■m- 



along a straight line in a uniform stream. Weinig's iii5)ortant approximation 

 holds: That the Intensity of the doublet distribution is roughly proportional 

 to the sectional-area curve of the body.*® 



We now distribute surface singularities over an elongated region of 

 a vertical plane (Figure 2). Again in a horizontal uniform stream a closed 

 surface is created, if the Integral of the strength of the source and sink 

 system, taken over the given region of the plane, is zero. One can prove that, 

 within certain limitations, the surface ordinate y^ of the resulting body at 

 a point X z , is roughly proportional to the doublet strength at the point, 

 and that the sectional area curve A(x) is approximately proportional to the 



Figure 2 - Generation of Bodies by Singularities 



integral of the doublet intensity taken over z. Under the same conditions the 

 strength of the sources and sinks is proportional to the slope of the surface 

 in the horizontal direction. 



Let the distribution over the plane be symmetrical with respect to 

 the X-axis, then the resulting body is also symmetrical with respect to the 

 xy plane. Within reasonable assumptions as to its character we can assert 

 that the maximum beam 2b is smaller than the height 2H. This is easily under- 

 stood In the limiting case of a body of revolution when the singularities are 

 concentrated on the axis; by definition 2b = 2H. By displacing an element of 

 the distribution away from the x-axis in the direction of the z-axis we ob- 

 viously increase the vertical dimension of the resulting body. 



To generate bodies characterized by 2b > 2H one must obviously dis- 

 tribute singularities in a horizontal (x,y) plane. Some quantitative rela- 

 tions may be estimated from the known results for a general ellipsoid; Figure 

 3. Assuming a > c > b, I.e., the vertical axis greater than the horizontal 

 axis in the y direction, it has been proved that the ellipsoid is generated by 

 a doublet system M(x,z), which is distributed over the focal ellipse In the 

 xz plane 



- b' 



= 1 



[7] 



