Sec. 45.1R 



FRICTION RESISTANCE CALCULATIONS 



115 



viscous flow, having in mind that sand-coated 

 surfaces give different variations of Cp with /?„ 

 than surfaces coated with sprayed plastic paints 



(f) General pattern of roughnesses, as viewed 

 normal to the surface, including spacing, density, 

 shadowing or shielding effects, and the like 



(g) Finally, it must be possible to ascertain the 

 roughness index easily and quickly in service and 

 to express it (or its results) in quantitative terms. 



Further development of the shadowgraph pro- 

 cedure described in Sec. 22.14 and illustrated in 

 Fig. 22.1, or of an equivalent procedure, should 

 give the heights of the roughness peaks above the 

 limen or above the adjacent surface, in terms of 

 the lengths of the shadows for a given inclination 

 of the light rays with reference to the surface as 

 a whole. With an inclination of say 15 deg it 

 could be assumed that any region covered by 

 shadow was in a separation zone and therefore 

 subject to — Ap's. It is not known, however, that 

 this is the proper angle or that the angle remains 

 constant. The slopes of the upstream sides of the 

 roughnesses could be determined generally by 

 their relative brightness although it is recognized 

 that the shadowgraph scheme breaks down for 

 an upstream face which lies at a large angle to 

 the limen, say 80 to 90 deg. The orientation of the 

 sloping surfaces with respect to the direction of 

 flow is easily recognized from a photograph taken 

 by this method although it is not so simple to 

 express this orientation in terms of angles or 

 numbers, especially as an average or effective 

 value for a given area. The spacing, density, and 

 general pattern of the roughnesses, as viewed 

 normal to the surface, is perhaps easiest of all to 

 visualize on the shadowgraph, although again 

 not so readily put in terms of numbers or scalar 

 quantities. 



It is not improbable that some sort of screen 

 or set of screens may be devised which, when 

 superposed on a shadowgraph, would give a 

 numerical or other roughness index of any given 

 surface. 



Whatever may be the method (s) ultimately 

 developed for expressing the physical roughness of 

 a surface, the index derived therefrom must be 

 compared with the hydrodynamic parameters of 

 the viscous flow taking place over that particular 

 surface to determine its roughness effect on friction 

 resistance. These may include the downstream 

 distance x from the leading edge of the body or 

 ship, the speed V of the body or ship or the 

 relative velocity U of the water past it, the thick- 



ness &[, of the laminar sublayer in way of the 

 roughnesses, the thickness 5 and characteristics 

 of the boundary layer, and the type of flow exist- 

 ing in the inner regions of that layer. 



45.18 Determination of the Allowances for 

 Roughness. It is necessary to estimate the fric- 

 tion resistance and both the effective and the 

 shaft powers early in the design stage. Often it 

 may not be known definitely of what material 

 the shell will be constructed, how smooth the 

 material will be, how the shell plates or planks 

 will be applied, what sort of workmanship is to 

 be expected, or what the eventual external coating 

 will be. If trial predictions only are involved the 

 hull will at least be clean and new, but not neces- 

 sarily smooth and fair. If an average service per- 

 formance is wanted, fouling allowances must be 

 estimated and added. 



For an intelligent application of the several sets , 

 of roughness allowances which have been de- 

 veloped to predict the service performance of a 

 ship, it is necessary to consider the existence of at 

 least six different regimes in the roughness setup. 

 From the knowledge so far gained (1955) it 

 appears that somewhat different physical laws 

 govern the viscous flow in these regimes and that 

 different sets of practical rules apply. The six 

 regimes may be described as: 



I. Zero ACf. , where, at sufficiently low values of 

 Rn , say up to 4 or 5 million, with a range of Cp 

 above about 3.3(10"''), roughness effects appear 

 to be small or nonexistent, at least for moderate 

 values of speed compared to length. For example, 

 it has long been known that ship models built for 

 routine resistance and self-propulsion tests re- 

 quired no special finish. It appears that small 

 racing sailboats are in the same category, except at 

 extremely low speeds, say less than 1 kt. 



II. Zero ACf , at all values of i2„ , where the model, 

 boat, or ship surfaces are hydrodynamically 

 smooth. Sees. 45.10 and 45.15 explain the circum- 

 stances under which the laminar sublayer thick- 

 nesses exceed the roughness heights by sufficient 

 margins so that this type of smoothness is 

 achieved. 



III. Small ACf , at all values of K„ throughout 

 the boat and ship range. In the lower or boat 

 portion of this range the roughness effects appear 

 to be small, especially at low speeds, despite the 

 existence of normal physical roughnesses. In the 

 upper or ship part of the range the use of self- 

 leveling coatings and the existence of certain 



