Pien and Strom-Tejsen 



operating condition the geometry of the free vortex sheet as well as the vorticity- 

 strength distribution on this sheet becomes almost immanageable unless drastic 

 simplification and assumptions are made. 



When the acceleration potential is used, the blade position is determined by 

 the advance velocity and the angular velocity and is independent of the blade 

 loading. Hence, the induced fluid velocity at the point under consideration is 

 proportional to the blade loading, and the principle of superposition can be ap- 

 plied. The contribution to the induced fluid velocity from each of the blade- 

 loading components can be computed separately. 



Furthermore, no limitation is needed on blade loading, blade geometry, or 

 blade motion. As long as the total time history of the blade loading and blade 

 position are known during any time period, the change in fluid velocity during 

 that time period at any point relative to the present position of the blade can be 

 computed. Therefore, the unsteady propeller problem can be dealt with in a 

 straightforward manner. 



If a propeller has several blades, or if several propellers or other lifting 

 surfaces operate simultaneously in the same vicinity, the computational work 

 may increase, but the basic concept of using an acceleration potential is the 

 same. 



In summary it can be stated that a useful tool, the exact acceleration poten- 

 tial, has been developed which greatly facilities development of a general theory 

 for marine propellers. However in this paper we shall limit ourselves to the 

 discussion of periodic propeller loading in the noncavitating condition only. 



Even though it is possible with the approach mentioned to include all the de- 

 tails of a blade element section in the formulation of our general propeller 

 theory, there is no reason to unduly complicate our problem beyond the practical 

 engineering necessity. For instance a great deal of computing time can be saved 

 if the pressure source or dipole distribution can be placed along a chord rather 

 than along a meanline. To find out whether such simplification will impair the 

 practical usefulness of our theory, information on airfoils as given in Ref . 23 

 have been studied with care. Figure 1 (taken from this reference) compares 

 theoretical and experimental pressure distributions on both sides of the foil. 

 The theoretical curves are computed on the assumption that the velocity distri- 

 bution about the foil is composed of three separate and independent components: 



1. The distribution corresponding to the velocity distribution over the basic 

 thickness form at zero angle of attack. 



2. The distribution corresponding to the load distribution of the meanline at 

 its ideal angle of attack. 



3. The distribution corresponding to the additional load distribution asso- 

 ciated with the angle of attack. 



Items 2 and 3 are computed on the basis of a thin foil theory where the aero- 

 dynamic singularities are distributed along a chord rather than along the meanline. 



94 



