Ship Maneuvering in Deep and Confined Waters 



In most practical applications the xz -plane is a plane of 

 symmetry, so that yc = Yb - ^ ^^^ ^xy - ^' Except in a few special 

 cases, such as when dealing with hydrofoil crafts, etc. — the dis- 

 cussion of which is outside the scope of this paper — other terms 

 may be safely ignored in view of the smallness of the products of 

 inertia and the perturbation velocities involved. 



The Merchant Type Displacement Ship 



In what follows the discussion is restricted to displacement 

 ships, for which m = pVq and V ~ V„ . Forward speed is always 

 associated with a sinkage and change of trim, most obvious as 

 "squatting" in waters of finite depth, but the manoeuvring dynamics 

 will be sufficiently well described by the equations in four degrees 

 of freedom, i.e. the surge, sway, roll and yaw. Then 



mj u - rv - X r +Zgrpj= X 

 mjv + ru + x^r - z^p f = Y 



(8.4) 

 ^xxP " •'•zx^ " J^2;q{v + ru) = K - mg(Zg - z^) s in <|) 



\^r - l^^-p + mxQ(v + ru) = N 



Whereas the initial roll as well as the steady outward heel 

 may be appreciable in case of say a highspeed destroyer these 

 angles are also known to be quite insignificant in the tanker case. 

 In steady turning a heel, proportional to - (L/Rc) * FnL . may produce 

 an effective camber of the waterline flow around a fine hull, but this 

 hardly applies to merchant ship forms. 



Leaving the roll equation the present deep-water model is 

 given as in Eq. (8.5). It shall be pointed out that the derivative Y^p 

 includes the potential -flow contribution X|| and the derivative N^V 

 the potential-flow contribution Y" , In the forward speed equation 

 X" is given a value that is smaller than its ideal value equal to - Y". 



(1 -XS)u = L-' .IxJ^u^+lV -^Xj^^^ung. T"(l-t) 



+ (1 +x;;)vi + L(xj + ix;;)i%L-V • -^x^vw^lvlv^ 



865 



