1 . THE REPRESENTATION OP SHIP FORMS 



1.1. THE GEOMETRY OF SHIPS 



Any treatise on theoretical naval architecture should begin with 

 (or at least include) a chapter on the representation of ship forms. This 

 could be called "The Geometry of Ships," although this terminology has some- 

 times been used for discussions of problems of statical stability. 



1.1.1. Graphical Method 



The generally used graphical method of representing ship surfaces 

 by "fairing" the lines is efficient from some viewpoints, as it leads within 

 a reasonable time to solutions which con^jly with the necessary conditions of 

 buoyancy, stability, etc. The resulting surfaces (lines) have a high degree 

 of smoothness within the practical degree of accuracy required when "spline 

 curves" (battens) are used. A curve is called "smooth" when the first deriv- 

 ative is continuous (the curve itself has no corners); we define the "order 

 of smoothness" of a curve as the order of the highest derivative which is con- 

 tinuous. A curve in which there is a continuous radius of curvature (a con- 

 tinuous second derivative) is smooth to the second order. Spline curves drawn 

 in the proper way should generally be smooth to a still higher order. This 

 can be easily understood since the curvature of the elastic line of a batten 

 is proportional to the bending moment; the graph of the bending moment remains 

 continuous, even if we apply to the batten horizontal concentrated loads by 

 weights— a procedure contrary to the idea of fairing under normal conditions. 

 On the other hand, discontinuities in the curvature of ship lines are admitted, 

 for instance, when using a combination of a straight line and a circular arc 

 for sections. 



These points will be considered later;* at the present it is suffi- 

 cient to state that a definite order of smoothness may be a necessary or de- 

 sirable condition for a ship line, but it is not a sufficient condition as is 

 well known from experiments and will be proved by theory. It is the purpose 

 of resistance research to develop criteria for good ship lines— lines deter- 

 mined by minimum resistance qualities. Because of the lack of rigorous re- 

 sults, however, earlier practice — guided by experience and other considera- 

 tions, some of arbitrary character — has introduced a working concept of "fair- 

 ness of lines," with which hulls should comply. 



*See Appendix 3, where it is shown that modern hydrodynamics supports the wisdom of artisanshlp in 

 shipbuilding. 



