Hydrofoil Motions in a Random Seaway 



V'a = U'(l+u-uj 



( 1 ( U - Ll ) 



2 » - 2 2 ^ ^ 



U rx(l + u-u) +U a,(l+u-u). 



(47) 



For small perturbations in u and u^ the u^ terms can be neglected thus 



Thus 



V, a = V^ % [1+2(G-G^)] + U„ ^dd+^-^w) 



a^[l+ 2(u- uj] + a^(l + G- uj. 



(48) 

 (49) 



In the drag terms there is the expression V- a^. This becomes 



V. a^ = U„ Cl + u-u^)' 



(1 + u-uJ. 



Sideslip angles are obtained in a similar manner to give 



/3j= [v+xi/j-z0-v 



w w^ 



(50) 



for fixed speed and 



/^total - /^dCl + U-Gj 



for varying speed. 



Only the expression for thrust remains to be derived before the final equa- 

 tions can be written. Two effects need to be considered: (1) the effect of 

 changes in throttle setting and (2) the effect of changes in water velocity at the 

 propeller. 



Let k be the increment of thrust horsepower available for a given change 

 in throttle setting, then the effect of a change in throttle setting can be expressed 

 as 



T = T„(l + k) . 



(51) 



If thrust is assumed to be a function of local water velocity at the propeller 

 when the throttle setting is constant, then an expression of the following form is 

 derived. 



623 



