c. Form a more general foundation for research on other problems in 

 naval architecture such as motions in a seaway, stability, etc. 



d. Reduce the work in the mold loft. (The author has made some contri- 

 butions to this idea without being able to claim much practical success.) 



The formal development is briefly reviewed in Appendix 1 . Although the 

 analytical approximation of a given hull may be a tedious problem, f.or some 

 scientific purposes quite simple expressions prove to be valuable. 



We locate the origin at the midship section, and the planes of ref- 

 erence are given by the vertical-center plane (X,Z), the load-waterline plane 

 {X,Y) and the midship-section plane (Y,Z); see Figure 1. In dealing with re- 

 sistance problems to a first approximation, we confine ourselves to the under- 

 water part of the hull. 



Figure 1 - Axes of Reference 



We denote as an "elementary" hull a form defined by a rectangular 

 longitudinal contour and an equation of the type 



Y=|x(x) Z(z) 



{^\ 



where X(x) and Z(z) are the dlmensionless equations of the load waterline and 

 midship section. It can be easily seen that for such hulls: 



[5] 



The sectional- area curve is afflne to the load waterline (their 

 equations differ only by a constant factor) 



Cp - «> - C,, - a 



[6] 



c. The sections are afflne to the midship section and the waterlines 

 to the load waterline. 



It is astonishing that such an elementary equation leads to quite 

 reasonable ship forms as long as the C„ = iS relationship is low; it is appro- 

 priate for investigating the Influence on wave resistance of the longitudinal 



