INTRODUCTION 

 HISTORY 



The determination of the flow about elongated bodies of revolution 

 is of great practical and theoretical importance in aero- and hydrodynamics. 

 Such knowledge is required in connection with bodies such as airships, tor- 

 pedoes, projectiles, airplane fuselages, pitot tubes, etc. Since it is well 

 known that for a streamlined body, moving in the direction of the axis of sym- 

 metry, the actual flow is very closely approximated by the potential (inviscid) 

 flow about the body, 1 numerous attempts have been made to find a convenient 

 theoretical method for obtaining numerical solutions of the potential flow 

 problem. 



At first the problem was attacked by indirect means. In 1871 

 Rankine 2 showed how one could obtain families of bodies of revolution of known 

 potential flow, generated by placing several point sources and sinks of vari- 

 ous strengths on the axis. This method was extended and used by D.W. Taylor 3 

 in 1894 and by G. Fuhrmann 4 in 1911- The latter also constructed models of 

 the computed forms and showed that the measured distributions of the pressures 

 over them agreed very well with the computed values except for a small region 

 at the downstream ends. More recently, in 19^. the Rankine method was em- 

 ployed by Munzer and Reichardt 5 to obtain bodies with flat pressure distribu- 

 tion curves, and a further refinement of the technique was published by 

 Riegels and Brandt. Most recently the indirect method has been employed to 

 obtain bodies generated by axisymmetric source-sink distributions on circum- 

 ferences, rings, disks, and cylinders. This development, which enabled bodies 

 with much blunter noses to be generated, was initiated by Weinstein in 19^8 



8 9 



and continued by van Tuyl and by Sadowsky and Sternberg in 1 950 • 



A method of solving the direct problem, i.e., to determine the flow 

 over a given body of revolution, appears to have been first published by 

 von Karmah 10 in 1927- von Karman reduced the problem to that of solving a 

 Predholm integral equation of the first kind for the axial source-sink distri- 

 bution which would generate the given body, and solved the integral equation 

 approximately by replacing it with a set of simultaneous linear equations. 

 Although this method has limited accuracy and becomes very laborious when, for 

 greater refinement, a large number of linear equations are employed, neverthe- 

 less it is the best known and most frequently used of the direct methods. A 

 modification of the von Karman method was published by Wijngaarden 11 in 19^8. 



Beferences are listed on page 59. 



