THEORY OF UNSTEADY 

 PROPELLER FORCES 



Ryusuke Yamazaki 



, ,^ . , Kyushu University 

 ..... Fukuoka, Japan 



ABSTRACT 



As the simplest example of the problem of unsteady propeller forces, a 

 treatment is presented for a ship or a submarine with a single pro- 

 peller and a single rudder being moved straight with a constant speed 

 in unrestricted still water by rotating the propeller with a constant 

 angular velocity. The velocity field is represented hydrodynamically 

 by a potential due to distributions of sources, doublets, and vortex sys- 

 tems so as to satisfy the boundary conditions on the hull, the rudder, 

 and the propeller in which mutual interactions among these three parts 

 are generally taken into account. The unsteady propeller forces are 

 subdivided into bearing forces, surface forces, and impulse forces, for 

 which general mathematical expressions are obtained. Finally numerical 

 examples are presented for the effects of propeller forms on the bearing 

 forces. 



INTRODUCTION - . 



When a ship is being moved straight with an almost constant speed on or 

 under still water by rotating the propeller steadily, the flow surrounding it fluc- 

 tuates with respect to time, since the propeller with a finite number of blades is 

 rotating in the nonuniform wake flow behind the hull. The unsteady forces and 

 moments of water acting on the hull, rudder, and propeller caused by the rotat- 

 ing propeller are called unsteady propeller forces. The forces can be divided 

 into two parts: one is the mean value of the forces with respect to time and is 

 connected mainly with the propulsion characteristics of the ship, and the other 

 is the fluctuating part of the forces whose magnitudes and periods are related 

 mainly to the vibration of the ship. These unsteady propeller forces are trans- 

 mitted to the ship hull either directly through a shaft bearing of the propeller or 

 indirectly through surfaces of che hull, rudder, etc., in the form of water pres- 

 sure. The former are called bearing forces, and the latter are called surface 

 forces. In particular the forces and moments acting on bodies such as a rudder 

 placed in the fluctuating propeller race may be called impulse forces (1). In the 

 existing papers about the unsteady propeller theories (2-6) some examples of 

 the bearing forces were calculated for given propellers in given nonuniform 

 flows without taking into account the interactions with the hull and rudder. How- 

 ever, the surface forces on the hull were calculated for the case where the ve- 

 locity field generated by the propeller replaced with simplified vortex lines 

 satisfied the boundary condition on the hull surface (7). Accordingly, both forces 



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