CM \1' i l-.K 



iMatlicinaticiil Methods of Calculating the 

 Pressure Resistance of Ships 



50.1 General 200 



50.2 Early Efforts to Aimlyze anil Calculate Ship 



Hosi.stance 207 



50.3 Moiiorn Dcvplopmentsi in the Calculation of 



Pressure Uc-iislancc duo to Wavcmakinp . 210 

 50-1 .\ii.sumption.': anil Liniitattonti Inherent in 



Presont-Day Calculations 212 



50.0 Formulation of the Velocity-Potential E.\- 



pression 214 



50.6 The Calculation of \Yavcni!ikingRcsiiitancc 215 



50.7 Components of the Calculated Wavemaking 



Resistance 21() 



50.8 Comparison of Calculated and E.xperimental 



Resistances 210 



50.9 Other Features Derived from Analytic Ship- 



Wave Relations 217 



50.10 Ship Forms Suitable for Wave-Resistance 



Calculations 219 



50.11 Necessary Improvements in Analytical and 



Mathematical Methods 219 



50.12 Practical Benefits of Calculating Ship Per- 



formance 220 



50.13 Reference Material on Theoretical Resist- 



ance Calculations 221 



50.1 General. 'I'lie iiiriuiiiiig and enterprising 

 marine architect ha.s long felt a need for a story 

 on the theoretical calculation of the wavemaking 

 resistance of a ship. He has known that mathe- 

 maticians, physicists, and even some naval 

 architects have been engaged on this project for 

 nearly a centurj' but that their work was on a 

 plane "sky-high" compared to his own. He has 

 realized, from looking at some of their simpler 

 graphs, that their results compared rather well 

 with experimental data from model ba.sins, well 

 enough to sustain a keen interest among workers 

 of their caliber. The forward-looking ship architect 

 and designer, imfamiliar with higher mathematics, 

 has wanted to know about the.sc things but could 

 not understand the papers that were being 

 written. He has felt, and justifiably so, that if the 

 story relating to the calculation of wave resistance 

 could not be made simple, it should at least be 

 made readable to him. Someone should take the 

 trouble to make it understandable to those who 

 had to spend their dajs fa.shioning and building 

 ships rather than covering sheets of paper with 

 mathematical ctjuations. 



Beginning in abinit 1950, several workers 

 prominent in the mathenuitical field .set out to 

 do just this. .Anumg their efforts may be men- 

 tioned: 



(a) The early paper of T. M. Havelock entitled 

 "Wave Patterns and Wave Hesistunrc!" (IN.\, 

 l'j;il, Vf.l. 7f;, pp. !:«) IIO] which, in the words 



uf ^^'. C. S. A\'iglcy, describes liie theory "without 

 mathematical complications" 



(b) The somewhat mathematical but nevertheless 

 xery readable paper presented by Professor Sir 

 Thomas H. Havelock on two occasions in 1950 

 in the United States, entitled "Wave Resistance 

 Theory and Its Application to Ship Problems" 

 [SXAME, 1951, pp. 13-24] 



(c) The rather brief but more general (and less 

 mathematical) account written bj' G. P. Weinblum 

 and entitled "The Practical Use of Theoretical 

 Studies in Wave Resistance" [MESR, Oct 1951, 

 pp. 49-52] 



(d) Weinblum's paper entitled "Analysis of Wave 

 Resistance," published as TMB Report 710 in 

 September 1950. On page 2 he states that the 

 purpose of the paper: 



". . . is to show to what extent theory has succeeded in 

 furnishing valuable practical re.iults and how the scope 

 of its applications can lie e.\t<'nded . . . 



"There is common agreement that theory \\t\s furnisheti 

 a valuable description of general phenomena; it is less 

 \\M known that it also has given us the proof of consider- 

 able practical value of how sensitive wave resistjinco can 

 be to changes, even small changes, in ship form." 



(c) The most interesting accotmt presentetl by 

 the mathematician-physicist-naval architect team 

 uf (!. MirkholT, M. \. Korvin-Kroukovsky, and 

 .1. Kotik ill (lii'ir "Theory of the Wave Resistance 

 of Ships," e.spcci.Mliy Pari I |S\.\MK, liOl, pp. 

 •S.Jil '.VM\]. 



The presciil cliiiptcr, piep.'ired by one ilelinitely 



JOG 



