5T 



5.4.4 Ships of Least Resistance 



Ship-resistance researdh will have reached its practical goal when 

 we will be able to indicate the form of least total resistance for any given 

 conditions of speed, displacement, etc. Theory emphasizes the well-known fact, 

 often forgotten by inventors, that there does not exist one ship form of least 

 resistance, but that optimum forms vary with Froude numbers and with other con- 

 ditions. So called optimum shapes like "pisciform" (fish form) w'lich have 

 been derived from considerations valid for an unbounded fluid lack any serious 

 background for surface ships. 



The problem of finding ships of least total resistance can be formu- 

 lated analytically; however, this formulation does not seem to be helpful as 

 long as no analytical expression for the viscous drag Is known. The friction- 

 al resistance may be assumed with reasonable accuracy to be proportional to 

 the wetted surface. 



Thus, the problem of calculating ships of least wave resistance ap- 

 pears to be the appropriate first step towards the solution of the more gen- 

 eral task. In fact, the wave resistance is the "component" most sensitive to 

 changes in form and is responsible for the dependence of optimum form upon 

 Froude number. We can hope, therefore, to obtain the most essential informa- 

 tion on ships of least resistance by solving the problem for the wave resist- 

 ance — an assumption which underlies Froude 's method. 



Prom the form of the resistance integrals for ships, submerged bod- 

 ies of revolution and pressure systems, it follows that the forms of least re- 

 sistance are symmetrical with respect to the midsection, since then the term 

 I^ (see Appendix 2, Equation [12]) becomes zero. 



Another deduction which will be needed later is that the resistance 

 of an asymmetric body is the same when moving ahead or astern. These results, 

 which are contrary to our general experience, are caused by the assumption of 

 an ideal medium; at high Froude numbers, however, the effect of viscosity is 

 small, so that for a restricted class of bodies symmetry may become an approx- 

 imate condition of least wave resistance as has been shown by experiments. 

 Actual ship forms suitable for very high speeds, however, do not comply with 

 the condition of symmetry, one reason for the departure from the results of 

 simplified hydrodynamic theory being the influence of the changed attitude of 

 the ship at such speeds (trim and bodily rise). 



Keeping in mind that the following results must be applied with 

 caution to actual conditions, we discuss methods used, the difficulties met 

 with, and the practical information obtained when trying to find ships of 

 least wave-making resistance. 



