Some Hydrodynamic Aspects of Ship Maneuverability 



Schiff, 1946). Recent experimental confirmation of this has been given by van 

 Leeuwen (1964) who performed oscillator tests both with and without the propel- 

 ler. This stabilizing influence can be explained in terms of the velocity field in- 

 cident upon a yawed propeller in an open stream; if the propeller and stern are 

 swung, e.g., to port, then a stabilizing (positive to starboard) force reaction will 

 be exerted by the propeller blades when they are in that part of their revolution 

 moving to port, and vice versa. But the angle of attack of the blade will be in- 

 creased by the drift angle when the blade is moving to port, and decreased when 

 it is moving to starboard (if the propeller is operating in normal ahead condi- 

 tions). Thus the net reaction on each blade over a complete cycle is a stabiliz- 

 ing force tending to return the stern to the original centerline. If the ship is 

 backing or the propeller is located so as to pull at the bow, the opposite conclu- 

 sion would result. 



Quantitative data on the performance of a propeller in an oblique flow are 

 available from the investigation of Gutsche (1964). The results show that for 

 moderate values of the advance ratio J the force vector due to the resultant of 

 the longitudinal and lateral propeller forces is rotated by approximately 50% of 

 the drift angle beyond the ship's instantaneous x axis (in other words about 50% 

 more than the rotation of the ship itself). However it is difficult to apply these 

 results directly to normal ships, and especially to single screw vessels with 

 large deadwood area, due to the interaction between the deadwood and the pro- 

 peller. The deadwood may be expected to straighten the flow into the propeller, 

 and thus the stabilizing side force due to the propeller will be reduced by a sig- 

 nificant amount. 



Similar interference phenomena must be considered in evaluating the im- 

 portant effects of the propeller slipstream on the rudder. This particular sub- 

 ject would be well suited to theoretical analysis. 



FREQUENCY EFFECTS IN GENERAL 



Most of the discussion of the previous sections pertains to steady-state hy- 

 drodynamic forces and moments acting on a yawed ship, and these can only be 

 useful if a pseudo-steady-state analysis is valid. Likewise the experimental 

 results of captive model tests generally are analyzed on the assumption that the 

 hydrodynamic force and moment depend only on the instantaneous velocity and 

 acceleration of the ship, as stated earlier, whereas strictly speaking it is nec- 

 essary to represent the force and moment as convolution integrals over the 

 previous time history of the motion. These "memory" effects of the fluid appear 

 in captive model tests as dependence of the force coefficients on the frequency 

 of oscillation. They stem both from the vorticity which is shed from the oscil- 

 lating hull and from the wave effects associated with the unsteady motion of the 

 hull at the free surface. The characteristic nondimensional frequency parameter 

 associated with the vortex wake is the reduced frequency - l v, while for surface 

 wave effects the corresponding parameter is v g. Here - is the radian fre- 

 quency of the oscillations, L is the ship length, V is the forward velocity and g 

 is the gravitational acceleration. For sufficiently small frequencies these two 

 parameters tend to zero and the pseudo- steady -state analysis is valid. 



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