19} 



HVnRODVNAMICS IX SHIP DESIGN' 



See. 49.S 



time inuncrnorial tli:it tlio urulerwatcr surface 

 of a .'ihip liull should be fair in the direct ion of 

 water flow along it. This was achioveil by eye in 

 the hewing process or by bending fore-and-aft 

 structural members such as planks into reasonabl}' 

 fair elastic curves. It is entirely possible, indeed 

 probable, that the hewer of old usetl flexible 

 wooden .strips or battens bent around the hull to 

 check his fairing, as does the womlcn-mmlel maker 

 of today. If so, these were the forerunners of the 

 flexible strips or splines later emplo^'ed for drawin};; 

 fair lines to which the shipwrights anil ship- 

 fitters were to work. 



It is often taken for granted that because a 

 heavj' sphne can not have an abrupt kink put 

 into it without splitting or breaking, it must 

 automatically produce a fair or smooth ship line. 

 Wliether carried to tliis extreme or not it is still 

 necessary, in order to achieve the maximum 

 degree of what G. P. Weinblum calls "geometrical 

 smoothness of the ship surface," to use the 

 stifTest spline which can be bent into the desired 

 curve, and to supplement the elastic uniformitj' 

 of the spline bj' sighting along it before drawing 

 the lijie. 



In the discussion which follows, adapted largely 

 from the work of Weinblum, his term "smooth- 

 ness" is eliminated. This makes it sj'nonymous 

 with his term "fairness" and avoids confusion \\\i\i 

 the use of ".smoothness" to describe the condition 

 of a .solid surface along which viscous How takes 

 place in a real liquid. 



It is difficult to describe or to specify fairness, 

 especially in a quantitative sense. Following 

 Weinblum, a curve may be called fair when its 

 first derivative with respect to a selected ship 

 axis, say dy/dx, is continuous. The order of 

 fairness of such a curve may be further defined 

 OS the order of the highest derivative which is 

 still continuous. Thus a curve in which there is a 

 continuous .second derivative d'y/dx' and con- 

 tinuous curvature; is fair to the second order 

 [Weinblum, (I. P., and Kendrirk, J., "On the 

 Geometry of the Ship, Part I," mii)iilil. TiMB 

 rep.). The following is ((uoted from pages 1(> and 

 17 of the referenced report, with "smoothness" 

 replaced by "fairness" and .some minor editing: 



"iSpline curvi.-a drawn in the pro|)cr way oliould be at 

 leant fair to tlio mpcoikI order or have continuoim curvature. 

 This followH inuiie<liali;ly from the proportionality of tlic 

 curvature of the eliuitic axis of a Hpline to the l>ending 

 moment on the Hpline. The Kraph of the tending momi-iit 

 and therefore the curvature remain continuouH oven 

 Ihougli horizontal conccnlrat4.-d loodii uro cxerU-d l>y wi-lKlit-t 



on the Kplinc. Since tlie draftsman endeavors to avoid 

 these concentrated loads in the process of fairing, the 

 order of fairness will generally bo higher than 2." 



Weinblum gives .several additional criteria for 

 fairness, among which may be mentioned: 



(a) A small number of points of inflection in any 

 quadrant between two ship axes normal to each 

 other, preferably only one such point 

 (h) Freedom from flat regions 

 ((■) M(Mlerate changes in the first and .second 

 derivatives. Weinblum goes on to point out that 

 I lie foregoing concepts of fairness, although 

 derived from experience and found u.seful in 

 practice, may fail completely to give indications 

 as to ship resistance, especially that due to wave- 

 making. 



The uncertainties associated with the fairing 

 of ship lines and the lack of fairness found in the 

 shapes of well-known ships were two reasons 

 which led to the study of longitudinal curvature 

 described in Chap. 4 of Volume I. Others were 

 the comments of W. J. M. Rankine in the 1860's 

 and 1870's relative to the curvature of stream 

 forms developed bj' the source-and-sink process, 

 the procedures used to shape airship hulls, and 

 the findings of aeronautical engineers in the shap- 

 ing of strut and similar sections. 



Rankine chose, for the waterline of a ship, a 

 streamline somewhat removed from the boundary 

 of a source-sink stream form. Here, along the 

 chosen streamline or lissoneoid, as he called it, 

 the curvature was such as to produce only three 

 changes in differential pressure as litiuid flowetl 

 along it, from well ahead to well astern. Around 

 the stream form itself there were five changes in 

 pressure undergone by a particle of liciuid in 

 moving from a great distance ahead to a great 

 distance astern ("An Investigation on Plane 

 Water-lines," Brit. A.ssn. Rep., 1803, pp. 180-182, 

 under Mechanical Science; Jour. Franklin Inst., 

 Jan-Jun 180-1, Vol. XLVII, Thinl Series, pp. 

 2l-2()]; see Sec. 50.2 and Fig. 50. A. 



For the no,so or en trainee portions of the hulls 

 of the U. S. Naval airships Ahron and Moron of 

 the 1930's, which were joined to parallel middle- 

 bodies, an elli]isoi(l of revolution of the third 

 order was employed. Based upon a length of 

 entrance a and a radius of middlebixly b, tho 

 ecjuation of the forebody outline in a longitudinal 

 plane pa.ssing through the axis was 



i' + // ' 



(JO.xix) 



