I9fi 



HVDRODVNAMKIS IN SHIP DKSir.N 



Sec. I'l.lO 



ola, x' = aij or j-' = bij, «'ith its viTtex at tln' 

 eiul of the straiRlit soft ion of trai-k. For a ship, 

 it involves a similar curve with its vertex at the 

 end of the straight or parallel portion of the ship 

 line. 



For a S-tlinil form, particularly a hotly of 

 revolution, perfect transition of this kind is 

 achievtHl liy joiiiinft a parallel cyliiulrical portion 

 with half of an ellipsoid of revolution defined by 

 the relationship jjiven in Eq. (4!).xL\) of Sec. 49.8 

 or by the identical relationship 



— + ^ = 1 



1 I'.l.wii) 



This is the c((iuition of the "i-dinil intersection of 

 the outer skin with a plane pa.ssing through the 

 a.\is, sketched in Fig. 49.D, and not of the ;{-(linil 



(31 »-Axis oi Body^'' 

 h — ' aorLg 



^(l7-t^ 



(49*XKi) 



Whani-O, -r£~0 Qndo-^O 



Fig. 49.D Skktch of Airship Nose Outline of 

 Third-Degree Eluptic Shape 



body surface. The origin of coordinates is on the 

 axis at the jvmction of the two portions; L^ is the 

 half-length of the ellipsoid, and Rh is its maximum 

 transverse radius, ec|ual to the radius of the 

 parallel portion. This corresponds to the com- 

 bination of no.se and niiddlebody portions of the 

 hulls of the airships Akron and Macon, mentioned 

 in the .section preceding. The longitudinal section 

 drawn on I'^ig. 49. D indicates tlu; extremely 

 gradual transition from the parallel niiddlebody 

 t(j the after portion of the entrance or no.sc. 



Upon double dilTerentialion with respect to r, 

 Eq. (49.xxii) reduces to the value of d'y/dx' 

 indicated on Fig. 49.13 as E(i. 49.xxiii). In this 

 ca.se, as shown on the figure, when x = 0, 

 d'l/'tlx' = and l/lfc is *'. I'he combination of 

 third-order ellipsoid and cylinder described in 

 the foregoing gave most gratifying resistance and 

 propulsi(jn results when used on the large rigid 

 airships nicntioncd. 



-Modern hull-<lcsigii procedure re(|uires that 

 equally good transitions be made, if practicable, 

 between the parts of fore-and-aft ship lines. 

 Further, the finished lines should be as fair as 

 modern technology can make them. This calls 

 for the use of some method for guaranteeing a 

 longitudinal curvature that will eliminate Ap 

 disturbances along these lines or that will indicate 

 the presence of localized i)re.s.sure dLsturbances 

 if they can not be avoided. Unfortunately, it is 

 not ea.sy for a human being to realize how sharp 

 this transition may be along the .side of a ship, 

 ecrtiiinly not as easily as it would be if he were 

 ill a train, jiniiifi around a geoinclrically similar 



cUI'X'r. 



'I'lir aerial \ iew of Fig. 49. E, taken of a moilern 

 (ill.").")) nieicliaiit siiip and reproduced with the 

 permi.ssioii of the Kockums IMekaniska Aktiebolag, 

 Maim<'), Sweden, illustrates this feature in a 

 rather extraordinary manner. It is almost possible 

 lo discern the Velox waves generated by the 

 liiiward-shoulder pressure disturbance, where the 

 hollow in the entrance waterline shifts rather 

 abruptly to the parallel waterline amidships 

 through a convex transition region of rather sharp 

 curvature. Methods of taking care of this situation, 

 for cases where there is no limitation on the 

 extreme beam and no parallel waterline is neces- 

 sary, are described in Sees. G7.2 and 67.3. 



49.10 Graphic Determination of the Dimen- 

 sionless Longitudinal Curvature of any Ship Line. 

 Details of the graphic procedure mentioned in 

 Sees. 4.4, 4.5, and 4.7, for determining 0-dind 

 longitudinal cur\'ature in waterlines, buttocks, 

 and diagonals, are given here. 



]?riefly, the 0-diml curvature of a designed 

 waterUne of a ship is determined for any selected 

 point along the length by the ratio 



Beam By at the section of maximum area 

 Length of 1-deg arc of the circle of curvature 



where both linear dimensions are given in the 

 ■same luiit of measurement. 



The value of Bx is taken directly from the ship 

 lines; it is the magnitude of the beam on the 

 drawing being analyzed, not that of the .ship 

 it.self. Determining the value of the denominator 

 in the ratio given is facilitated by drawing on 

 transparent film, by photograjjhic reiiroduction 

 or the equivalent, a .series of arcs of circles of 

 varied radii, comprising the range of curvature 

 to be expected in any body or shi]) lines to be 

 analyzeil. ()|)posite eaeh such arc is marketl, in 



