Some Hydrodynamic Aspects of Ship Maneuverability 



my direction at the Paris Tank in 1949-50, is included a photograph of a paint 

 test. This photograph shows that in turning condition, a concentrated bound 

 vortex may exist near the bow and that a free vortex originates as a conse- 

 quence. The same phenomenon may occur in yawed condition but the field of 

 velocities induced would be different. 



Moreover, when a ship is turning, the local angle of attack varies along the 

 length of the ship. The transverse flow, when the ship is turning to port comes 

 from port on the forebody and from starboard amidship and on the aft body. 

 When the radius of gyration is small, there are string eddies on the port side 

 near the stern. 



In spite of the above considerations, I wish to state that I am in agreement 

 with Dr. Newman's opinion. But the reasons why I agree with him may be more 

 pragmatic. 



The phenomena being very intricate, we have to test various mathematical 

 models to examine the predictions to which they lead, and to choose accordingly 

 the model that we will finally adopt for the class of ships that we have under 

 consideration. In particular, the structure of the expressions of the force and 

 moment acting on the ship is likely to vary from one class of ship to another; in 

 addition, the order of magnitude of the numerical values of the coefficients are 

 bound to change substantially. Generally speaking, the flow can be idealized, 

 but in a manner specific of each type of ship. 



The ship herself must not be too much idealized if we want to obtain suffi- 

 ciently accurate predictions for practical purposes. It is well known, for in- 

 stance that the behavior of a ship is very sensitive to differences in the block 

 coefficient, the angle of entrance, the extent of the deadwood, and so on. 



The controversy that Dr. Newman mentions in page 213 of his paper is fa- 

 miliar to me. This controversy originates in the fact that, if the force and mo- 

 ment are considered as nonanalytic, the use of Taylor series expansions is not 

 permissible. But limited expansions are polynomial, and it is always possible 

 to use polynomial expressions provided the functions, which are to be approxi- 

 mated, are continuous. Another controversy concerns the low aspect ratio wing 

 theory. This theory is useful, but it is necessary that it take into account the 

 effect of the angular velocity. 



In my opinion the real problem is to represent the force and moment by ex- 

 pressions which contain as few terms as possible, while ensuring the smallest 

 discrepancy with respect to the results of the experiments, and which lead to 

 the best understanding of the effects of the shape of the hull and of the appendages 

 on the behavior of the maneuvering ship. For instance, Casal's thesis seems 

 particularly interesting because it helps to understand why, in yawed condition, 

 the force is acting near the bow and even ahead of the bow while, in turning con- 

 dition, it is acting behind the middle transverse section. For analogous reasons, 

 the dimensionless expressions of the force and moment must be able to account 

 for their rapid variation when l 2R, that is the reduced angular velocity, is in 

 the vicinity of the zero value. 



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