Sec. 'iO.13 



CALCULATION OF WAVEMAKING RESISTANCE 



221 



(g) The definite knowledge that, under certain 

 conditions, which are as yet unfortunately not 

 too well defined, small changes in the longitudinal 

 distribution of displacement, indicated by the 

 customary section-area curve, produce relatively 

 large changes in wavemaking resistance. Similarly, 

 that small variations in surface-waterline shape 

 may produce unexpectedly large changes in this 

 resistance. 



The work done along these lines during the 

 period 1945-1955, at least in the United States, 

 has given a new impetus to the mathematical de- 

 lineation of ship lines, described in Chap. 49. In 

 particular, it has initiated studies of the problems 

 of fairing the Imes of ships, so that this may be 

 done impersonally — automatically, if need be — in 

 a manner which mil benefit the overall hydro- 

 dynamic performance of the ship. 



The discussion of this chapter may well be 

 concluded by some comments of G. P. Weinblum, 

 to be found on pages 2 and 3 of TMB Report 710, 

 pubUshed in September 1950: 



"Experienced experimenters are often somewhat 

 bewildered b.y the fact that the wave resistance may vary 

 appreciably for different but reasonable types of hnes, 

 although all the form parameters generally considered 

 as decisive are identical. From a theoretical viewpoint 

 this appears to be quite natural, since the wave resistance 

 depends to a first approximation upon a complicated 

 function of the surface slope in the longitudinal direction, 

 i.e., on derivatives. On the other hand, the most commonly 

 used (hull) coefficients are integrals, which even when 

 kept constant still admit of very wide variations of the 

 slopes. We realize now why the solution of the basic 

 problem of the model basins mentioned above — to estab- 

 lish the resistance as a function of the form — remains 

 almost hopeless as long as the ship surfaces (or at least 

 their most important features) are not defined in a rigorous 

 way by mathematical expressions. Hence, our first task 

 must be to find equations for the ship surface, continuing 

 the work of D. W. Taylor." 



50.13 Reference Material on Theoretical Re- 

 sistance Calculations. Supplementing the re- 

 marks in Sec. 50.2 concerning early efforts to 

 analyze and to calculate ship resistance, there are 

 given here a few of the references which contain 

 interesting accounts of this work. They do not 

 include the Rankme references mentioned in the 

 text of Sec. 50.2: 



(1) An excellent and most readable summary of the work 

 done prior to 1869 relative to the calculation of 

 ship resistance by formula is to be found in the 

 report of the Committee of the British Association 

 headed by C. W. Merrificld and counting among its 

 members Professor W. J. M. Rankine and Mr. 



William Froude, Brit. Assn. Rep., 1869, pp. 11-21. 



(2) Of the work (and workers) which followed that of 



Rankine, an excellent summary is to be found in a 

 paper by A. W. Johns entitled "Approximate 

 Formulae for Determining the Resistance of Ships" 

 [INA, 1907, pp. 181-197]. In this paper Johns 

 mentions the formulas of: 



(a) Middendorf, published in 1879 and given by 

 Wilda in "Marine Engineering," 1906 



(b) Admiral Fournier of France. His formula is 

 pubUshed in English, with comments, in INA, 1907, 

 page 190. 



(c) D. W. Taylor, quoted and commented upon 

 briefly in SNAME, 1894, Vol. 2, page 14.3. 



(3) Lorenz, H., "Beitrag zur Theorie des Schiffswider- 



standes (Contribution to the Theory of Ship 

 Resistance)," Zeit. des Ver. Deutsch. Ing., 16 Nov 

 1907, No. 46 



(4) Rothe, "Bemerkungen zur Schiffswiderstandstheorie 



von H. Lorenz (Note on the Theory of Ship 

 Resistance of H. Lorenz)," Schiffbau, 8 Jan 1909, 

 Vol. 9, pp. 253-354; 2 Jan 1909, pp. 289-290. 



The technical literature covering the modern 

 (20th century) analytic attempts to calculate the 

 resistance of ships and to predict other aspects of 

 their performance, as set forth in this chapter, is 

 amazingly extensive. There are listed here only 

 a few of the references which contain large 

 bibliographies: 



(5) Weinblum, G. P., TMB Rep. 710, Sep 1950. Pages 



98-102 Ust 116 items, principally by authors. The 

 individual references are extremely sketchy. 



(6) Wilhamson, R. R., "Bibliography on Theoretical 



Calculation of Wave Resistance," ETT, Stevens 

 (unpublished and undated). This contains 62 

 items, listed by authors. 



(7) Lunde, J. K., "On the Linearized Theory of Wave 



Resistance for Displacement Ships in Steady and 

 Accelerated Motion," SNAME, 1951, pp. 25-85. 

 Pages 75-76 list 55 items. 



(8) Guilloton, R., "Potential Theory of Wave Resistance 



of Sfiips, with Tables for its Calculation," SNAME, 

 1951, pp. 86-128. On pages 120-123 there is a 

 section entitled "Bibhography," listing 91 items 

 in seven different categories. In spite of the com- 

 pleteness of this list it does not give the subjects or 

 titles of the papers. 



(9) Korvin-Kroukovsky, B. V., and Jacobs, W. R., 



"Calculation of the Wavemaking Resistance of 

 Ships of Normal Commercial Form by GuUloton's 

 Method and Comparison with Experimental 

 Data," ETT, Stevens, Rep. 541, Aug 1954. Pages 

 51-53 fist 29 items. 



(10) Birkhoff, G., Korvin-&oukovsky, B. V., and Kotik, 



J., "Theory of the Wave Resistance of Ships," 

 SNAME, 1954, pp. 359-396. Pages 384 and 385 

 list 47 items. This list brings the bibliography on 

 the subject practically up to date (1955), except 

 for the items to follow. 



(11) Sezawa, K., "Wave Resistance of a Submerged Body 



in a Shallow Sea," Paper 610, Proceedings, World 



