Sohmi-tke and Jones 



Equations of Motion for Surface -Piercing Hydrofoil Ships 



The equations of motion listed below are written with respect 

 to the axis system illustrated in Figure 10. The origin is at the C.G. 

 and in the reference condition of steady symmetric flight in calm 

 water at speed U , the x-axis is directed horizontally forward, the 

 z-axis vertically upward and the y-axis to port. The pitch angle 

 is positive for downward rotation of the bow. 



Pitch : I__0 = 2 (-L.x. cosT. - D.z. + M. cosH) - 

 Y v ii i ii i i 



T (x T sin7 - z T cos 7 ) 



(1) 



Heave : 



• • 



m (w - U 6) = 2 L. cos T. + Tsin 7 - W (2) 



O ! 1 



Surge: m(u-g0) = T cos y - 2D. (3) 



Sideslip: m (v + U r + g<*>) = - 2 L. sinr. (4) 



o 11 



Roll : I $ = 2L. (y. cos T . + z. sinT.) (5) 



X 111 11 



Yaw: I r = 2(D.Y. -L.x. sin T . + M. sini:) (6) 



z 1111 1 1 1 



where summation of lift (Lj), drag (Dj^) and pitching moment (Mj^) 

 is over all foil and strut elements, individually located at (x^, y^, z^). 

 W is all-up-weight and the line of action of thrust (T) passes through 

 (x-p , z-p ). The following sign convention is adopted for dihedral and 

 anhedral angles : 



for a port dihedral foil of angle I t^-d ' ^- = ^nxa 



for a stbd. dihedral foil of angle F , T. = T 



B DS i DS 



300 



