Division The finite segment correction ΔF (Exposure levels LE only)

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The adjusted baseline noise exposure level relates to an aircraft in continuous, straight, steady level flight (albeit with a bank angle ε that is inconsistent with straight flight). Applying the (negative) finite segment correction Δ_F = 10 · lg(F), where F is the energy fraction, further adjusts the level to what it would be if the aircraft traversed the finite segment only (or were completely silent for the remainder of the infinite flight path).

The energy fraction term accounts for the pronounced longitudinal directivity of aircraft noise and the angle subtended by the segment at the observer position. Although the processes that cause the directionality are very complex, studies have shown that the resulting contours are quite insensitive to the precise directional characteristics assumed. The expression for Δ _F below is based on a fourth-power 90-degree dipole model of sound radiation. It is assumed to be unaffected by lateral directivity and attenuation. How this correction is derived is described in detail in Appendix E.

The energy fraction F is a function of the ‘view’ triangle OS₁S₂ defined in Figures 2.7.j to 2.7.l such that:

Δ_{F} = 10 \times \lg [\frac{1}{π} (\frac{α_{2}}{1 + α_{2}^{2}} + \arctan α_{2} - \frac{α_{1}}{1 + α_{2}^{1}} - \arctan α_{1})]

(2.7.45)

with

α_{1} = - \frac{q}{d_{λ}}

;

α_{2} = - \frac{q - λ}{d_{λ}}

;

d_{λ} = d_{0} \times 10^{[L_{E∞} ({P,d}_{p}) - L_{\max} ({P,d}_{p})] ∕ 10}

;

d_{0} = \frac{2}{π} \times V_{ref} \times t_{0}

where d_λ is known as the ‘scaled distance’ (see Appendix E). Note that L_max(P, d_p) is the maximum level, from NPD data, for perpendicular distance d_p , NOT the segment L_max .

It is advised to apply a lower limit of – 150 dB to Δ _F .

In the particular case of observer locations behind every takeoff ground-roll segment and every landing ground-roll segment, a reduced form of the noise fraction expressed in equation (2.7.45) is used, which corresponds to the specific case of q = 0. This is computed using

Δ_{F′} = {10 log}_{10} [(1 ∕ π) [α_{2} ∕ (1 + α_{2}^{2}) + \tan^{- 1} α_{2}] 10^{ΔSOR ∕ 10}]

(2.7.46)

where α₂ = λ/d_λ and Δ_SOR is the start-of-roll directivity function defined by equations (2.7.51) and (2.7.52).

The rationale for using this particular form of noise fraction is further explained in the section below, as part of the start-of-roll directivity application method.

Notes on Division 2.7.19

Footnotes

f1: NPD specifications require that the data be based on measurements of steady straight flight, not necessarily level; to create the necessary flight conditions, the test aircraft flight path can be inclined to the horizontal. However, as will be seen, inclined paths lead to computational difficulties and, when using the data for modelling, it is convenient to visualise the source paths as being both straight and level.