Norrbin 



a nominal blockage ratio of 1:4 for ships in northbound transit at a 

 maximum speed of 13 kiloinetres per hour, corresponding to a mean 

 back-flow velocity of some 1.5 m/s . 



Today new limits are imposed by the depths of ocean sills as 

 well as by the depths and widths of open sea port approaches. The 

 potential dangers of a large oil tanker navigating in such waters 

 under, say, the influence of an unexpected change of cross current 

 must not be denied. Whatever nautical experience the master or 

 pilot may possess , he is still in need of actual data and of means to 

 convert this information to helm and engine orders. Automatic 

 systems on a predictor basis are likely to appear in a near future, [ 3] . 



In the planning for dredged entrance channels and harbour 

 turning basins the maneuvering properties of the ships must no longer 

 be overlooked. The upper drawing of Fig. 4, reproduced from 

 Ref. [ 4] , shows part of the plan view and a typical section of the 

 buoyed channel for 200 000 tdw tankers unloading at a new oil ter- 

 minal. Before entering the 90° starboard turn the speed is brought 

 down to less than 2 knots, and the tanker then proceeds under slow 

 acceleration by own power. Braking tugs are used on quarters, 

 and forward tugs assist in the S-bend. The lower diagram of Fig. 4 

 is taken from SSPA records of yaw rates in the passage; the initial 

 curvature corresponds to r' = 0»175, and the maximum rate of 

 change of angular velocity is of the order of 0.0005 °/s at a forward 

 speed of 2.3 knots. 



In general the lateral forces on the ship will all increase as 

 water depth turns smaller, and the dynamical stability is also likely 

 to increase. From extensive measurements by Fujino it appears, 

 however, that the picture is not so simple, and that for some ships 

 there may be a "dangerous" range of depth-to-draught ratios, in which 

 the dynamic stability gets lost, [5]. 



Recent model tests indicate that the large-value non-linearities, 

 such as the lateral cross-flow drag at high values of drift, do increase 

 even more than the linear contributions governing the inherent stability 

 conditions. Whereas these non-linearities may be omitted in the 

 mathematical model of the ship in a canal the bank effects here intro- 

 duce destabilizing forces, that are again highly non-linear. 



The effects of well-known forces experienced by a ship sailing 

 parallel to the bank of a canal are clearly apparent in the record from 

 a Suez Canal transit here reproduced in Fig. 5, [ 6] . (The positions 

 in the canal as well as the width between beach lines were derived 

 from triangulation by use of two simple sighting instruinents designed 

 for the purpose.) Upon approach to the Km 5 7 bend the ship is slightly 

 to port of the canal centre line. The pilot orders port helm for two 

 minutes, by which the ship is pushed away from the near bank and the 

 desired port turn is also initiated. Back on centre line the ship 

 mainly turns with the caned. In spite of a starboard checking rudder 



814 



