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Derivation of Formulations 1 and 1A of FarassatFormulations 1 and 1A are the solutions of the Ffowcs Williams-Hawkings (FW-H) equation with surface sources only when the surface moves at subsonic speed. Both formulations have been successfully used for helicopter rotor and propeller noise prediction for many years although we now recommend using Formulation 1A for this purpose. Formulation 1 has an observer time derivative that is taken numerically, and thus, increasing execution time on a computer and reducing the accuracy of the results. After some discussion of the Green's function of the wave equation, we derive Formulation 1 which is the basis of deriving Formulation 1A. We will then show how to take this observer time derivative analytically to get Formulation 1A. We give here the most detailed derivation of these formulations. Once you see the whole derivation, you will ask yourself why you did not do it yourself!
Document ID
Acquisition Source
Langley Research Center
Document Type
Technical Memorandum (TM)
Farassat, F.
(NASA Langley Research Center Hampton, VA, United States)
Date Acquired
August 23, 2013
Publication Date
March 1, 2007
Subject Category
Report/Patent Number
Funding Number(s)
WBS: WBS 561581.02.07.07
Distribution Limits
Work of the US Gov. Public Use Permitted.
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