13 



the symmetrical (even) terms 77 , //* are the main parts, obviously in 





drj^ dri 



+ 



d* 



9« 



the odd terms dy /d$, a* become the main part. 



2.3. CONNECTION BETWEEN STRENGTH OP SINGULARITIES AND BODY SHAPE 



The next consideration is to establish the dimension factors u. 

 and a . The flux through the midship section may be written as 



= C( 



a ' 



)7Tb 2 U 



[7: 



Here the coefficient C(b/a, n*) is, as indicated, a function of the elonga- 

 tion ratio b/a = D/L and of the shape of the distribution^*. For very large 

 elongations C(b/a, n*) -*1 , but for shapes and values b/a used in actual op- 

 eration C differs from one. 



A closer investigation of the coefficient C will be given elsewhere 

 by L. Landweber; for the present purpose we introduce C as a correction fac- 

 tor which improves the accuracy of Munk's or Weinig's approximate affinity 

 theorem mentioned on page 5. The dependence of C upon fi* , although apparent- 

 ly negligible within the range of presently used submarine hull forms, shows 

 some interesting features. Earlier brief investigations lead to the follow- 

 ing table for C(b/a, n*) (Reference 5). 







b/a = D/L 





1A 



1/6 



1/8 



1/10 







/»*(«) 



*d 



C(b/a,^*) 



(1 -* 2 ) 2 



0.533 



1 .172 



1.093 



1.060 



1.0^3 



1 



1 -* 2 



O.660 



1 .192 



1.092 



i .054 



1 .036 



1 



l - 3.o825| 8 + 0.165s 10 + 1.9175s 12 



0.820 



- 





1 .0124 



1.008 



1 



Prom these results we gather that C(b/a, ft*) values for normal 

 submarine shapes apparently can be estimated from the spheroid; an empirical 



