A New Appraisal of Strip Theory 

 2. This brings me to the second point I wish to raise. Why is 



U„ ; X dx , 



o J dx 



"pseudo- three-dimensional," whereas its equivalent - u^//x(x)dx is not? 

 As shown in our 1957 SNA paper, if one integrates by parts 



r -^^^ xdx = r xd^x) = - r M(x)dx 



and therefore 



e(^e) - - N(x) xdx + 2u^ /x(x) dx + u^ ^^ x dx 

 = - I N(x) X dx + Uj^ /j.(x) dx 



which is equivalent to the value of e(M^) in your "new approach," as well as to 

 Havelock's and Haskind's coefficient of in the heaving force equation. 



In the Korvin-Kroukovsky approach, the coefficient of z in tiie pitching 

 moment equation is 



E(a)^) = - TnCx) xdx + u^ f ^^^ xdx 

 = - N(x) X dx - u^ Lu(x) dx 



the second term of which is missing in your "new approach," but is present in 

 Havelock's and in Haskind's developments. Similarly, it can be shown that the 

 Korvin-KrovLkovsky coefficients B(co^) and C, after integrating by parts, become 



BC^e) = [ N(x) x^dx - 2u^ r/x(x)xdx - u„ J ^^^ x^dx 



= J N(x) x^dx 



C = pg TbCx) x^dx - j^ TnCx) xdx + uj f ^^j^ xdx 



= pg j B(x) x^ dx - u^ N(x) x dx - u^^^ I fj(x) dx . 



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