10 



2. RESISTANCE 



When analyzing the wave resistance, some remarks on ship resistance 

 in general are necessary. We ignore the air resistance, which may be quite an 

 important item but is outside the scope of these considerations. 



Proude developed his well known method of using model experiments by 

 starting from the idea that it is comparatively easy to calculate the fric- 

 tional drag and impossible to compute the wave resistance. He tacitly assumed 

 that the different "components" of resistance can be superposed with reason- 

 able accuracy, i.e., that their mutual influence Is relatively the same for 

 the model and the ship. The "eddy" or "separation" resistance, although ob- 

 viously due to viscosity, is merged into the residual resistance and its co- 

 efficient considered to be independent of scale effect; it was assumed to be 

 small for good ship forms. 



These assumptions have led to a practical technique used all over 

 the world. Prom the viewpoint of hydrodynamics, however, matters are somewhat 

 different. Here the frictional resistance due to viscosity effects is in prin- 

 ciple a more complex problem (involving the solution of Navier-Stokes equa- 

 tions) than the wave making force which arises in an ideal fluid. The gener- 

 ation of surface waves in a viscous medium is a problem which has not yet been 

 investigated by theory, so that the hypothesis of the mutual independence of 

 the resistance components from scale effect (model and ship) cannot be quan- 

 titatively discussed in the light of rational mechanics. 



The "eddy" resistance due to viscosity is a function of some appro- 

 priate Reynolds number. Prom the reasoning given in Appendix 3, a serious 

 scale effect can be expected when model data are converted to the ship, al- 

 though it is assumed that the character of separation does not change when 

 full turbulence has been reached over the model surface. In aerodynamics, 

 contrary to Proude 's procedure, frictional and "eddy" resistance are treated 

 together as viscous drag. 



These undetailed remarks indicate now difficult it is to analyze 

 rigorously the wave resistance of the ship using model experiments. Por most 

 types of ships wave resistance is only a small part of the total resistance 

 and as the amount of viscous drag is known only to a relatively low order of 

 accuracy, the wave-resistance values obtained by subtraction are liable to be 

 quite erroneous. 



To put things on a more rigorous foundation we define the following 

 kinds of resistance: 



a. Prictional resistance is the tangential resistance due to viscous 

 forces. It differs in principle from the resistance of the equivalent plate 

 having the same wetted surface, this difference being denoted by frictional 



