Distribution of Hydrodynamic Forces on a Shipmodel 



Fh ^ - ( J ^'^A 'K - (I N'dx^ z^ - PgA^z^ (6) 



where A^ is the waterplane area. The moment produced by the force on the 

 strip is given by 



K = - ''Fh = (^^') '^o + (n'x - Vx ^) z„ + 2pgxyz^ . (7) 



Because 



f X ^ dx = -m , 

 J dx 



L 



we find for the whole ship 



Mjj = M xm'dxj Zq + (J N'xdx + VmJ z^ + PgS^z^ (8) 



where S^ is the statical moment of the waterplane area. 



For a pitching ship the vertical speed of the strip at x with regard to the 

 water will be - x(9 + Vi9, and the acceleration is -•^e^■ 2Vi9. The vertical force on 

 the strip will be 



Fp = - -^ m'C-x^ + V5) - N'(-x0 + V^) - 2/Ogyx5 , 



or 



Fp = m'x^ + fN'x-2Vm' -xV ^j \ hpgyx + V^ ^ -N'v)^. (9) 



The total hydromechanical force on the pitching ship will be 



Fp = [ I m'xdxj ^ + I j N'xdx-VmJ^ + ( p g S^ - V | N'dx J(9. (10) 



The moment produced by the force on the strip is given by 



Mp = -xFp = -m'x2^ - fN'x2-2Vm'x-x2v ^)^- f2pgyx2+ V^x ^ - N'Vx)^. (H) 



The total moment on the pitching ship will be 



■ I J m'x^dxj^ - I f N'x^dx p - (pgl^- V^m-vJ N'xdx'j^ , (12) 



239 



Mp 



