Sec. 50.11 



CALCULATION OF WAVEMAKING RESISTANCE 



219 



(13) Effect of vertical distribution of displace- 

 ment. 



Weinblum, G. P., TMB Rep. 710, Sep 19.50, pp. 50-56. 

 Covers influence of the midship-section coefficient, 

 shape of sections, shape of waterlines, section-area 

 curve, bulb bows, and cruiser sterns. 



50.10 Ship Forms Suitable for Wave-Resist- 

 ance Calculations. The simplified ship of J. H. 

 Michell's 1898 paper was little more than a 

 friction form with somewhat convex sides. Many 

 of the forms subsequently used resembled deep 

 canoes more than real ships. This was largely 

 because the slopes of the fore-and-aft lines of 

 these "ships" were small, and because the source- 

 sink distribution, when employed, was for many 

 years limited to positions on the centerplane. 

 Possibly the greater part of the forms were 

 selected because their boundaries could be defined 

 by mathematical formulas based upon the ship 

 axes. If the expressions were not to become too 

 involved, appreciable limitations were imposed on 

 the shapes represented by them. Body plans and 

 other lines drawings of these forms are illustrated 

 by: 



(1) Wigley, W. C. S., and Lunde, J. K., INA, 1948, Vol. 90, 



Fig. 1, p. 97; also Havelock, T. H., SNAME, 1951, 

 Fig. 6, p. 18, and BirkhofT, G., SNAME, 1954, Fig. 5, 

 p. 366 



(2) Guilloton, R., INA, 1948, Vol. 90, Fig. 2, p. 52 and 



Fig. 3, p. 54. 



While they are not to be classed as ships, the 

 thin friction forms and thick planes used in 

 friction-resistance tests in model basins lend 

 themselves admirably to the calculation of their 

 wavemaking resistance. No matter how thin they 

 may be constructed they are rarely free of wave- 

 making at the higher speeds. 



Of late years, the calculation technique has 

 progressed to the point where combined radial 

 and uniform flow can be utilized to produce hull 

 shapes not unlike those of actual ships. Fig. 3.Q 

 of Sec. 3.13 of Volume I illustrates such a form 

 designed by J. K. Lunde and made the subject of 

 rather extensive studies [INA, 1949, Vol. 91, 

 Figs. 1 and 2, pp. 186-187]. 



To produce a 3-diml ship of this type, simple 

 enough from the naval architect's viewpoint but 

 extremely complex when translated into radial- 

 flow and uniform-flow stream functions, may 

 require as many as 30 pairs of sources and 20 

 pairs of sinks. The sources of each pair are dis- 

 posed symmetrically about but offset from the 



centerplane, as are the sinks, with offset distances 

 which vary from pair to pair. 



While the labor involved in the numerical 

 calculations increases with the number of radial- 

 flow points or singularities, it is diminished 

 appreciably by the use of certain tables now in 

 existence. It can possibly be reduced further in 

 the future by the generous use of computing 

 machines. 



A remark made by W. J. M. Rankine on page 83 

 of his 1866 book entitled "Shipbuilding: Theo- 

 retical and Practical" applies to many phases of 

 predicting ship performance other than the one 

 discussed in this chapter: 



". . . as for misshapen and ill-proportioned vessels, there 

 does not exist any theory capable of giving their resistance 

 by previous computation." 



50.11 Necessary Improvements in Analytical 

 and Mathematical Methods. All workers in the 

 field of theoretical and analytical wave-resistance 

 calculations now (1956) agree that there are 

 appreciable discrepancies between the derived 

 and observed resistance data for most of the 

 forms concerned. While these are hardly first-order 

 differences, and while the wavemaking resistances 

 of models can not be measured independently, 

 the variations are large enough to indicate that 

 all the hydrodynamic actions have probably not 

 been taken into account. One of these is the slope 

 drag (or thrust), due to the position of the vessel 

 on the back (or front) of a wave of its own Velox 

 system. This may be the reason for the increased 

 resistance of the destroyer model of Fig. 50. D at 

 Froude numbers above about 0.48, T, = 1.61. 



Moreover, it is recognized at the outset that 

 the major viscous effects are neglected, as are all 

 the interactions listed as (d), (e), and (f) in Sec. 

 12.1. It is entirely possible that the hydrodynamic 

 actions mentioned previously are not recognized 

 in routine analytic and experimental studies of 

 resistance and propulsion, let alone in calculations 

 of wavemaking resistance. 



Because of the severe limitations imposed by 

 many analytical methods, such as the necessity 

 for retaining the same type of transverse section 

 from stem to stern of the ship being worked upon, 

 the use of I'adically different procedures is being 

 studied. One of these is the slender-body theory, 

 widely employed by aerodynamicists but hitherto 

 not applied to surface-ship forms. Without going 

 into details, this method is based upon the assump- 

 tions that: 



