208 



iiM)ii()iiv\ \Mi(:s i\ siiii' nisicx 



Sec. 50.2 



purely analytic point of view. He slarled with 

 a two-dimensional body in an unliniitotl liquid 

 and then brought it to the surface, so to speak. 

 When he did so he realized that surface waves 

 would be formed but of these "principal vertical 

 disturbances" he assumed them "to be so small, 

 compared with the dimensions of the bodj', as 

 not to produce any appreciable error in the 

 consoijuencos of the supposition of (licjuid) 

 motion in plane layers" [Phil. Trans., Hoy. Soc, 

 London, 1S04, pp. 383-384]. 



Whatever may be said of Rankinc's sense of 

 values and of physical laws in this matter, he 

 did succeed in deriving mathematically an 

 infinite series of 2-diml and 3-dinil shapes for 

 which not only the boundarj' coordinates but the 

 velocity and pressure distribution could be calcu- 

 lated. It seems reasonable to suppose that 

 eventually he hoped to be able to calculate their 

 resistances to motion in a li(|uid. With the 

 assistance of Clerk Maxwell, as related previously 

 in Sec. 2.11, he devised graphic and geometric 

 methods of drawing the outlines of these oval 

 forms, called here Rankinc stream forms, as well 

 as the procedures for constructing the streamlines 

 around them. Rankine's endeavors [Phil. Trans., 

 Roy. Soc, 18G1 and 1871] constitute, so far as 

 known, the first scientific attempt to take into 

 account the prime factors of velocity and pressure 

 around a ship hull. Tjiis important .scientific 



contribution cinlKRlicii Kankine's invention of 

 the concept of radial flow, later to be known in 

 some (luartcrs as source-sink (low, and subse- 

 quently to be utilized to some extent in practically 

 all attacks on the wave-resistance problem from 

 1890 to the present. While it is reporteil that 

 G. R. JvirchholT emploj-ed the artifice of sources 

 and sinks in analytic hydrodynamics as early as 

 1845 [Rou.se, II., and Ince, S., "History of 

 Hydraulics," La Ilouille Blanche, B/19'}'), Chap. 

 9, p. 201], Rankine's search for the fundamental 

 velocitj' and pressure relationships in the sur- 

 rounding flow laid the groundwork for the u.seful 

 features of this concept today. 



One interesting feature of Rankine's work, 

 seldom brought to mind in these years, is that 

 while he considered the oval shapes resulting 

 from his new procedure to be general forms of 

 waterlines, it was not at all his intention that the 

 blunt-ended "neoids" or stream-form outlines 

 generated by placing a source-sink pair in a 

 uniform stream be incorporated a.s waterlines in 

 actual ships. lie proposed instead that one of the 

 stream surfaces lying iji the litiuid outboard of 

 the oval form, comprising both hollow regions 

 and convex shoulders, be u.sed as the hull surface 

 at the ship waterline. To this shape of boundary, 

 represented by the trace Ls — Lb in diagram 1 

 of Fig. 50. A, or by any streamline farther removed 

 from the stream form, he gave the name "lis.sone- 



\ I>nniuM ny !^hkami.inim in 2-Diml Flow, Ii-i.uarRATiNO Rankinb's Libsonroid, wrrn IxtNorruDiNAL 



I'UKSHIIKH VaIUATIONB 



