266 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 53.5 



plate were completely submerged, and then 

 halving this value. 



Without going further into the analytic hydro- 

 dynamics of planing, set forth in detail in many 

 of the references listed in Sec. 53.8, it is stated 

 simply that the dynamic lift exerted normal to a 

 flat inclined plate of length L and breadth B, 

 in contact with a hquid surface on its under side 

 only, is expressed by 



Li, normal to plate = ^ pB'V^a (53. i) 



o 



where a is the angle of attack or trim by the stern 

 and Lz) is not, as customary, measured normal to 

 the direction of motion. 



The dynamic lift to be expected from a simple 

 planing surface, defined as one with straight 

 buttocks and keel and a constant rise-of-floor 

 angle j8, running at a trim angle d, may be derived 

 more precisely in terms of equations set up by 

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

 W. F. Lehman [ETT Rep. 360, Aug 1949]. These 

 equations, with their representation in graph 

 form, are used by A. B. Murray in his paper "The 

 Hydrodynamics of Planing Hulls" [SNAME, 

 1950, Fig. 11, p. 666]. 



The dynamic lift is expressed in terms of 

 0-diml dynamic-lift coefficients Cdl , using 

 (CdlJo for a planing surface with zero rise of 

 floor and {Cul)^ for one with a rise-of-floor angle /3. 

 The equations for these coefficients are, strictly 

 speaking, dimensionless in that all the factors 

 composing them have dimensions of zero. Never- 

 theless, the fact that the trim angle 6, expressed 

 as T(tau) in the references, appears to the 1.1 

 power and the term {Cdl)o to the 0.6 power 

 seems to indicate that other terms as yet unknown 

 should eventually be embodied in the equations. 



Expressed in standard and ATTC notation 

 these equations are: 



(1) 



W (or A) Cj^ 



'•^DL — — Z „2 



(53. ii) 



where Be is the mean chine beam, Cld is the load 

 coefficient, and Cy is the speed coefficient, pre- 

 viously defined 



(2) For a flat, inclined plate, having a rise-of- 

 floor angle /3 of zero and a trim of d deg, 



(C^l)o = e'M0.0120\"' + 



0.0095X' 



ci 



(53.iii) 



of floor and X (lambda) is the ratio of the mean 

 wetted length L^,^ to the mean chine beam Be 

 (3) For a V-surface having a constant rise-of- 

 floor angle of /3 deg, 



{C^l), = (C^l)o - 0.0065^[(C«^)„]" 



(53. iv) 



where {Cdl)o is the lift coefficient for a zero rise 



Graphs giving the relationships between these 

 variables, convenient for the use of a planing-craf t 

 designer, are drawn in Fig. 53.B, adapted from 

 diagrams previously pubUshed in the references 

 listed earlier in this section. 



The method of using the equations listed and 

 the accompanying graphs is described by A. B. 

 Murray [SNAME, 1950, pp. 669-670] and is 

 illustrated for a specific design of planing-type 

 motorboat in Sec. 77.26. 



53.5 Typical Pressure Distribution and Mag- 

 nitude on Planing-Craft Bottoms. Diagrams 

 showing typical transverse and longitudinal pres- 

 sure distributions on the wetted bottoms of 

 planing forms, similar to those reproduced in 

 Figs. 13.B and 13.D on pages 205 and 207 of 

 Volume I, are rather plentiful in the technical 

 Hterature. They are to be found in many of the 

 references of Chaps. 13 and 30 and of Sec. 53.8 

 of the present chapter. For example, the graphs 

 of longitudinal -|-Ap distribution pubhshed by 



A. B. Murray [SNAME, 1950, Fig. 19 on p. 675] 

 are taken from data developed by W. Sottorf, in 

 a paper Usted as reference (21) of Sec. 53.8. 



Assuming a V-bottom craft, the transverse 

 pressure distribution is characterized by peak 

 pressures over the regions of origin of the port 

 and starboard spray roots, along the diagonal 

 stagnation loci depicted in Fig. 13.D. At small 

 immersions of the keel, all the pressure is con- 

 centrated near the centerplane. At greater 

 immersions the two pressure concentrations move 

 outward toward the chines. 



Reliable specific data on the distribution of 

 pressure and the magnitude of the pressure 

 intensities on the bottoms of planing craft having 

 given characteristics, especially when subjected 

 to heavy impact in waves, are relatively meager. 

 Much of the available information is in a classified 

 status, so that the naval architect is forced to fall 

 back upon the results of theoretical analysis or 

 upon pubhshed data concerning measurements on 

 the hulls of seaplanes and flying boats. 



For the determination of CP positions in 

 specific cases the equations and graphs set up by 



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

 W. F. Lehman are useful [ETT Rep. 360, Aug 



