IL'O 



HYDRODYNAMICS IN Sllll' l)i;si(;N 



Sec. 45.20 



no prc-poiuli'raiu'c of foiiliiin cfTocIs along tlic 

 waterlino. 



This boinp the case, the laminar sublayers over 

 the two hulls, at the same absolute speed for each 

 hull, will have only a slightly greater thickness 

 5t on the large ship than on the small one, 

 indicated in Fig. 45.F of Sec. 45.10. For the higher 

 speed at which it is presumed the larger ship 

 will run, its laminar sublayer will be thinner than 

 on the smaller ship. This means, for example, 

 that a group of barnacles of a given size and 

 ilistrilnition will have a greater roughness effect 

 on the large, fast ship than an identical group of 

 identical barnacles on the small, slow ship. If 

 this physical reasoning is correct, the effect of a 

 given amount of fouling in unit surface area of the 

 hull decreases slowly with the increase in ship 

 length but it increases rapidly with the increase 

 in magnitude of the speed term U in the Reynolds 

 number UL/v. 



It can not be said, therefore, that a fouling 

 rate and a fouling effect determined for a sm-'ll 

 craft will be valid for a large one, and ^'ice versa, 

 any more than the effect of a given roughness is 

 independent of ship size and speed. 



Even though all other conditions remain the 

 same, there is almost certainly some non-linearity 

 of the roughness effects ■nith time out of dock. An 

 older curve of several decades ago, given in 

 reference (15) of Sec. 45.21, indicates a moderate 

 ri.se immediately after undocking, a rate less than 

 the average for the intermediate period, say 

 from 2 to 4 months, and a rapidly increasing rise 

 at the end of the interval, from about 5 months to 

 months. On the other hand, results of experi- 

 ments by \V. IMcEntoe, reported in reference (3) 

 of Sec. 45.21, gave rates that were almost exactly 

 the opposite [Taylor, D. W., S and P, 1943, Fig. 

 43, p. 38]. Later and possibly more accurate data 

 indicate that the increa.sc in A^Cr for the first 

 few days and weeks out of dock may be slightly 

 le.s.s than the average while the increase under 

 conditions favorable for marine growth, during a 

 later portion of the docking period, may be greater 

 than the average. If the .ship is left moored or at 

 anchor to accumulate ^ marine growths having 

 thickncs-ses of inches or even feet, AyCr probably 

 reaches a maximum value by the time the hull 

 surface is completehj covered with a growth 0.1 

 or 0.2 ft thick. It may not become larger no 

 matter how dcnst; or thick the growth. However, 

 the weight displacement and the volume dis- 



placement both increa.sc perceptibly as the growth 

 thickens. Should the ship have to be propelled or 

 towed while fouled it is effectively larger than 

 when clean and requires additional power in 

 proportion, over and above that due to the fouling 

 roughness. Ships have been known to pick up 

 from 100 to 300 or more tons of marine growth 

 when heavilj' fouled. The effective, equivalent 

 increa.se in volume of water displaced is probably 

 still larger. 



All additive allowances for fouling effect should 

 constitute increases in the "clean, new" friction 

 drag Rr of a ship. This is not ahvays the case 

 when ship data arc reported. In fact, some reports 

 are so ambiguous as not to specify the quantity 

 which increases with the fouling. Stictly speaking, 

 the magnitude of the friction drag is not known 

 for any ship but it can be calculated by the 

 methods described elsewhere in this chapter. It 

 can be estimated as a percentage of the total 

 towrope resistance for the type of ship in question. 

 If corresponding changes in the power and speed 

 are wanted, they may be predicted by the methods 

 described in Chap. 60 for the estimate of power 

 and speed on a new design. 



In this connection it must be remembered that 

 an increase in roughness due to fouling increases 

 the thickness of the boundary layer at the pro- 

 pulsion-de\ace positions. This in turn almost 

 invariably increases the average-wake fraction 

 over the thrust-producing area Aa of the pro- 

 pulsion device. Furthermore, the additional 

 resistance means augmented thrust, higher thrust 

 loading, and undoubtedly a lowered efficiency of 

 propulsion. Estimates of increased shaft power 

 due to fouling are not ahvays accurately predicted, 

 therefore, on a basis of model tests run with an 

 overload allowance only for a clean, new hull 

 surface. 



45.20 The Prediction of Fouling Effects on 

 Ship Resistance. Simimarizing the elTects of 

 fouling on shi]) resistance, dist'u.ssed in Sec. 45.19, 

 the principal factors appear to be: 



(1) The type and nature of the fouling which 

 adheres to the .ship hull 



(2) The history of the operation of the ship 

 during any one interval between dockings, taking 

 account of the length of time out of dock, and 

 including the kind and temperature of the water 



(3) The fouling rates, cycles, and other features 

 a.ssociated with the historyfof ojMTation. These 

 rates vary widely in the different parts of tho 



