126 



IIVDRODYNAMICS IN SHIF' PFSIGN 



Src.4^.22 



(29) W'win. v.. v., "How to Dotcrmiiio KfToolji of Ship 



Bottom Fouling." TIip I/Jg, May HMK, pp. 50, 52 



(30) Bamnby, K. C, "Kronomic Con«cqueniH«« of Foul- 



ing," IN A. 1950, p. J 15 



(31) Toild, F. II,, "Skin Friction ncnintanoo and tho 



KfliTtn of .»<urf.i.c HouKhnoss," T.MB Hop. 729, 

 Sop 1950. Till- gniph nt the end of thin re|)ort 

 iihows that X-i'y for various c-oatings is approxi- 

 mately roniitaiit over the range of W, roveretl by 

 the normal ship s|)ee<l range, .\llhough not brought 

 out by this report, the ^yCf for moilerate fouling 

 is found to vary in nuieh the same way. 



(32) Courh, It. H., "Preliminary Report of Friction Piano 



Hcsistnnco Test.s of Anti-Fouliiig Ship Bottom 

 Paintfl," T.MB Hep. 789, Aug 1951. Figs. 2 and 3 

 of this reiHJrt indieate that at some low value of 

 the HcynoKIs number, probably in the vicinity of 

 3.5 million, the .irO- values for G types of bottom 

 coatings for ."hip hulls, varying from yellow zinc 

 chromatc to Norfolk hot plastic, would probably 

 Ix- in the vicinity of zero. .\t /f, values of from 25 

 to 30 million the SfCp values for each of the G 

 coatings become practically constant and remain 

 so up to a Reynolds number of about 40 to 45 

 million. 

 (.33) Kielhorn, W. V., "Military Biological Oceanogra- 

 phy," rSNI, S<-p 1951, pp. 947-953, esp. pp. 

 947-94S and 951 



(34) "Marine Fouling and Its Prevention," Report 580 



of the WoimIs Hole Oceanographic Institution, 

 published by I'SN'l, Annapolis, 19.52 



(35) AmLsberg, II., abstract of a report by Prof. Aertssen 



on the ext<'nsive full-scale test.s conducted in 1951 

 and 19.52 on tho Tervaele, formerly the Pomona 

 Victory, including the results of fouling on several 

 voyages, Ilan.sa, 9 May 1953, p. 793. 



45.22 The Calculation of the Friction Drag of 

 a Ship. The friction ro.si.stancc of ii .ship under 

 analysis or design is calculated by the general 

 Eq. (45.ii) of Sec. A'^.l, Ry = <3r.S(C, -|- ^JAfV). 

 Here CV is the flat, smooth-piatc .specific friction 

 resistance at a given li, , 2ACV is (A, -|- Aj -}- 

 Ap + A., -f- Af + Af)Cr , and A, and Aj are 

 the allowances for transverse and loiiKitndinal 

 curvature, respectively. 



Beginning with the ram pres.sure q, ecjual to 

 0.5pV\ Tables 4l.d and 41.e give values of q 

 in lb per ft" for standard fresh and .salt water, 

 respectively, at .">!) dcg 1'', I.") dcg (", over a very 

 large range of ship speeds. 



Tlur wetted surface .S isdctcrinincd as described 

 in Kec. 4.'>. 12 preceding. If eaih api)endage whiih 

 hud an appreciable wetted area moved through 

 the wuti-r i»y it.self, it would theoretically create 

 it* own boundary layer, independent of the others 

 ttrxl of till! hull proper. It would then have its 

 own Heynolils number, ba.scd upon il.s length in 

 the dirci'tion of inotieui. It wouli! al.su have its 



own (',• value, depending upon its R, . The ship 

 friction drag would then be a summation of a 

 bare-hull drag plus a separate friction drag for 

 each appendage. These (V values would be high 

 becau.se of the short lengths and the small HJh. 

 Occasionally there may be a special appendage, 

 exposed to undisturbed flow, which extends for a 

 considerable distance from the hull, somewhat 

 like a deep drag pipe on a .self-propelled dredge. 

 Such a one may reijuire this treatment. In the 

 main, however, ship appendages lie partlj' within 

 the hull boundary layer, they do not generate 

 their own layers exclusively, and the average 

 velocities over them are lower than the ship speed. 



It is found acceptable, anti it is customary, to 

 use the ship value of R„ for all appendages having 

 appreciable lengths and wetted areas, hence the 

 ii.sual summation of all wetted surfaces into a 

 single value of »S'. The appendages which are 

 short enough to give z-Rcyiiolds numbers less 

 than about 15 million, especially those which are 

 thick in proportion to their length in the direction 

 of flow, are considered to have no separate 

 friction drag. Their pressure drags are predicted 

 as described in Chap. 5.5. 



For the actual friction-drag calculations for a 

 ship, a .series of values of .shii) speed l' is .selected, 

 extending from the lowest speeii of interest to 

 beyond the maximum-.speed point. This enables 

 the plotting of curves of Ry and Py on V. Using 

 the selected speeds and the waterline length of 

 the ship, values of R„ are taken from Tables 45. a 

 or 45. b for either standard fresh or sixlt water, 

 respectively. If the water is not standard, the 

 /i'„'s are calculated. 



The values of the flat, smooth-plate, turliulcnt- 

 flow coefficient Cy for the A'FfC 1947 ^Schoen- 

 herr) meanline are picked for the given values 

 of /?„ from Table 45. d. In Tables 45. c and 45. d 

 the numerical values of Cy are listed in terms of 

 thousands, called for convenience llious. The 

 values of Reynolds number are given in millions. 

 The tabulated values of Cy are therefore to be 

 multii)lied by 10"' and tho.se of /e, by lO". 



For other friction formulations listed in Sec. 

 l.')..S the Cy values are calculated for the desired 

 R„ values or are picked from other tables. 



Incrca-scs to be made to take care of curvature, 

 either lotigitudiiuil or traiisvcr.se or both, are 

 applied at this stage. 



'J'he total rotighnc.ss allowance -Af ',• is .selected 

 on the ba.sis of the general rules laid down in 

 .Sees. 45. IS and I.".. JO. 



