472 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 66.9 



the Telfer merit factor M, is represented by 

 values of WV^/igLPg) for a range of Froude 

 numbers squared. Taking the 515-ft or middle 

 length of ABC ship as the example, for which 

 Fl is 0.0727, the broken meanUne of Fig. 34.1 

 gives a tentative merit factor M of about 9.5. 

 Using the dimensional Eq. (34.xxv) of Sec. 34.10, 



Ps = 0.61 



L{M) 



= 0.61 



(17,300)(20.5)' 



(5 15) (9. 5) 

 18,582 horses. 



Since the 20.5-kt speed is to be made at 0.95 of 

 maximum designed power, by item (22) of Table 

 64.d, this power is 18,582/0.95 = 19,560 horses. 

 Using the alternative weight-speed-power factor 

 WV/Ps of Fig. 60.U, for an Fl of 0.0727, the 

 broken meanhne gives a value of about 125. 

 Then, with the dimensional formula on Fig. 60.U, 



Ps = 6. 



17,300(20.5) 

 125 



= 19,520 horses. 



The designed maximum power estimate is then 

 19,520/0.95 = 20,550 horses. 



It is emphasized that, when making estimates 

 from the meanlines, one assumes that a ship of 

 modern design is to perform no better than the 

 average of a number of older ships. Further, since 

 the merit-factor ordinates of both Figs. 34.1 and 

 60. U are logarithmic, a value picked among the 

 spots for the better ships may easily be from 20 

 to 40 per cent better than the average. This means 

 estimated powers of from 20 to 40 per cent below 

 those calculated in the preceding paragraphs. 



The third estimate is made by the use of the 

 ATTC 1947 or Schoenherr friction line, the ATTC 

 1947 roughness allowance ACp of 0.4(10"^), 

 and the Taylor Standard Series data as reworked 

 by M. Gertler [TMB Rep. 806, Govt. Print. Off., 

 Wash., Mar 1954]. 



At this point it is necessary to take account of 

 the average temperature of the sea water in which 

 the ship is to run, specified in item (18) of Table 

 64. c. For this temperature, 68 deg F, the value of 

 the mass density p(rho) of salt water, from Table 

 X3.e, is 1.9882 slugs per ft'. The kinematic 

 viscosity j'(nu), from Table X3.h, is 1.1372(10"') 

 ft^ per sec. The former is 0.99884 times the value 

 of p = 1.9905 slugs per ft' for the standard con- 

 dition of temperature 59 deg F, wliile the latter 

 is 0.88726 times the value of j- = 1.2817(10"') 

 ft" per sec for the same standard temperature. 

 The former ratio is suflSciently close to 1.000 for 



all preliminary-design purposes. The latter ratio 

 is some II per cent less than 1.000, but its effect 

 on Cf at the large ship Reynolds numbers is 

 small. Since the effect of the 68-deg kinematic 

 viscosity is to diminish the calculated friction 

 resistance, its use is somewhat questionable in a 

 preliminary design. For these reasons, and 

 because the "standard" values of p and v for 59 

 deg F are easily remembered, the latter are 

 employed throughout Part 4 of the book. 



Entering the large-scale portion of Fig. 45.H 

 with a Cx of 0.96 and a B/H of 2.92 for the 515-ft 

 ship, the wetted-surface coefficient Cs is found 

 to be 2.618. The fi rst a pproximati on to the wett ed 

 area is then CsV^ = 2.618 \/605,500(515) = 

 46,231 ftl From Table 45.b the Reynolds number 

 R„ is about 1391 million for the 515-ft length, for 

 the 20.5-kt speed of 34.62 ft per sec, and for a 

 kinematic viscosity v in "standard" salt water of 

 1.2817(10"') ft' per sec. From Table 45.d the 

 value of Cf is 1.470(10"'). Adding a roughness 

 allowance ACp of 0.4(10"') for a clean, new ship 

 of as-yet-undetermined shape or surface condition, 

 gives Cf + ACf. = 1.870(10"'). 



Entering the appropriate graph of the B/H = 

 3.00 group of the reworked Taylor Standard 

 Series contours, reproduced in Fig. 56. D of Sec. 

 56.5, for Cp = 0.62, T„ = 0.903, F„ = 0.268, and 

 F/(O.IOL)' = 4.433, the value of Cn is found to 

 be 1.25(10"'). Entering the B/H = 2.25 group 

 with the same values, Cr is 1.21(10"'). Since 

 B/H is actually 2.92, Cr is found by linear inter- 

 polation to be approximately 1.246(10"'). At the 

 20.5-kt speed, therefore, the specific friction 

 resistance is considerably more than half of the 

 total resistance, namely 1.870(10"') as compared 

 to (1.870. -I- 1.246)10"' = 3.116(10"'). The 

 amount of wetted surface is therefore something 

 to be watched carefully in the design. 



The total drag Rt oi the bare underwater hull 

 is estimated from Eq. (45.ii) of Sec. 45.7, namely 

 Rt = (p/2)7'S(C« -I- Cf. + ACf) = 55(1.246 -f- 

 1.470 + 0.4)10"', where for the first approxima- 

 tion p is taken as 1.9905 slugs per ft' for salt 

 water. Then Rt = 0.99525(34.62)^(46,231)3.116 

 (10"') = 171,830 lb, whence 



Pe = 



RtV 

 550 



171,830(34.62) 

 550 



= 10,816 horses. 



A round figure is 10,820 horses. 



As a check calculation by Taylor's original 

 method [S and P, 1943, pp. 59-60], the friction 

 resistance per ton of displacement is found by 



