ABSTRACT 



The force and moment on a body placed in an arbitrary steady potential 

 flow were found by Lagally when the body can be represented by a system of 

 singularities interior to the surface of the body. They were found to be simple 

 functions of the strengths of the singularities and the character of the undis- 

 turbed stream in the neighborhood of the singularities. In the present paper, - 

 this result is rederived and extended to the case in which the body is subject 

 to an arbitrary non-steady motion (including rotation) in a stream which is chang- 

 ing with time. The force and moment are found to be the "Lagally force and 

 mom.ent" plus additional components. These additional components are given 

 for the force as simple functions of the singularities used in establishing the 

 boundary condition and of the motion of the body, but an integration over the sur- 

 face of the body is required for the moment. 



INTRODUCTION 



The determination of the force and moment acting on a body placed in a non-uniform po- 

 tential flow of an ideal fluid has received considerable attention, the problem being of consid- 

 erable importance in both aerodynamic and hydrodynamic applications. 



There have been two essentially different approaches to the question. In the first, the 

 flow is assumed to be only slightly non-uniform, and the dynamic action is found in terms of 

 virtual mass. Thus the problem is reduced to the case of motion in a uniform stream. Lord 

 Kelvin^ solved the important special case of the sphere as early as 1873, but G.I. Taylor^'^ 

 was the first to make an extensive study of arbitrary bodies. His analysis, which applied to a 

 steady state system only, included some discussion of the moment. ToUmien developed a 

 solution for the force and moment in terms of the "Kelvin impulses" and extended the discus- 

 sion of force to include the case of uniform translation in a steady non-uniform stream.'* These 

 results have been rederived by Pistolesi ^ who found an error in ToUmien's formula for the 

 moment. 



The second approach considers the boundary condition at the surface of the body to be 

 established by means of a system of singularities within the body. The force and moment are 

 then found in terms of the strengths of the singularities and the character of the basic stream 

 in the neighborhood of the singularities. Hence, this method is not restricted to slightly non- 

 uniform streamSjbut is limited to those cases in which a suitable system of singularities can 

 be found which simulates the presence of the body. This is the approach used in the present 

 paper. 



References are listed on page 48. 



