Further development of 3-D rotary-wing acoustic directivity using a spherical harmonic representation

Date of Award


Degree Name

Ph.D. in Mechanical Engineering


Department of Mechanical and Aerospace Engineering


Advisor: Reza Kashani


Mathematical models of 3-D acoustic directivity for helicopters have been used to describe the acoustic source characteristics used in acoustic propagation models. Spherical harmonics have been applied to this problem by a group of researchers at the Swiss Federal Laboratory (EMPA). Analysis of their techniques has yielded a number of potential enhancements that could be performed on the basis model. This dissertation details further development of the spherical harmonic techniques for 3-D acoustic directivity for helicopters. These further developments include methods for removal of contaminated data, methods for achieving averaged spherical harmonic source representations, and methods for interpolating between spherical harmonic source representations of two different acoustic source conditions. Finally, a representation of the iv correlation and adequacy of the model is provides that examines the spherical harmonic model across frequency and measurement location. The correlation and adequacy of the new methods has been demonstrated using an acoustic dipole. This acoustic source has directivity patterns inherent in its representation. This dipole has been exercised to show that the interpolation of source definitions permitted the motion of acoustic hot zones, a vital property in describing rotary-wing source directivity. Results from this analysis leads to the planning and execution of a physical measurement of a UH-1 helicopter. The source directivity patterns of the UH-1 have been constructed using measurements from Aeroacoustic Research Complex (ARC) facility at White Sands Missile Range. The author as applied all the new methods described in this dissertation on the full scale UH-1 data set. Examination of the data shows the contaminated data is successfully removed; the averaging of the source definitions maintains the correlations that are seen in individual source descriptions; interpolation of the spherical harmonic directivity patterns are also shown to be successful. Finally the correlation and adequacy of the new methods, using predicted versus measured charts over a wide range of conditions, is examined. Review of these charts shows areas where the new model/methods are not sufficient. These areas are used to describe limitations of measurement and analysis techniques and spherical harmonic model descriptions.


Acoustic localization Mathematical models, Rotors (Helicopters) Mathematical models, Spherical harmonics Mathematical models

Rights Statement

Copyright 2012, author