Ill 



nvnRODVNA.MK.S IN SHIP DESIGN 



Sec. n.n 



TABLIC lo.e — 1'Xiiivaij;\t Sand Roughnkrs V'ai,i;i-;s 

 Kf OF H. M. Weitbrecht 



The listed vftlues of Kx for "now, painted hull plates, 

 inclusive of butts, seams, and rivot heads . . ." apply to the 

 types of ships indirate<i. 



(a) Sporting and racing craft, torpedo- 



boats and destroyers 0.10 mm 0.004 in 



(b) CrossK-hanncl ships, cruisers, 



battleships 0.15 0.006 



(c) Mail shijxs, fiu<t liners, carefully 



built cargo ships 0.20 O.OOS 



(d) Carpo ships of less careful work- 



manship, tugs 0.2.5 0.010 



theory. In this work Weitbrecht used the values 

 given in Table 45.e. 



In a more recent paper H. Sasajinia and E. 

 Yoshida pointed out rather convincingly that 

 the t.vpc of roughness embodied in the hull 

 coatings of most large ships (not necessarily 

 including fouling roughness), is not the t3'pe 

 which produces a constant Cf value at large 

 values of /?„ [Int. Shipbldg. Prog., 1955, Vol. 2, 

 No. 13, pp. 441-450]. In other words, since the 

 derived friction-resistance values for full-scale 

 tests appear to involve a constant increment of Cf 

 and not a constant total CV , the effective rough- 

 ness is of a t3'pe different from the sand roughness 

 of Nikuradse's pipes. They reason that the in- 

 crease in friction drag is due to a waviness in 

 which there is a degree of pressure and separation 

 drag, ahead of and behind the roughnesses, which 

 adds to the normal viscous drag. This means 

 that the dynamic effects on the ship, varj'ing as 

 V', form only a part of the friction drag of the 

 rough hull surface, and not all of it. 



The feature responsible for this dilTcrcncc in 

 effect is, according to the reasoning of Sasajima 

 and Yoshida, the effective slope of the roughnesses 

 in the direction of the flow. For example, the 

 slope of a wavy surface is less than that of a 

 sand-roughened surface. In fact, according to 

 their findings, the slope or the steepness of the 

 roughness elenioiit.s is more important than their 

 absohitc height. It is interesting in this connection 

 to c|uote their conclusion "g" on page 450 of the 

 reference: "The roughness effect of paint seems 

 to be almost completely determined by an 

 clement of the smallest height but the steepest 

 Blop(!." They derive curves for various roughness 

 effects which appear to conform, rea.sonably well, 

 to the curvf.s derived from fuil-H<'ale tests. 



45.17 Practical Definitions of Surface Rough- 



ness. Sec. 5.21 of Volume I describes some of the 

 known — or suspected — aspects of viscous flow 

 over a rough solid surface and the effect of these 

 features on the friction drag generated at the 

 surface. In particular, it outlines briefly the new 

 approach to the viscou.s-flow problems presented 

 by rough surfaces on the inside of pipes and 

 conduits, devised by H. N. Morris [ASCE, 

 Hydraulics Div., Jan 1954, Vol. 80, Separate 390]. 

 Fig. 45..I is a diagram prepared bj' the present 



Clear Circumferential 

 Space Between 

 Rouqhness 

 Elements, 

 Meosured ot 

 inner Periphery 

 Of y 



Conduit, 15 s 



n is Number of 



Roucjhness "" ^ -^ ^^~^;^- -^^^^ Radius rg is 



Elements in o ^ ^^ "-^ d/e less the 



h IS Rouqhness Heiqhl ' u ■ i.. l. 



l-jpicol Periphery I ' Heiqnt h 



Rouohness Elements Shown Are Entirely Schemotic 



Fig. 45.J Definition Sketch for Roughness Pabam- 

 ETER-s OF H. N. MoRms, Applied to the Inside of 



A TlBE 



author as a definition sketch to illustrate the 

 dimensions used by Morris to represent the 

 roughness characteristics mentioned in his paper. 

 The roughness projections shown in this diagram 

 are purely schematic; Morris gives no dimension 

 for them other than their height /i. 



It is pointed out in Sec. 22.14 that what might 

 Ije termed the roughness index of a surface, more 

 or loss regardless of its shape, must take account 

 of at least seven factors, repeated here for con- 

 venient reference. It is possible, in fact probable, 

 that it must take account of others as yet un- 

 recognized or unknown: 



(a) Height of roughness peaks above the limen 

 or reference surface, in terms of mean heights 

 (averaged by some suitable method), maximum 

 heights, and a statistical or significant hciglit 

 (!)) Slopes of the roughnesses, on botli tlie u])- 

 stream and the downstream sides 



(c) Orientation of the sloping surfaces with 

 respect to the litiuid-flow direction 



(d) Spacing of roughnes.ses in the flow direction, 

 probably with respect to the roughness heights. 

 This corresponds to the distance ,\ in l''ig. 15., I, 

 or to the ratio A li. 



(i) Type of roughness projections as affecting the 



