Prediction of Steering and Manoeuvring of Ships 



to starboard. Forward and aft OUT @ forces, resulting from positive sway- 

 velocity (or negative drift-angle) are largely functions of lift, due to circulation 

 built up around the hull, which acts at approximately the quarter-chord point, 

 i.e., close to the forward Y gauge for a 6-m model. 



Addition and subtraction of the in-phase force components according to 

 Eqs. (15) give the side force and turning moment due to sway-acceleration. The 

 slopes of straight lines used to fair these data give the terms Y^ - m and N;, - mx^, 

 again including the effects of the model mass, the elimination of which results in 

 the hydrodynamic derivatives Y^ and N^ . 



Out-of -phase force components resulting from sway velocity or drift angle 

 are generally to some extent frequency and/or amplitude dependent and are dis- 

 carded in favor of results obtained from tests made with steady drift angles in 

 the static mode. 



Integration and Interpretation of Nonlinear Forces 



It has been assumed in the foregoing that the periodic forces measured in 

 "pure yaw" and "pure &way" tests are proportional to the motions. This is, 

 however, not a necessary condition for the use of the integration technique de- 

 scribed but was introduced to simplify the discussion. When the forces are 

 related to the motions in a nonlinear fashion, the same principles can be used 

 to obtain the nonlinear hydrodynamic coefficients. 



Suppose, for instance, that for a particular hull the hydrodynamic force or 

 moment resulting from yaw velocity is of the character shown in the top of Fig. 18. 



Fig. 18 - Nonlinear force 

 response to steady- state 

 yawing motion (top) and to 

 sinusoidal yawing motion 

 (bottom) 



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