Division Lateral attenuation Λ(β,ℓ) (infinite flight path)

Tabulated NPD event levels relate to steady level flight and are generally based on measurements made 1,2 m over soft level ground beneath the aircraft; the distance parameter is effectively height above the surface. Any effect of the surface on event noise levels beneath the aircraft, that might cause the tabulated levels to differ from free-field values^f1, is assumed to be inherent in the data (i.e. in the shape of the level vs. distance relationships).

To the side of the flight path, the distance parameter is the minimum slant distance — the length of the normal from the receiver to the flight path. At any lateral position the noise level will generally be less than at the same distance immediately below the aircraft. Apart from lateral directivity or ‘installation effects’ described above is due to an excess lateral attenuation which causes the sound level to fall more rapidly with distance than indicated by the NPD curves. A previous, widely used method for modelling lateral propagation of aircraft noise was developed by the Society of Automotive Engineers (SAE) in AIR-1751 and the algorithms described below are based on improvements SAE now recommends AIR-5662. Lateral attenuation is a reflection effect, due to interference between directly radiated sound and that which reflects from the surface. It depends on the nature of the surface and can cause significant reductions in observed sound levels at low elevation angles. It is also very strongly affected by sound refraction, steady and unsteady, caused by wind and temperature gradients and turbulence which are themselves attributable to the presence of the surface^f2. The mechanism of surface reflection is well understood and, for uniform atmospheric and surface conditions, it can be described theoretically with some precision. However, atmospheric and surface non-uniformities — which are not amenable to simple theoretical analysis — have a profound effect on the reflection effect, tending to ‘spread’ it to higher elevation angles; thus the theory is of limited applicability. SAE work to develop a better understanding of surface effects is continuing and this is expected to lead to better models. Until these are developed, the following methodology, described in AIR-5662, is recommended for calculating lateral attenuation. It is confined to the case of sound propagation over soft level ground which is appropriate for the great majority of civil airports. Adjustments to account for the effects of a hard ground surface (or, acoustically equivalent, water) are still under development.

The methodology is built on the substantial body of experimental data on sound propagation from aircraft with fuselage-mounted engines in straight (non-turning), steady, level flight reported originally in AIR-1751. Making the assumption that, for level flight, air-to-ground attenuation depends on (i) elevation angle β measured in the vertical plane and (ii) lateral displacement from the aircraft ground track ℓ, the data were analysed to obtain an empirical function for the total lateral adjustment Λ _T (β,ℓ) (= lateral event level minus the level at the same distance beneath the aircraft).

As the term Λ _T (β,ℓ) accounted for lateral directivity as well as lateral attenuation, the latter can be extracted by subtraction. Describing lateral directivity by equation (2.7.37), with the fuselage-mount coefficients and with φ replaced by β (appropriate to non-turning flight), the lateral attenuation becomes:

where β and ℓ are measured as depicted in Figure 2.7.m in a plane normal to the infinite flight path which, for level flight, is also vertical.

Although Λ(β,ℓ) could be calculated directly using equation (2.7.39) with Λ _T (β,ℓ) taken from AIR-1751, a more efficient relationship is recommended. This is the following empirical approximation adapted from AIR-5662:

where Γ(ℓ) is a distance factor given by

and Λ(β) is long-range air-to-ground lateral attenuation given by

The expression for lateral attenuation Λ(β,ℓ), equation (2.7.40), which is assumed to hold good for all aircraft, propeller aircraft as well as fuselage-mount and wing-mount jets, is shown graphically in Figure 2.7.o.

Under certain circumstances (with terrain), it is possible for β to be less than zero. In such cases it is recommended that Λ(β) = 10,57.