ship Maneuvering in Deep and Confined Waters 



The mean width of the canal at the station considered is 



2W = W. - Wq = -—V- * L (10,3) 



where the parameter ratio in the right member is constant for all 

 lateral positions of the ship in the cross section. Expecially, when 

 ship on £entre-line so that "Hs = " "Hp = ^o/^' there is L/ZW = 'n^/4. 

 In fact 'n/4 alone is an acceptable approximation to the "ship 

 length-to- canal width" parameter ratio also at ship positions slightly 

 off- set from the centre-line: with y© = W/4 ti/4 over-estimates the 

 ratio L/ZW = 110/4 with less than 7 per cent. As a consequence r\ 

 and t, may be used to define an approximate blockage ratio 



BT _ 1 . B T)^ 



2Wh 



4 L T~ri 



(10.4) 



For small t, the blockage ratio is proportional to r[t,, 

 for large t, to y\ alone. 



Force Representation 



The asymmetric forces appearing in presence of a single wall 

 or in a canal are highly increased by an increase of the under-keel 

 clearance parameter, and the general model will include complex 

 couplings. If a single canal depth is studied on basis of special 

 nnodel tests it is of course possible to express the wall effect forces 

 in terms of t| and r]^ only. Although the geometry of the inflow 

 to the propeller may be modified in confined water it is assumed that 

 the control derivatives remain unchanged and that changes of rudder 

 forces are due to changes of screw loading only. 



When suitable theoretical and experimental information 

 becomes available it shall be possible to include the effects of ship 

 motions towards the wall and of the angular orientation along it. At 

 present solutions to the problem of motions oblique to a wall seem 

 to be known only for elementary singularities such as circular 

 cylinders and spheres, [97], In particular, these results give a re- 

 pulsion by the wall on the body moving toward or away from it, but, 

 again of course, an attraction on the body moving parallel to it. 



For the present investigation it shall be assumed that the 

 effects of the walls on a ship moving not to close to them will be 

 approximated by the quasi- steady asymraetry, and that the added 

 masses may be taken as those derived for low-frequency oscillations 

 in the centre of the confinement. 



In the previous Section was shown that the attraction force 



879 



