Tuck and Taylor 



2 



k = Acq tanh qoh (4.11) 



and this pole must be avoided by passing beneath it in order that the 

 waves are behind the ship. 



Thus the real part of A (k) may be written as a Cauchy 



I 



principal value integral, which can be evaluated by standard numeri- 

 cal quadratures , whereas the imaginary pa 

 from the residue at the pole, and we have 



cal quadratures , whereas the imaginary part of A (k) can be obtained 



TT/C q^ dq^ 



rz. 7^ k dk ' 



Kh < 1 



JA*(k) = <; (4.12) 



0, /Ch > 1. 



Once A is determined, g(x) follows by further numerical quad- 

 ratures from (4.9), if actual numerical values of g(x) are required. 



However, our main aim is to find the forces on the ship, 

 which follow from g(x) via the pressure distribution, given by 



p(x,y,z) = p^(x,y,z) - pUg'(x) (4.13) 



where p (x,y,z) is the pressure on a double body in an infinite 

 fluid. Hence the vertical force is 



F3 = F^- pU \ dx B(x)g'(x) 

 ^ -i 



4 IT J.co 



= Ff-|^\ dkk2s*(k) B*(k) A*(k), (4.14) 



and the trim moment is 



pi 

 F5 = F^ +pU \ dxxB(x)g'(x) 



2 rt^ 



d p"^ 



= Ff +P^ \ dkkV(k) xB*(k) A*(k), (4.15) 



where F^, F^ are the corresponding quantities for the "subnnerged" 

 half of the infinite fluid double body, B(x) is again the waterplane 



64 2 



