Recent Progress in the Calculation of Potential Flows 



the bearing, and this inability to penetrate leads to the condition Bqj/Bn = o over 

 the surface. Here again we find a classical Neumann problem. Roger Bourke 

 studied such a bearing at Stanford University for his Ph.D. dissertation (13). It 

 is a body of revolution and is shown in Fig. 18. By using the methods of this 

 paper he first calculated the relation between the current and the displacement. 

 A comparison of theory and experiment is included in Fig. 18. Agreement is 

 within experimental accuracy. He then studied the stability problem by analyz- 

 ing other displacements (rotational and sideways) and obtained the same good 

 agreement between theory and experiment. 



2.8 r 



■/)2.6 



Q. 



i2,2 

 a. 



"20 



cr 

 O 



^ 1.8 



Q 

 Z 



S 16 



THEORY 

 EXPERIMENTAI 



TOP CAPACITOR- 



INPUT 

 CAPACITOR 



/ 



BOTTOM CAPACITOR- 



01 02 03 04 



GAP'-CM 



Fig. 18 - A superconducting bearing suspended 

 in a magnetic field. The graph on the left com- 

 pares theory and experiment for displacement 

 in the axial direction. - , 



REFERENCES 



1. Hess, J. L., and Smith, A. M. O., "Calculation of Potential Flows About 

 Arbitrary Bodies," Progress in the Aeronautical Sciences, Vol. 8, New 

 York: Pergamon Press, 1966 



2. Kellogg, O. D., "Foundations of Potential Theory," New York: Ungar, 

 1929 (also available through Dover Publications, New York) 



3. Gentry, A. E., "Aerodynamic Characteristics of Arbitrary Three- 

 Dimensional Shapes at Hypersonic Speeds," Aerospace Proceedings 1966, 

 Vol. 1, New York and Washington, D. C: Spartan Books 



4. Giesing, J. P., "Nonlinear Two-Dimensional Unsteady Potential Flow with 

 Lift," J. Aircraft 5(No. 2), 135-143 (Mar. -Apr. 1968) 



361 



