1. to •obtain well-defined expressions for the ship forms, which admit especially of 

 clearly defined variations in these forms . . . 



2. to enable us to perform resistance, seaworthiness and similar calculations in a 

 simple and systematical manner. 



... in the writer's opinion a reasonable evaluation of the existing theories (of wave resist- 

 ance and sea-going qualities) could be reached by using graphically-defined parent hulls, by 

 approximating these forms mathematically and using the latter for the calculations involved.. 

 . . . This reasoning together with some difficulties ... in representing full sections justifies 

 the use of empirical lines at present . . . The idea of the proposed wave resistance calcu- 

 lations is essentially two-fold: we intend to make a contribution to the analysis of the experi- 

 mentally-obtained resistance curves and to indicate what improvements in the parent forms 

 are suggested by theory. Especially the latter purpose can become rather interesting. On 

 the other hand, since we are dealing with a first order theory, valuable checks of its validity 

 may be obtained from systematic experiments. 



. . . Finally, the series work may make use of other procedures applied in hydrodynam- 

 ics and thus stimulate the whole field of model research. It does not give credit to theoretical 

 naval architecture and to general hydrodynamics that in text books on the latter subject the 

 ship has nearly disappeared." 



In view of such opinions, the basic lines of Series 60 were developed empirically 

 and defined graphically, and Dr. Weinblum showed in his discussion how the waterlines and 

 sections could be closely represented by polynomial expressions. 



Today much effort is being applied to the problem of representing a ship form mathe- 

 matically, either by means of sections and waterlines or as a three-dimensional surface, for 

 use on a digital computer. ^^'^^'^^ Such an approach would enable calculations of wave- 

 making resistance, velocity distribution, and motions in waves to be made very quickly and 

 permit examination of many alternative ideas. In the particular case of calculations of wave- 

 making resistance, these will still suffer in the absolute sense from limitations in the theory, 

 particularly as regards the inclusion of viscosity effects, but they should furnish a guide to 

 the experimenter in the choice of hull changes likely to reduce wavemaking resistance. It 

 must be remembered, however, that in the type of ship with which this research is concerned, 

 the wavemaking resistance is, in general, only a small part of the total. By fining the entrance 

 for example, it may well be that the reduction in wavemaking resistance will be equalled or 

 even exceeded by an increase in viscous form drag and eddymaking occasioned by the corres- 

 pondingly fuller stern. On the other hand, the wavemaking resistance is the part over which 

 we have most control since it depends essentially on the hull shape, and every use should be 

 made of any guidance that mathematical work can provide as to the type and character of 

 changes likely to reduce it. This approach will be most fruitful in high-speed ships, but at 

 present it seems that for low -speed cargo ships we must in the final analysis still have 

 resort to experiments. 



XIII-4 



