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1 Ministerlo de Marina CANAL DE EXPERIENCIAS HIDRODINAMICAS, EL PARDO A - HULL AND PROPELLER NON-DIMENSIONAL VALUES Conversion Factors when using systems of units which are not consistent / M A D R I D

CONTENTS Huix NON-DIMENSIONAL VALUES : TABLE 1. Conversion factors for Length-volume ratio. 2- " Surf ace-volume ratio. 3.' Fullness coefficients. 4. " " Length Proude Number. 5.

3 CONTENTS Huix NON-DIMENSIONAL VALUES : TABLE 1. Conversion factors for Length-volume ratio. 2- " Surf ace-volume ratio. 3.' Fullness coefficients. 4. " " Length Proude Number. 5. Volume Froude Number, 6- " " R. E. Froude Speed-length constant. Baker Speed-prismatic-length constant. " (K)R. E. Froude 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 Relationships between the various speed-bases. 15- resistance-parameters. 16- resistance-paramieters and R/A. PROPELLER NON-DIMENSIONAL VAUJES: TABLE 17. Conversion factors for J Advance coefficient. 18. " " Propeller Froude Number. 19. " kr Thrust coefficient. 20. " kq Torque coefficient. 21. " Power coefficient. 22. " " (f Speed pararneter. 23. " or Thrust parameter. 24. " IX Torque parameter. 25. " Thrust load.

The following physical constants have been taken: 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 ft' s= y =

4 The following physical constants have been taken: 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 ft' s= y = 1000 kg m-^" y. = 1/35,91 ton ft' Of the above values, those in metric units are used at El Pardo; those in English units were generally used by Baker. 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, km h-' 1 HP (English) ft lb 1 Knot 1, ft s-^

5 HULL NON-DIMENSIONAL VALUES

$TABLE 1 ^ LENGTH-VOLUME RATIO V) L Definition ; ƒ {form), = : A -.,1/3 A Units 1.008 693 Ml t Salt water 0.$

7 TABLE 1 ^ LENGTH-VOLUME RATIO V) L Definition ; ƒ {form), = : A -.,1/3 A Units Ml t Salt water n Ton 10 leg 1 m t Fresh water it lb n Ton V) (m) in the 'circular constant' notation of R. E. Froude.

$SURFACE-VOLUME RATIO (*) Definition ~ ; f {form) B _ = A. ^ 2/3 B ^S/S - A B Units - 1.017 260 t - r \ ëait water 0.093 4.$

8 SURFACE-VOLUME RATIO (*) Definition ~ ; f {form) B _ = A. ^ 2/3 B ^S/S - A B Units t - r \ ëait water Ton mi kg t Freeh water ft' lb Ton (*) (s) In the 'circular constant' notation of R. E. Froude.

TABLE 3 FULLNESS COEPFICIENrS Definition 6 LBT V V ; fif orm, simumrity) S = A LBT 9 = A. (E) L A Units - A L B T 0.

9 TABLE 3 FULLNESS COEPFICIENrS Definition 6 LBT V V ; fif orm, simumrity) S = A LBT 9 = A. (E) L A Units - A L B T t Vl m ni Salt water 35 Ton ft ft fti kg ra m m 1 t m ni m m2 - - Fresh water lb Ton ft ft ft ft ft ft ft^ fti \ r

10 TABLE 4 FROUDE NUMBER (LENGTH FROUDE NUMBER) V Definition - ; Speed-lengtli base in Fronde's law. Practical form A. -A Unitu g = 9.81 m s-a flr = 32.185 3 = 9.80 tl 32.153 ft s- 0.

10 10 TABLE 4 FROUDE NUMBER (LENGTH FROUDE NUMBER) V Definition - ; Speed-lengtli base in Fronde's law. Practical form A. -A Unitu g = 9.81 m s-a flr = = 9.80 tl ft s VI 8-> km mido ill m m ft.9-1 ft ft ft , Knot ft

TABLE 5 ii VOLUME FROUDE NUMBER V Definition ; Speed-volume base in Fronde's law. Practical fonn 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.

11 TABLE 5 ii VOLUME FROUDE NUMBER V Definition ; Speed-volume base in Fronde's law. Practical fonn A. (V or A) '-'^ A Units 0 = g = Q.80 m flr = fts-i « V V w' t Sa!t water Knot Knot Ton m e-i t km h-i t nudo t Fresh water ft^ Knot ft^ /is-i lb fts-i Ton I Kmt Ton - j i

12 TABLE 6 R. E. FROUDE SPEED-LENGTH CON.STANT - V Definition - VgL ^/4.^r ; Speed-length base in Fronde's law. Practical form A. V A Vnits (J ~ 9.81 m s-2 (/ = 9.80 «i s-2.9 =32.185 ft s-i ƒ/=32.

12 12 TABLE 6 R. E. FROUDE SPEED-LENGTH CON.STANT - V Definition - VgL ^/4.^r ; Speed-length base in Fronde's law. Practical form A. V A Vnits (J ~ 9.81 m s-2 (/ = 9.80 «i s-2.9 = ft s-i ƒ/= fts--' V Vi s-i m km 7i-i >n m Jt s-i ft ft min-'^ ft Kmt

TABLE 7 i3 BAKER SPEED-PRISMATIC-LENGTH CONSTANT. y Definition ^ = 7 - V^n ; Speed-Iengtiï base in Fronde's law. VgvL Practical form A. V A Units (J 9.81 m s-2 (/ = 32.185 ft s-i y = 9.80 m s-"~»=:32.

13 TABLE 7 i3 BAKER SPEED-PRISMATIC-LENGTH CONSTANT. y Definition ^ = 7 - V^n ; Speed-Iengtiï base in Fronde's law. VgvL Practical form A. V A Units (J 9.81 m s-2 (/ = ft s-i y = 9.80 m s-"~»=: ƒ* s-2 V L Ml.9-1 m kin h-i m nuclo in I ft s-i ft ft min-i ft Knot ft

^ ^ TABLE 8 R. E. FROUDE SPEED-VOLUME CONSTANT V Definition V43r ; Speed-volume base in Fronde's law. Practical form A V (V ora)^'*' Units <; = 9.81 w.s-2 3 = 32.185 fts- fif c=: 9.80 tns-i 0 = 32.

14 ^ ^ TABLE 8 R. E. FROUDE SPEED-VOLUME CONSTANT V Definition V43r ; Speed-volume base in Fronde's law. Practical form A V (V ora)^'*' Units <; = 9.81 w.s-2 3 = fts- fif c=: 9.80 tns-i 0 = fta nudo nudo Salt water Knot Knot Ton l.lsl m Ö-1 km /j-i mtdo «l3 m» Fresh water , ft s-i Knot ft s-i ft s-i Knot ft' ft^ lb Ton Ton

TABLE 9 is RESISTANCE COEFFICIENT (WETTED-SURFACE RESISTANCE COEFFICIENT) R Definition ; f(fomi, S, Sfl) 2 R P Practical forma A,. ; A2. 8V' 8V' Units B P 8 V, w.. 0.072 255 17 10.

15 TABLE 9 is RESISTANCE COEFFICIENT (WETTED-SURFACE RESISTANCE COEFFICIENT) R Definition ; f(fomi, S, Sfl) 2 R P Practical forma A,. ; A2. 8V' 8V' Units B P 8 V, w kg GV mi nude -. Salt water lb HP fti Knot kg CV mi kg cv mi kg CV mi mido Freah water lb HP fti fts-^ lb HP fti : Knot Table 9 also appliey to the "Area resistance coefficient" R/. Prtictical forms A,. R/<g) V~- ; A^P/^ V

$TABLE lö VOLUME RESISTANCE COEFFICIENT R Definition ; /(/orm, %, 3Ï) 2 R : p Practical forms A,. ^ ; A-,. {vora)2/3y2 (y or A)^'''^" U n i t s A.-, (P) R... P J V V 0.072 255 17 10.$

16 TABLE lö VOLUME RESISTANCE COEFFICIENT R Definition ; /(/orm, %, 3Ï) 2 R : p Practical forms A,. ^ ; A-,. {vora)2/3y2 (y or A)^'''^" U n i t s A.-, (P) R... P J V V "kg OV nudo i ky OV \ t nudo Salt water lb HP Knot lb HP Ton Knot ky CV t m s-i ky CV t km h-i ky CV m-- t nudo Fi'esh - water lb HP ft' -. ft s-i lb HP ft' Knot lb HP lb ft s-i lb HP Ton ft s-i lb HP Ton Knot

$TABLE 11 17 R. E. FROUDE RESISTANCE CONSTANT Definition R 1000 jiform, S. 3Ï) Practical forms A, R (p or A)=/=.7^ ; A2. (v- ora)2/3f= A, (B) ^2 (P) U n { t i- R 2.874 942 2.924 563 419.130 9 426.$

17 TABLE R. E. FROUDE RESISTANCE CONSTANT Definition R 1000 jiform, S. 3Ï) Practical forms A, R (p or A)=/=.7^ ; A2. (v- ora)2/3f= A, (B) ^2 (P) U n { t i- R kg kg CV CV nudo mtdo Salt water lb 2b HP HP I ff _ Ton Knot Knot kg kg kg CV CV CV m3 in s-i km h-i nndo Fresh water lb lb lb lb lb HP HP HP HP HP ft'- ft" i lb Ton Ton ft s-i Knot ft s-i ft s-i Knot

$153 ft U n t s A, (B) A, (P) A, {R) A, (P) R P ^ \ A V 9.81 735.750 0 9.80 735.0 kg GV m i kg 0.009 81 0.735 750 0 0.009 80 0.735 kg GV m! t 0.127 137 6 34.327 13 0.127 008 0 34.$

18 18 TABLE 12 TELFER RESISTANCE COEFFICIENT R g L Definition ; /(form, S, RL P L Practical forms A,. ; A,. A F= A y m s - g ~ 9.80 m s -.<; = ft g ~ ft U n t s A, (B) A, (P) A, {R) A, (P) R P ^ \ A V kg GV m i kg kg GV m! t kg CV m t km ;i ' ha CV m t nudo Ih HP ft lb fts " lb HP ft Ton fts ' O lb HP ft Ton knot 1

TABLE 13 RESISTANCE-DISPLACEMENT RATIO Definition - ; Hforni, S, 9t) R Practical forms A,. ; A.. A A P AV Aj (R) U 71 it s I R A P v 1 75.

19 TABLE 13 RESISTANCE-DISPLACEMENT RATIO Definition - ; Hforni, S, 9t) R Practical forms A,. ; A.. A A P AV Aj (R) U 71 it s I R A P v kg kg OV m s-i C.OOl kg t ov m s-i t ov km h t ov nudo lb lb HP ft s-i lb Ton HP Knot

20 20

21 21

TABLE 14 RELATIONSHIPS. ^. X IsL X V J. 1 0.28200 V 1 0.28209 1/ ^ 3.

22 TABLE 14 RELATIONSHIPS. ^. X IsL X V J V / ^ [/ / Example: = X

BETWEEN THE VARIOUS SPEED-BASES P X K) X 0.39894 ]/9 0.

23 BETWEEN THE VARIOUS SPEED-BASES P X K) X ]/ /9,1/ ]/

24 24 TABLE 15 RELATIONSHIPS B E T W E E N R X R p Vi - 6?) R p Vi K P Vi 11 s p Vi,3/S 2 R p 7 y2/3.2/8 c = /, RgL 0.5 LS 2^, 0.5,1/a Example: R i2 X

THE VARIOUS RESISTANCE-PARAMETERS X j 0.025 133 ' 2 0.

25 THE VARIOUS RESISTANCE-PARAMETERS X j ' m L 1 79,577 L L 0,012.56r, 1 1 / 1 1

26 26 TABLE 16 RELATIONSHIPS B E T W E E N T H E VARIOUS RESISTANCE- PARAMETERS AND B/A,1/3 2/;. pvi 01' 2 pvi B / L gv or 2 pvi R 2(p. or 2 ya 2/3 g V 1/3 ya ' ';r gl 1000 ya 1000 B X V- gh ya -1/3 ya i/i;

27 PROPELLER NON-DIMENSIONAL VALUES

29 TABLE 17.7 ADVANCE COEFFICIENT Definition ~ ; basic parameter in Newton's law. nd Practical form A. nd A U n i t s n D 1 HI. S-1 i: p. a. rn 60 m s-i r. p. m. m undo /. p. s. ni nudo T. p. m. tn 1 ft s-i r. p. 9. ft 12 ft r. p. a. inch Knot r. p. m. ft /

$30 TABLE 18 PROPELLER FROUDE NUMBER Definition n ; basic parameter in Fronde's law. Practical form A. n \/D A U n i t s - - g = 9.81»!. s-2 g = 32.185 ft s-2 (/ = 9.80 w.$

30 30 TABLE 18 PROPELLER FROUDE NUMBER 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 = ft s-2 (/ = 9.80 w.s-2 3 = 32,153 ft s-i n D r. p. s. r. p. Hi. m. m r. p. s. r. p. s. r. p. m. ft inch ft

TABLE 19 si fcr THRUST COEFFICIENT T Definition fcr = ; f(form, J, ^, 31) («') T Practical form A. A V n i t s n D,0.009 561 399 k(j r. p. s. m 34.421 04 kg r. J). ni. m Salt water 1 810.865 lb r. p. in.

31 TABLE 19 si fcr THRUST COEFFICIENT T Definition fcr = ; f(form, J, ^, 31) («') T Practical form A. A V n i t s n D, k(j r. p. s. m kg r. J). ni. m Salt water lb r. p. in. ft kg r. p. s. m kg r. p. m. m Fresh water lb r. p. s. ft lb r. p. s. inch lb T. p: TO. ft - (*) If both over critical flow and sufficient immersion are provided, Ufonn, J) approximately.

sa TABLE 20 Icq TORQUE COEFFICIENT Q Definition ; /(form, J, S, Dl) ( ) Q Practical forms A^. ; A2. P A, (Q) A, tp) U )l i t n Q P n D 0.009 561 399 0.114 130 8 m kg CV r. p. s.

32 sa TABLE 20 Icq TORQUE COEFFICIENT Q Definition ; /(form, J, S, Dl) ( ) Q Practical forms A^. ; A2. P A, (Q) A, tp) U )l i t n Q P n D m kg CV r. p. s. '111 34, m kg CV r p. m. m Salt watoi' ft lb IIP r p. m. ft n kg CV r. p. s. m 35, m kg CV r p. m. m Fresh water ft lb HP r. p. s. ft S ft lb HP r. p. s. inch ft lb HP r p. m. ft I,') If both over critical flow and sufficient Immersion are provided, Kforrm J) approximately.

TABLE 21 33 POWER COEFFICIENT P Definition- = 2irkQ ; fif orm, J, g, 91) (*) Practical form A. n' P 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.

33 TABLE POWER COEFFICIENT P Definition- = 2irkQ ; fif orm, J, g, 91) (*) Practical form A. n' P A U n i t s P n D [ m kg s-^ r. p. s. m av r, p. m. m Salt water X IO2 HP r. p. m. ft O m kg s-i r. p. s. m CV r. p. s. r GV r. p. m. m Fresh water 0, lb ft s-i r. p. s. ft lb ft S-3 r. p. s. inch X 102 HP r, p. m. ft (*) If both over ci-itlcal flow and sufficient immersion are provided, ftform, J) approximately.

TABLE 22 <(, SPEED PARAMETER Definition Vc pd' Q J Vfc( ; fiform, J, S, 91) (*) Practical forms A,. V Q ; A,.V iq) A,{P) V n i ts D Q P 10.226 79 2.960 046 m s-i m TO kg CV 2.840 775 0.

34 TABLE 22 <(, SPEED PARAMETER Definition Vc pd' Q J Vfc( ; fiform, J, S, 91) (*) Practical forms A,. V Q ; A,.V iq) A,{P) V n i ts D Q P m s-i m TO kg CV fom h-i m m kg CV mido m TO- kg CV Salt water ft s-i ft ft lb HP ft min-i ft ft lb HP Knot ft ft lb HP ni s-i m m kg CV km 7i-i m m kg ov Fresh water ft s-i ft ft lb HP ft s-i inch ft lb HP ft min-i ft ft lb HP (*) If both over critical flow and sufficient immersion are provided, fifomi, J) approximately.

TABLE 23 35 <r THRUST PARAMETER Definition TD 1 7c 7 2 TT Q 27r kq J ; fiform, J,d,m) (*) Practical forms Ai. TD A,. T D n Q A (P) U n i t s T D Q n P 0.159 154 9 0.013 333 33 0.

35 TABLE <r THRUST PARAMETER Definition TD 1 7c 7 2 TT Q 27r kq J ; fiform, J,d,m) (*) Practical forms Ai. TD A,. T D n Q A (P) U n i t s T D Q n P kg kg m m m kg r. p. s. r. p. m. CV CV " lb lb lb inch ft ft ft lb ft lb r. p. s. r. p. s. r. p. m. HP HP HP (*) If both over critical flow and sufficient immersion are provided, f(fonn, J) approximately.

36 TABLE 24 /A TORQUE PARAMEl^R 1 Definition n / Q V/C( f(form, J, s, m) n Practical forma A,. n Q ; A, A^ (P) Units 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.

36 36 TABLE 24 /A TORQUE PARAMEl^R 1 Definition n / Q V/C( f(form, J, s, m) n Practical forma A,. n Q ; A, A^ (P) Units n D Q P r. p. s. m m kg CV r. 2). m. m 'm kg ov Salt water r. p. s. ft ft lb HP r. p. 7)1. ft ft lb HP r. p. 's. nr ' n kg CV r. p. in. m rn kg OV Fresh water r. p. s. inch ft lb HP ' >: p. s. ft jt lb HP r. p. m. ft fi lb HP (*) If hoth over critical flow ajid sufficient immersion are provided, fiform, J) approximately.

TABLE 25 37 THRUST LOAD T 8 kt Definition =. ; fiform, J, 8, 91) (*) pve^ TTD' TT r~ 2 4 Practical form A. T A Units T D 0.024 347 90 kg m s-i m 0.091 998 32 kg nudo ni Sait water 1.

37 TABLE THRUST LOAD T 8 kt Definition =. ; fiform, J, 8, 91) (*) pve^ TTD' TT r~ 2 4 Practical form A. T A Units T D kg m s-i m kg nudo ni Sait water lb ft s-i ft lb Knot ft < kg m 5-1 m kg km h-i m Fresh water lb ft 8-1 " ft lb ft s-1 inch (*) If both over critical flow and sufficient immersion are provided, fiform, J) approximately.

38 3S

Exhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No

Exhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No xhibit 2-9/3/15 Invie Filing Pge 1841 f Pge 366 Dket. 44498 F u v 7? u ' 1 L ffi s xs L. s 91 S'.e q ; t w W yn S. s t = p '1 F? 5! 4 ` p V -', {} f6 3 j v > ; gl. li -. " F LL tfi = g us J 3 y 4 @" V)