Hydrofoil Motions in a Random Seaway 



For example consider a point on a surface piercing foil element as shown 

 in Fig. (iv). The velocity normal to the foil element is 



Vi = ± I - (v + xi/i - z<;6 - v^ cos <?> " w^ sin fp) sin P 



+ (vi - xd - V sin c/j - w^ cos c/;-) cos I ' 1 ( f t/sec) . ( ' ' ) 



i i 



The angle of attack is 



u. 



u. 



The sideslip angle is 



toil o 



(v + xi/i-z^-v^ cos<^-w^ sin(^)sinr+(w-x5+y0+v^ sinc/)-w^ cosc^) cos F 



for small perturbations sin (p ^ and cos c^ % 1.0, U- % u^. Therefore 



(78) 



ttr . , = a 



-foil 



V X- z • ''vi\ . ^ f VI X ■ y ■ ''.. , „ 



+ Tr'P-jT-'t>-Tr) si.nr+ {rr - rr ^ + tt 4> - rr- cos i 



and 



^ V o II ~ w 



x0 = I (|- X 0j = ^ ; 



but U^ = V, therefore 



xxh - X . 



^ U ^ 



o 



Therefore 



'^foil = °-o - [~ (v + x0 - zc^ - v^) sin r + w - x^ + y0 - wj cos Pj. ('^^ 

 Thus for left- and right-hand foil elements 



629 



