39 



Let us study the S(y) function for a given polynomial, say (2,4,6; 

 ^;t) Figure 24 and (3,4,6;^;t) Figure 25; the parameter t = t = const. 

 Curves for different prismatics intersect at fixed points; the abscissas of 

 these points are given by zero values of the curves A^S(y), and are constants 

 for a basic family; the ordinates vary with varying t, but are constants for 

 t = t = const. 







When all maxima of an S(y) curve coincide with such fixed points, we 

 obviously obtain a curve with small amplitudes and good resistance qualities 

 over the whole range of Froude numbers. When such a coincidence occurs only 

 for one or several points the particular curve may be advantageous over a lim- 

 ited speed range. For t = const and a given Froude number F there is a value 

 of the prismatic which corresponds to a minimum resistance; a further reduc- 

 tion of <l> means a deterioration of the resistance properties. This agrees 

 with experiments. Prom Taylor's Standard Series the prismatic of least spe- 

 cific resistance appears to be something like 0-52 for moderate Froude numbers 

 (second hump); following theory for hollow forms with t = 0, the minimum is 

 somewhat lower as can be easily inferred from the S[y) curves. 



We investigate now the influence of the curvature parameter K on the 

 resistance. We compare for this purpose the family (2,4,6;^;!) with the re- 

 lated (2,3,4;0;1), keeping for simplicity the tangent value t constant and 

 equal to one. The curvature at the midsection is K = -2a2 ■ 



77 = (2, 3, 4; 0.6; 1) = (2, 4, 6; 0.6; 1 ) =. 1 - 1 .51^ + 0.5?* [22] 



is common to both families. If we let0<O.6,it can be shown that for equal val- 

 ues of 4> the coefficient a is higher in (2,3,4) than in (2,4,6), hence the 

 form (2,3,4,) has, ceteris paribus , a higher curvature at the midsection. 

 When ^>0.6, the reverse holds. 



Take the curves corresponding to ^ = O.56; it is seen from Figure 

 13 that they differ only slightly. However, the functions S(y) or S^(y) dif- 

 fer very much in the region n > y > 8,and we must expect that the resistance 

 associated with (2,4,6; O.56; 1) will be much lower over an extended range of 

 Froude numbers . 



A crucial test with rather wide consequences therefore appeared to 

 be possible; it was performed at the Berlin Tank-'-"'' and yielded a beautiful 

 agreement between calculation and experiment, see Figure l4. Model 1370 was 

 developed from the sectional-area curve (2,4,6; O.56; 1) and Model 1337 (2,3, 

 4; 0.56; 1). Unfortunately, because of a widely spread but ill advised thrift, 

 the original readings have not been published, but the author testifies that 

 every effort was made to obtain reliable results. Furthermore, the results 



