216 



n\i)Rc)i)\N.\Mit;.s IN smv design 



.SVf. 50.7 



INA, 1952, \'ol. ".II, i>. 3i;?fr; RirkhofT, C, Kon'in- 

 Kroukovsky, B. V.. ami Kotik, J., SNAMK, 

 1954, pp. 359-.3961. Tlii.s nictliod has the disad- 

 vantage that it is difficult to measure or record 

 the profile positions accurately. The profile 

 appears to shift in any one run, even when the 

 model is moving at nominally constant speed. 

 Further, the difTerences in profile positions for 

 successive speotls are small. 



G. P. Weinblum gives a summary of most of 

 these methods, in more mathematical terms, in 

 Appendix 2 of TMB Poport 710, September 1!).")(), 

 pages 89-94. 



It has been shown liy Lumlr that all six 

 methods lead to exactly the same result if carried 

 out correctly. Further, that for a thin ship the 

 methods of Havelock and Guilloton give identical 

 results. 



The derivation of the resistance equations by 

 anj- of these six methods, as well as the calcu- 

 lation of the resistance for a range of speed, is 

 exceedingly involved. No attempt is made to 

 give it here but those who \\'ish to pursue this 

 matter further may find the work carried out in 

 several ways in the references quoted in Sec. 50.13. 



One could wi.sh that the ingenuity of the workers 

 in the analytic field had been matched bj' those 

 in the experimental field, and that there were an 

 equal number of methods by which the resistance 

 and other characteristics of a towing model could 

 be determined. Further, that when so determined, 

 the values would all be equal! 



50.7 Components of the Calculated Wavemak- 

 ing Resistance. The matiifniatic cxiirc^sions for 

 resistance derived by the processes mentioned, 

 for shapes which lend themselves to this operation, 

 can sometimes be broken down into four or more 

 parts. These represent the components due to 

 separate wave systems formed at the bow and 

 stem and along the sides, plus the interference 

 efTects between these components. Exactly the 

 same unraveling process may be applied to the 

 expressions for the surface elevation (or depres- 

 sion) of the combined gravity-wave system. 



As an example. Fig. 50.C gives the formula 

 derived by T. H. Havelock for the wavemaking 

 resistance of the essentially 2-diml and sym- 

 metrical form shown there, made up of two 

 parabolic watcrlines having their vortexes at 

 midlenglh |1XA, 1934, Ei|. (28), pp. 441-142|. 

 Thi.H formula consists of a constant factor times 

 a V" term times the sum of five terms whose 



significance is dcscrilunl in the diagram. It is to 

 be noted that the fourth and fifth terms of the 

 series are negative, indicating an everpresent 

 benefit from the interferences of all except the 

 bow and stern wave patterns. The general and 

 physical reasons for this are explained in Sec. 

 10.14 and other sections of that chapter. 



Furthermore, the last three terms contain a 

 sine and two cosines which vary with K(kappa) = 

 g/V, hence these terms have values which are 

 said to oscillate with speed. The oscillations give 

 rise to the well-known hum|)s and hollows in the 

 curves of resistance due to wavemaking. ilhis- 

 liated in diagram .3 of Fig. ."lO.B. 



50.8 Comparison of Calculated and Experi- 

 mental Resistances. As an indication of the cor- 

 relation obtainctl between the calculated and 

 experimental values of resistance derived from a 

 model which resembles an actual ship. Fig. 50.D 

 gives the (c)-curves, based on total resistance, for 

 the destroyer model devised by J. K. Lunde and 



i(k»ppa) ^'■~^C}^^"'^'^''i^ ^Z"-^**^^ °^ Havelock 

 " g/t* of HQvelod<^*~~'' ' I ' —""""^ffeferertce - V of this 

 Referente - o/V of thie fioore f jqure 



PRESSURE RESISTANCE DUE TO WAVEMAKING 

 rr (l +II*III+Er+Y), where 



Term I (S 



2 / V^ Y 



lofasu/ • ^^'' ""'sto't* D"E. to the Bow and the 

 Stern Wove Rjtterns. Assumed 

 to Exist Indepandenlivy 



^ '^Ts io/O.SLW ' "^' Re»i»ton« Due to the Wove Rjt- 

 terns from the Two Curved Sides, 

 Existinq Indepsndentiv 



Term m 15 (-/q^lJ / ^ coi^ 9 cos[2«.(0 5L)38ce]de, the 



Pesistonce Due to the Interferenc 

 of the Bow ond the Stern 

 Wove Potterns 



Term E, (-) 2 (-fo5|_\ ) / ^ cos ♦e sin [Z *i (05L)sec e] de , the 



Resistance Due to the Inlerferen 



of Bow or Stem Wavt Fbtterns 



With Entrance or Run Rittcm 



Term "^ • '■ Malpil^ '^"^'^ sin[2»i(a5L)sece]de, the 



Resistance Due to Mutual Interference 

 of the Wove RrtUirns of the 

 fntronce and the Run 



Fid. 5().{; TAnULATION OK TyI'ICAI, C-OMPONENTS 



OK Wavemakino Resistance 



