128 



HYDRODYNAMICS IN SlIII' Dl SICX 



Srr. ^.21 



found on hulls of this kind, so that there is no 

 comjiensation for the convcx-furvature effects. 

 I^ndweber's transverse curvature correction, de- 

 scribed in Soc. 45.14, becomes rather absurdly 

 large for sharp chines, or even for these chines if 

 they are assumed to be rounded to a small 

 radius. In these cases the increase in 7?^ is known 

 to be positive, but it is difficult to estimate. 



On discontinuous-section forms, coves are 

 generally associated with chines in pairs, so that 

 the increased friction drag caused by the convex 

 chine is partly or wholly offset bj' the decreased 

 friction in the concave area. For discontinuous 

 sections of not abnormal shape, such as those 

 illustrated in Figs. 76. E and 76. F, it is acceptable 

 to compute the entire wetted surface and to 

 consider that it bfloiiR.s to a hull of normal form. 



45.24 The Friction Resistance of a Planing 

 Hull. A planing hull that benefits bj' dynamic 

 lift rises out of the water as the F„ incrca.ses and 

 loses wetted surface by this process. If friction 

 drag is to be taken into account it is then neces- 

 sary, either on a model or on the craft itself, to 

 determine the length, shape, and position of the 

 wetted portion of the bottom and to compute the 

 actual wetted area. Only those regions over (or 

 under) which the water moves at the same order 

 of relative speed as the planing craft are included 

 as effective wetted areas. Those wetted by thin 

 spray sheets moving forward or predominantly 

 sideward are excluded. Furthermore, unless the 

 model runs at the same trim as the full-scale 

 craft, either by the action of forces from its own 

 propulsion devices or equivalent forces applied 

 during the test run, the wetted surfaces are not 

 comparable. 



It is often feasible to locate, by photographs 

 or visual observation, on either the model or the 

 full-scale craft, the forward end of the wetted 

 surface along the keel. It is usually easy to "spot" 

 the corresponding points along the chines. Having 

 these three points fixed reasonably well, the wetted 

 surface is readily outlined and its area determined. 



A length is necessary to fix the approximate 

 values of F. and /?, in the planing condition. This 

 ifl usually taken as the mean wetted length Lws , 

 the arithmetic mean of the wetted keel and the 

 wetted chine lengths. 



These matters, including a method of predicting 

 the wettctl length and wett«!d area, an; discus-sed 

 in detail in Sees. 53.6 and 77.27, to which the 

 reader is referred for specific information on this 

 type of water craft. 



45.25 Friction Drag of a Craft Moored in a 

 Stream. .\ friction-drag problem ari.ses in con- 

 nection with the mooring of i)()ntoon-bridge 

 floats, barges, lighters, and lightships where swift 

 currents prevail and adefpiate ground tackle must 

 be provided. In flood conditions this situation is 

 intensified. In these cases the Froude number F^ 

 or Taylor quotient T, is usually small and most 

 of the drag is due to friction. The friction drag due 

 to current may be a maximum when the wind 

 drag is zero. 



The fact that a vessel is andiorcMl or held 

 stationary in a moving stream, rather than ])vill('(| 

 or pushed at the same relative speed through 

 stationary water, has no appreciable effect upon 

 its friction resistance. It does not alter the method 

 of calculating the friction drag, provided the 

 flowing water contains no great amount of large- 

 scale turbulence. It is to be remembered, however, 

 that a stationary surface vessel near the center 

 of a fast-moving stream, of not-too-large cro.ss 

 section compared to that of the vessel, has a 

 relative velocity in the center which is greater 

 than the average velocity of the stream. This is 

 because the velocities in the boundary layer 

 along the banks and over the stream bed are le.s,s 

 than the average velocity. The same phenomenon 

 occurs in a pipe where there is a boundary layer 

 all around the inside wall surfaces and the center- 

 line velocity exceeds the average velocity [Rouse, 

 H., EMF, 1946, p. 197]. If the bed clearance under 

 the vessel is small, as for a deep vessel moored in 

 a shallow river, the relative water velocity under 

 the bottom is probablj- greater than the average 

 current velocity. 



Subject to the foregoing, and assuiuing that 

 the ship axis lies in the direction of stream flow, 

 the computation procedures of Sec. 45.22 suffice 

 for calculating the friction drag. 



If the craft is moored at both enils and does 

 not lie in the direction of the stream, friction 

 resistance plays only a small part and the forces 

 on the moorings must be determined by other 

 methods [TMB unclassified Rep. R-332, "Wind 

 Tunnel Tests to Determine Air Load on Multiple- 

 Ship Moorings for Destroyers of the DD 692 

 Class," by M. K. Long, Doc 191.-)]. 



45.26 Selected Bibliography on Friction Re- 

 sistance. For convenient reference there are 

 listed in this section a incxlerate lunuber of the 

 multitude of titles in any nuKlern bibliography on 

 friction resistance. Textbooks are listed in the In- 

 troduction of Volume I and arc not imludcd here. 



