Beck and Tuck 
APPENDIX II 
COMPUTATION PROCEDURE FOR VERTICAL PLANE INTEGRALS 
The task of evaluating the integrals (3.2) is simplified by 
re-casting them in a Fourier transform manner, Thus 
co 
ipa di * oT et 
= = Ate A AI, 1 
0 
where 
a Coy = if dxA.( x ) spe : (AII. 2) 
a bar denotes a complex conjugate, and we adopt the convention that 
Lory (hi She V heen = iq/ rd? - 1 . The result (AII.1) follows from 
the integrals 
1 
2 dA 
SCZ) 5, ————- _ cos Az 
: i : Ns, Ge 
and 
co 
Z. 
Yee? \= 2 a4 Gcosi Zz , 
0 T nN = t 
1 
mithaE hepa re 
0 0 0 
The Fourier transforms AS (which are incidentally also re- 
quired for the Froude-Krylov forces Tjg in (3.1) ) are obtained by 
a modification of Filon's quadrature (Tuck, 1967). Data concerning 
A;(x) (i.e. beam B(x) and section area S(x)) is supplied at given 
(not necessarily equally spaced) values of x. Data actually used was 
read directly from the table for the Series 60, block 0.80 parent 
form (Todd, 1963) at 25 stations. The Filon quadrature maintains 
uniform accuracy as the parameter \ increases, 
The integration with respect to \ in (AII.1) is carried out 
separately for 0<A < 1 and 1<) <o. In both cases there isa 
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