Ship Maneuvering in Deep and Confined Waters 



Time is scaled as square root of length. Human response 

 time may be "scaled" within certain limits only. The 4j(6)- diagrams 

 of Fig. 2 demonstrate results of simulated steering of the tanker 

 prototype sdready referred to, as well as of her fictive models of 

 four different sizes. (Note that curves run anti- clockwise with time.) 

 The smallest "model" is in scale 1:100, i.e. it has a length of 3.1 m, 

 which should permit free-sailing tests in several in-door facilities. 

 The two helmsmen, which each one seem to represent one kind of 

 steering philosophy and who were allowed a short training period in 

 each case, both failed to maintain the proper control of the two 

 smaller "models. " 



The control of a ship on a straight course is governed mainly 

 by the effective inertia, by the yaw damping moment, by the rudder 

 force available, and by the time this force is applied. A mathemati- 

 cal model intended for studies of manual or automatic steering may 

 therefore be quite simple; in contrast to the test basin model it may 

 include proper corrections for the large scale effects often present 

 in rudder force data. (Cf. Section VII.) 



Figure 3 repeats the original simulator ij;(6)-curves from 

 real-time straight running, recorded by use of the "complete" 

 mathematical model, but it also presents results from tests with a 

 linear model as well as with a model, which contains no other hydro- 

 dynamic contributions than those in lateral added inertias and rudder 

 forces. No major differences were experienced in using these three 

 models of increasing simplicity. 



On Manoeuvring in Confined Waters 



Manoeuvring, involving yaw rates and drift velocities, which 

 are not small compared to the forward speed, demands a mathemati- 

 cal model of considerable complexity. A useful presentation of non- 

 linear characteristics has been given by Mandel , [ 2], One particular 

 non-linear model designed to include manoeuvres in confined waters 

 will be more fully discussed in subsequent Sections of this paper. 



The average depth of the oceans is some 3800 m. But ocean 

 voyages start and terminate at ports behind the shallow waters of the 

 inner continental shelves. Additional confinements are presented 

 by many of the important gateways of world trading, such as the 

 Straits of Dover and Malacca, the Panama Canal, and the Suez Canal 

 now closed. 



The maximum draughts of "large" ships have always been 

 limited by bottom depths of docks and harbours, and of canals and 

 canal locks. With few exceptions the requirements placed on under- 

 keel clearances — by ship owners or by authorities — have been 

 chosen solely with a view to prevent actual ship grounding or exces- 

 sive canal bed erosions. Thus the Suez Canal Authorities accepted 



811 



