220 



iivnuonN \ \Mi( s i\ siiii' nrsK;\ 



SVr. 10.12 



(a) All trniisvcrso tliiiiciisiinis aio assiiin<'<l to !)(> 

 small in comparist)n with tlie length 



(b) The elevations of the Velox wave system, 

 caused by the passjige of the slender body through 

 the water, are as*!umed to be eonccntrated along 

 the j-axis, as if the wa\e system were shifted 

 inward due to a transverse collapse of the body 

 to zero beam. 



Xntwithstaniling the modifications to simplify 

 the problem, the mathematical equations are still 

 formidable, the procedure has not yet (lOoti) been 

 refined, nor have the results received more than 

 preliminary experimental verification. However, 

 the method ha-s the great advantage of lending 

 itself to performance predictions on ship forms 

 with any type or shape of transverse section, and 

 with radical changes in transverse section along 

 tlie length, such as that which occurs at a transom 

 stern. Furthermore, preliminary indications are 

 tliat a great many actual ship forms fail within 

 the "slender-body" category. 



50.12 Practical Benefits of Calculating Ship 

 Performance, ^'iewed from that point in the 

 progress cunx' which has been reached to date 

 (195G), the most valuable promise which the 

 analytical and mathematical method now offers 

 to the practical designer is its indication of the 

 relative influence of various shape parameters on 

 the behavior of ship hulls. Wlien the progress is 

 such that adequate mathematical expressions can 

 be .set up for ship and liquid motions, the influence 

 of the.se shape parameters and of particular 

 a.ssumptions and conditions will be made readily 

 apparent and be expressed cjuickly in numerical 

 or engineering terms. This is exactly the function 

 of the tide-predicting machine which, when it is 

 supplied with the basic information and its 

 wheels arc set going, rolls out the data for tide 

 tables with effortless ease. 



If the miKlel-tcsting tcchnifiue is advantageous 

 becau.sc of its relatively low cost, (luick answers, 

 and ability to lake all physical actions into 

 account, the machinc-cahulating method promises 

 a saving in time and labor and a greater degree of 

 freedom in .setting up the basic conditions. The 

 factors in a mathematical expression can be given 

 any reasonable values, they can be given greater 

 or less weight, as appears to be called for, or they 

 can be omitted entirely. 



As to the indication of the influence of various 

 shape parameters of a ship hull, the analytic 

 ulljick hiia alremJy to it.s cre<lit a considerable 

 number of importiinl and u.'seful conclusions and 



contributions. Whether these c(juld have been 

 achieved by other methods or whether they had 

 already been discovered by observation, deduc- 

 tion, intuition, or experimentation is somewhat 

 beside the point. The fact is that they came out of 

 the analytic "machine" with negligible assistance 

 from other sources. 



Among the conclusions aiul contributions may 

 be liste<l: 



(a) The combination tlivergcnt- and transverse- 

 wave pattern due to a moving pressure disturb- 

 ance, as developed by Lord Kelvin and as worked 

 on by E. Hogner, T. H. Havclock, and others 



(b) Extensive knowledge of the phj'sical reasons 

 for the oscillatory \'ariations in the pressure 

 resistance due to wavemaking, resulting in the 

 well-known humijs and hollows of residuary- 

 resistance and wavemaking-resistancc curves 



(c) The reduction in pressure resistance due to 

 wavemaking as the displacement volume is taken 

 away from the vicinity of the surface waterline 

 and moved farther down 



(d) A greater appreciation of the necessity for 

 fairness in all ship lines, principallj' those parallel- 

 ing the water flow 



(e) The phy.sical and theoretical explanation for 

 the beneficial action of the bulb bow in the reduc- 

 tion of pressure resistance due to wavemaking 



(f) Knowledge as to separate contributions to 

 the wavemaking resistance made by the diverging 

 and the transverse waves of the Velox system. 

 Fig. .50.F, adapted from J. K. Lunde (SNAME, 

 1951, Fig. 7, p. 72], indicates this feature most 

 vividly for a rather wide range of Froude numbers. 



020 (lis — ?53o — 535 — SSS — 545 — 535 — SU 065 



Froudt Number 



/VsT 



Fio. 50.F Gkaimis Indicating Sei-ar.\te Contri- 



iii'TiriNM Mai>k iiy tick Divkroino and tiik Transverse 



Wavks to thk ToTAr, Wavbuakino Resistanci3 



