It is not easy to give a reasonable definition of the real meaning 

 of "fairness." As applied to a ciirve some features characterizing this prop- 

 erty are: (a) Conditions of monotonic increase or decrease, (b) avoidance of 

 flat parts, (c) lack of abrupt change in the curve and its first and second 

 derivative, and (d ) the possession of a finite number of points of inflection. 



The basis of the idea of fairness is the fact that a trained human 

 eye is very sensitive to any peculiarities of curves. It will be proved later 

 that fairness has not given us reliable indications as to the resistance qual- 

 ities of forms, although the concept can be useful from resistance and stnivC- 

 tural viewpoints. The well known resistance qualities of bulbs and "swan- 

 necks" furnish a good illustration of how far the idea of fairness must be mod- 

 ified in the light of present knowledge. 



The disadvantages of the graphical method of ship design are: (a) 

 The necessity of laying off to a large scale, and (b) the unsuitability of 

 graphical representations for establishing general laws for wave resistance, 

 behavior in a seaway, and so on. 



1.1.2. Description by Coefficients and Lines 



The "Explanatory Notes for Project Number 2"^^ issued by The Society 

 of Naval Architects and Marine Engineers contain a consistent system of form 

 parameters and lines which are assumed to be known. 



Use is made of dimenslonless representation: Dimension factors are 

 separated from the pure form or shape defined as the ratio of hull ordlnates 

 y to half- beam B/2, etc. The dimensions can be expressed by the absolute 

 length L and two ratios as L:B,B:H; the shape can be approximately described 

 by suitable Integral or differential properties (coefficients of fineness, 

 tangents, curvatures). Thus two sets of important parameters are obtained 

 which, within a certain range, can be treated independently, as will be 

 demonstrated. In the light of this tendency there does not seem to be any 

 advantage in the use of such expressions as — us'Ts' where the pure form con- 

 stants and the parameters derived from dimensions are mixed, except for a 

 first orientation; for practical work the use of ratios, like L/B, B/H, and 

 Cg = (5 (which are all known) is preferable.* Our purpose is to approximate 

 the ship form by as many characteristic parameters as possible, not to merge 

 several known parameters into one. 



*As a matter of courtesy, symbols like C ,C .proposed by the Sub-committee of the SNAME, are men- 

 tioned here beside the well established Greek letters which are used throughout the report. For actual 

 work Greek letters have a definite advantage over the C coefficients by reducing the prohibitive' number 

 of subscripts. 



