Ship Maneuveving in Beep and Confined Waters 



■■•r " ■'■V ~ f _ -y" ~ v" ^°' '' 



to be a suitable measure for the degree of stability. In particular it 

 provides a good illustration when studying the effects onto the stability 

 characteristics of changes in the stability derivatives. 



Most modern large tankers are slightly unstable, or marginal 

 stable, i.e. 1^ = ly. For such ships the pivoting point position is 

 given by the simple relation 



-^ = - -^n^ (8.8) 



which may be approximated by OP/L = 0._45 + (l/3)(5pp(B/T) - 2). 

 For a typical tanker this corresponds to OP/L = 0.5. (The formula 

 in fact indicates an acceptable value also for the destroyer, about 

 0.3.) Again, the pivoting point position — or the drift angle P — 

 is a critical parameter to study when entering shallow waters. 



IX. CONFINED WATER FLOW PHENOMENA AND SOME RESULTS 

 FROM THEORY 



Mostly on Resistance 



In his notes for a third volume of "Hydrodynamics in Ship 

 Design" Saunders collected a number of citations, ranging from 

 Scott- Russel to Moody, which all illustrate the classical picture of 

 ship behaviour in confined waters as it has been derived from obser- 

 vations in full scale and in model tests, [ 73] . He also concluded that, 

 by i960, the ventures and progresses made in analytical studies of 

 ship manoeuvring in shallow waters remained scarce. One exception 

 was offered by the papers by Brard, [ 74] . The problems of inter- 

 action between meeting or passing ships, or between ships travelling 

 abreast — closely related to the bank effect problem of the single 

 ship — had been dealt with by Weinblum [ 75] , Havelock [ 76] , and 

 Silverstein [ 77] . 



Undoubtedly much more effort had by then been devoted to 

 the changes of frictioncil and wave resistance of ships in axial motion 

 in confined waters, and an important survey and contribution had 

 been given by Schuster [ 78] . 



Ocean-going ships generally move at low speeds in shallow 

 or narrow waterways, and hence the deformation of the wave system 

 is small. According to Schuster the wave resistance is not notably 

 affected by a limited depth for speeds below F^^^^ = 0.7, at which 

 speed the excentricity of the orbital ellipse corresponds to a diameter 



867 



