A NUMBER of approaches to the calculation of rotor downwash have already been discussed. Broadly spsaking, the methods of Castles and DeLeeuw and Squire and Mangler are the same. In both methods the downwash at the rotor disk is assumed to be perpetrated in a helical downwash sheet which, as the slipstream, extends below the rotor to infinity. The downwash in the disk due to the bound vortices, and the additional downwash in the disk which is induced by the helical sheets in the slipstream (Castles and DeLeeuw substitute downwash rings for helices, in the interest of mathematical simplicity) is calculated, on the assumption of an infinite number of lightly loaded blades. The final results of Castles and DeLeeuw on the one hand, and Squire and Mangier on the other, are in very wide disagresment. This disagreement is principally due to the fact that, whereas the first investigation assumes constant circulation along the blade (ideal twist and taper), Mangier and Squire assume a ‘practical’ variation of the form likely to be encountered on an untwisted untapered blade. We conclude that the radial distribution of lift on a helicopter blade will have a profound effect on the downwash pattern: which in turn will affect the calculated lift.
Payne, P. (1957), "Helicopter Longitudinal Stability: Some Contributions to Existing Theory", Aircraft Engineering and Aerospace Technology, Vol. 29 No. 5, pp. 143-150. https://doi.org/10.1108/eb032826Download as .RIS
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