Spherical Harmonics, Splines, and Wavelets

Freeden, Willi; Schreiner, Michael

doi:10.1007/978-3-662-46900-2_101-1

Cited by 1 publication

(1 citation statement)

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“…All 16 of these integrals are similar, and their calculation follows the same procedure. Definitions and the theory of spherical harmonics and associated properties may be found in classical works, such as [30,31]. The integrals may then be simplified into integrals involving combinations of trigonometric functions that can easily be evaluated using techniques such integration by parts.…”

Section: Modeling Source Directivity Function Using Spherical Harmonicsmentioning

confidence: 99%

Closed-Form Analytical Approach for Calculating Noise Contours of Directive Aircraft Noise Sources

et al. 2023

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This paper extends the simplified airport noise model Rapid Aviation Noise Evaluator (RANE) [Torija et al., Journal of the Acoustical Society of America, Vol. 141, No. 2, 2017, pp. 981–995], adding capability of including fully nonisotropic noise sources. This extended tool, RANE v2, is developed as a part of multidisciplinary acoustic assessment of novel aircraft, in order to produce ground contours around airports and helipads. Version 2 extends the capability of RANE to accommodate predictions of future air vehicles implementing propulsion systems solution with inherent directional properties. The model uses three-dimensional noise emission surfaces around a series of discretized segments that represent the aircraft flightpath. The main inputs are the sources’ sound power level, the distance from the flightpath at which a level is observed, and the source three-dimensional directivity. The directivity function may take analytical or numerical form, allowing for experimental data inputs. This paper demonstrates the use of spherical harmonics as a form of directivity function with a closed-form analytical solution for calculating the noise exposure contours. Results and comparison against the Federal Aviation Administration’s Aviation Environmental Design Tool module for helicopter community noise indicate that exposure contour coordinates can be estimated for high and low noise exposure levels. The incorporation of source directivity allows for the assessment of lateral attenuation, engine installation effects, and transition operations (for vertical to horizontal flight and vice versa) via the assumption of individual source directivities and, therefore, complex noise surfaces. As a consequence of the analytical nature of the model, low computational requirements allow for fast exploration of the design space and parametric studies, with minimal input requirements. The capabilities of RANE v2 are demonstrated by predicting noise footprints for three helicopters, each of different size, performance, and directivity characteristics.

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Section: Modeling Source Directivity Function Using Spherical Harmonicsmentioning

confidence: 99%