ship Maneuvering in Deep and Confined Waters 



Typical estimates for tankers give as a guide value a relative 

 increase in forward resistance due to a rudder deflection of 5 

 radians AX(6)/X(u) ~ 3.5 or 5 * 5 . For small sinusoidal helm 

 angles on a straight course the quasi-stationary application gives 

 AX(5)/X(u) ~ 1.75 or 26^ , which may be compared with the relation 

 given from propulsion tests with a Mariner ship model in Japan, 

 AT(5)/T = 2 • 6a^, [ 54] . 



At propeller advance conditions removed from the steady 

 forward motion state the induced rudder drag will be given by 

 4^cc88* |c|c6 , where c = c(u,n) is the effective flow velocity 

 past the rudder and where the coefficient 4X"(.§§ is proportional 

 to the control derivative a'YccS a-nd to the ratio a./ 7^. In com- 

 puter applications a soft-type limiter will be used to simulate the 

 conditions for a stalled flow. 



The viscous lift experienced by a slender ship hull in oblique 

 translation is also accompanied by an induced drag, but the axial 

 component of the resultant force still is expected to be positive. 

 (According to the zero-aspect-ratio wing analogy the resultant force 

 will bisect the angle between the normal to the hull and the normal 

 to the flow. With increasing aspect ratios the resultants move 

 towards the normal to the flow.) The break-down of the ideal flow 

 over the stern causes a change of viscous pressure resistance, 

 however, and wave-making effects will cause a further increase of 

 forward resistance. 



These effects are here illustrated in Fig, 1 7 by results of 

 axial force measurements on the surface ship model and the sub- 

 merged double-body form otherwise described in Ref. [ 18] . From 

 an inspection of these and other surface ship model experiments it 

 Is suggested to use a term 



X(u,v) =-^X^^^;i|v|v2 (6.8) 



to represent the axial force due to lateral drift. An approximate 

 value of the derivative is given by e^uvw ~ " 200. 



851 



