Hydrofoil Motions in a Randonn Seaway 

 U = (u^ + u) 

 P = (Po + P) 



etc. The hydrofoil reference condition will be with the axes of the craft hori- 

 zontal and with the craft travelling symmetrically in the Ox direction. Thus 



V =w =p =q =r -6 - (h - . 

 o o "^o ^o o o ^o 



^^ is usually put equal to 0. However, any arbitrary value may be assigned 

 without affecting the equations of motion. 



Making small angle approximations and substituting the perturbation varia- 

 bles in the foregoing equations we have Euler's equations for small perturba- 

 tions. 



Linear Motions and Forces 



mil = X - mg g" (16) 



m [v + (u^ + u) r] = Y + mg (17) 



m [w - (u^ + u) q] = Z + mg (18) 



Angular Motions and Moments 



Ap - Ef = L (19) 



Bq = M (20) 



Cf - Ep = N (21) 



Velocities Along Space Axes 



Xg = (u^ + u) COS - V sin \p (22) 



Yg = (u^ + u) sin \p + V cos (23) 



z^ = - (u^+ u) + w (24) 



Relations between Angular Velocities 



P = 4> (25) 



q ^ e (26) 



r - . (27) 



617 



