Prediction of Steering and Manoeuvring of Ships 



the particular ship in question and can be used without reservation within the 

 performance envelope corresponding to the ship's rudder action, instead of only 

 being valid within a limited area. 



In designing the experimental program, emphasis should be placed on the 

 more important terms. In general, the six linear velocity-dependent terms, Y^, 

 Nv> ^T> "^Sf 3iid Ng , are predominant, while acceleration-dependent, higher-order, 

 and crosscoupling terms are of lesser influence (though many are far from negli- 

 gible) in the accurate prediction of manoeuvres. 



The larger hydrodynamic acceleration-dependent terms, Y^ and N;., are of 

 the same order of magnitude as their related mass m and inertia l^ values, 

 which effectively doubles their accuracy. Acceleration terms are, furthermore, 

 influential only in transitional manoeuvres, having no influence during steady 

 turning states. 



Sufficient experimental measurements should be made to justify the use of 

 least-squares fairing procedures. If too few points are used, the fairing ex- 

 pression may give a good fit without truly representing the trend of the actual 

 curves. 



It is generally recognized that the propeller slipstream has a considerable 

 influence on the characteristics of the rudder coefficients. In carrying out the 

 model tests, it is consequently important to scale the slipstream as accurately 

 as possible, for instance by executing the tests for a propeller rpm correspond- 

 ing to the ship propulsion-point as opposed to that of the model. When a ship 

 enters a manoeuvre, its speed will reduce and the propeller rpm will conse- 

 quently vary somewhat, the variation being dependent on the type of engine and 

 the engine control settings maintained during the manoeuvre. If it is simply 

 assumed that a constant propeller rpm is maintained during the entire ship 

 manoeuvre, the model tests carried out to measure the speed-dependent coeffi- 

 cients such as Yj^j and Y.^^^ can simply be made with the model propeller rpm 

 maintained at the value corresponding to the initial speed of the ship. It is also 

 possible, however, as will be discussed later, to compute the variations of pro- 

 peller rpm which occur as a ship reduces speed and to obtain speed-dependent 

 coefficients which correspond to specified machinery types and control settings. 



Analysis of Force Measurements 



In the last stage of the testing procedure, the forces and moments meas- 

 ured in the course of the various planar-motion mechanism tests, are analyzed 

 to yield the different hydrodynamic coefficients. The analysis consists, in prin- 

 ciple, of fairing the experimental data, using the mathematical model as the 

 approximating function, and obtaining the hydrodynamic coefficients as those 

 coefficients which give the best fit to the measured values. 



The results from a "static drift angle" test would, for example, consist of 

 measurements of X and Y forces and the N moment as functions of drift angle 

 and rudder angle. According to the mathematical model, these forces and mo- 

 ments are described by the expressions 



351 



