Davis and Oates 



The vertical component w^ has a phase angle \ = 90 ° relative to the wave 

 amplitude; the horizontal component u^ has a phase angle 0^^ = ° and is in 

 phase with the waves. 



When there is more than one foil then there will be a phase lag between the 

 forward and rear foil units. If we denote the forward and rear foils by the sub- 

 scripts (f) and (r) respectively and the phase lag is d) then we have the general 

 expression based on 



^ 27tL ,. 



<v - — - — radians , 



A. 



where L = distance between front and rear foils (feet), 



cos (a)t-<I)) = cos ojt cos <^ + sin cot sin $ (10) 



oj sin (wt - <!)) = CO sin cot cos O - oj cos o)t sin O . (H) 



The equations for the wave and the orbital velocity components at the front 

 and rear foils can now be written, viz: 



Wave Amplitude I 



^(F) - ^o '^°^ oot (22) 



Vertical Component of Orbital Velocity 



( i" ) 



(R) 



+ ajZ^ sin (f^t - O.jj. ) = +^^(2^^ sin cot cos '^'cr-, - Z^ cos oot sin <I'/rn) • (25) 



Horizontal Component of Orbital Velocity 



+ <ijZ cos cot (26) 



'(F) 



'(R) 



wZ^ cos ('^t-O^gp = &;(Z^ cos a)t cos <I),j^, + Z^sinwt sin <I'crn) • (27) 



The computer block diagram for simulating the above seaway is given in 

 Fig. 7 for a front foil and a main foil, with the main foil split into three ele- 

 ments, left foil, centre foil, and right foil, denoted by the subscripts (l), (c), 

 and (r) respectively. 



632 



