{
  "url": "https://openlegislation.uk/eu-directive-2015-996/annex/division-ASSESSMENT/division-2/division-2.5/division-2.5.3/division-4",
  "json_url": "https://openlegislation.uk/eu-directive-2015-996/annex/division-ASSESSMENT/division-2/division-2.5/division-2.5.3/division-4.json",
  "legislation": "eudr/2015/996",
  "legislation_title": "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)",
  "legislation_url": "https://openlegislation.uk/eu-directive-2015-996",
  "path": "annex/division/ASSESSMENT/division/2/division/2.5/division/2.5.3/division/4",
  "kind": "division",
  "number": null,
  "heading": "Calculation of the mean plane",
  "text": "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:\nak = (Hk + 1 – Hk )/(xk + 1 – xk )\n(2.5.2)\nbk = (Hk · xk + 1 – Hk + 1 · xk )/(xk + 1 – xk )\nThe 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.\nUsing:\nA = 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\n(2.5.3)\nB = ∑ 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\nThe coefficients of the straight line are given by:\na = 3 2 A − B x n + x 1 x n − x 1 3\n(2.5.4)\nb = 2 x 3 n − x 3 1 x n − x 1 4 B − 3 x n + x 1 x n − x 1 3 A\nWhere segments with xk + 1 = xk shall be ignored when evaluating eq. 2.5.3.",
  "extent": "E+W+S+N.I.",
  "status": null,
  "version": "current",
  "annotations": [],
  "outstanding_effects": [],
  "provenance": {
    "source": "legislation.gov.uk",
    "source_url": "https://www.legislation.gov.uk/eudr/2015/996/annex/division/ASSESSMENT/division/2/division/2.5/division/2.5.3/division/4",
    "retrieved_at": "2026-11-01T15:21:38.862218+00:00"
  },
  "licence": "Open Government Licence v3.0",
  "licence_url": "https://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/",
  "attribution": "Contains public sector information licensed under the Open Government Licence v3.0. Source: legislation.gov.uk, The National Archives."
}