Sec. 49.R 



MATHEMATICyXL LINES FOR SHIPS 



193 



0.5 0.338 0.277 0.215 0.154 OOSZ. <£ 0.09E 0.154 0.215 0.277 a338 0.5 



Waterline Positions are in Fractions of Draft; Buttock Positions are m Fractions of Half-Beam 



Fig. 49. C Body Plan op Ship with Mathematical Lines Following the Taylor Method 

 From Sta. 2 through Sta. 14, both inclusive, the lines of the hull represented here are entirely of mathematical derivation. 



The body plan of Fig. 49. C, illustrating a 

 tentative form for a multiple-screw vessel of 

 modern (1954) design, is a good illustration of 

 what can be done with D. W. Taylor's system of 

 mathematical lines. From Sta. 2 to Sta. 14, both 

 inclusive, the hull form is entirely of mathematical 

 derivation. Beyond those stations the reverse 

 curves and changes in curvature call for the 

 customary graphic layout and fairing procedure. 



For information, the principal 0-diml form 

 coefficients of the hull of Fig. 49. C are: 



Cp = 0.560 

 Cx = 0.976 

 Cw = 0.684 

 Cn = 0.547 

 LCB = 0.5051L 



(O.IOL) 



In common with many other tools of the marine 

 architect, mathematical lines are specialized 

 rather than all-purpose affairs. In this respect, 

 however, they may often do well what the others 

 can not do at all. For example: 



(1) Mathematical methods lend themselves to 

 working in 0-diml terms 



(2) The formulas lend themselves to machine 

 calculations, enabling many ordinates — or abscis- 

 sas — to be calculated in a given time, and making 



any subsequent curve drawing more precise. The 

 computing, lajdng off, and drawing may be 

 performed by not-too-skilled operators, and by 

 those not fully indoctrinated in naval architecture. 



(3) It is possible, as explained in Sees. 49.13 

 and 49.14, to fair the principal ship lines of a set 

 by mathematical methods, and to produce fair 

 full-scale offsets for those principal lines in the 

 design stage. Further, it is possible, by desk- 

 machine calculation, to shift from fair station 

 offsets to fair frame offsets, greatly facilitating 

 the laying down of the full-scale lines. 



(4) A mathematical curve is more readily and 

 accurately transferred from small scale on a 

 drawing to full scale in the loft than is a graphical 

 curve 



(5) It is possible, for analytical projects, to Avork 

 on the mathematical formulas mth a number of 

 mathematical (not. human) operators, such as 

 those which give slopes, rate of change of slopes, 

 and moments. 



In general it may be said that graphic represen- 

 tations are unsuitable for analytic investigations, 

 in which modern hydrodynamic parameters are 

 used, general laws are to be established, and 

 predictions of performance are to be made 

 [Weinblum, G. P., TMB Rep. 710, Sep 1950, p. 5]. 

 Formulas and equations are needed for this work. 



49.8 Value and Relationship of Fairness and 

 Curvature. There has been an inherent realiza- 

 tion among ship designers and shipbuilders since 



