268 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. ^3.6 



1949]. Both eciiiatioiis and graphs are reproduced 

 by A. B. Murray [SNAME, 1950, Fig. 10, p. 665]. 

 The distance of the center of pressure CP from 

 the traihng edge of the planing surface, assumed 

 at the after perpendicular AP, is expressed as 



The .r-distance [CP to AP] = K(L„.s)\" (53.v) 



where L^s is the mean wetted length, X is the 

 ratio LjTs/Bc , and K is a function of the angle 

 of trim 6 and of the rise-of-floor angle /3. This 

 relation is 



K = 



0.84 + 0.015/3 



(53 .vi) 



where /3 and 6 are both expressed in degrees. 

 The exponents n and m are derived from 



„ = -(0.05 + O.Olg) (Sa.vii) 



m = 0.125 + 0.0042/3 (53.viii) 



where /3 is again expressed in degrees. 



Graphs giving the relationships between these 

 variables, in convenient form, are drawn in Fig. 

 53. C, adapted from diagrams pre\'iously published 

 in the references quoted. 



The method of using the equations listed and 

 the accompanjdng graphs is described by A. B. 

 Murray [SNAME, 1950, pp. 670-671] and is 

 illustrated for a specific design of full-planing 

 motorboat in Sec. 77.26. 



53.6 Wetted Length, Wetted Surface, and 

 Friction Resistance. Diagrams indicating the 

 general position and shape of the wetted area 

 under a planing craft when running at or near its 

 designed speed are found in Chaps. 13 and 30. The 

 changes in wetted surface and wetted length at 

 speed are discussed briefly in Sec. 30.8. Since these 

 features are important factors in predicting per- 

 formance, the method of estimating or determining 

 them, in a running rather than an at-rest condi- 

 tion, requires further explanation. 



The shape and extent of the wetted area of the 

 bottom or dynamic-support surface of a planing 

 craft is rather easily determined by running a 

 model under a given set of conditions. This method 

 is, however, open to the objection that a model 

 which is towed and not self-propelled may not 

 run at the proper trim for the prototype because 

 the vertical forces exerted by the propeller (s) are 

 missing. A change in trim almost always means 

 a change in both wetted length and wetted area, 

 possibly a change in the center-of -pressure position 

 as well. 



A. B. Murray illustrates the ETT method of 

 determining wetted chine and keel lengths for a 

 towed model [SNAME, 1950, Figs. 14 and 15, 

 pp. 672-673]. Both wetted length and wetted 

 area may be determined by fish-eye views made 

 photographically, using a painted grid on the 

 under surface of the model and a water box, 

 underwater mirror, or other suitable setup [ETT, 

 Stevens, Rep. 378, Sep 1951, pp. 46-47]. The 

 general shape of the wetted area for a V-bottom 

 craft is the same, illustrated by Figs. 13. D, 30. A, 

 30.C, 30.F, and 77. P. Small-size photographs 

 and diagrams, in the form of fish-eye views 

 .published by A. G. Smith, show the general shapes 

 of the wetted area and of the spray roots under 

 V-bottom planing forms with a 25-deg rise of 

 floor and a 6-deg trim by the stern [5th ICSTS, 

 1949, pp. 70-73 and Figs. 1-5]. 



C. W. Spooner, in his unpublished report "Speed 

 and Power of Motorboats up to a Speed-Length 

 Ratio of 3," dated October 1950, gives a table 

 listing the principal characteristics and wetted- 

 surface area of a considerable number of motorboat 

 designs. In his Fig. 13 he includes tentative 

 graphs for estimating the wetted surface of craft 

 of this type, based on a coefficient S/{LB), which 

 increases slowly \vith fatness ratio V/{0.lOLy. 

 For a motorboat mth a single centerline skeg the 

 coefficient is: 



0.950 at a fatness ratio of 4.0 

 0.984 at a fatness ratio of 6.0 

 1.01 at a fatness ratio of 8.0, 



where L and B are presumably in ft, and »Sr is in 

 ft^. For a bare hull the corresponding coefficient 

 values are 0.860, 0.889, and 0.911, respectively. 



J. P. Latimer gives the layouts, lines, principal 

 characteristics, and wetted surface for a USCG 

 40-ft utility boat ["Characteristics of Coast 

 Guard Powered Boats," SNAME, Ches. Sect., 

 13 Oct 1951]. 



Contour charts for determining wetted areas 

 of the EMB Series 50 models, applicable as first 

 approximations of the wetted areas of other 

 V-bottom planing craft having speed-length T", 

 values of from 2.0 to 6.0, are described and pub- 

 lished on pages 6 and 85-94 of TMB Report 

 R-47, revised edition, March 1949. 



Further data may be found in a paper by 

 B. V. Korvin-Kroukovsky, D. Savitsky, and 

 W. F. Lehman, entitled "Wetted Area and Center 

 of Pressure of Planing Surfaces" [ETT, Stevens, 

 Rep. 360, Aug 1949]. 



