lateral attenuation¶

class description¶

lateral_attenuation.lateral_attenuation(settings: Dict[str, Any], beta: numpy.ndarray, x_obs: numpy.ndarray) → numpy.ndarray[source]¶

Compute lateral attenuation coefficients.

Parameters

settings (Dict[str, Any]) – pyna settings
beta (np.ndarray) – elevation angle [deg]
x_obs (np.ndarray) – observer location [m, m, m]

Returns

Lambda

Type

np.ndarray

theory¶

The engine installation term, \(E_{\textrm{engine}}\), is given by:

\[\begin{split}E_{\textrm{engine}} = \begin{cases} 10\log_{10}\left[\frac{(0.0039 \cos^2\phi_d + \sin^2\phi_d) ^ {0.062}}{(0.8786 * \sin^2(2 \phi_d) + \cos^2(2 \phi_d))}\right] & \textrm{if engines are mounted under the wing} \\ 10\log_{10}\left[(0.1225 \cos^2\phi_d + \sin^2\phi_d) ^ {0.329}\right] & \textrm{if engines are fuselage mounted} \\ 0 & \textrm{if propeller engines} \\ \end{cases}\end{split}\]

Assuming the aircraft is flying horizontally (zero bank angle), the depression angle, \(\phi_d\), is equal to the elevation angle, \(\beta\). The attenuation caused by ground and refraction-scattering effects, \(A_{\textrm{grs}}\), is given by:

\[\begin{split}A_{\textrm{grs}} = \begin{cases} 1.137 - 0.0229 \beta + 9.72 \exp(-0.142 \beta) & \textrm{if} \quad \beta \leq 50 \textrm{deg}\\ 0& \textrm{else}\\ \end{cases}\end{split}\]

The overall lateral ground attenuation, \(g\), over a lateral length, \(l\), is given by:

\[\begin{split}g = \begin{cases} 11.83 (1 - \exp(-0.00274l)) & \textrm{if} \quad 0. \leq l \leq 914\textrm{m} \\ 10.86 & \textrm{if} \quad l > 914\textrm{m} \\ \end{cases}\end{split}\]

The lateral attenuation factor, \(\Lambda\), is given by:

\[\Lambda = 10^{0.1(E_{\textrm{engine}} - \frac{g A_{\textrm{grs}}}{10.86})}\]

Note that the lateral attenuation factor is 0 for observers underneath the flight path. Finally, the lateral attenuation are applied to the mean-square acoustic pressure of each sub-band \(j\) using:

\[<p^2_{\textrm{lateral-attenuation}}>_j \ = \Lambda <p^2_{\textrm{ground-effects}}>_j\]

To avoid double book-keeping of the empirical lateral attenuation effects and the ground reflection effects, the ground reflection effects should only be applied from the noise source up to the center-line. The ground reflection and lateral attenuation section can then be combined using:

\[<p^2_{\textrm{lateral-attenuation}}>_j \ = \Lambda G_{\textrm{center-line}} <p^2_{\textrm{absorb}}>_j\]