M. C. Eames 



While much attention has been given in recent years to refinement of the 

 linearized theory of wave resistance as initially formulated by Michell and developed by 

 Havelock and others, and now there is evidence of some success in Russia and Japan 

 of handling the formidable mathematics of non-linearized solutions, the fact remains 

 that comparatively little has been done in the opposite direction. By this is meant the 

 simplification of solution to the point where first approximations to the wave resistance 

 of an actual ship form may be carried out in the preliminary design stages, calculated 

 by naval architects as opposed to mathematicians (or complex computing machines). 



It is, of course, unlikely that an accurate wave resistance calculation for a prac- 

 tical ship form will ever be reduced to the simplicity of, for example, a stability calcula- 

 tion, but the present writer believes that an approximation which is sufficiently close to 

 yield a useful result in a comparative sense, is possible. 



An approach which was developed by the present writer in 1952 will be briefly 

 outlined by way of illustration. It should be clearly pointed out however, that the tech- 

 nique remains largely unproven, since other commitments have so far prevented the 

 writer from concluding the work. 



The ship is treated in a number of horizontal layers, the layer including the 

 waterline being by far the most significant. By direct substitution of ordinates from the 

 lines plan as coefficients in simple polynomials, these layers are then represented mathe- 

 matically with a fair degree of accuracy. A refinement consists of adding to the ordi- 

 nates in the after body so as to take into account the growth of the boundary layer 

 according to the ideas expressed by Havelock in his 1948 paper to the Institution of 

 Naval Architects. 



The linearized Michell solution, in one of the forms developed by Havelock can 

 be written directly in terms of relatively simple integrals involving these layer polynom- 

 ials, as has been shown in a particular case by Weinblum, who has also tabulated values 

 for one of the resulting integrals. 



The other integral has been tabulated by the present writer and the Weinblum 

 table extended to cover the range of practical interest. (The polynomials used by the 

 writer involve higher powers than those considered by Weinblum, thereby increasing 

 the accuracy of representation of the ship form.) 



The procedure is then purely automatic and can be conveniently arranged in a 

 tabular form of calculation well within the capabilities of a calculations-draughtsman. 



Consideration of some work by Emerson applying Havelock's well known source 

 and sink compartmentisation of the ship has shown that very few vertical subdivisions 

 of the ship are necessary to give a satisfactory result, provided the layer containing the 

 waterline is kept narrow. Thus the amount of arithmetic involved in the method pro- 

 posed by the writer need not be excessive, and one obvious advantage of the technique 

 over that of the source and sink calculation is that systematic variations of hull lines can 

 be more readily performed and traced through the calculation so that their significance 

 on the final result is more clearly understood. 



Finally it might be remarked that if, for initial estimates, a two layer horizontal 

 subdivision is adopted, it is possible to modify the method so that the only ordinates 

 required to perform the calculation are those of the waterline, and those of the curve 

 of section areas — the two basic curves from which line plans are usually derived. This 

 immediately suggests a technique for rapidly comparing fundamental differences of hull 

 form from the wave resistance point of view at the very outset of a design, which might 

 be of particular value where other requirements dictated a rather radical departure from 

 "normal" ship forms. 



It is not suggested that calculations of the form outlined above will ever reach a 

 state whereby they would replace the techniques of the model experiment, but it is felt 

 that they could constitute a useful control on such work, and in many cases serve to 

 reduce the number of models required by suggesting the most promising hull forms 

 thereby reducing the range of possibilities. 



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