Prediction of Steering and Manoeuvring of Ships 



example the interaction effects between two ships passing in a shallow canal. 

 The difficulty in handling the more complex situations arises not, however, as a 

 result of the mathematical model, which even in a very general case is almost 

 ideally suited to computer solution, but rather in the determination of the hydro- 

 dynamic coefficients of the equations of motion. 



Although some of the hydrodynamic coefficients can be approximated the- 

 oretically, the only reliable way at this time of obtaining values with the accu- 

 racy needed for quantitative simulation is to conduct captive model tests. This 

 state of affairs has the merit of great flexibility. As theory progresses, more 

 and more coefficients will be obtainable by calculation and fewer experiments 

 will be necessary. In the meantime, the orderly experimental approach neces- 

 sitated by the structure of the mathematical model is conducive to systematic 

 and progressive collation of data, itself tending to make testing redundant and 

 to stimulate the creation of useful theoretical concepts. 



MATHEMATICAL MODEL 



The mathematical model at present in use at HyA for simulation of steering 

 and manoeuvring characteristics of surface ships is based on the general equa- 

 tions of motion of a rigid body moving in the horizontal plane. The detailed 

 derivation of these equations in terms of the now commonly accepted notation 

 (1,2) employed in steering and manoeuvrability work is given by Abkowitz (3). 

 For a body having freedom in surge, sway, and yaw but restricted in heave, pitch, 

 and roll* the equations, developed for a coordinate system fixed in the symmetry 

 plane of the body, are 



X = m(u - rv - XqT ^) 



Y = m(v+ ru + x^r) (1) 



N = ^ z^ ^ mX(-,(v+ ru) , 



where terms on the right side describe mass and inertial responses, and the left 

 side expresses the external hydrodynamic forces and moments acting on the 

 body (see Fig. 1). 



The hydrodynamic forces and moments are functions of body geometry, 

 motions, and orientation. For a given body with a single control surface, mov- 

 ing in unrestricted water, they may be expressed as the general functions 



f (u, V, r , u, V, r , S) , \^) 



*Rolling and heel have been neglected in the present model, since they are felt 

 to have little influence on the prediction of steering and manoeuvring charac- 

 teristics, with the possible exception of fast warships, which heel appreciably 

 in turns. 



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