188 



MYnROnVNAMICS IN Sllll' DI.SIC.N 



Src. 19.3 



Sorii-.s, \ol. XIA I, PI). :U-. H.V.I aiul .SSO ;{•)(>. 

 with Pis. U ami 111), i-nablwl him to lak-ulatc the 

 fiimpU'to set of offsets for a ship body plan 

 represent iiiR an underwater form with a numerical 

 value of block cocfHcient C/, selectetl in advanre. 

 He describes, on page 358 of the reference: 



"... a vessel coiistrurtcil wholly by the paraluilir nictlicxJ; 

 pvery rrosa soctioti or friiini' is ii paniliolii; tlio friiinu 

 ilruwiiiK or lio<ly plan is laid ilown direct from caleillation 

 without refen'iiee to water-lines or diaKonals and without 

 exiTcise of tjisto." 



lie was able, with this mathcmatic method, to 

 use reversetl i)arabolas for hollow waterlincs, to 

 calculate both the horizontal and the vertical 

 position of the center of buoyancy CB, and to 

 draw a curve of displacement volume on a basis 

 of draft. His methods are explained in detail in 

 the reference cite<l and are illustratetl by examples. 

 Xystrom even goes so far as to tell, on ]ian;e :).")S 

 of the reference, how: 



". . . to form the displacement so as to present the least 

 possil>lc resistance wlien forced throiigli water. The 

 immer.sotl area of each frame (station) should increase or 

 diminish in a certain series, found theoretically to lie thai 

 the sfiuarc root of the sections (areas) should be ordinates 

 in a parabola, the exponent of which depends on the 

 desired fulness of the displacement (block coefficient)." 



The words in parent lieses arc those of I lie prcscMit 

 author. 



Subsequent papers by Nystrom, all on the same 

 general subject, appear in references (.S) and (4) 

 listed in Sec. A\)M. 



Shortly after the Wasliinglon Model Ha.sin was 

 put in operation in I'.KK) I). W. Taylor developc^d 

 a mathematic "method of deriving (luickly the 

 lines of a nuxlel i)o.sse.ssing certain desired charac- 

 teristics, and . . . practicable; anil easy methods of 

 sysU'malically varying characteristics of models 

 . . ." ISXAMI-:, IIKW, pp. 24:3-2C7]. This method 

 covered the delineation of waterlincs, section 

 lines, and section-area curves. A somewhat 

 difTcrent mathematic method of producing water- 

 lines, section-area ciu'ves, and body plans, closely 

 resembling llio.se of actual ships, was proposed by 

 J. N. Warrington .shortly tlicnnrirr |S\A.Mi;, 

 1909, pp. 41I~J52|. 



Another decade of development by Taylor, 

 following lii.s original concepts, produced tlu; 

 paper entitled "(Calculations for Ships' Kornis 

 and the I^ight Thrown by Model l']xpeiiments 

 upon Resistance, Propulsion and Uolling of Ships" 

 I'l'rans. Int. lOng'g. ("ong., Nav. Arch, and Miir. 

 Mng., San Francisco, Hll.'i). In this revised and 



aniplilied prr)cedure, .separate fornnilas are u.se<l 

 for waterlincs and sections. The curve familias for 

 fine sections are 4th-tlegiee parabolas; those for 

 full sections are hyperbolas. The entrance and the 

 run, extending from the bow and stern, respec- 

 tively, to the section of maxinnun area, are 

 treated separately, because the origins of the 

 mathematical curves are taken at the bow and at 

 the stern. The families of curves representing 

 waterlincs and section-area curves are given bj' 

 oth-ilegree polynomials with five arbitrary param- 

 eters, of the type y = tx ■{■ ax' -\- bx^ -f- ex* -\- dx''. 

 It was apparently' Taylor's intention to give a 

 shape to the waterlinc curves that would inii)art 

 a predctemiined amount of lateral or normal 

 acceleration to the water flowing aroimd them. 



Xo parallel body is mentioned in Taylor's paper 

 although there is of course no difficulty in separat- 

 ing (he hull at the section of maximum area and 

 inserting any desired length of cylindrical prism 

 luuing the maxinunn-section shajje. 



Taylor's method is entirely suitable for practical 

 ami shipyard u.se; in fact, it has been used off 

 iiiiij nil for drawing model and ship lines at 

 Wa.shiugton for the past 50 years. A number of 

 I'. S. naval vessels have been constructed to 

 the.sc lines. The body plan of a modern design, 

 most of which was delineated by Taylor's metlKul, 

 is reproduced in Fig. 4i).C of Sec. 40.7. 



l']laboraling u\wn the quotation in a preceding 

 l)aragiaph from D. W. Taylor's Um SXAME 

 paper, his met hod makes it |)o.ssible, by the u.se of 

 eqiiidilTerent or progressive values for the i)aram- 

 eters, to develop any desired mnnlicr of ship 

 forms in a series. This was of inestimable value 

 in the preparation of lines for large groups of 

 models such as the Taylor Standard Series. 

 Using this method the series became scientifically 

 .systematic, with the minimum of elTort on the 

 l)art not only of those who planned it but tho.se 

 who had to draw the lines for each model. 



An excellent sui)i)lementary slalement by 

 (;. P. Weinblmn |TMli Hep. "•*'. ^n) I'-'ot), p. 7), 

 from which the following is jjaraphra.sed, .says 

 dial T;i\liir developed mathematical formulas, 

 mil uiili (he idea that they gave the lines of a 

 ship of mininnnn resistance but sim|)ly to obtain 

 lines po.s.se.s,sing desired shapes. This statement is 

 important. Contrary to .some attempts to a.scribe 

 magic ])roperlies to certain analytically delined 

 curves like trochoids and sine curves, the principle 

 of .systemali/ation was the decisive argument for 

 llieir .'tdnptiiin. 



