The e x i s t i n g propeller theories are valid for an i n c o m p r e s s i b l e inviscid fluids range. In t h e p r e s e n t paper, t h e k n o w n G 1 a u e r t's propeller theories are t r a n s f e r r e d into t h e c o m p r e s s i b l e inviscid fluids region. All t h e disc o n t i n u i t y p h e n o m e n a are e x c l u d e d f r o m the considerations. F o u r element a r y theories will be discussed: axial m o m e n t u m -, general m o m e n t u m -, i m p r o v e d general m o m e n t u m -, a n d v o r t e x theory. The a p p l i c a t i o n of some a p p r o x i m a t e
m e t h o d s of solution, like P i s t o 1 e s i's m e t h o d , to compressible range will be s h o w n . In a first a p p r o x i m a t i o n , B e t z's t h e o r y of propellers of h i g h e s t efficiency m a y be applied to propellers m o v i n g in a c o m p r e s s i b l e m e d i u m , w i t h t h e a s s u m p t i o n t h a t t h e c o n d i t i o n s existing in t h e propeller's w a k e are invariable a n d t h a t t h e c o m p r e s s i b i l i t y p h e n o m e n a are r e s t r i c t e d to t h e close n e i g h b o u r h o o d of the propeller w i t h t h e d e n s i t y in t h e propeller's plane differing f r o m t h a t one in the wake. There are indications, however, t h a t B e t z's t h e o r e m should be revised for compressible r a n g e since t h e F r o u d e -F i n s t e r w a l d e r t h e o r e m , on w h i c h t h e p r e v i o u s one is based, breaks d o w n for compressible fluids as F r a n k 1 h a d shown,
Introduclion. The existing G 1 a u e r t's propeller theories, valid for incompressible inviscid fluids, were transferred into the compressible inviscid fluids region 1). All of the discontinuity phenomena are excluded from the considerations. Four elementary theories will be discussed: axial momentum theory, general momentum theory, improved general momentum theory, and vortex theory. In general, one may distinguish three parameters characterising the work of a propeller: density of the air in the plane of the propeller disc, aerodynamic coefficients of a propeller blade element and the inflow *) The paper is based upon an investigation which was carried out by the author in the University of Illinois for the Aeroproducts Division of General Motor Company, under the sponsorship of the Air Material Command, U. S. Air Force.