Hull and propeller non-dimensional values - Conversion Factors - when using systems of units which are not consistent

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Ministerlo de Marina

C A N A L DE E X P E R I E N C I A S H I D R O D I N A M I C A S , EL P A R D O

• A -•

HULL A N D

P

ROPELLER

N

O N - D I M E N S I O N A L

V

A L U E S

C o n v e r s i o n F a c t o r s

when using systems of units which a r e not consistent

/

M A D R I D

1 9 5 1

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C O N T E N T S

H u i x N O N - D I M E N S I O N A L V A L U E S :

T A B L E 1.—Conversion factors f o r Length-volume ratio.

2- — " S u r f ace-volume ratio.

3 — .' Fullness coefficients.

4. — " " L e n g t h Proude Number.

5. — Volume Froude Number,

6-— " " © R . E . Froude Speed-length

cons-tant.

— " @ B a k e r Speed-prismatic-length

cons-tant.

— " (K)R. E . F r o u d e Speed-volume cons¬

" tant.

^-— " » Wetted-surface resistance coefficient,

10- — " Volxune-resistance coefficient,

11- — " "

0 R . E . Fi'oude Resistance constant.

12. — Teifep resistance coefficient.

13. — „ Resistance-displacement ratio. .

14. —Relationships between the various speed-bases.

15- — resistance-parameters.

16- — resistance-paramieters

and

R / A .

P R O P E L L E R N O N - D I M E N S I O N A L V A U J E S :

T A B L E 17.—Conversion factors f o r J Advance coefficient.

18.—

"

_{" Propeller Froude Number.}

19.—

_{" kr T h r u s t coefficient.}

20.—

_{" kQ Torque coefficient.}

21.—

_{" Power coefficient.}

22.—

"

_{" (f}

_{Speed pararneter.}

23.—

" or T h r u s t parameter.

24.—

_{" IX}

_{Torque parameter.}

25.—

" T h r u s t load.

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The following physical constants have been t a k e n :

Salt water

**P - 104,5872 Teg mr's"- p = 1,988 lb ft* s^'**

y = 102Q kg m-' y = 1/35 ton ft-'

EVesh water

P ^ 101,9368 kg 's' p ^ 1,938 lb f t ' s=

y = 1000 kg m-^" y. = 1/35,91 ton f t '

Of the above values, those in metric units are used at E l Pardo;

those in E n g l i s h units were generally used by B a k e r . These latter are

slightly lower, but the differences are negligeable (less than one per

thousand).

In each of the following tables, the geometrical and physical factors,

from which the non-dimensional value depends, are given. Spaces for

eventual additions have been provided,

1 CV (metric) - 75 m kg 1 nude 1,852 010 km h-'

1 HP ( E n g l i s h ) - 550 f t lb 1 Knot 1,688 889 f t s-^

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L E N G T H - V O L U M E R A T I O V ) L Definition • ; ƒ {form) , = : A -. — ,1/3 A Units A • Salt water 1.008 693 Ml t • Salt water 0.305 710 7 n Ton 10 leg 1 m t Fresh water Fresh water 3.965 923 it lb 0.303 106 3 n Ton

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S U R F A C E - V O L U M E R A T I O (*) Definition ~ ; f {form) B B _ = A . ^ 2/3 ^ S / S A Units

-A B • -1.017 260 _t -r _\ ë a i t water ë a i t water 0.093 4.59 08 Ton 100 1 mi kg t Freeh water Freeh water 15.728 55 0.091 873 43 ft' lb Ton

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Definition 6 —

FULLNESS COEPFICIENrS

V V LBT S = A LBT 9 = A . ; f i f orm, simUmrity) (E) L A U n i t s A - A L B T 0.974 658 8 t Vl m ni Salt water Salt water 35 _Ton _ft _ft _fti 0.001 kg ra m m 1 -t -m ni m m2 Fresh water Fresh water 0.016 031 35.91 r \ 25 lb Ton ft ft ft ft ft ft ft^ fti

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10 _{T A B L E 4}

F R O U D E N U M B E R ( L E N G T H F R O U D E N U M B E R )

V

Definition -

; Speed-lengtli base in Fronde's law.

Practical form A .

g = 9.81 m s-a flr = 32.185 0.319 275 4 0.088 687 61 0.164 250 3 0.176 267 9 0.002 937 798 0.297 696 9 -A 3 = 9.80 tl 32.153 ft s-0.319 438 2 0.088 732 84 0.164 334 1 0.176 357 8 0.002 939 296 0,297 848 7 Unitu VI

8->

km mido ft

.9-1

ft Knot ill m m ft ft ft

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V O L U M E F R O U D E N U M B E R

V

Definition • •• • — — ; Speed-volume base in Fronde's law.

P r a c t i c a l f o n n A . ———— (V or A) '-'^ A Units 0 = 9.81 . g = Q.80 m flr = 32.185 fts-i «7 — 32 153 V V 0.164 250 3 _{0.164 334 1} w ' 0.164 954 4 _{0.165 038 5} _t Sa!t water Sa!t water 0.297 696 9 _{0.297 848 7} Knot . ™ 0.164 599 9 _{0.164 683 8} _Knot _Ton 0.319 275 4 _{0.319 438 2} m e-i t 0.088 687 62 0.088 732 85 km h-i t • -0.164 250 3 _{0.164 334 1} _nudo _t F r e s h water • F r e s h water 0.176 267 9 _{0.176 357 8} _ft^ 0.297 696 9 _{0.297 848 7} Knot ft^ 0.351 030 7 0.351 209 8 / i s - i — lb 0.097 044 42 _{0.097 093 91} _fts-i _Ton -0.163 897 3 I -0.163 980 9 Kmt j i Ton

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12 T A B L E 6

© R. E . F R O U D E S P E E D - L E N G T H C O N . S T A N T

-

V

Definition - ^/4•.^r ; Speed-length base in Fronde's law.

VgL

V

Practical form A .

A Vnits (J ~ 9.81 m s-2 (/ = 9.80 «i s-2 .9 =32.185 ft s-i ƒ / = 3 2 . 1 5 3 fts--' V 1.131 802 1.132 379 Vi s-i m 0.314 389 4 0.314 549 7 km 7i-i >n 0.582 252 4 0.582 549 3 m 0.624 853 6 0.625 172 3 Jt s-i ft 0.010 414 23 0.010 419 54 ft min-'^ ft 1.055 308 1.055 846 Kmt

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® B A K E R S P E E D - P R I S M A T I C - L E N G T H C O N S T A N T .

y

Definition ^ = 7 - V^n ; Speed-Iengtiï base in Fronde's law.

VgvL

I

Practical form A .

V

•

Practical form A .

A Units (J — 9.81 m s-2 (/ = 32.185 f t s-i y = 9.80 m s-"~ » = : 3 2 . 1 5 3 ƒ* s-2 V L 0.800 304 7 0.800 712 9 •Ml .9-1 m 0.222 306 9 0.222 420 3 kin h-i m 0.411 714 6 0.411 924 5 nuclo in 0.441 838 1 0.442 063 4 ft s-i ft 0.007 383 968 0.007 367 7 ft min-i ft 0.746 215 5 0.746 596 1 Knot _ft

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^•^ T A B L E 8

® R . E . F R O U D E S P E E D - V O L U M E C O N S T A N T

V

Definition V43r ; Speed-volume base in Fronde's law.

V P r a c t i c a l f o r m A (V orA)^'*' Salt water <; = 9.81 w.s-2 3 = 32.185 fts-0.582 252 4 0.584 748 5 1.055 308 0.583 491 5 l . l S l 802 0.314 389 4 0.582 252 4 Fresh water _{0.624 853 6} 1.055 308 1.244 372 0.344 013 6 0.581 000 8 fif c=: 9.80 tns-i 0 = 32.153 fta-0.582 549 3 0.585 046 7 1.055 846 0.583 789 1 1.132 379 0.314 549 7 0.582 549 3 0.625 172 3 1,055 846 1.245 006 0.344 189 0 0.581 297 1 Units nudo nudo Knot Knot m Ö-1 km / j - i mtdo « l 3 m» ft s-i Knot ft s-i ft s-i Knot ft' ft^ Ton lb Ton Ton

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R E S I S T A N C E C O E F F I C I E N T ( W E T T E D - S U R F A C E R E S I S T A N C E C O E F F I C I E N T ) R Definition ; f ( f o m i , S, Sfl) 2 R P P r a c t i c a l forma A , . — ; A2 . — 8V' 8V' U n i t s B P 8 V , w. . 0.072 255 17 10.533 91 kg GV mi nude Salt water - . Salt water 0.352 704 1 -114.860 8 lb HP fti Knot • 0.019 619 95 0.254 274 7 0.074 133 82 1.471 497 68.654 18 10.807 79 kg kg kg CV cv CV mi mi mi mido Freah water Freah water 1.031 989 0.361 803 6 567.594 0 117.824 2 lb lb HP HP fti fti : fts-^ Knot

Table 9 also appliey to the "Area resistance coefficient" R/.

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T A B L E l ö V O L U M E R E S I S T A N C E C O E F F I C I E N T R Definition ; / ( / o r m , %, 3Ï) 2 R : p P r a c t i c a l f o r m s A, . ^ ; A-, . {vorA)2/3y2 (y or A)^'''^" A.-, (P) U n i t s • A.-, (P) R .... P J V V 0.072 255 17 10.533 91 "kg OV nudo 0.073 502 28 i 0.715 72 ky OV \ _t _nudo Salt water 0.352 704 1 114.860 8 lb HP — Knot 0.032 963 40 10.734 79 lb HP Ton Knot 0.019 619 95 1.471 497 ky CV t m s-i 0.254 274 7 68.654 18 ky CV t km h-i 0.074 133 82 10.807 79 ky CV m-- t nudo Fi'esh -water 1.031 989 567.594 0 lb HP ft' - —. _{ft s-i} 0.361 803 6 117.824 2 lb HP ft' — Knot 16.231 69 8 927.433 lb HP — lb ft s-i 0.094 812 38 52.146 82 lb HP — Ton ft s-i 0.033 240 13 10.824 91 lb HP Ton Knot

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© R. E . F R O U D E R E S I S T A N C E C O N S T A N T R 1000 17 Definition P r a c t i c a l forms A , R jiform, S. 3Ï) (p or A)=/=.7^ ; A2 . Salt water A, (B) 2.874 942 2.924 563 ^ 2 (P) 419.130 9 426.365 1 14.033 65 1.311 572 4 570.168 427.123 7 Fresh water 0.780 653 2 10.117 27 2.949 691 41.061 55 14.395 71 845.838 5 3.772 465 1.322 583 (v- orA)2/3F= U n { t i-R kg kg lb 2b CV CV HP _{f f} HP I _ nudo mtdo 58.548 99 kg 2 731.663 430.028 4 22 583.85 4 688.075 355 211.3 2 074.856 430.709 6 kg kg CV CV CV lb lb lb lb lb HP HP HP HP HP m3 Ton Knot Knot in s-i km h-i nndo ft'-ft" i lb Ton Ton ft s-i Knot ft s-i ft s-i Knot

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18 T A B L E 12 T E L F E R R E S I S T A N C E C O E F F I C I E N T R g L Definition ; /(form, S , RL P L P r a c t i c a l f o r m s A , . — ; A , . — A F= A y 0 9.81 m s—- g ~ 9.80 m s—- _{U n t s} .<; = 32.185 ft g ~ 32.153 ft A, (B) A, (P) A, {R) A, (P) R P ^ \ A V 9.81 735.750 0 9.80 735.0 kg GV m i kg 0.009 81 0.735 750 0 0.009 80 0.735 kg GV m ! t 0.127 137 6 34.327 13 0.127 008 0 34.292 14 kg CV •m t km ;i—' 0.037 066 99 5.403 908 0.037 029 20 5.398 399 ha CV m t nudo 32.185 17 701.75 32.153 17 €84.15 Ih HP ft lb fts—" 0.014 308 31 7.902 567 0.014 354 02 7.894 709 lb HP ft Ton fts—' 0.005 037 364 1.640 458 O.005 032 355 1.638 827 lb HP ft 1 Ton knot

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R E S I S T A N C E - D I S P L A C E M E N T R A T I O

Definition — - ; Hforni, S, 9t)

A

R P

Practical forms A, . — — ; A. .

A A V U 71 it s A j (R)

_I

R _A P

v

1 75.000 00 kg kg OV m s-i C.OOl 000 0 0.075 000 0 kg t

ov

m s-i — 0.270 000 0 — t

ov

km h-1 0.145 787 6

t

ov

nudo 1 550.000 0 lb lb HP ft s-i • 0.000 446 428 6 0.145 382 9 lb Ton HP Knot

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T A B L E 1 4 R E L A T I O N S H I P S . ^. X

IsL

_1/

E x a m p l e : = © X 0.28209

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B E T W E E N T H E V A R I O U S S P E E D - B A S E S P X 0.39894 ]/9 0..39894 / 9 ,1/3 1.4142 ]/9 1.4142 K ) X 0.28209 0.28209 0.70711 1 1

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24 _{T A B L E 1 5} R E L A T I O N S H I P S B E T W E E N R — X R p Vi - 6?) R p Vi K P Vi 11

s

p Vi 2 R p y2/3 7 c = RgL .2/8 39.789 .2/,1 L S 0.5 39.789 2^, ,3/S 39.789 0.5 ,1/a E x a m p l e : R i2 X

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T H E V A R I O U S R E S I S T A N C E - P A R A M E T E R S

© X

j

0.025 133 ' 2 0.025 133 — • m 37. 0.025 133 2 -L 1 79,577 L • • L 0,012 .56r, _ _ — 1 • / • 1 1 • 1 •

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26 T A B L E 1 6 R E L A T I O N S H I P S B E T W E E N T H E V A R I O U S R E S I S T A N C E -P A R A M E T E R S A N D B / A pVi B pVi R pVi ,1/3 „ 2/; . 01' 2 £/ L gv — or 2 2(p . — or 2 — 2/3 g

V 1/3

ya

©'

©-

1000 4';r gL 1000

ya

1000 B X V-gh

ya

-1/3

ya

i/i;

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.7 A D V A N C E C O E F F I C I E N T

Definition —~ ; basic parameter in Newton's law.

nD

Practical form A .

nD

U n i t s A n D 1 H I . S-1 i: p. a. rn 60 m s-i r. p. m. m 0.514 447 2 undo /•. p. s. ni 30.866 83 nudo T. p. m. tn 1 ft s-i r. p. 9. ft 12 ft r. p. a. inch 101.833 3 Knot r. p. m. ft /

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30 T A B L E 1 8

P R O P E L L E R F R O U D E N U M B E R

Definition n

; basic parameter in Fronde's law.

Practical form A . n \/D

A U n i t s - - • g = 9.81 »!. s-2 g •= 32.185 ft s-2 (/ = 9.80 w.s-2 3 = 32,153 ft s-i n D 0.319 275 4 0.005 321 257 0.319 438 2 0.005 323 97 r. p. s. r. p. Hi. m. m. 0.176 267 9 0.050 884 15 0.002 937 798 0.176 357 8 0.050 910 11 0.002 939 296 r. p. s. r. p. s. r. p. m. ft inch ft

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fcr T H R U S T C O E F F I C I E N T T

Definition fcr = ; f(form, J, ^, 31) («')

T

Practical form A . •——

V n i t s A n D ,0.009 561 399 k(j r. p. s. m 34.421 04 kg r. J). ni. m Salt water water 1 810.865 lb r. p. in. ft 0.008 810 000 kg r. p. s. m 35.316 00 kg r. p. m. m Fresh water 0.515 995 9 lb r. p. s. ft 10 699.69 lb r. p. s. inch 1 857.585 -lb T. p: TO. ft

(*) I f both over critical flow and sufficient immersion are provided, Ufonn, J) approximately.

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sa T A B L E 20

Icq TORQUE C O E F F I C I E N T

Q

Definition ; /(form, J, S, Dl) (•)

Q P

Practical forms A^ . ; A2 . —

A , (Q) A , tP) U )l i t n A , (Q) A , tP) Q P n D 0.009 561 399 0.114 130 8 •m kg CV r. p. s. '111 34,421 04 24 6 52.25 m kg CV r p. m. m Salt watoi' Salt watoi' 1 810.865 9 510 867. ft lb IIP r p. m. _ft 0.009 810 000 0.117 098 2 7n kg CV r. p. s. m 35,316 00 25 293.21 m kg CV r p. m. m F r e s h water 0.515 995 9 45.167 80 ft lb HP r. p. s. ft 123 39S.28 11 239 194. ft lb HP r. p. s. inch 1 857.585 9 756 245. ft lb HP r p. m . ft

I,') If both over critical flow and sufficient Immersion are provided, Kforrm J) approximately.

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P O W E R C O E F F I C I E N T P D e f i n i t i o n - = 2irkQ ; f i f orm, J , g, 91) (*) P P r a c t i c a l f o r m A . — n' A U n i t s P n D 0.009 501 399 m kg s-^ [ _{r. p. s.} m 154 894.7 av r, p. m. m • Salt water • 597 585.4 X IO2 • HP r. p. m. _ft O.009 810 00 m kg s-i r. p. s. m 0.735 750 0 CV r. p. s. r. 158 922.0 GV r. p. m. m Fresh water Fresh water 0,515 995 9 lb ft s-i r. p. s. ft 128 396.3 lb ft S-3 r. p. s. inch 613 003.1 X 102 HP r, p. m. ft

(*) I f both over ci-itlcal flow and sufficient immersion are provided, ftform, J) approximately.

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Definition Vc

T A B L E 22 <(, S P E E D P A R A M E T E R

pD' J

Q

Vfc(

**; fiform, J, S, 91) (*)**

Practical forms A , . V„

Q

; A,.V„

iQ) A,{P) V n i t s iQ) A,{P) D Q P 10.226 79 2.960 046 m s-i m

TO

kg

CV

2.840 775 0.822 235 1

fom

h-i m m kg

CV

5.261 143 1.522 787 mido m TO- kg

CV

Salt water 1.409 965 0.150 701 3 ft

s-i

ft ft lb HP 0.023 499 42 0.002 511 688 ft min-i ft ft lb HP 2.381 274 0.254 517 8 Knot ft ft lb HP 10.096 38 2.922 300 ni s-i m m kg

CV

2.804 550 0.811 750 1 km 7i-i m m kg

ov

F r e s h water 1.392 121 0.148 794 1 ft s-i ft ft lb HP 0.033 489 22 0.003 579 429 ft s-i inch ft lb HP 0.023 202 02 0.002 479 901 ft min-i ft ft lb HP

(*) I f both over critical flow and sufficient immersion are provided, fifomi, J) approximately.

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TD D e f i n i t i o n <r T H R U S T P A R A M E T E R 1 7c 7 2 TT Q 27r P r a c t i c a l forms Ai . kQ J TD ; f i f o r m , J,d,m) (*) T D n A, . Q A„ (P) U n i t s A„ (P) T D _Q n P 0.159 154 9 0.013 333 33 0.000 222 222 2 kg kg m m m kg r. p. s. r. p. m. •CV CV " 0.013 262 91 0.159 154 9 0.000 151 515 2 0.001 818 182 0.000 030 303 03 lb lb lb inch ft ft ft lb ft lb r. p. s. r. p. s. r. p. m. HP HP HP

(*) I f both over critical flow and sufficient immersion are provided, f(fonn, J) approximately.

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36 Definition n T A B L E 24 /A T O R Q U E P A R A M E l ^ R 1 / Q V/C( f ( f o r m , J , s, m) n P r a c t i c a l forma A, . n Q ; A, U n i t s A^ ( P ) n D Q P 10.226 79 2.980 046 r. p. s. m m kg CV 0.170 445 5 0.006 369 003 r. 2). m. m 'm kg ov Salt water 1.409 965 0.150 701 3 r. p. s. ft ft lb HP 0.023 499 42 0.000 324 257 5 r. p. 7)1. ft ft lb HP 10.096 38 2.922 300 r . p. 's. nr '•n kg CV 0.168 273 0 0.006 287 787 r. p. in. m rn kg OV F r e s h water 0.002 790 768 0.000 298 285 8 r. p. s. inch ft lb HP 1.392 121 0.148 794 1' •>: p. s. ft jt lb HP 0.023 202 02 0.000 320 153 8 r. p. m. ft fi lb HP

(*) I f hoth over critical flow ajid sufficient immersion are provided, fiform, J) approximately.

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• T H R U S T L O A D T 8 kT Definition — = . ; fiform, J , 8, 91) (*) pVe^ TTD' TT r~ 2 4 T P r a c t i c a l f o r m A . — U n i t s • A T D 0.024 347 90 kg m s-i m 0.091 998 32 kg nudo ni Sait water 1.280 925 lb ft s-i ft 0.449 077 8. lb Knot < ft 0.024 980 96 kg m 5 - 1 m 0.323 753 2 kg km h-i m Fresh water Fresh water 1.313 973 lb ft 8 - 1 " _ft 189.212 1 lb ft s - 1 inch

(*) I f both over critical flow and sufficient immersion are provided, fiform, J) approximately.

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