Pavdoussis 



two-dimensional, (b) boundary-layer effects, and (c) the use of fins. 

 The tow-rope pull P Is equal to the tension in the cylinder at x = 0, 

 plus the form drag at the nose. I.e. 



P = iMU^c, + Cg + c^l./D). 



Substituting P Into the above equations and assuming y and v to 

 be constant over the Intervals of Integration, we obtain 



[El|^.f,Mu(|^.u|^) 



+ A Mu'lc^ ^ + c, + Cj) ^ + (m + f,M)x, ^\_^ =0, (11) 



where 



1 r^' 1 r'' 



X = -^ \ S(x) dx and x„ = -5 \ S(x) dx. 



Here M = pS, and S and D are quantities pertaining to the cylindri- 

 cal part of the body. 



In the above the forces arising from form drag were taken to 

 be In the x-dlrectlon. If they are taJsen to be along the cylinder, 

 then terms ic,MU^(8y/8x) and icgMU^ay/Sx) should be added to 

 Eqs. (11) and (12), respectively. 



The other two boundary conditions are obtained by making the 

 reasonable assumption that there are no bending moments at x = 

 and X = L , or 



[|^]..o=[I^L=<'- <'^' 



The adveuitages In this method of analysis. In which the shape 

 characteristics of nose and tall were absorbed in the two parameters 

 f , and fg, are obvious. The disadvantages are equally obvious: al- 

 though we can estimate f , and fg, we cannot easily calculate them. 



988 



