# Commission Directive (EU) 2015/996 of 19 May 2015 establishing common noise assessment methods according to Directive 2002/49/EC of the European Parliament and of the Council (Text with EEA relevance), Division: Calculation of the mean plane

Extent: E+W+S+N.I.

In the plane of the path, the topography (including terrain, mounds, embankments and other man-made obstacles, buildings, …) may be described by an ordered set of discrete points (xk, Hk ); k є {1,…,n}. This set of points defines a polyline, or equivalently, a sequence of straight segments Hk = akx + bk, x є [xk, xk + 1 ]; k є {1,…n}, where:
ak = (Hk + 1 – Hk )/(xk + 1 – xk )
(2.5.2)
bk = (Hk · xk + 1 – Hk + 1 · xk )/(xk + 1 – xk )
The mean plane is represented by the straight line Z = ax + b; x є [x 1, xn ], which is adjusted to the polyline by means of a least-square approximation. The equation of the mean line can be worked out analytically.
Using:
A = 2 3 ∑ k = 1 n − 1 a k x 3 k + 1 − x 3 k + ∑ k = 1 n − 1 b k x 2 k + 1 − x 2 k
(2.5.3)
B = ∑ k = 1 n − 1 a k x 2 k + 1 − x 2 k + 2 ∑ k = 1 n − 1 b k x k + 1 − x k
The coefficients of the straight line are given by:
a = 3 2 A − B x n + x 1 x n − x 1 3
(2.5.4)
b = 2 x 3 n − x 3 1 x n − x 1 4 B − 3 x n + x 1 x n − x 1 3 A
Where segments with xk + 1 = xk shall be ignored when evaluating eq. 2.5.3.

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Source: https://www.legislation.gov.uk/eudr/2015/996/annex/division/ASSESSMENT/division/2/division/2.5/division/2.5.3/division/4 (the official version)
Page: https://openlegislation.uk/eu-directive-2015-996/annex/division-ASSESSMENT/division-2/division-2.5/division-2.5.3/division-4
Contains public sector information licensed under the Open Government Licence v3.0. Source: legislation.gov.uk, The National Archives.