24 





*(*) 



<t> 



t 



1) 



(i - | 2 ) 2 



0.533 







2) 



i - i .5 £ 2 + 0.5 I 4 



0.6 



1 



3) 



i - e 



2/3 



2 



4) 



1 - 1 4 



0.8 



4 



5) 



1 -* 6 



6/7 = 0.857 



6 



6) 



1 -* 8 



8/9 



8 



Figure 4 shows these sectional-area curves and Figures 6, 7 an ^ 

 8 the corresponding resistance coefficients as functions of y - 1/2F 2 , with 

 an additional non-equidistant scale for F. The choice of y as independent 

 variable yields an appropriate picture of the wave-resistance values at high 

 speeds. 



From the Figures 6, 7 and 8 a rather complete understanding of the 

 wave-resistance properties of various symmetrical forms can be derived. Ref- 

 erence is also made to Figure 12 and the pertaining discussions in the text. 

 The influence of the depths of immersion follows immediately from a comparison 

 of Figures 6 through 8; also, cross curves can be plotted over f/L as the 

 independent variable. Figure 11 shows this dependency for k7r\ , which is 

 the resistance function of a spheroid A*(£) = 1 -. £ 2 , with y = 1 /2F 2 as 

 parameter. We note that with increasing depth the resistance drops more 

 quickly at small than at large Froude numbers F. This is rather obvious; 

 it will be discussed later more thoroughly that the most indicative parameter 

 is the ratio f/X , where X the length of the free wave is X = 27rF 2 L. 



In Figures 9 and 1 the resistance curves for three depths of im- 

 mersion have been reduced to approximately the same maximum ordinates. This 

 rather artificial approach yields a clear idea about the shift of the last 

 hump (of its steep rise as well as of the position of its maximum) to higher 

 Froude numbers with increasing depth of immersion; it further emphasizes 

 again that the rate of decay of the wave resistance with increasing depth is 

 much higher for low Froude numbers than for high ones. 



Figure 12 represents a coefficient r = R./A a 2 /2C 2 b 2 = r /<f> . For 

 approximately constant C 2 (very elongated bodies) and given a 2 /b 2 ratio, 

 r ~ R/4, i.e., the figure yields a comparison of the resistance per unit 

 displacement for various forms. 



The discussion of the various graphs leads to the following summary 

 results: 



