0.35..................... 8 3. Propeller with 2 blades and AEiAo = 0.40..................... 9 4. Propeller with 2 blades and AE/Ao = 0.45..................... 10 S. Propeller with 2 blades and AE/Ao = 0.50..................... 11 6. Propeller with 2 blades and AE/Ao = 0.55..................... 12 7. Propeller with 2 blades and AE/Ao = 0.60 ' 13 8. Propeller with 2 blades and AE/Ao = 0.65..................... 14 9. Propeller with 2 blades and AEiAo = 0.70..................... 15

10. 11. 12.

13. 14. 15. 16.

17.

18.

19. 20.

21.

22. 23.

24. 25.

26. 27.

28. 29. 30. 31. 32.

Propeller with 2 blades and AE/Ao = 0.75 Propeller with 2 blades and AE/Ao = 0.80 Propeller with 2 blades and AE/Ao = 0.85

" Propeller with 2 blades and AE/Ao = 0.90 Propeller with 2 blades and AE/Ao = 0.95 Propeller with 2 blades and AE/Ao = 1.00 Propeller with 2 blades and AE/Ao = 1.05

Propeller with 3 blades and AE/Ao = 0.30 Propeller with 3 blades and AEiAo = 0.35 Propeller with 3 blades and AE/Ao = 0.40 Propeller with 3 blades and AE/Ao = 0.45 Propeller with 3 blades and AE/Ao = 0.50 Propeller with 3 blades and AE/Ao = 0.55 Propeller with 3 blades and AE/Ao = 0.60 Propeller with 3 blades and AE/Ao = 0.65 Propeller with 3 blades and AE/Ao = 0.70 Propeller with 3 blades and AE/Ao = 0.75 Propeller with 3 blades and AE/Ao = 0.80 Propeller with 3 blades and AE/Ao = 0.85 Propeller with 3 blades and AE/Ao = 0.90 Propeller with 3 blades and AE/Ao = 0.95 Propeller with 3 blades and AE/Ao = 1.00 Propeller with 3 blades and AE/Ao = 1.05

-ix-

16 17

18

19 20 21

22

23 24

25 26 27

28 29

30

31 32 33 34

35 36

37 38

Figure No.

33.

34.

35. 36. 37. 38. 39. 40. 41.

42. 43.

44.

45. 46.

47.

48.

49.

50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62.

63.

64.

65. 66.

Propeller with 4 blades and AE/Ao = 0.30 Propeller with 4 blades and AE/Ao = 0.35 Propeller with 4 blades and AE/Ao = 0.40 Propeller with 4 blades and AE/Ao = 0.45 Propeller with 4 blades and AEiAo = 0.50 propeller with 4 blades and AE/Ao = 0.55 Propeller with 4 blades and AE/Ao = 0.60 Propeller with 4 blades and AE/Ao = 0.65 Propeller with 4 blades and AE/Ao = 0.70 Propeller with 4 blades and AE/Ao = 0.75 Propeller with 4 blades and AE/Ao = 0.80 Propeller with 4 blades and AE/Ao 0.85 Propeller with 4 blades and AE/Ao = 0.90 Propeller with 4 blades and AE/Ao = 0.95 Propeller with 4 blades and AE/Ao = 1.00 Propeller with 4 blades and AE/Ao = 1.05

Propeller with 5 blades and AE/Ao = 0.30 Propeller with 5 blades and AE/Ao = 0.35 Propeller with 5 blades and AE/Ao = 0.40 Propeller with 5 blades and AE/Ao = 0.45 Propeller with 5 blades and AE/Ao = 0.50 Propeller with 5 blades and AE/Ao = 0.55 Propeller with 5 blades and AE/Ao = 0.60 Propeller with 5 blades and AE/Ao = 0.65 Propeller with 5 blades and AE/Ao = 0.70 Propeller with 5 blades and AEiAo = 0.75 Propeller with 5 blades and AE/Ao = 0.80 Propeller with 5 blades and AE/Ao = 0.85 Propeller with 5 blades and AE/Ao = 0.90 Propeller with 5 blades and AE/Ao = 0.95

Propeller with 5 blades and AE/Ao = 1.00 Propeller with 5 blades and AE/Ao = 1.05 .

Propeller with 6 blades and AE/Ao = 0.30 Propeller with 6 blades and AE/Ao = 0.35

-x-

Page

39

40 41

42

43 44

45 46

47

48

49

SO 51

52

53 54

55 56 57 58 59 60 61 62

63 64

65 66

67 68

69

70

71

72

Figure No.

67. 68. 69. 70. 71.

72.

73. 74. 75. 76. 77.

78.

79. 80.

Propeller with 6 blades and AE/Ao = 0.40 Propeller with 6 blades and AE/Ao = 0.45 Propeller with 6 blades and AE/Ao = 0.50 Propeller with 6 blades and AE/Ao = 0.55 Propeller with 6 blades and AElAo = 0.60 Propeller with 6 blades and AE/Ao = 0.65 Propeller with 6 blades and AE/Ao = 0.70 Propeller with 6 blades and AE/Ao = 0.75 Propeller with 6 blades and AE/Ao = 0.80 Propeller with 6 blades and AE/Ao = 0.85 Propeller with 6 blades and AE/Ao = 0.90 Propeller with 6 blades and AE/Ao = 0.95 Propeller with 6 blades and AE/Ao = 1.00 Propeller with 6 blades and AE/Ao = 1.05

Page

73 74

75 76 77

78

79 80 81

82

83

84 85

86

81. Propeller with 7 blades and AE/Ao = 0.30..................... g7 82. Propeller with 7 blades and AE/Aa = 0.35..................... 88 83.

84.

85. 86.

Propeller with 7 blades and AE/Ao = 0.40 Propeller with 7 blades and AE/Ao = 0.45 Propeller with 7 blades and AE/Ao = 0.50 Propeller with 7 blades and AE/Ao = 0.55

89

90 91 92

87. Propeller with 7 blades and AE/Ao = 0.60..................... 93 88. Propeller with 7 blades and AE/Ao = 0.65..................... 94 89. Propeller with 7 blades and AE/Ao = 0.70..................... 95 90. Propeller with 7 blades and AE/Ao = 0.75..................... 96 91. Propeller with 7 blades and AE/Ao = 0.80..................... 97 92. Propeller with 7 blades and AElAo = 0.85..................... 98 93. Propeller with 7 blades and AElAo = 0.90..................... 99 94. Propeller with 7 blades and AE/Ao = 0.95..................... 100 95. Propeller with 7 blades and AE/Ao = 1.00..................... 101 96. Propeller with 7 blades and AE/Ao = 1.05..................... 102

-xi-

D

J

n

P/D Q Re

Greek Symbols

n

p

NOMENCLATURE

blade area ratio coefficient in the ~ polynomial expression coefficient in the KT polynomial expression propeller diameter advance coefficient torque coefficient

thrust coefficient propeller revolutions per second pitch-diameter ratio propeller torque Reynolds number propeller thrust thickness to cord ratio for propeller blades speed of advance number of blades

open-water propeller efficiency fluid density

-xii-

INTRODUCTION

The open-water propeller characteristics conventionally are presented in the form of the thrust and torque coefficients KT and KQ in terms of the advance coefficient J where

T Krr = pn2D4 (1)

KQ = _Q-pn2D5 (2 )

J VA

= nD (3 )

where

T is the propeller thrust, Q is the propeller torque, p is the fluid density, n is the number of propeller revolutions per second, D is the propeller diameter and

VA is the speed of a~vance.

The open-water efficiency of the propeller is

(4 )

The thrust and torque coefficients can be written as:

AE t , Z , Re , -) Ao c (5)

and

~ fQ(J , P AE

, Z , Re , ~) -D Ao c

(6)

where P/D is the pitch diameter ratio

AE/Ao is the blade area ratio Z is the number of propeller blades

-1-

Re is the Reynolds number of a characteristic radius (0.75 R) tic is the ratio of the maximum propeller blade thickness to the

length of the cord at a characteristic radius (0.75 R)

KT and KQ can be expressed in terms of polynomials of J, and Z (see Table 1) [1].

P D

The Reynolds number effect on the propeller characteristics has been taken into account using Lerbs method [2]. The Reynolds number corrections for ~ and KQ 'are polynomial expressions of Re, P/D, AEiAo and J (see Table 2).

Finally the effect of variation of blade thickness on propeller charac-teristics can be represented as a change in the Reynolds number and need not be formulated in a polynomial form (1].

-2-

K.r, ~ POLYNOMIALS AND REYNOLDS NUMBER CORRECTIONS

The polynomials for KT and ~ derived with multiple regression analy-sis are

KT = 2: cT s,t,u,v (J)S (P/D)t (AEiAo)U (Z)V (7) s,t,u,v

Ko = 2: cQ s,t,u,v (J)S (P/O)t (AEiAo)U ( Z)V (8) s,t,u,v

The coefficients CT s,t,u,v and CQ s,t,u,v and terms s,t,u,v are given in Table 1.

For Reynolds number greater than 2x10 6 the open water propeller charac-teristics should be corrected. The corrections

AKT(Re, J, P/O, AEiAo, z) (9)

and

AKQ(Re, J, P/O, AEiAo, z) ( 10)

are given in Table 2.

-3-

TABLE 1

Coefficients and terms of the ~ and Kg polynomials for the Wageningen B-screw Series for Rn=2x106. Reproduced from [ 1]

K.r= 2: cT .(J)S.(P/D)t.(AE/Ao)u.(zV) s,t,u,v Kg= s,t,u,v cQ .(J)S.(P/D)t.(AE/Ao)u.(zV) s,t,u,v

T s t U v cQ s t u v K.r Cs,t,u,v (J) (P/D) (AE/Ao) (Z) s,t,u,v (J) (P/D) (AE/Ao) ( z)

+0.00880496 0 0 0 0 +0.00379368 0 0 0 0 -0.204554 1 0 0 0 +0.00886523 2 0 0 0 +0.166351 0 1 0 0 -0.032241 1 1 0 0 +0.158114 0 2 0 0 +0.00344778 0 2 0 0 -0.147581 2 0 1 0 -0.0408811 0 1 1 0 -0.481497 1 1 1 0 -0.108009 1 1 1 0 +0.415437 0 2 1 0 -0.0885381 2 1 1 0 +0.0144043 0 0 0 1 +0.188561 0 2 1 0 -0.0530054 2 0 0 1 -0.00370871 1 0 0 1 +0.0143481 0 1 0 1 +0.00513696 0 1 0 1 +0.0606826 1 1 0 1 +0.0209449 1 1 0 1 -0.0125894 0 0 1 1 +0.00474319 2 1 0 1 +0.0109689 1 0 1 1 -0.00723408 2 0 1 1 -0.133698 0 3 0 0 +0.00438388 1 1 1 1 +0.00638407 0 6 0 0 -0.0269403 0 2 1 1 -0.00132718 2 6 0 0 +0.0558082 3 0 1 0 +0.168496 3 0 1 0 +0.0161886 0 3 1 0 -0.0507214 0 0 2 0 +0.00318086 1 3 1 0 +0.0854559 2 0 2 0 +0.015896 0 0 2 0 -0.0504475 3 0 2 0 +0.0471729 1 0 2 0 +0.010465 1 6 2 0 +0.0196283 3 0 2 0 -0.00648272 2 6 2 0 -0.0502782 0 1 2 0 -0.00841728 0 3 0 1 -0.030055 3 1 2 0 +0.0168424 1 3 0 1 +0.0417122 2 2 2 0 -0.00102296 3 3 0 1 -0.0397722 0 3 2 0 -0.0317791 0 3 1 1 -0.00350024 0 6 2 0 +0.018604 1 0 2 1 -0.0106854 3 0 0 1 -0.00410798 0 2 2 1 +0.00110903 3 3 0 1 -0.000606848 0 0 0 2 -0.000313912 0 6 0 1 -0.0049819 1 0 0 2 +0.0035985 3 0 1 1 +0.0025983 2 0 0 2 -0.00142121 0 6 1 1 -0.000560528 3 0 0 2 -0.00383637 1 0 2 1 -0.00163652 1 2 0 2 +0.0126803 0 2 2 1 -0.000328787 1 6 0 2 -0.00318278 2 3 2 1 +0.000116502 2 6 0 2 +0.00334268 0 6 2 1 +0.000690904 0 0 1 2 -0.00183491 1 1 0 2 +0.00421749 0 3 1 2 +0.000112451 3 2 0 2 +0.0000565229 3 6 1 2 -0.0000297228 3 6 0 2 -0.00146564 0 3 2 2 +0.000269551 1 0 1 2

+0.00083265 2 0 1 2 +0.00155334 0 2 1 2 +0.000302683 0 6 1 2 -0.0001843 0 0 2 2

2 x 10 6 -0.000425399 0 3 2 2

Rn = +0.0000869243 3 3 2 2 -0.0004659 0 6 2 2 +0.0000554194 1 6 2 2

-4-

TABLE 2

Polynomials for Reynolds number effect (above Rn = 2x106) on KT and KQ

~KT = 0.000353485

-0.00333758(AE/Ao)J2 -0.00478125(AE/AO) (P/D)J +0.000257792(logRn-0.301)2(AE/Ao)J2 +0.0000643192(logRn-0.301)(P/D)6J2 -0.0000110636(logRn-0.301)2(p/D)6J 2 -0.0000276305(logRn-0.301)2 z (AE/Ao )J2 +0.0000954(logRn-0.301)z(AE/AO) (P/D)J +0.0000032049(logRn-0.301)Z2(AEiAo) (P/D)3J

~~ = -0.000591412

+0.00696898(P/D) -0.0000666654z(P/D)6 +0.0160818(AE/Ao)2 -0.000938091(logRn-0.301) (P/D) -0.00059593(logRn-0.301)(P/D)2 +0.0000782099{logRn-0.301)2(p/D)2 +0.0000052199(logRn-0.301)z(AE/Ao)J2 -0.00000088528(logRn-0.301)2 z (AE/Ao) (P/D)J +0.0000230171(logRn-0.301)z(P/D)6 -0.00000184341(logRn-0.301)2 z (P/D)6 -0.00400252(logRn-0.301) (AE/AO) 2 +0.000220915(logRn-0.301)2(AE/Ao)2

LIMITATIONS OF APPLICABILITY OF THE REGRESSION POLYNOMIALS

The derived regression polynomials can be used to evaluate the thrust and torque coefficients for

and

0.5 ( PID ( 1.40

( 11 )

(12)

( 13 )

However, at the extremes of the above ranges the results are not fully reliable. For instance the thrust coefficient ~ displays a local maximum for low values of J, high number of blades, low blade area ratio and high pitch-diameter ratio. This minor error is due to regression analysis.

96 open-water propeller characteristics curves are included in this re-port. For each set of blades between 2 and 7, sixteen graphs have been plot-ted for blade area ratio varying between 0.30 and 1.05 in steps of 0.05 and pitch diameter ratio varying between 0.50 and 1.40 in steps of 0.10. These graphs have been plotted with the aid of the Michigan Computer Center plotting routines which are included in the public file *PLOTSYS [3].

REFERENCES

1. Oosterveld, M.W.C. and P. Van Oosanen, "Further Computer-Analyzed Data of the Wageningen B-Screw Series," IV International Symposium on Ship Auto-mation, Genova, Italy, Nov. 1974.

2. Lerbs, H.W., "On the Effect of Scale and Roughness on Free Running Pro-pellers," Journal ASME, 1951.

3. MTS Volume 11: "Plot Description System," University of Michigan Compu-ting Center, 1978.

-6-

m)O.:1.:BOJ 3n0C101 9l'0 ,l'O 80'0 vO'O 00'0

(f) ~ 0::: W ..-l ..-l W CL 025 0:::('1") a..c:i Cf)1I WO Her: ........ 0:::' ; W~ ~ (f) ~ I LlJ

en 0 0 -.::t U Z~"': dLlJ

WOD U Oer:!- Z Z-.J "' 0: Hmo 0 If) > ZN 0 W 'iT 00: Oc:::O II1c..o 0:o, od :3lJ..CL

.-i

L.J...I 0::: 0 :::l ~

m>l1.:L~30J 3nOClOl OGO 9l0 GlO 800 rOO

c.n 0::: W .....J .....J W Q..o OLD 0:::("1') 0...0 c.n II W O H CC 0:::' W~ c.n I

CO 0 ~ c.n~

Zw woo wCCr-Z...J HCO o LD Z(\Jo W II wO:::O 0:0' 3LLo....

N

I..LJ c:::

~

m)ll::L~30J 3nOdOl O~O 91"0 ~l'O 80'0 vO'O 00'0

(f) 0::: N W .; --1 --1 W 0.... 0 00 O:::"

m>O.:Lf30J 3nOClOl 9l'O 2:l'O 80'0 rO'O

(f) 0:::: W -l -l W ~ 0-0 OUJ o::::..q-

0 O-c:i .... (f)1I WO HCI 0::::"' wE!E (f) I

en 0 -.::t

Z~"": WOO C')CIf-Z-l HCIJO Z ~ W 0Jo C') II ([0::0 0", 3LLCl..

.::r

l.J..J 0:=: ::::> (.!:)

-LL.

OO'l 08'0 09'0 Or'O OG'O AJN3IJI.:L~3 (1)ll.:l.:l30J lSnClHl

-10-

O~'D

-; l.J..

OJ l.J.. a W 0 oU CO Ow

U Z CI

"' > 0 0 oCI (0

",0 0

0 "

m>l)jj30J 3nOClOl Oc'O gra cl'O 80'0 rO'o 00'0

a ~ .

(f) 0:: W --.J a --.J N W D-o 00 O:::Lf) D-c:i c: (f)1I a WO a Ha: -o::~ '" -; Wa: l..L. (f) l..L. I W

CO 0 0 ~ au Z~""': CO Ow WoO ci U c...:)a:1- Z Z..J a: HCI)~

'" >

Z ' 0 W No c oa: c...:) II c.o C[c:::o 0"-.. 3l..L.o...

I.f"\

WJ e:::: a => ~ (.,!:) a -u..

a ~ ______ ~ ______ ~ __ ~~~~~~~~~~~~4N

d

00'1 08'0 09'0 Ov'O O~'O AJN3IJIjj3 (1)l)jj30J lSnClHl

-11-

m>O.:J.:J30J 3nO~Ol OG"O Gl"O 80"0 fO"O 00'0

(.f) ee w --.l --.l W 0....0 Ol[) eel[) o....d (f)1I Wo HCI ee~ WCI (f) I

cn 0 -.::t (f)"":

Zw Woo werl-Z...J HCO o l[) Z(\Jd W 11 wo:::o a: 0-....... 3LLo...

(.Q

I.J..J c::

~ ) 0

LL LL

IX) W 0 0 oU co Ow

r- U 0 z a: > ~ 0 0 0 a:

-1-

THRUST COEFF(KT) EFFICIENCY 0.20 0.40 0.60 0.80 1.00

o t ! 'I )~~ "I."" "0:3' f\.) '-\.,,7':

-v1-

THRUST COEFF(KT) 0.20 0.40

EFFICIENCY 0.60 0.80

P !! ~"I'{ ">f

-Sl-


o


I "W~fl f\.) r I~'k'w{>< .... f / ,. I I I I II ~ o II Tit}, r /

1.00

.."

.....

G'> c:: :::0 rT1

t.D

TI g ~~~ o ~OD < D~Q TI ~ m z . ~z n ~mH mo rz . ~~o n- 00 o mm m ~~z ~

a OJ I (f) ~1Il rTl::::o "H ~1Il o 1I(f)

Il Il L

0.00 0.04 0.08 0.12 TORQUE COEFF(KQ) 0.16

0.20

au '::::0 cia au

III r r III ::::0 (f)

OG'O

(f) 0:: W

~ -' W 0....0 OLD o::r-0....0 (f) II WO Ha: o::~ Wa: (f) I 0 m ~

(f)"": ZLJJ woo c...Ja:1-Z....J HCO o LD Z~O W II c...JO:::O crO"," 3LLo..

C ....-4

LL.J c:::: ::::l c..:>

-u...

00'1

(o)0:):)30J 3nOCJ01 91'0 Gl '0 80'0 vo'O

08'0 09'0 AJN3IJI:):)3 Ov'O OG'O (l>1l.::1:)30J lSnCJH1

-16-

00'0

-;

W U Z C[ > 0 C[

0

OG'O

UJ 0::: W -l -l W 0.... 0 00 0:::00 0....0 UJII W O H eI o:::~ WeI UJ I 0 CD

-.;;t

zt8"": Woo c...Ja:f-Z---l Hmo If) ZNci W II c...Jo::o ITo ......... 3l..l..o....

....-i

....-i

W 0:::

~ c..o

-u..

OO'l

(O)l):L:ElOJ 3nOtJOl 9l'O Gl'O 80'0

08'0 09'0 AJN3IJI.i:J3

Ov'O OG'O (l)l):L:J30J lSntJHl

-17-

00'0

")

W U Z ([ > 0

0([ (0

cio

0

m>ll.=3.:ElOJ 3nOtJOl 9l'O cl'O 80'0 vo'o 00'0

(f) 0::: W .-J .-J W 0-0 OLD o:::ca 0-0 (f) II WO Ha:

"""") o:::~ Wa: lL. (f) lL. I W 0 0 CD

-.::t U (j)""": Zw woo CJa:1-Z-.J HCO o . LD ZNO W II CJcr::o CIo,,-3l.J..Q..

N ......-t

UJ 0::: :::l l!:)

-u..

OO"l 08'0 09"0 Ov'O 02;"0 AJN3IJI.=3.=33 (1)1).=3.=330J lSntJHl

-18-

0.00

-61-



0.04 0.08 0.12 0.16 TORQUE COEFF(KO)

1.00

-n -G'l c= ;:0 rn I--' \.N

-o'TlL: ,on O:::OC)

II fll ~f\)z UlaJH Cl rz --I])C) OOfll

rTlz ~(f) ~ OJ CI I

0.20

(j) ])fll rTl:::o 'H :::Ofll 1I(j)

Clu w:::o CIa Cl u

fll r r rn :::0 (j)

(o>O.::J.::J30J 3nOtlOl OG'O 2:1 '0 80'0 vO'O

(J) 0::: W -1 -1 W (Lo OlJ) 0:::0") (La (J) II W O Ha:

-") o:::~ Wa: (J) I 0 en ~ 2~""'= ~c:i W woo o U wa:1- z 2---1 a: Hmo > lJ) 2Na 0 w II oIT wo:o (0 ITo'.... 3Ll...Q...

.:::r

....-i

LI..J 0::: :::::> (..!)

---LJ..

o ~ ________ +-__ -+ __ -+~~~~ __ ++~~-+~~~ri-~+---+N

OO'l 08'0 09'0 AJN3IJI:1:13

o

OV'O OG'O (1)0:1:130J lSm:1H1

-20-

m>j)~~30J 3nOClOl 9l'O cl'O 80'0 00'0

(f) cr:: W

~ ~ W 0.... 0 00 cr::o 0...."": (f) II WO Ha: ) cr::' W~ (f) I 0 Q)

-.:::t (j)"":

Zw WOO Oa:f-Z--1 Hmo Lf") ZNO W II 00:::0 ([0' 3u..o....

L.f'I .-!

I.J..J 0:::

~ t.!J

-u..

OO'l 08'0 09'0 ov'o m:'o AJN3IJI~.::J3 (1)D.:J.:J30J lSnClHl

-21-

c:P.00 o o

-II=-

-cc-

THRUST COEFF(KT) 0.20 DAD


o I J' ~~~~ , { (I l ; ; ; ; ') (( (I' I I / rv If I, ,,) )} ~ o

P 0')

:0 0 0 ? <

-.J

:0 z n 0 rn ;" p ngg 0 fTl 11 11 ,-..

L : ...- ~o

0 0

I'V 7 71 / 0 :::::::::::::=t 7

II / ~ / ~ . '" ~ 0

0.00 0.04 0.08 0.12 0.16 TOROUE COEFF(KQ)

1.00

.,.,

-G'l c= :;::0 l"T'l

~ 01

IJ""'I:: "on o::::OC) II rn .0 I\) Z

~OJH rz

-IIlC) oOrn

fTl ;-,(f)z .::::. OJ 0 I

CD JJrn fTl:::lJ "H 5 rn II CD

;-'-0 0:::lJ UlO 0-0

rn r r rn :::lJ CD

0.20

FIGURE 17. WRGENINGEN B-SERIES PROPELLERS FOR 3 BLADES AE/AO= 0.300 P 10=0.50 TO 1.40 =

N 0, 10

w >-~ 0 Uo z W H U

0 H

N~ LL LLO -:LL w~ =LL =

W 1 N 0 U

w l-I :::::.:::::

w LL oo=:J LL= ~o W"": = 0:::: 0=

0 U

I-l-

(f) =:J

\ I \ \ ..q-~~ ~~~-~s2:1~~'::::::"\--- ___ 1 \ ~ = ----

r- I 1 1':>-1 "'t--I:>-I 1>-:1 =:""""1 r--=:-I =.........., 1>' =:"""""'1 1:S 0.20 0.40 0:60 0.6 0.S07 0.8 1.00. 9 l.0. MLl 1.2 __ 1.3 1.4 0

RDVRNCE COEFF(J)

OG'O

(f) 0:: W -.J -.J W 0-0 OLD O:::('Y') 0-0 (f)1I WO Ha: o:::~ Wee (f) I

co 0 ~ zt3~ woo Oa:~ Z-.J Hmo LD Z('Y')o W II 00:::0 CIo,,-3LLCL

00 rl

l.J...J 0::: :::::l c..!:l

l.J....

00'l

m~l.:L:L30J 3nOCjOl 9l'O 2:l'o 80'0 rO'O

08'0 09'0 AJN3IJI.::l.::l3

OV'O OG'O (1~).::l.::l30J lSnCjHl

-24-

00'0

.........

""""') LL LL W 0 u

w u Z CI > 0 0:

(Q>l).:L:f30J 3nO~Ol OGOO 9100 G[OO 800 rOOO

c..n 0::: W ...J ...J W 0... 0 00 c:: o:::-.::t ... 0...0

c..n ll W o Ha:: 0::: ......... w~ c..n I

m 0 -.::t

(f)"": Zw woo lJa::l-Z-' Hmo Lf) Z(Y')o W II lJc:::o 0:0 ......... ::3LL..o.. .

en ......-I

L.L.J 0::

~ l!:l -I.J..

OOOt 080 090 0170 0(:0 AJN3IJI.:L:l3 (1)ll.:l.:l30J lSn~Hl

-25-

000

"""')

'" LL

0 LL W 0

oU '"'CO COw

U Z

'" CI

0 > 0

oCI

0 ..q-0

0 N 0

m>n~.:BOJ 3nOdOl OG'O 9l'0 Gl'O 80'0 vO'O

(f) 0:: W .-J .-J W CLo Olf)

o::~ CLo

':

(f)" WO HO: 0::"' W~ (f) I a m ~

(J)~ Zw WoO 00:1-Z.-J HCO o If) Z(Y)o W " 00::0 ([a"' 3LL.Q..

0 N

LJ..J 0::: ::::::l t.!:l -u..

OO'l 08'0 09'0 Ov'O OG'O AJN3IJI~~3 (1)D~~30J lSndHl

-26-

00'0

.........

J

oOW U Z IT > 0 IT

0 ~ 0

0 N 0

m>Il.:L::!30J 3nOCJOl 9l"0 (;l'O 80'0 vO'O

(f) 0::: W -.J -.J W 0- 0 00 0:::1,[') 0-0 (f)1I W O H CC o:::~ Wcc (f) I

en a ~ ztij-= WOO C)CCI-Z....J HCO o I,[') ZMO W II C)o:::O cr:0,,", ::Il.La..

1"'"'"1 N

LL.l c:::: =>

~ -.

L.L.

OO'l 08'0 09'0 Ov'O 0(;'0 AJN3IJI.:I.:I3 (1)D.:L::!30J lSnCJHl

-27-

OD'D

J LL LL W 0

5u ~dW

U Z cr:

'" > 0 0 ocr: (D

0 '

m)n~J:JOJ 3nOtjOl OG'O 91'0 G1'0 80'0 vO'o

(f) 0::: W ....J ....J W 0....0 OlJ"') 0:::lJ"') 0....0 (f)1I W O HCI o:::~ WCI (f) I

m CI

""'" ztfj"": woo C)CII-Z-l HCO o Z ~ w(Y)o C) II ([0::0

0'-3LL.D-

0 0 00: (,C

",0 0

0 -.:t 0

0 N 0

m>!l:J:J30J 3nOtjOl 91'0 (;1'0 80'0 rO'O 00'0

(f) 0:::: W --1 --1 W CL o 00 o::::c..o Q..,c:i (f) II WO Ha:

") o::::~ Wa: (f) I 0 m ~

(J)""": Zw WOO Qa:1-Z--.J HmO Ln ZMc:i W II Qo:: o ([0"-. 3l.LQ..

r-r'I N

L.J..J 0::::: =:l O:J:J30J lSntjHl

-29-

(f) 0:: W -1 -1 W 0...0 OLf) 0::(0 o...c::::i (f) II WO Her: o::~ Wer: (f) I

CO

-L.L..

0(:'0

00'1

(o>l1.:L::l30J 3nOClOl 91'0 (:1'0 80'0 vO'O

08'0 09'0 AJN3IJI.::l.::l3

OV'O OG'O (1)ll.::l.::l30J lSnClHl

-30-

00'0

-1t:-



P r'0 0

; !1!/:1!ff!it!~1/1 I 1/1 I I I I I _ 1 J ~I ! Ii 'I '/ IV II ~ u:rT~7 v I I I I 1 p en

])Cb 0 '" < ]) z 0 n

" rnp

n~ o ~ rn 11 11 .--.. 0

L '"

g II I /1 1/ 1/11 z:=:::::::=1 :- 7 \\

~IJ/J/J =::::::P""" ;" 7

I { .s:::.. } I ........=: I' ~ o ::::::>'

0.00 0.04 0.08 0.12 0.16 TOROUE COEFF(KOl

1.00

..,.,

GJ c= ;;:0 rn

N V1

-o"1l~ '0]) O:::OC")

II rn PW Z Ul OJH rz -ITIC") oOrn

rTlz --,,(f) .

~ OJ 0 I Cf)

TIrn rTl::;o 'H ~rn "Cf)

0-0 ~::;o 00' 0-0

rn r r rn ::;0 Cf)

0.20

-ZE-

THRUST COEFF(KTl 0.20 DAD

EFFICIENCY O.SO 0.80

~~///// I -=1 e= 17') I

0.00 0.04 0.08 0.12 0.16 TOROUE COEFF(KOl

1.00

II -C1 c:: :::c rn

N en

u'Tl~ ......... 0]) O::::OC) II rn pw Z c.nroH Cl rz ~:DC) oOrn JTlZ ~U) ~ OJ Cl I

0.20

(f) :::Drn JTl:::o ......... H :::Drn o 1I(f) Clu '....J:::o c.no Cl u

rn I I rn :::0 (f)

-n:-



TI o < TI

p . I" I\) I I I i .L~~(>el"~ I J Ii I , I II I I . o ~- I .1 , } r r r I

;z: , :Ii n , "I :;:)

(/) 0::: W --.J --.J W CLo OlD 0:::00 CLo (/)11 WO Ha: o:::~ Wa: (/) I

OJ 0 -=:t (f)""':

Zw WOO lJa:1-Z.....J Hmo Z U1 w(Y')o lJ II a 0:: 0 0""-::Il.J...Q..

co N

lJ...J ~ :::J (.!:)

-u..

on

(o~l:1:130J 3nOdOl 2:1'0 80'0

08'0 09'0 "JN3IJI:1.::l3

Ov'O 0(:'0 (1~l:1:130J lSndHl

-34-

00'0

"""') lL.. lL.. W 0 U

W u Z IT > 0 IT

e

e N c::i

oo~

(j') 0:: W .-J .-J W !l.o 00 0::01 !l.o (j')11 W O HO: 0:: .......... W~ (j') I

CO 0 "

(f) 0::: W -1 -1 W a.... 0 01J) 0:::0") a....c::i

OG'O

OO'l

m>n.:tBOJ 3nOClOl 9l'O Gl'O 80'0 vO'O

08'0 09'0 AJN3IJI.::L:l3

Ov'O OG'O (1)n:L:l30J lSnClHl

-36-

O~'D

02:'0

()") 0::: W .-J .-J W 0.... 0 00 0:::0

o....~ ()") II WO Ha: 0:::" W~ ()") I

m 0 -.:;t

zt3~ Woo lJa:1-Z--' Hmo Z lJ1 W(Y)o lJ II cco::: o 0" 3LLo...

....-i

"'" L.J..J c::: => to!:)

-u..

OO'l

(O)l).:j.:j30J 3nO(jOl 9l'o ~l'o 80'0 ro'o

08'0 09'0 AJN3IJI~~3

Or'O 02:'0 (1)l)~~30J lSn(jHl

-37-

OD'D

.-

") LL LL W 0 u

-8E-


"T1

-G"l c=: ;:0 f"!1

IJ.J N

"'lJ"ilI::

:DO 0 <

,oJ:)

:D

O:::OC")

Z

II rn

n

!=lw z

rnpo

~OJH

n~

rz -/IlC")

0

oOrn

rn

rrl

il

;-,(f)z

"Tl

.j:::,. OJ

-

0

L

t

(J) Ilrn rrl:;JJ 'H ~rn II(J)

;-'""'0 O:;JJ UlO 0-0

rn r r rn :;JJ (J)

0.00 0.04 0.08 0.12 0.16 0.20 TOROUE COEFF(KQ)

(/) 0::: W -'

-' w a.... 0 00 O:::(Y) a....c:i (/)11 WO HC[ o:::~ WC[ (f) I

CD 0 ...;;t

Z~~ WOO uC[f-

Z~ HmO LJ) Z~c:i W II uo::O ITo'... 3LLCl.

!'I"'I !'I"'I

L.I.J , c::::

=:: to!:)

-LJ..

m>D~~30J 3nOtlOl GlO 80"0 vOO 000

-; LL LL W 0 U

Ow

..r

~-------+--------4-------~~~~~~~-L++--4~

U Z IT > 0 IT

OOt 08"0 Og'O AJN3IJI~~3

OVO OG'O (1)n~~30J lSntlHl

-39-

OG'O

(J) 0::: W

~ ~ W 0.....0 Ol.[) O:::(Y') 0.....0 (J) II W O H ee o:::~ Wee (J) I

CO 0 -.:r (f)~

Zw woo weer-Z....J HCO o l.[) Z-.:rc::i W II wo:::o ceo,,-3LLCl.

~ I'f'\

L.L.J 0::: :=l

0,'0

(f) 0::: W ---1 ---1 W 0... 0 00 o:::-.;:r-0...0 (f) II W O Ha: o:::~ Wa: (f) I 0 CD

-.;:r-

Zt:J~ WOO wa:1-Z..-J Hmo IJ') Z-.;:r-o W II wo:::o CIa",", 3li..CL

Ln

"'"' L.W e::::

~ ~

-u..

OO'l

(o)!).J.J30J 3nOcml 9l'O 'l'O 80'0 vO'O

08'0 09'0 AJN3IJI.J.J3

Ov'O 0(;'0 (1)!).J.J30J lSnCjHl

-41-

00'0

----;

w U Z cr: > 0 cr:

(f) 0:: W

~ ~ W O-Cl OU") 0::""" 0-0 (f)1I W O H cr 0::;:U Wcr (f) I Cl m

-.:::t

Z~""': WOO Ocrf-Z-.J Hm Cl If) Z",,"O W II 00::0 CCO ......... 3l..L.o....

t.O I't"'\

W c::::

~ l..!:l

-u...

OO'l

(o>l).=l.=l30J 3nOdOl 9l'O cl'O 80'0 vO'O

08'0 09'0 AJN3IJI.::l.::l3

OV'O Oc'O (1)l).::l.::l30J lSndHl

-42-

OD'D

j

W U Z a: > 0 a:

OG'O

(/') 0::: W --.J --.J W (La 00 O:::Ln (La (/')11 W O Her o:::~ Wer (/') I

co a -.::t

(J)""': ZLLJ WOO

wer~ Z--.J Hmo Ln Z-.::ta W \I wo:::o ([0'-.. 3l.LCL

r--.... f'('\

L.J..J 0:: =' ~ -u....

OO'l

m>l)~~30J 3nOtjOl 9l'O Gl'O 80'0

08'0 09'0 AJN3IJI~~3

OP'O 0(:'0 (1)l)~~30J lSntjHl

-43-

00'0

-; LL LL W 0 U

W u z a: > 0 a:

m>D.:j.:j30J 3nO~Ol 91'0 cl'O 80'0 vO'O 00'0

(f) 0::: W -.J -.J W 0....0 oU") o::::U") 0....0 (f) II W O Her: o:::~ -; Wer: (f) I 0 m

-.::t (f)~

Zw WOO (.Jer:I-Z-l HeIl U") Z-.::to W II (.Jcr:o CI:o"" 31.LQ..

co !'r\

l.J..I 0::: =:l t.!:)

-Ll.

OO'l 08'0 09'0 Ov'O oc'o AJN3IJI.:j.:j3 (L>D.:j.:j30J lSn~Hl

-44-

(o>1):l:l30J 3nOCjOl 9l0 (TO 800 rOO 000

(f) 0:::: W -l -l W 0... 0 00 o::::c.o 0...0 (f) II W O HC[

") o::::~ WC[ LL (f) LL I W

m 0 0 -.:::t oU (j)"": co

Zw ,oW WOO 0 U wC[t-- Z Z..J 0: Hmo > II) Z-.:::to 0 W II 00: wo:::O (0 ([0-....... 3l..J..CL

en /'Ii

w 0 0::: '

U'") 0:: W -.J -.J W

~Cl OLD 0::

(j) 0:: W -1 -1 W 0... 0 00 o::r-0...0 (j)1I WO H([ 0::"" W~ (j) I

CO 0 -.::t (J)~

Zw Woo 0([1-Z-1 Hmo UJ Z-.::to W II 00:::0 CI:o"" 3l..L.Q..

....-i

.;r

L1.J 0:::: -(.!:)

u....

m>0:l:l30J 3nO~01 91'0 (TO 80'0 vo'o OD'D

0 ~

0 N

0 0

"""') '-'

IJ.. IJ.. W 0

oU co Ow

U Z a: > 0

oa: (0

0 ~

o ~-------+--------~~~~+-~~~~~~~~~-+~

00'1 08'0 09'0 OV'O OG'O AJN3IJI:l:l3 (1)0:l:l30J lSntJH1

-47-

(j) er::: w

~ ~ w 0....0 OLf) er:::r--0....0 (j)1I W O H CC er:::~ Wcc (j) I

CD 0 -.::t

(f)""": Zw WoO D.::J.::J30J 3nO(jOl 9l'O i::l'O 80'0 vO'O

08'0 09'0 "JN3IJI.::J.::J3

OV'OOG'O (1)D.::J.::J30J lSn(jHl

-48-

OD'D

0 ~ -

0 ('\J -

") lJ.. lJ.. W a

oU co Ow

U z 0: > 0

00: (lJ 0

0 ~ c:::i

Oc'O

(J) 0::: W .-J .-J W L1-0 00 0:::00 L1-o (J) II WO H([ 0:::;:U WIT (J) I 0 en " 0

ooCI c.o 0

0 "

-05-


EFFICIENCY 0.60 0.80 1.00

p ~ I----;:-;~j'f'}~~)~~~~'t'~~~~~~~~~~~~~~~~~~~~~----------1----------------o i ."''' .JP\.~' J 'I ( t ; J / (I I j ) ."

-c::n ;1: :; 'I V II\~* f / I c ~I :::0 ["T1 n r .'/ ,r ,1 ~J /

~ ~

""'O'T]~ ,on p D:::OC')

II rn en P~z :::0 O? o '" UlCIJH < Cl rz :::0 __ :DC) Z oDrn n fTlz rno ;--(f) o:l ~ ill nco Cl

1 0

'"

c..n rn :TIrn

.,.,

fTl:::o .,., 'H

-L :TIrn 1Ic..n Cl u 00:::0 CJlO Cl u

rn r r rn :::0 c..n

/ ....

...

0.00 0.04 0.08 0.12 0.16 0.20 TOROUE COEFF(KO)

OG'O

(/) 0:: W .-J -.J W 0.... 0 00 0::01 o....c:i (/) II W O H cc o::~ Wcc (/) I

m 0 ~ (f)""':

Zw woo

wCC~ Z...J HCO o lJ) Z~c:i W II wo:::o CIo,-3l.Lo....

LI"'I .:::r

w 0::: => (.!:)

-L.I...

m>O~~30J3nOcOl 2:l'O 80'0 vO'O

08'0 09'0 ;\JN3IJI~~3

OV'O OG'O (l>D~~30J lSncHl

-51-

00'0

LL LL W a u

W u Z a: > 0 a:

(f) 0::: W .-J .-J W (La OU) o:::m (Lei (f) II WO HO: o:::~ Wo: (f) I

en a "

m)D.:l.:l30J 3nO~Ol OGO 9l'0 G[O 800 rOO 000

(f) cr.: W ---.J ---.J W 0... 0 00 cr.:o 0..."-= (f) II WO Ha:

") cr.:~ Wa: lJ...

.(f) lJ... I W

m 0 0 ~ u zt8"-= WOO

Ow

-vs-

THRUST COEFF(KT) dlOO 0.20 0.40


:::0 o < :::0

. .",.....

P I '> " I , r ( I I I I I , rv I r I ~~~ ... J'~< 7 ) I.} It 7 .17 7 } o

Z " "L-( .... h...,.\--n , OJ I' / .'1 :> rn 0 ~ 1/ '"dd:- ,'-'==1 I. ; ; n o rn "Tl "Tl L

0.00 0.04 0.08 0.12 TOROUE COEFF(KO)

0.16

1.00

II -Cj) c= :::0 rrt

...t::' 00

v"1l~ '-...on o::OC") II rrl ~.j:>..z UlDJH rz -jTIC") OOrrl

rnz ;-"(/) .j:>.. o

0.20

OJ I

c.n TIrrl rn:::D '-...H TIrrl o 1Ic.n --0 o:::D UlO 0-0

rrl r r rrl :::D c.n

(f) 0:: W .-J .-J W 0.... 0 00 O:::(Y) 0....0 (f) II W O Ha: o::~ Wa: (f) I

CO 0 ..:t

(j)""': Zw woo

C)a:~ Z-' Hmo L() ZLf)O W II C)o:o ([0"'-31..l.-o...

en .::T

w 0::: :::l (.!:)

-L.L

(O)!).:L::I30J 3nOtl01 91'0

OG'O

(j") 0::: W

~ ~ W 0....0 OLD O:::(Y) 0....0 (j") II WO Ha: 0::: ......... W~ (j") I

CO 0 -.::t

Z~'-: WOO ua:f-Z...J Hmo Z ~ w LDo u II c:cO:: O 0 ......... 3u..CL

c l.1'\

W c::: ----~ -u..

OO'l

9l'O

08'0 09'0 AJN3IJI.:I.:I3

to'O

-56-

00'0

"""') LL LL W 0 U

0 "

(j) 0:::: W --.J .-J W CL o 00 0::::'

(/) 0:: W .-J .-J W Il.o Ol) o::-.::t Il.o (/)11 WO H CC 0::' W~ (/) I

CO 0 -.::t

(j)"": Zw woo OCCf-Z....J Hmo l) Zl)O W II 00:::0 0:0' 31.J..0-

,N I.J"\

l.J.l 0:::

~ (.!:)

-u..

OO'l

m>D~.:ijOJ 3nOCjOl (:['0 80'0

08'0 09'0 AJN3IJI~~3

-58-

00'0

-; ........

LL co LL 0 W

0 as U

oOW U Z IT \0 > 0 0

oIT c.o

":0 0

0 '

m)D.:l.:l30J 3nOClOl OGO 9l0 Gl"O 800 rOO 000

(f) cr: W .-J .-J W CL o 00 cr:Ln CLei (/)11 W O H ee cr:~ -; Wee li... (f) li... I W

m 0 0 ~ oU (f)"": co r- Zw oOw woo U C)eel- Z Z-.J 0: Hmo > Z ~ 0 W Lno 00: C) II c.o a: a:: 0 0'-.. :3LL.o....

F'f"\ l.{",

LI..l 0 ~ "'d" :=J d l.!:l

lL,

o r-------~--------_+--~+r~+rr_~~~~~~_r--~N

OOl 080 Ogo AJN3IJI.:l.:l3

o

OrO OGO (1)l1.:l.:l30J lSnClHl

-59-

(f) 0::: W -1 -1 W 0...0 OLD O::LD 0...0 (f)1I W O Ha: 0::"'-W~ (f) I

CO 0 ...;:t

zt3....: Woo wa:r-Z-1 Hmo LD ZLDd W " wo:::o ([0"'-3LL..CL

.::t' I..l"\

loW 0::: :::::l c..,::l -..

u...

m~)~~jOJ jnOClOl 9l'0 cl'O 80'0 00'0

.--

") l..l-lL. W 0

oU co

w U Z a: > 0

oCI c.o

0 ~ d

o ~------~---------+--~~~~~~~~~N+~~--4d

OO'l 08'0 09'0 AJNjIJI~~j

O~"O 0(:'0 Oo"iF (l~)~~jOJ lSnC1Hl

-60-

m>l)~~30J 3nOtJOl 91'0 ,TO 80'0 00'0

(1) 0:: W -.J -.J W 0... 0 00 0::r:.D o....d (1)1\ WO H CC o::~ l..J... Wcc (1) l..J... I W

en 0 0 ..q- 5u (f)"""': Zw ,ow woo 0 U wCCr- Z Z-.J ([ HCO o > Lf) ZLf)O 0 W 1\ 0([ wo::o (,0 ITo,," 3LL.o...

Lon If'I

W 0 ex: "

(O)l):j:j30J 3nOtlOl 9l'O 2:['0 80'0 00'0

(f) 0::: W ....J ....J W 0-0 Olf) 0::: CD 0-0 (f)1I WO HCI ) 0:::;:U WCI (f) I 0 CO

-.::t

m>O.::l.::l30J 3nO(jOl 9l'O

OG'O

Cf) 0::: W -.J -.J W Q..a OU") o:::r--Q..o Cf) [[ W O Ha: 0:::'""-W~ Cf) I 0 m ::t z~'-: Woo C)a::r-

Z~ Hmo U") ZU")o W [I C)o::o 0:0'""-~1.LQ..

oc U"'\

l.J..l 0:::

== l!:l -L.L..

m>D.=j.=j30J 3nOtjOl 91'0 cl'O 80'0 vO'O

08'0 09'0 AJN3.IJI.:L:J3

OV'O OG'O (l>l).=j.::J30J lSntjHl

-64-

00'0

0 (\J

0 ~ - )

Ow ~ u

z 0: >

"' 0 0 0:

(O>lU.:l30J 3nOdOl OG'O 91"0 Gl'O 80'0 vO'O 00'0

(f) 0::: W

~ ~ W 0.... 0 00 0:::00 o....c:i (f)1I W o HCI o:::~ WCI (f) I

CO 0 ~ Z~""': woo DCIf-Z...J Hmo U") ZU")c:i W II Do:::o cro ......... 3LLo....

O"l LI'\

\.JJ 0:: =::l

~ -u..

o ~--------~--------~~------+---------~----~~4~

0 N

0 0

0

00 a: to

0 ~ 0

o r---------r-------~r_~~~~+r+_~~~~~--~--~N

o

OO'l 08'0 09'0 AJN3IJI.:l.:l3

OV'O OG'O OO'~ (1)l).:l.:l30J lSndHl

-65-

if) 0:::: W

~ ~ W 0...0 OlI) 0::::00 0...0

-

m>D.::Lf30J 3nOtjOl cl'o 80'0

o ~------~--------~~~-----+---------+-----r-r-t~

o ~------~---r~--~~--~-=-+---------+~~~~-tN

.--I'-t~t-f:r:7'71 0 ~------~----~r-~----~~~=---~~++-+r-~~-t0

o r-------~~----~~_+~~~++.r~~~~~~_+--_+N

o

o ~------~----~~~~~~~~~~~~_r~~~--~O

00'1f'

-66-

OGOO

(J) 0:::: W -.J -.J W 0- 0 00 0::::0"l Q...a (J)IJ W o Ha: 0::::'"'" w~ (j') I

CO 0 -.;;t (f)~

Zw woo Oa:f-Z....J Hmo Lf) ZLf)a W II 00::0 ITo,"", 3u....o... I""""'i I.D

W e:::

~ ~

-u..

OOOl

(o>ll:l:l30J 3nOtJOl 9100 GlOO 800

080 OgoO AJN3IJI:l:l3

OroO OGoO (1)l)~~30J lSntJHl

-67-

00'0

0 '

(f) 0:::: W ---1 ---1 W D-a OLD 0::::0") D-o (f)1I WO HCI O::::~ WCI (f) I

en 0 o::::t Z(J")'-: W~O C)CII--Z...J HCO o If) Zlf)o W II C)o:::o 0:0'-::II..J..O-

N l.O

W c::: =::I l!:l

u....

00'1

(O)ll.J.J30J 3nOClOl 91'0 GI'O 80'0 rO'O

08'0 09'0 AJN3IJI~~3

Ov'O 0(;'0 (1)l).J~30J lsnClHl

-68-

00'0

0 .".

..-:

.......

'""') ~ ~ W

'" 0

c'ou 00 Ow

r- U 0 Z

IT > 0 ~"O IT (0

0 .".

-69-


P N 0

jl/~!'/IV/ ! I.' I / / ."

-G') c: ::t:I m 0") \.N

-o.,.,~ ,oJ] O:::lJC)

:D 0", II rn 0 pCJl z < CJl coH :D 0 rz z

.... ....,TIC) n oOrn rnp rrlz ;-,(/)

~ OJ I (f)

TIrn "'I I I I, It'll/I I ~ Y \\ rrl:::o L 'H 6 rn

,,(f)

;-,u 0:::0 0 u

rn I I rn :::0 (f)

0.00 0.04 0.08 0.12 0.16 0.20 TOROUE COEFF(KQ)

m>ll.:J.:J30J 3nOCJOl Oc'O 9100 cloO 80'0 vO'O 00'0

(j) 0:: W -.J -.J W 0... 0 OLf) 0::0 0...'-:

(j)1I W O HC[ ) o::~ Wc[ LL (j) LL I W

CO 0 OJ 0 """

'oU (f)'-: Oro Zw Ow WOO u C)C[r Z Z....J IT Hmo > Z ~ 0 WLf)o IT C) /I crO:: O 0'"'-3LLCL .::r c..o

I...W 0::

~ ~

-u..

~ ________ ~ ____ ~ __ ~~~~~~~~~~~~r+~ __ ~N

oot 080 Og'O AJN3IJI.:J.:J3

Ov'O OcO (1)l).:J.:J30J lSn~Hl

-70-

U) 0::: W

~ ~ W 0- 0 00 O:::M 0-0 U)II WO HO: 0:::'""-W~ U) I

CO 0 ~ (f)~

Zw Woo 00:1-Z-.J Hmo IJ') Zc.oo W II 00:::0 0:0'""-3u..CL

LI"'\ 1.0

W c::::

--c.!:l

-u..

m>l)~.:BOJ 3nOtJOl 9tO 2:1"0 80"0 00"0

0 o::t"

-

0 N

0 0

-

""") -.....;

LL LL W 0

as U Ow

U Z cr: > 0

ocr: (0

0 o::t"

o

r-------~--------~------~~~~~~~~rT~--~~ o

OO"l 08"0 09"0 Ov'O 0(;"0 AJN3IJI~~3 (1)l)~~30J lSntJHl

-71-

(o>O.:l.:l30J 3nO~01 O~'O 9l'0 ~1'0 80'0 vO'O 00'0

(J) 0:::: W -I --l W 0..0 OlJ) O::::M 0..0 (J) II WO Her: o::::~ Wer: (J) I 0 CO

-.:t (f)~ Zw W WOO U wcrl- Z Z...J cr: Hmo > lJ)

0 Zc.oo W II ocr: wa:::o cr:o'-.. 3LLO-

lD lD

W 0::: =:! c..:;l

-I..L.

(,0 ",0 0

0 "

(o>l).:L:L30J 3nOtJOl (TO 800 vOO 000

(f) 0::: W -.J -.J W CL o 00

O:::~ CLei (f)1I W O HIT ) O:::~ WIT (f) I 0 OJ ~

(J)""': Zw ":0 W WOO 0 U lJITr Z Z.....J IT Hmo > Z ~ 0 Wc.oo oIT lJ II (0 C[c:t:O

0"-... :3LLo...

r--... l..D

w 0 0::: ~

~ 0 L!:!

-LL

o

~--------r---------r---~~~~~~~~~~~~--+N o

aOl 080 090 avo OGO AJN3IJL:L:B (1)l1.:LJ30J lsntJHl

-73-

(f) cr::: W -1 -1 W 0....0 OLn o:::-.::t 0....0 (f) II WO HIT cr:::~ WIT (f) I

en 0 -.::t

(J)"":' Zw WOO eJITf-Z...J Hmo Z ~ WlO o eJ II a:cr:::o 0"'-. 3l.Lo..

cc (,Q

lJ.J 0::: -

l:l -u....

00'1

(o)0.:l.:l30J 3nOtJOl 9l'O 2:l'O 80'0

08'0 09'0 AJN3IJI:l:l3

Ov'O O~'O (1)I).:l.:l30J lSnClHl

-74-

00'0

-;

(j) 0:::: W --.J --.J W CL o 00 O:::Lf) CLei (j) II W O Ha: o:::~ Wa: (j) I

CD 0 ~ U)~

Zw woo Oa:f-Z.-J HCO o Lf) Zeoei W II 00::0 CIo". 3LLo...

Oi t.O

l.J...J 0::::

---~

---u..

OO'l

m>ll.:1:ElOJ 3nO~Ol 9l'O Gl '0 80'0 vO'O

08'0 09'0 AJN3IJI.:1.:13

Ov'O 02:'0 (l>1).:1.:130J lSn~H1

-75-

00'0

0 ~

0 N

0 '=!

) LL LL W 0

5u ,,-ow c U

z ([ >

c 0 0([ ((J 0

0 ~

(J) 0:::. W ~ ~ W (Lo OLI) O:::LI) (Lei (J) II WO Her: o:::~ Wer: (J) I

CO 0 ~ (J)~ Zw

WOO 0er:1-Z-..J HCDo LI) Z(!)ei W II 00:::0 a:o"-.. 3lJ...CL

0 r--..,

l.LJ 0::: ::J

(f) 0.:: W --1 --1 W 0.... 0 00 o.::c.o 0....0 (f) II WO Ha: o.::~ Wa: (f) I 0 CO

-.;t

Z~~ WOO Qa:1-Z-.J HCO o UJ Zc.oo W II Qo:::O 0:0""-3LLO-

......t

'" UJ 0::: -(.!J

-LL

(O)1):L:fjOJ 3nO~Ol

(J) 0::: W --.J --.J W 0....0 OLD o:::c..o o...ci (J)II Wo Ha: o:::~ WeI (J) I

CO 0 ""

-6L-

THRUST COEFF(KT) ,0.20 0.40


CI tv I ",?-XF

(f) 0::: W

~ ...J W CLo Oll") o:::r--CLa (f) II WO Ha: o:::~ Wa: (f) I

CO a ~ CJ)""":

Zw WOO wa:1-Z-l Hmo Z ~ wc.oo w II crCt::O 0"'-. 3lLCL

.:::T r--..

l.J..J 0:: --'

~

u...

m>D:1:130J 3nOdOl 9l'O 2:l'O 80'0 vO'O 00'0

0 -:r

'" M

0 N

0 0

""") LL LL W 0

oU co Ow

U Z CI >

"' 0

00 CI 1..0 d

0 ~ 0

o r---------r---------~+_H_~~+n~~~~~~~4---+~

OO'l Ov'O O~'O oo'IF (l)1):1:130J lSndH1

-80-

-18-


p ;m'~' 0 V: /,1/11116~~ II I c::: .t>. ;:c 0 :i :) l'l ,II (, fT1

~ V1

u"T1~ '0]) o:::OC)

J) 0,0 II rn 0 0\ pm z < c.nroH ::D rz z

--i:::DC) n

'" oOrn nlp rnz ;-Cf)

+:>. OJ I (f)

:::Drn :orI' /' /11 / I / I ./' I \ A \ rn:::o L

'H E;rn 1I(f)

pv 00:::0 00 0-0

rn r r rn :::0 en

0.00 0.04 0.08 0.12 0.16 0.20 TOROUE COEFF(KQ)

(f) 0::: W .-J .-J W (La Oll) 0:::00 (Lei (f) II W O Her: 0::: ........ W~ (f) I

CO a "

(f) 0:::: W --.J .-J W 0- 0 00 0::0'") 0...0 (f) II W O HCI o::~ WCI (f) I

m 0 'OJ"

(1)""": Zw WOO OCIr-Z-' Hmo IJ) ZillO W II 00::0 ITO'-::3l.LCL

,...."

,...."

I.JJ c::: :::::l

~

L.L.

OO'l

(Q~)~~30J 3nOClOl 9['0 (;['0 80'0 vO'O

08'0 09'0 AJN3IJI~~3

Ov'O 0(;'0 (1~)~~30J lSnClHl

-83-

00'0

j LL LL W 0

ooU CD Ow

U Z IT > 0 IT

0 '

m>D:l.:L30J 3nOCJOl 0~'0 9[ '0 ~!'O 80'0 vo'O 00'0

if) 0::: W ..-J --l W L1-o OLf) o:::m L1-d (/)11 W O Her:

--; 0::: ......... W~ LL (/) LL I W

CO 0 0 oo:::t oU (J")~ CD

Zw Ow WOO U Oer:r- Z Z-' 0: H m G5 > Z(OQ 0 W II a: 00::0 0:0'-.... 3LLo....

00

'" l.J.J 0 e::: -=t

-

0 ~

-u...

o r-------~------~~rr+-~~,r+-TP~~~~~~--~d

00'[ 08'0 09'0 "JN3IJI:l:l3

Ov'O O~O U>D:l:l30J lSnCJHl

-84-

en 0::: W ....J ....J W 0- 0 0 0 0:::0 0-"": en II W O Ha: o:::~ Wa: en I

CD 0 "

(O)J).i::J30J 3nOc.JOl 02:'0 9l'O 2:l'O 80'0 vO'O 00'0

(f) 0::: W .-J .-J W 0.... 0 OlJ) 0:::0 0....""": (f) II W O Ha:

') o:::~ Wa: LL (f) LL I W

m 0 OJ 0

-.::t ou (j)""": co Zw Ow Woo u C)a:1- Z Z....J IT HCO o > lJ) Zc.oo 0 W II IT C)cr:o 0:0"-3LLo..

0 co

l.J..J 0 0:: --=:r

-

~ -L.I...

OO'l 08'0 Og'O Ov'O 02:'0 AJN3IJL:LJ3 (1)JL:LJ30J lSnc.JHl

-86-

(Q>lL:tf30J 3nOtjOl OG'O 9l'0

(J) 0::: W -.J -.J W 0-0 OLf) O:::(Y') 0-0 (/)11 W o Ha: o:::~ Wa: (J) I

CO 0 ~ .

Z~-Woo C)a:r-Z.......J HCO o Lf) Zr-o W II C)o::o 0:0 ......... 3l1...CL

N oc

LL.J 0::: :=J

m>O:::J:::J30J 3rOtJOl 9l0 c:tO 800 1700 000

0 '

(J) 0::: W -.J -.J W Q...o OLD

o:::~ a... a (J)II WO Her: o:::~ Wer: (J) I

CO 0 ~ Z~"": WOO lJer:1-Z-l Hmo Z ~ wr--o lJ II crO::: O 0'-31..l..Q...

.::r 00

L.LJ c:::

~ ~ -u..

OOl

m>D.:L:f30J 3nO~Ol 9['0

OG'O

(/) cr: W -l -l W 0..... 0 00 o:::Lf) CLei (/)11 W O Her: o:::~ Wer: (/) I

CO 0 ::t Z~~ WOO

~a:f-Z--l Hmo Z ~ Wr--o ~ II a:cr:::O 0'

:31.J..D..

I.f'\ oc

l.J..I 0::: =>

~

-u...

m>lU:l30J 3nO~Ol 9l'0 Gl"O 80"0 vO'O

08"0 09'0 AJN3IJI:l:l3

Ov'O OG'O (1)l):l:l30J lSn~Hl

-91-

00'0

0 ~

0 N

~

0 0

~

") LL LL W 0

OoU co Ow

U Z IT > 0

00 IT CD

0 ~ 0

()) 0::: W .-J .-J W Q..o OlJ) 0:::lJ) Q..ci ()) II WO H CC o:::~ Wcc ()) I

en 0 ~ Z~'-: Woo OCCr-Z-' Hmo lJ) zr--ci W " 00::0 0:0'-... 3LLo...

t.O 00

W 0:::: =:l

~

-u...

m>0:l.:f30J 3nOtjOl 9!'O Gl '0 80'0 vO'O 00'0

") lL. lL. W 0

oU co Ow

0 " 0 IT

OO'l 08'0 09'0 "JN3IJI:l:l3

Ov'O 0(:'0 (1)0:l:l30J lSntjHl

-92-

(o)O.=J.=J30J 3nOtlOl OGO 9l0 2:l0 800 vOO 000

o r---------+-------~_r--~~~_+----------~--~~~+~

(/) 0::: W ---1 0 ---1 ("\I W 0- 0 00 0:::(0 0-0 (/)11 0 WO 0 HIT ~ 0:::" ) W~ ll.. (/) ll.. I W

CO 0 0 -.:;t OOU

(f)""": CD Zw Ow WOO U wITI- Z Z...J cr Hmo > Z ~ 0 wr'o ~ocr w II (0 ([0::0 c:i 0" 3l.L..0-

"" 00

LJ.J 0 e:::: ~ => c:i (.!:)

-u..

OOl 080 090 OVO OGO ,\JN3IJI:l:l3 (1)D:l:l30J lSntlHl

-93-

(J") 0::: W --.l --.l W 0-0 OLf) 0:::(0 O-d (J")II Wo Ha: 0:::' W~ (J") I

OJ 0 ...::t (j")~

Zw WoO C)a:!-Z....J HCO o Lf) Zr-d W II C)o::o CI:o, 3lL.0-

OC CO

1.J..J 0::: =:l L!:'

lJ...

(O>D:L:j30J 3nOd01 9l'O (:l'O 80'0 00'0

a ~--------+----------r--~~---+----------~--~~~~~

a N

~

....

a a

,......

") LL L!.. W

'" 0 oa U

CO Ow

U Z 0: > 0 ~a 0:

CD a

a ~

, I I

a N a

a r-----____ +-______ ~~-U~-k~~~~~--~~~~--~~a

OO'l 08'0 09'0 "JN3IJI:I:l3

Ov'O 0(:'0 OO'~ (1)O:l:l30J lSnClHl

-94-

L

dJoo ~

-S6-



P I ~0(>~

-o1lL: ,oJ) 0:::00

1\ rn P~z CJ1roH rz -I])C) oOrn

rTlz ~(J) .

~ OJ o I

0.20

en ])rn rTl::o 'H ])rn II(/)

u ~::o ClO Cl u

rn I I rn ::0 (/)

en cr::: W -.J -.J W 0-0 Oli") cr:::r--0-0 (/)/1 W o Ha: cr:::~ Wa: (/) I m 0

-.:::r (f)~

Zw woo lJa:f-Z....J HCO o li") Zr--o W II lJa:::o CIa"" 3l.LQ...

0 O"l

W c::::: ::=I

J:) o < J:) z n

-L6-

THRUST COEFF(KT) EFFICIENCY 0.20 0.40 0.60 0.80

p '),,, I ,! I II I f\.) 'R'?~N:' ... ... Pi?< r ,I , 'i F ) I f o

o ~ 'i I .f/ I 1 I' ;" l\)v,*'uf'\'/K;';' /' o

rn 0, 7 I V' "'1 \ ~ n~:o~/ i +---f="rll ~ :7 \:\ o rn 11 11 .......

L

0.00 0.04 0.08 O. i2 0.16 TOROUE COEFF(KQ)

1.00

" c:;") c= :::0 f"T"I

l..D I-"

u"Tll:: '0I) O:::OC) II rn p....jZ c.r1 coH rz --.,::oc) oOrn

r11Z -"if) .

~ OJ o I

0.20

(f) ::orn r11:::o 'H TIrn o II(/) 0-0 00:::0 00 0-0

rn r r rn :::0 (/)

(f) 0::: W -.J -.J W 0-.0 OlI) 0::: co 0-0 (f)1I WO Ha: 0:::" W~ (f) I

en 0 ~ (f)~

Zw WOO Oa:f-Z--1 Hmo lI) Zr--O W II C)0:::0

m>D.:1.:l30J 3nOtlOl 91'0 1:1'0 80'0 vo'O 00'0

(/) 0:::. W .-J -.J W CL o 00 0:::.0') CLd (/)11 WO Ha: .--.. o:::.~ -; Wa: LL (/) LL I W

CO 0 0 ~ oU (J)"": co Zw Ow WOO U C)a:f- Z Z-.l a: Hmo > UJ zr--d 0 w "

a: C)c::o 0:0""' :3l.J....CL

""" en

l.J..I 0 a:: ...:r => 0 t.!:)

-w-I , , ,

0 N

OO't 08'0 09'0 Ov'O O~O ;l.JN3IJI.:1.:13 (1)/).:1.:130J lSntlHl

-99-

(/) 0:: W -1 -1 W CLo OLD 0::01 CLei (/)11 Wo HCI o::~ WCI (/) I

CO a -.:::t

(f)"":' Zw WoO

(/) 0::: W -l ..--1 W CL 0 0 0::::5 CL"":

(/)" W O HCI: 0:::'"' W~ (/) I 0 m ~

Z(f)"": W WOO

lJCI:1-Z...J HCDo L{) Zr---o W II (.:10::0 CIO,", 3lL..CL

LrI O"l

l.J..J 0:: =:l D.:1.:l30J 3nOtlOl Gl0 800 rOOD

080 OgoO ~JN3IJI:I:l3

OVOO OGoO a)D:I:l30J lSntlHl

-101-

I I I ,

000

;

Ow U Z cr:: > 0 a:

"O:t d

N

m>ll.:L::J30J 3nO~Ol 0(;'0 (;1'0 80'0 to'O 00'0

0 ' lJ") Zr-ci 0 W II "'-0 ([ lJa:::o 0(0 0:0"'-..

3L!...o....

I.D en

Ll..l 0 0::: '

1IIIIIIIIIIIIIIIIIfl)lrlllllll~ll~ll1illiil"lllllllllllIIII 3 9015 02229 2968

Curvas Kt Kq de B Series Wageningen

Documents

Transcript of Curvas Kt Kq de B Series Wageningen