Sec. 45.19 



FRICTION-RESISTANCE CALCULATIONS 



119 



the water in which the ship has been floating. 

 Unless an external coating is proof against most 

 types of fouling, an estimate based only on time 

 out of dock is precarious at the best, considering 

 all the variables involved. The basis for fouling 

 effect should be one of history, modified in degree 

 to conform to the anti-fouling properties of the 

 outside coatings on the underwater hull. The 

 history embodies a combination of ship location in 

 the navigable waters of the globe, ship operation, 

 elapsed time, the seasons during which the ship 

 is exposed, and the portion of the fouling cycle 

 in each water area which is involved, if this is 

 known. 



Assuming that the location, the events, and 

 the time history are fully recorded, it is found 

 that the fouling rates, fouling types, and fouling 

 effects are variable because of seasonal, cyclic, 

 or other factors pertaining to marine life. Fur- 

 thermore, in making predictions of future fouling 

 effects it is possible only to estimate a probable 

 history for any given period. With our present 

 (1955) knowledge, an average result is the best 

 that can be expected in the prediction of fouling 

 resistance. 



It has been the custom in the past to reckon 

 the effect of fouling as a percentage increase in 

 the friction resistance Rf , va. the effective power 

 Pe , or in the shaft power F,, . Occasionally it is 

 expressed as a percentage of the total resistance 

 Rt or of the friction power Pf but with the dis- 

 advantage that, of the five quantities mentioned, 

 only the shaft power is known with any degree of 

 accuracy on ships in operation. Actually, be- 

 cause the friction resistance of certain not-too- 

 smooth ships of the past — and some of the 

 present — consisted of some tanvis resistance 

 (varying with the Reynolds number), with a large 

 amount of tanqua resistance (varying as V^), 

 there was some logic in expressing the resistance 

 increase due to fouling as a percentage increase 

 of the total resistance. 



Modern knowledge indicates that the average 

 flat, smooth-plate specific friction resistance Cf 

 decreases as the ship size and speed increase. By 

 all indications, the ApCp values for fouling as 

 well as for other types of roughness decrease 

 somewhat with the size (length) but they increase 

 rapidly with the designed speed of the ship, as 

 described in Sec. 45.10. For a tug or ti'awler Cp 

 is say 2.3(10~^) at an i2„ of 50 million whereas for 

 a fast liner it is only 1.3(10"') at R„ = 4,000 

 million. At the same time a "tapering" ACp new- 



ship allowance for plating, structural, and coating 

 roughness, described in Sec. 45.18 preceding, is 

 of the order of only 0.25(10"') for the tug whereas 

 it is about 0.39(10"') for the liner. 



The roughness drag of fouling is predominantly 

 a tanqua resistance proportional to V^ and is 

 largely independent of /?„ , except possibly at 

 low R„ values. It is not a function of the tanvis 

 resistance and should therefore not appear as a 

 percentage of the latter. 



The use of a formula with additive specific 

 resistance terms, as in Eq. (45. ii) of Sec. 45.7, 

 requires that the roughness effects of the fouling 

 be considered as a primary function of the size, 

 shape, and distribution of the fouling roughnesses 

 on the hull surface. They may be a secondary 

 function of Reynolds number, at low R„ values, 

 only because of a laminar sublayer which either 

 persists over fouling .that is not excessively rough 

 or which is increased in effective thickness by 

 some physical action as yet unknown. 



To reduce the observed fouling effects to terms 

 of an additive ApCp factor by the older methods 

 is difficult. For most of the cases on record, the 

 propeller thrusts were not measured and the 

 actual ship friction resistances were not known. 

 Furthermore, there is no way to determine how 

 much of these resistances was due to plating, 

 structural, and coating roughnesses, exclusive of 

 fouling. The operation is greatly facilitated by 

 the use of the specific resistances Ct = Cr -{■ 

 Cp -\- SACp , if it is assumed that the specific 

 residuary resistance Cr remains constant regard- 

 less of the extent of fouling. The flat, smooth- 

 plate specific friction resistance Cp remains 

 constant by derivation. Therefore any increase 

 in Ct over the clean-bottom value is a change due 

 to fouling and may be represented by ApCp as a 

 first approximation. This procedure takes no 

 account, for example, of a ApCp or a AcCp that 

 may be diminished because heavy fouling covers 

 up original plating or coating roughnesses. 



It may be presumed that, for a large and a 

 small ship having exactly the same underwater 

 coating, the same exposure position with refer- 

 ence to the adjacent water bodies and currents, 

 and the same fouling history, the fouling will be 

 exactly the same on the underwater surface of 

 each. In other words, the marine growths will be 

 of the same absolute shape and size and will be 

 distributed in the same manner over each unit 

 of area. If each craft has about the same hull 

 shape and a reasonably large draft, there will be 



