# 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: Definition

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

The roughness level Lr is defined as 10 times the logarithm to the base 10 of the square of the mean square value r2 of the roughness of the running surface of a rail or a wheel in the direction of motion (longitudinal level) measured in μm over a certain rail length or the entire wheel diameter, divided by the square of the reference value r 2 0 :
L r = 10 × lg r r 0 2 dB
(2.3.6)
where
r 0 1 μm
r r.m.s. of the vertical displacement difference of the contact surface to the mean level
The roughness level Lr is typically obtained as a spectrum of wavelength λ and it shall be converted to a frequency spectrum f = v/λ, where f is the centre band frequency of a given 1/3 octave band in Hz, λ is the wavelength in m, and v is the train speed in km/h. The roughness spectrum as a function of frequency shifts along the frequency axis for different speeds. In general cases, after conversion to the frequency spectrum by means of the speed, it is necessary to obtain new 1/3 octave band spectra values averaging between two corresponding 1/3 octave bands in the wavelength domain. To estimate the total effective roughness frequency spectrum corresponding to the appropriate train speed, the two corresponding 1/3 octave bands defined in the wavelength domain shall be averaged energetically and proportionally.
The rail roughness level (track side roughness) for the i-th wave-number band is defined as Lr,TR,i
By analogy, the wheel roughness level (vehicle side roughness) for the i-th wave-number band is defined as Lr,VEH,i .
The total and effective roughness level for wave-number band i (LR,tot,i ) is defined as the energy sum of the roughness levels of the rail and that of the wheel plus the A3(λ) contact filter to take into account the filtering effect of the contact patch between the rail and the wheel, and is in dB:
L R,TOT,i = 10 × lg 10 L r,TR,i ∕ 10 + 10 L r,VEH,i ∕ 10 + A 3, i
(2.3.7)
where expressed as a function of the i-th wave-number band corresponding to the wavelength λ.
The contact filter depends on the rail and wheel type and the load.
The total effective roughness for the j-th track section and each t-th vehicle type at its corresponding v speed shall be used in the method.

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Source: https://www.legislation.gov.uk/eudr/2015/996/annex/division/ASSESSMENT/division/2/division/2.3/division/2.3.2/division/3/division/1 (the official version)
Page: https://openlegislation.uk/eu-directive-2015-996/annex/division-ASSESSMENT/division-2/division-2.3/division-2.3.2/division-3/division-1
Contains public sector information licensed under the Open Government Licence v3.0. Source: legislation.gov.uk, The National Archives.