A great success has been achieved in naval architecture by the use 

 of integral curves of which the sectional-area curve is perhaps the most 

 important . 



1.1.3. Equations of Ship Surfaces 



Quite a number of attempts have been nade to define ship lines by 

 ma:thematical equations, with different purposes in view. There is no need to 

 dwell on Chapman's parabolas, which can be found in every handbook. Obviously 

 they are almost impractical, as they contain only one parameter, i.e., their 

 shape is fixed by the area coefficient alone. One should therefore eliminate 

 them as a method for design, notwithstanding the fact that they have formed 

 the starting point for all further work on the exact representation of ship 

 form. 



According to D.W. Taylor's own statement,"*^ he developed "Mathemat- 

 ical formulae not with the idea that they give lines of least resistance but 

 simply to obtain lines possessing desired shape." This statement is important; 

 contrary to some attempts to ascribe magic properties to certain analytically 

 defined curves like trochoids, sine curves, etc., the principle of systemi- 

 zation is put forward as the decisive argument for ^their adoption. Formulas 

 are given for waterlines and sections separately, no parallel body having been 

 apparently envisaged, although there is no difficulty in inserting this fea- 

 ture. Pore and afterbodies are treated separately; the origin is situated at 

 the bow or stern, respectively. The family of curves intended to represent 

 waterlines and sectional-area curves is given by a fifth-degree polynomial 

 with three arbitrary parameters; the discussion of the properties of this fam- 

 ily is performed in classical style and is perhaps the most refined contribu- 

 tion to our problem. The lines are perfectly suitable for practical use. 



Unfortunately, Taylor's work is not very suitable for theoretical 

 investigations since the equations of waterlines and sections are not linked 

 together into equations of surfaces and fore and afterbody are treated separ- 

 ately. Nevertheless, it is a great loss to the profession that his basic pub- 

 lication*^ has remained almost unknown; otherwise model research would have 

 obtained a more systenatic character, as earlier stated. 



A system of ship-hull equations has been developed for broader pur- 

 pose s-"-"^'^""* in which expressions were sought which would: 



a. Be suitable for fixing and systematizing ship forms. 



b. Give a basis for investigating systematically wave-resistance qual- 

 ities of ships and eventually lead to forms of least (low) resistance. 



