Mooring and Positioning of Vehicles in a Seaway 



Z^ = - N,z + N,^0 , (7) 



where 



2 nil 

 \ 



and 



Nz = Pco(^)'y^''A,'de, (8) 



N.0 = 9^{^^^ 'A'ede . (9) 



Similar treatments yield the lateral damping force, pitch damping 

 moment, etc. 



In the initial discussion of damping, emphasis was placed upon 

 energy dissipation due to wave generation. Actually, viscous effects 

 also manifest themselves and contribute to dcimping. The contribu- 

 tion of the viscous damping term is quite negligible* for most motions, 

 with the possible exception of roll. Roll damping due to wave genera- 

 tion is often small for most normal ships and viscous effects (or 

 other drag mechanisms, such as eddy-making) assume greater 

 importance, especially if the ship is fitted with bilge keels. In that 

 case, the roll damping is often of nonlinear form, and an approxi- 

 mation is used to determine some equivalent linear representation. 

 Knowledge obtained from model experiments [ 7] was used to deter- 

 mine the value of roll damping used in treating the illustrative ship 

 case in this paper. 



The hydrostatic restoring forces and moments are, as the 

 name implies, due to buoyancy effects arising from static displace- 

 ments. The only displacements that will result in hydrostatic 

 restoring effects are heave, pitch and roll. On the basis of linear 

 theory, the local hydrostatic vertical force change due to vertical 

 displacements is 



^=- pgB*(z - ee), (10) 



where the ship is assumed to be almost wall- sided near the inter- 

 section with the free surface, and the effective buoyancy change 

 comes from the total immersion. Similarly, the hydrostatic 

 restoring pitch moment is 



dMh _ t dZh i^A\ 



1025 



