Bessho 



15. McLachlan, N.W., "Theory and Application of Mathieu Functions," Oxford, 

 1951 



16. Thwaites, B., "Incompressible Aerodynamics," Oxford, 1960 



17. Reinecke, H., "Die praktische Bedeutung einiger grundlegender theoretischer 

 Erkenntnisse fur die Wahl der Hauptabmessungen und fur die Projektierung 

 von Gleitbooten," Schiffstechnik, Vol. 65, No. 13 (1966) 



18. Maruo, H., "Calculation of the Wave Resistance of Ships, the Draught of 

 Which is as Small as the Beam," J. Zosen Kyokai, Vol. 112 (1962) 



19. Bessho, M., "Wave-Free Distributions and their Applications," Interna- 

 tional Seminar on Theoretical Wave Resistance, Vol. 2, Univ. of Michigan, 

 1963 



DISCUSSION 



G. P. Weinblum 



Institut fur Schiffbau der Universitdt Hamburg 



Hamburg, Germany 



Science is subject to fashion as much as other human activities. Recently 

 the thin ship and surrogates have completely dominated the field, but in the 

 twenties (and earlier) the pressure system has been considered as being an 

 equally important hydrodynamic model (at least in principle) as the Michell 

 ship, especially suitable for picturing fast shallow -draft and planing vessels. 

 By Dr. Bessho's paper a sound equilibrium has been established. The present 

 speaker had emphasized the similarity of the Hogner and the Michell integral 

 (Zamm, 1930) and thus inspired Sir Thomas Havelock to derive the simple rela- 

 tion between source-sink distributions a and pressure systems p 



^mpga = c 



3x 



With the usual notations (c = speed of advance) (Havelock, collected papers, p. 

 373). The line distribution established by Dr. Bessho for a rectangular pres- 

 sure domain follows from this equation. 



Somewhat later (1935) von Karman has shown that the induced resistance of 

 a finite-span wing can be derived from Hogner's integral for vanishing gL/c ^ or 

 vanishing g in Bessho's formulation, thus anticipating Maruo's result in his 

 splendid papers on planing surfaces. His analysis of pressure systems and cor- 

 responding form of planing hulls should be developed. A useful scheme had been 

 developed by H. Wagner, who connected planing surface and wing phenomena. 



790 



