70 



Theoretical solutions of the problem are due to Keldysh and Sedow^" 

 and Sretensky.^' Using the latter 's formula, some estimates were made of the 

 effect upon the wave resistance of different size models with a parabolic 

 waterline in rectangular tanks. ■'■'"' When properly extended, such evaluations 

 should lead to correction factors for the influence of the limited cross sec- 

 tion. Obviously the task is much more complicated than the corresponding one 

 in wind tunnels. To cover adequately the whole field we need results for: 



a. The whole useful range of Proude numbers. 



b. Different ratios h/b. 



c. Different ratios L/b. 



d. Different characteristic ship forms. 



Preliminary calculations indicate that we have to distinguish roughly between 

 deep- and shallow-water conditions (say h/b « O.5 and h/b < 0.1). For deep- 

 water tanks we distinguish between conditions far from the critical speed 

 (F, = 1) and near to it. When F, < O.7 and L/b < O.5 the limited breadth of 



tanks does not seem to influence the wave resistance appreciably, although a 



97 

 recent publication by Wigley does not support even this assumption. 



A wave resistance increase up to 15 percent has been found at high 

 Froude numbers when using a model length ratio L/b = 1 instead of L/b = 0.5- 

 Generally, an increase in resistance due to tank walls is found, when the re- 

 sistance curve for infinite liquid has a tendency to rise. At some Froude 

 numbers the resistance in the canal is smaller than in open water. Models 

 with a length L = b are liable to furnish totally "wrong" resistance results 

 at some Froude numbers when applied to deep-water conditions. 



When the intended correction factors will be available we shall be 

 able to Indicate upper limits of model sizes as given by wave phenomena, while 

 lower limits are fixed by conditions of viscous flow. 



Somewhat surprising results are found for shallow-water conditions, 

 F, = 0.9: Keeping the canal breadth b constant but doubling both the size 

 of the model (II) and the water depth (h/L = const) the calculated wave- 

 resistance coefficient of the large model was nearly twice that of the small 

 one. Figure 35- The values were 



I II 



h/b = 0.05 h^/b = 0.1 



L/b = 0.5 L/b = 1 



h/L =0.1 remaining the same in both cases. But even for Arrangement I the 

 resistance coefficient is some 55 percent higher than for the corresponding 

 case where b ->- <» and h/b ->• 0. 



