no 



JIVDRODVN AMK.S !\ Mill' DESIGN 



Seciyi-f 



\\ liiri till- I'xiifl iinili'iwiilor volume V is ditti- 

 iniiiotl by pliinimetcr, iisiiiR the fair lines of the 

 ship, it is foimd to be 575,847 ft'; the correspoiui- 

 iiig wetted surface 5, by Kq. (45.vii), is 44,831 ft'. 

 This is very close to the value determined by the 

 more precise method described in the next para- 

 graph. 



The calculation of wetted surface, using (1) the 

 measure<l girths at 21 stations, (2) a combination 

 of the Simpson and trapezoidal rules, and (3) no 

 correction for obliciuity, gives a value of S for the 

 bare hull, incluiling the cutwater shown on Fig. 

 67.E, of 44,883 ft'. It is found, for this ship, that 

 the wetted surface is about 1.2 per cent higher 

 when using two half-stations at each end in 

 addition to the customary 21 stations. However, 

 the precision here is much greater than for the 

 friction-resistance coefficient Cp , especially when 

 roughness is taken into account. 



The original estimate of net bilge-keel area of 

 Sec. 6G.9, assuming a keel length of 200 ft, a 

 width of 3 ft, and a girthwisc span at the base of 

 1 ft, is 2,400 - 400 = 2,000 ft'. Using the bilge- 

 keel design of Fig. 73. N, with a length of 193.5 ft, 

 a width of 3.5 ft, and a girthwise span of 1.25 ft 

 at the base, the net area is calculated to be 

 2,743 - 489 = 2,254 ft=. Incidentally, the 

 Reynolds number R, for a bilge-keel length of 

 193.5 ft is 



R. 



VL ^ (20.5)(l.fl889)(193.5) 

 V 1.2817(10") 



= 522.7 million. 



The wetted surface of the rudder and rudder 

 horn, calculated from the dimensions given in 

 Fig. 74. K, and a.ssuming the wetted area to be 

 twice the projected area, is found to be 748 ft^. 



The only separation zone expected around the 

 underwater hull is that abaft the transom. The 

 area of the after side of the transom is therefore 

 not included in the wctted-surface calculation, 

 using niea.sured girths. No deduct ioii is tlicrcforo 

 necessary for it. 



Xo allowance is made in this calculation, nor 

 is any customary, for the change in welted surface 

 due to substitution of the wave profile at designed 

 speed for the at-rest watcrlinc as an upper 

 boundary of the wetted area. 



The iiull area covered by tlir li\rd luddi r Imrn 

 i.s about 10 ft^ 



The actual wetted .surfiicc of the tnin.som-stcrn 

 AlU' whip, with all appendages, in ft', is: 



Hare-hull surface, plus cutwater, 



from girths 44,883 



Hilgc keels (2 of), surface expo.scd to 



water 2,743 



Rudder and fixeil rudiler horn 748 



Deduction for hull area covered by 



bilge keels —489 



Deduction for hull area covered In- 



rudder horn —10 



Net total, ft', 47,875 



As an indication of the absolute thickness S of 

 the boundary layer for the ABC ship, a .series of 

 values are calculated by the flat, . smooth-plate, 

 turbulent-flow formula S = 0.38(x)(R,y"- of 

 Fig. 5.R and plotted in Fig. 45.1. A note on the 



ABC Tronaan-Stem Peamn Spi ed Astj inea .s_|05 kt.-o- J'S_6i<tp«r mc 



, ,, ] Thickness is Cokukited b» ine FiotPlole _; 



R,-I35III0;; I Formula ,„r Turbulent no« 6- 038WBi" 



jond b^ ERtropololion For beyond lis Normol" 



Limits a;- I 2817(10 ')ri^ per set for SoltWller- 



FiG. 45.1 Variation ok Boundahy-Layeb Thickness 

 wrrH i-DisTANCE FROM Stem kok .\BC Ship 



graph emphasizes that this formula is extrapolated 

 far beyond its usual limits. It should be empha- 

 sized further that, since this is a flat-plate formula, 

 the assumption is made that the wetted area on 

 each side of the ship is the same as that on one 

 side of a thin plank of the same length, namely 

 510 ft. The formula employed takes no account 

 of either longitudinal or transverse curvature in 

 the ship, or of roughness, so that the thickness 

 values for ship ranges indicated on the plot may 

 be altered rather drastically when the ship values 

 are actually known. l']ven then, they could be 

 considered as only average or tj'pical, because the 

 local boundar3--layer thickness, at a given .r-di.s- 

 tance from the stem, varies with the local radius 

 of curvature, both longitudinal and transverse. 



45.14 Estimating the Allowances for Curva- 

 ture. For ('--tinialing tlio ;i|)|)i()ximate ciTcct of 

 coiiicx transver.se curvature of a body or ship 

 form, di.scus.sed in Sec. (>.S of N'olume I, use is 

 made of Land Weber's fornnila |TiMli Hep. tiSK, 

 Mar 1919, p. 7] for the increa.se in friction drag 

 of a .semi-subnicrgcd cylinder n\ rr (lie friction 



