61 



mathematical difficulties. A further step can be made by using some correc- 

 tions for viscosity, as shown later, but taking into consideration the some- 

 what arbitrary character of these corrections no results of general value can 

 be achieved. 



6. INFLUENCE OP VISCOSITY 



So far emphasis has been put on the wave resistance of symmetrical 

 ships, since in an ideal fluid the even terms of the surface equation contrib- 

 ute the principal part of the resistance as long as normal forms are consid- 

 ered. The resistance "component" corresponding to the antisymmetrical part 

 is computed in the same way as for the main part by slightly different func- 

 tions; the two components can be simply superposed. As mentioned before, in 

 an ideal fluid the wave resistance of asymmetrical bodies is the same when 

 moving either ahead or astern. 



Obviously, this paradox does not hold for a real liquid. When asym- 

 metrical variations of the surface are made, resistance calculations valid 

 for an ideal fluid in many cases do not agree with the facts even as to sign. 

 Thus, the classical problem of determining the optimum longitudinal position 

 of the center of buoyancy Involves the consideration of viscous effects. 



Because of our restricted theoretical knowledge, we have to rely 

 upon experimental data; but attempts have been made to deduce from such data 

 more general results. The phenomenological approach used is based mainly on 

 measuring the resistance of asymmetrical models run in both directions. The 

 most important experiments are due to Wigley. 



Some practical deductions can be obtained from some earlier work at 

 the Berlin Tank. •'■"^ By using four symmetrical models appertaining to the family 

 {2,h,6;^; T) with (^ = 0-52, O.56, O.6O, 0.64 and two asymmetrical models 

 4= 0.56, 0.60 run in both directions {^^ = <^ = 0.04), the following deductions 

 were obtained: 



a. For the fuller model <z) = O.6O the shifting of the center of buoyancy 

 aft proved to be advantageous except for F > 0.4. 



b. For the finer model <z) = O.56 the aftward movement of the LCB gave 

 a model worse than the symmetrical basic model . 



c. Thus the Influence "on the resistance of the shifting of the LCB for 

 given Proude numbers depends on the form (equation) of the original surface 

 and the method of moving the LCB (equation of odd members added). As a rule 

 resistance properties of asymmetrical ships cannot be described by the posi- 

 tion of LCB (or the difference <^„ ~ '^h) alone. 



