71 



Near the critical speed, model results must be converted cautiously 

 into full-size data valid for unlimited breadth. On the other hand, at 

 P, = 0.8 the resistance of the models discussed is practically uninfluenced 

 by the finite breadth b. 



fei= 



Figure 35 - Models in Shallow Water Basins 



Having in mind the oscillatory character of wave effects, one cannot 

 expect too much from the Equation [32]; perhaps at the best it can explain the 

 earlier rise of the resistance curve due to the finite cross section near the 

 critical speed. Some experiments made at the Hamburg Tank appear to support 

 the theoretical reasoning.^* Comstock and Hancock's paper^^ will furnish val- 

 uable checks, although it is thought that the influence of the finite cross 

 section on wave resistance has in principle a more complicated character than 

 represented by the curves on Figure l8 of the paper quoted. 



9. EXTENSION OF THEORY* 



Not all shapes of bodies of revolution can be represented by singu- 

 larities distributed over the axis. A fortiore, not all ship forms can be gen- 

 erated by sources and sinks distributed over the center plane; even the H/B 

 ratio attainable by this procedure is limited to H/B > 0.5- Furthermore, it 

 is impossible to expect that highly curved parts of the hull such as the 

 bilges can be obtained by a plane distribution. 



A first attempt to escape from this restriction was the introduction 

 of volume singularities proposed by Hogner.^" His "interpolation formula" 

 agrees in the limit of vanishing draft or vanishing beam with his integral or 

 Michell's integral, respectively. 



Havelock has criticized Hogner's attempt from theoretical considera- 

 tions;*® nevertheless, a closer agreement between calculation and experiment 

 can be expected by its use. Some numerical work based on the "interpolation 

 formula" showed results which, although not unfavorable ^ were not conclusive. 

 Unfortunately, we do not know what kind of body results from the singulari- 

 ties assumed. Another ingenious proposal was linked by Hogner;^^ who sug- 

 gested applying influence lines to resistance research. 



*ThiE chapter can be omitted by readers interested only In practical results . 



