Giddings and Wermter 

 The equations are: 



1 (ojt + 1 



I<^h^ + k<^h<^ + Izh^" + k,,z + I,j,h + B,h + k^h = K^k.T^^e ^ 



where 



= pitch amplitude radians, positive bow up 



z = heave amplitude feet, positive up 



h = change in tank water level from equilibrium, feet, positive up 



l^^ = pitch inertia of ship, tank mass and "added mass" 



1^2 = heave inertia of ship, tank mass and "added mass" 



I ,. = tank mass = pk^s 



A^ = area of tank free surface 



S = f ^ds 



J..T 



H = draft to bottom of tank 



A = cross section (waterplane) area of tank at any vertical 

 location 



P = mass density of seawater 



B_^,B^,B^ = linear damping coefficients in pitch, heave and of tank water 

 motion 



^<P4,'^zz = pitch and heave "stiffnesses" excluding the tank free surface 

 effect 



kt = P^^o> "tank" stiffness 



¥ = tank volume 



't = distance of tank center of gravity from ship center of 

 gravity, positive forward 



794 



