Ship Maneuvering in Deep and Confined Waters 



ship steering transfer function is obscured by the viscous frequency- 

 dependence, (Cf. Section IX.) 



The steady motion of a full form may also be accompanied 

 by a non- steady separation and shedding of vortices, which will 

 violate captive measurements , or it will modify the force field and 

 be a cause of unpredictable scale effects. In Ref. [44] Nomoto 

 drew the attention to an "unusual" kind of separation, which had 

 been observed not on the leeward but on the outer side of the after- 

 body of turning models. (Later on he reported the same phenomenon 

 taking place on full scale ships combining high block coefficients and 

 low length-to-beam ratios.) This separation may be responsible 

 for an almost constant increase in yaw damping moment — see 

 diagram in Fig. 14a — and so indirectly for the small- rate non- 

 linearity displayed in the yaw- rate- versus -helm diagram from spiral 

 tests with these hulls. 



Unsymmetrical separation may also take place on a hull 

 moving along a straight line with a small angle of drift. If transverse 

 force and moment both are mainly linear functions of angle of drift 

 the centre of pressure will remain in a forward position, only 

 gradually moving aft with onset of viscous crossflow. A three- 

 dimensional separation, which suddenly develops on one side of the 

 hull, may explain the strange behaviour of the centre-of-pressure 

 curve of a tanker model tested by Bottomley [45] , here reproduced 

 in Fig. 14b. New tests with modern hulls sometimes indicate 

 similar trends. 



It is fully possible to approximate these effects by a small - 

 value non-linearity term in the mathematical model, which may 

 then be used, say, for the prediction of a ship behaviour which is 

 extremely sensitive to winds of varying directions [46]; if the sepa- 

 ration is peculiar to the model only this prediction is meaningless , 

 however. 



Large-Value Non-Linearities in Lateral Forces 



The predominant non-linearities present in the lateral forces 

 are due to viscous cross-flow resistances, and they can only be 

 established by experimental procedures. It will be assumed that 

 the empirical relationships may be expressed by finite polynomials, 

 derived by curve -fitting, and that these same relationships therefore 

 also may be fully defined by a finite number of terms in the Taylor 

 expansions. This convention motivates the use of appropriate 

 numerical factors in front of the derivatives within the hydrodynamic 

 coefficients. 



From pure athwartship towing it is possible to define a Y- 

 force -Cq • LT • v , the sign of which is governed by |v|/v. Thus 

 Y(v2, |v|/v) = i\^(,^,/^)* v2 |v|/v, or, for convenience, iY,^,^ iv|v. 



845 



