All input values affecting the emission level of a source shall be determined with at least the accuracy corresponding to an uncertainty of ± 2dB(A) in the emission level of the source (leaving all other parameters unchanged).

In the application of the method, the input data shall reflect the actual usage. In general there shall be no reliance on default input values or assumptions. Default input values and assumptions are accepted if the collection of real data is associated with disproportionately high costs.

Software used to perform the calculations shall prove compliance with the methods herewith described by means of certification of results against test cases.

The road traffic noise source shall be determined by combining the noise emission of each individual vehicle forming the traffic flow. These vehicles are grouped into five separate categories with regard to their characteristics of noise emission:

• Category 1

  Light motor vehicles

• Category 2

  Medium heavy vehicles

• Category 3

  Heavy vehicles

• Category 4

  Powered two-wheelers

• Category 5

  Open category

In the case of powered two-wheelers, two separate subclasses are defined for mopeds and more powerful motorcycles, since they operate in very different driving modes and their numbers usually vary widely.

The first four categories shall be used, and the fifth category is optional. It is foreseen for new vehicles that may be developed in the future and may be sufficiently different in their noise emission to require an additional category to be defined. This category could cover, for example, electric or hybrid vehicles or any vehicle developed in the future substantially different from those in categories 1 to 4.

The details of the different vehicle classes are given in Table [2.2.a].

In this method, each vehicle (category 1, 2, 3, 4 and 5) is represented by one single point source radiating uniformly into the 2-π half space above the ground. The first reflection on the road surface is treated implicitly. As depicted in Figure [2.2.a], this point source is placed 0,05 m above the road surface.

The traffic flow is represented by a source line. In the modelling of a road with multiple lanes, each lane should ideally be represented by a source line placed in the centre of each lane. However, it is also acceptable to model one source line in the middle of a two way road or one source line per carriageway in the outer lane of multi-lane roads.

The rolling noise sound power level in the frequency band i for a vehicle of class m = 1,2 or 3 is defined as:

$L_{\mathrm{WR,i,m}}=A_{\mathrm{R,i,m}}+B_{\mathrm{R,i,m}}\times \lg \left(\frac{v_m}{v_{\mathrm{ref}}}\right)+{\mathrm{\Delta L}}_{\mathrm{WR,i,m}}$

(2.2.4)

The coefficients A_R,i,m and B_R,i,m are given in octave bands for each vehicle category and for a reference speed v_ref  = 70 km/h. ΔL_WR,i,m corresponds to the sum of the correction coefficients to be applied to the rolling noise emission for specific road or vehicle conditions deviating from the reference conditions:

ΔL_WR,road,i,m accounts for the effect on rolling noise of a road surface with acoustic properties different from those of the virtual reference surface as defined in Chapter 2.2.2. It includes both the effect on propagation and on generation.

ΔL_{studded tyres,i,m} is a correction coefficient accounting for the higher rolling noise of light vehicles equipped with studded tyres.

ΔL_WR,acc,i,m accounts for the effect on rolling noise of a crossing with traffic lights or a roundabout. It integrates the effect on noise of the speed variation.

ΔL_W,temp is a correction term for an average temperature τ different from the reference temperature τ_ref = 20 °C.

In situations where a significant number of light vehicles in the traffic flow use studded tyres during several months every year, the induced effect on rolling noise shall be taken into account. For each vehicle of category m = 1 equipped with studded tyres, a speed-dependent increase in rolling noise emission is evaluated by:

where coefficients a_i and b_i are given for each octave band.

The increase in rolling noise emission shall only be attributed according to the proportion of light vehicles with studded tyres and during a limited period T_s (in months) over the year. If Q_stud,ratio is the average ratio of the total volume of light vehicles per hour equipped with studded tyres during the period T_s (in months), then the yearly average proportion of vehicles equipped with studded tyres p_s is expressed by:

$p_s=Q_{\mathrm{stud,ratio}}\times \frac{T_s}{12}$

(2.2.7)

The resulting correction to be applied to the rolling sound power emission due to the use of studded tyres for vehicles of category m = 1 in frequency band i shall be:

${\mathrm{\Delta L}}_{\mathrm{studdedtyres,i,m}=1}=10\times \lg \left[\left(1-p_s\right)+p_s{10}^{\frac{{\Delta }_{\mathrm{stud,i,m}=1}}{10}}\right]$

(2.2.8)

For vehicles of all other categories no correction shall be applied:

The air temperature affects rolling noise emission; the rolling sound power level decreases when the air temperature increases. This effect is introduced in the road surface correction. Road surface corrections are usually evaluated at an air temperature of τ_ref = 20 °C. In the case of a different yearly average air temperature °C, the road surface noise shall be corrected by:

The correction term is positive (i.e. noise increases) for temperatures lower than 20 °C and negative (i.e. noise decreases) for higher temperatures. The coefficient K depends on the road surface and the tyre characteristics and in general exhibits some frequency dependence. A generic coefficient K_{m = 1} = 0,08 dB/°C for light vehicles (category 1) and K_{m = 2} = K_{m = 3} = 0,04 dB/°C for heavy vehicles (categories 2 and 3) shall be applied for all road surfaces. The correction coefficient shall be applied equally on all octave bands from 63 to 8 000 Hz.

The propulsion noise emission includes all contributions from engine, exhaust, gears, air intake, etc. The propulsion noise sound power level in the frequency band i for a vehicle of class m is defined as:

$L_{\mathrm{WP,i,m}}=A_{\mathrm{P,i,m}}+B_{\mathrm{P,i,m}}\times \frac{\left(v_m-v_{\mathrm{ref}}\right)}{v_{\mathrm{ref}}}+{\mathrm{\Delta L}}_{\mathrm{WP,i,m}}$

(2.2.11)

The coefficients A_P,i,m and B_P,i,m are given in octave bands for each vehicle category and for a reference speed v_ref  = 70 km/h.

ΔL_WP,i,m corresponds to the sum of the correction coefficients to be applied to the propulsion noise emission for specific driving conditions or regional conditions deviating from the reference conditions:

ΔL_WP,road,i,m accounts for the effect of the road surface on the propulsion noise via absorption. The calculation shall be performed according to Chapter 2.2.6.

ΔL_WP,acc,i,m and ΔL_WP,grad,i,m account for the effect of road gradients and of vehicle acceleration and deceleration at intersections. They shall be calculated according to Chapters 2.2.4 and 2.2.5 respectively.

The road gradient has two effects on the noise emission of the vehicle: first, it affects the vehicle speed and thus the rolling and propulsion noise emission of the vehicle; second, it affects both the engine load and the engine speed via the choice of gear and thus the propulsion noise emission of the vehicle. Only the effect on the propulsion noise is considered in this section, where a steady speed is assumed.

The effect of the road gradient on the propulsion noise is taken into account by a correction term ΔL_WP,grad,m which is a function of the slope s (in %), the vehicle speed v_m (in km/h) and the vehicle class m. In the case of a bi-directional traffic flow, it is necessary to split the flow into two components and correct half for uphill and half for downhill. The correction term is attributed to all octave bands equally:

• For m = 1

  ΔLWP,grad,i,m = 1 (vm ) =	$\frac{\mathrm{Min}\left(\mathrm{12\; \%;}-s\right)-\mathrm{6\; \%}}{\mathrm{1\; \%}}$	for s < – 6 %	(2.2.13)
  	0	for – 6 % ≤ s ≤ 2 %
  	$\frac{\mathrm{Min}\left(\mathrm{12\; \%;}s\right)-\mathrm{2\; \%}}{\mathrm{1,5\; \%}}\times \frac{v_m}{100}$	for s > 2 %

• For m = 2

  ΔLWP,grad,i,m = 2 (vm ) =	$\frac{\mathrm{Min}\left(\mathrm{12\; \%;}-s\right)-\mathrm{4\; \%}}{\mathrm{0,7\; \%}}\times \frac{v_m-20}{100}$	for s < – 4 %	(2.2.14)
  	0	for – 4 % ≤ s ≤ 0 %
  	$\frac{\mathrm{Min}\left(\mathrm{12\; \%;}s\right)}{\mathrm{1\; \%}}\times \frac{v_m}{100}$	for s > 0 %

• For m = 3

  ΔLWP,grad,i,m = 3 (vm ) =	$\frac{\mathrm{Min}\left(\mathrm{12\; \%;}-s\right)-\mathrm{4\; \%}}{\mathrm{0,5\; \%}}\times \frac{v_m-10}{100}$	for s < – 4 %	(2.2.15)
  	0	for – 4 % ≤ s ≤ 0 %
  	$\frac{\mathrm{Min}\left(\mathrm{12\; \%;}s\right)}{\mathrm{0,8\; \%}}\times \frac{v_m}{100}$	for s > 0 %

• For m = 4

  ΔLWP,grad,i,m = 4 = 0

  (2.2.16)

The correction ΔL_WP,grad,m implicitly includes the effect of slope on speed.

For road surfaces with acoustic properties different from those of the reference surface, a spectral correction term for both rolling noise and propulsion noise shall be applied.

The road surface correction term for the rolling noise emission is given by:

${\mathrm{\Delta L}}_{\mathrm{WR,road,i,m}}={\alpha }_{\mathrm{i,m}}+{\beta }_m\times \lg \left(\frac{v_m}{v_{\mathrm{ref}}}\right)$

(2.2.19)

where

• α_i,m is the spectral correction in dB at reference speed v_ref for category m (1, 2 or 3) and spectral band i.

• β_m is the speed effect on the rolling noise reduction for category m (1, 2 or 3) and is identical for all frequency bands.

The road surface correction term for the propulsion noise emission is given by:

Absorbing surfaces decrease the propulsion noise, while non-absorbing surfaces do not increase it.

The noise characteristics of road surfaces vary with age and the level of maintenance, with a tendency to become louder over time. In this method the road surface parameters are derived to be representative for the acoustic performance of the road surface type averaged over its representative lifetime and assuming proper maintenance.

The existing tracks may differ because there are several elements contributing to and characterising their acoustic properties. The track types used in this method are listed in Table [2.3.b] below. Some of the elements have a large influence on acoustic properties, while others have only secondary effects. In general, the most relevant elements influencing the railway noise emission are: railhead roughness, rail pad stiffness, track base, rail joints and radius of curvature of the track. Alternatively, the overall track properties can be defined and, in this case, the railhead roughness and the track decay rate according to ISO 3095 are the two acoustically essential parameters, plus the radius of curvature of the track.

A track section is defined as a part of a single track, on a railway line or station or depot, on which the track's physical properties and basic components do not change.

Table [2.3.b] defines a common language to describe the track types included in the source database.

The different equivalent noise line sources are placed at different heights and at the centre of the track. All heights are referred to the plane tangent to the two upper surfaces of the two rails.

The equivalent sources include different physical sources (index p). These physical sources are divided into different categories depending on the generation mechanism, and are: (1) rolling noise (including not only rail and track base vibration and wheel vibration but also, where present, superstructure noise of the freight vehicles); (2) traction noise; (3) aerodynamic noise; (4) impact noise (from crossings, switches and junctions); (5) squeal noise and (6) noise due to additional effects such as bridges and viaducts.

1. (1)

   The roughness of wheels and railheads, through three transmission paths to the radiating surfaces (rails, wheels and superstructure), constitutes the rolling noise. This is allocated to h = 0,5 m (radiating surfaces A) to represent the track contribution, including the effects of the surface of the tracks, especially slab tracks (in accordance with the propagation part), to represent the wheel contribution and to represent the contribution of the superstructure of the vehicle to noise (in freight trains).

2. (2)

   The equivalent source heights for traction noise vary between 0,5 m (source A) and 4,0 m (source B), depending on the physical position of the component concerned. Sources such as gear transmissions and electric motors will often be at an axle height of 0,5 m (source A). Louvres and cooling outlets can be at various heights; engine exhausts for diesel-powered vehicles are often at a roof height of 4,0 m (source B). Other traction sources such as fans or diesel engine blocks may be at a height of 0,5 m (source A) or 4,0 m (source B). If the exact source height is in between the model heights, the sound energy is distributed proportionately over the nearest adjacent source heights.

   For this reason, two source heights are foreseen by the method at 0,5 m (source A), 4,0 m (source B), and the equivalent sound power associated with each is distributed between the two depending on the specific configuration of the sources on the unit type.

3. (3)

   Aerodynamic noise effects are associated with the source at 0,5 m (representing the shrouds and the screens, source A), and the source at 4,0 m (modelling all over roof apparatus and pantograph, source B). The choice of 4,0 m for pantograph effects is known to be a simple model, and has to be considered carefully if the objective is to choose an appropriate noise barrier height.

4. (4)

   Impact noise is associated with the source at 0,5 m (source A).

5. (5)

   Squeal noise is associated with the sources at 0,5 m (source A).

6. (6)

   Bridge noise is associated with the source at 0,5 m (source A).

The vehicle contribution and the track contribution to rolling noise are separated into four essential elements: wheel roughness, rail roughness, vehicle transfer function to the wheels and to the superstructure (vessels) and track transfer function. Wheel and rail roughness represent the cause of the excitation of the vibration at the contact point between the rail and the wheel, and the transfer functions are two empirical or modelled functions that represent the entire complex phenomena of the mechanical vibration and sound generation on the surfaces of the wheel, the rail, the sleeper and the track substructure. This separation reflects the physical evidence that roughness present on a rail may excite the vibration of the rail, but it will also excite the vibration of the wheel and vice versa. Not including one of these four parameters would prevent the decoupling of the classification of tracks and trains.

Three speed-independent transfer functions, L_H,TR,i L_H,VEH,i and L_H,VEH,SUP,i , are defined: the first for each j-th track section and the second two for each t-th vehicle type. They relate the total effective roughness level with the sound power of the track, the wheels and the superstructure respectively.

The superstructure contribution is considered only for freight wagons, therefore only for vehicle type ‘a’.

For rolling noise, therefore, the contributions from the track and from the vehicle are fully described by these transfer functions and by the total effective roughness level. When a train is idling, rolling noise shall be excluded.

For sound power per vehicle the rolling noise is calculated at axle height, and has as an input the total effective roughness level L_R,TOT,i as a function of the vehicle speed v, the track, vehicle and superstructure transfer functions L_H,TR,i , L_H,VEH,i and L_H,VEH,SUP,i , and the total number of axles N_a :

for h = 1:

where N_a is the number of axles per vehicle for the t-th vehicle type.

A minimum speed of 50 km/h (30 km/h only for trams and light metro) shall be used to determine the total effective roughness and therefore the sound power of the vehicles (this speed does not affect the vehicle flow calculation) to compensate for the potential error introduced by the simplification of rolling noise definition, braking noise definition and impact noise from crossings and switches definition.

Impact noise can be caused by crossings, switches and rail joints or points. It can vary in magnitude and can dominate rolling noise. Impact noise shall be considered for jointed tracks. For impact noise due to switches, crossings and joints in track sections with a speed of less than 50 km/h (30 km/h only for trams and light metro), since the minimum speed of 50 km/h (30 km/h only for trams and light metro) is used to include more effects according to the description of the rolling noise chapter, modelling shall be avoided. Impact noise modelling shall also be avoided under running condition c = 2 (idling).

Impact noise is included in the rolling noise term by (energy) adding a supplementary fictitious impact roughness level to the total effective roughness level on each specific j-th track section where it is present. In this case a new L_{R,TOT + IMPACT,i} shall be used in place of L_R,TOT,i and it will then become:

$L_{\mathrm{R,TOT}+\mathrm{IMPACT,i}}=10\times \lg \left({10}^{L_{\mathrm{R,TOT,i}}∕10}+{10}^{L_{\mathrm{R,IMPACT,i}}∕10}\right)$

dB

(2.3.11)

L_R,IMPACT,i is a 1/3 octave band spectrum (as a function of frequency). To obtain this frequency spectrum, a spectrum is given as a function of wavelength λ and shall be converted to the required spectrum as a function of frequency using the relation λ = v/f, where f is the 1/3 octave band centre frequency in Hz and v is the s-th vehicle speed of the t-th vehicle type in km/h.

Impact noise will depend on the severity and number of impacts per unit length or joint density, so in the case where multiple impacts are given, the impact roughness level to be used in the equation above shall be calculated as follows:

$L_{\mathrm{R,IMPACT,i}}=L_{\mathrm{R,\; IMPACT}-\mathrm{SINGLE,i}}+10\times \lg \left(\frac{n_l}{\mathrm{0,01}}\right)$

dB

(2.3.12)

where L_{R,IMPACT–SINGLE,i} is the impact roughness level as given for a single impact and n_l is the joint density.

The default impact roughness level is given for a joint density n_l = 0,01 m^–1, which is one joint per each 100 m of track. Situations with different numbers of joints shall be approximated by adjusting the joint density n_l . It should be noted that when modelling the track layout and segmentation, the rail joint density shall be taken into account, i.e. it may be necessary to take a separate source segment for a stretch of track with more joints. The L_W,0 of track, wheel/bogie and superstructure contribution are incremented by means of the L_R,IMPACT,i for +/– 50 m before and after the rail joint. In the case of a series of joints, the increase is extended to between – 50 m before the first joint and + 50 m after the last joint.

The applicability of these sound power spectra shall normally be verified on-site.

For jointed tracks, a default n_l of 0,01 shall be used.

Curve squeal is a special source that is only relevant for curves and is therefore localised. As it can be significant, an appropriate description is required. Curve squeal is generally dependent on curvature, friction conditions, train speed and track-wheel geometry and dynamics. The emission level to be used is determined for curves with radius below or equal to 500 m and for sharper curves and branch-outs of points with radii below 300 m. The noise emission should be specific to each type of rolling stock, as certain wheel and bogie types may be significantly less prone to squeal than others.

The applicability of these sound power spectra shall normally be verified on-site, especially for trams.

Taking a simple approach, squeal noise shall be considered by adding 8 dB for R < 300 m and 5 dB for 300 m < R < 500 m to the rolling noise sound power spectra for all frequencies. Squeal contribution shall be applied on railway track sections where the radius is within the ranges mentioned above for at least a 50 m length of track.

Although traction noise is generally specific to each characteristic operating condition amongst constant speed, deceleration, acceleration and idling, the only two conditions modelled are constant speed (that is valid as well when the train is decelerating or when it is accelerating) and idling. The source strength modelled only corresponds to maximum load conditions and this results in the quantities L_W,0,const,i = L_W,0,idling,i . Also, the L_W,0,idling,i corresponds to the contribution of all physical sources of a given vehicle attributable to a specific height, as described in 2.3.1.

The L_W,0,idling,i is expressed as a static noise source in the idling position, for the duration of the idling condition, and to be used modelled as a fixed point source as described in the following chapter for industrial noise. It shall be considered only if trains are idling for more than 0,5 hours.

These quantities can either be obtained from measurements of all sources at each operating condition, or the partial sources can be characterised individually, determining their parameter dependency and relative strength. This may be done by means of measurements on a stationary vehicle, by varying shaft speeds of the traction equipment, following ISO 3095:2005. As far as relevant, several traction noise sources have to be characterised which might not be all directly depending on the train speed:

• noise from the power train, such as diesel engines (including inlet, exhaust and engine block), gear transmission, electrical generators, mainly dependent on engine round per minute speed (rpm), and electrical sources such as converters, which may be mostly load-dependent,

• noise from fans and cooling systems, depending on fan rpm; in some cases fans can be directly coupled to the driveline,

• intermittent sources such as compressors, valves and others with a characteristic duration of operation and corresponding duty cycle correction for the noise emission.

As each of these sources can behave differently at each operating condition, the traction noise shall be specified accordingly. The source strength is obtained from measurements under controlled conditions. In general, locomotives will tend to show more variation in loading as the number of vehicles hauled and thereby the power output can vary significantly, whereas fixed train formations such as electric motored units (EMUs), diesel motored units (DMUs) and high-speed trains have a better defined load.

There is no a priori attribution of the source sound power to the source heights, and this choice shall depend on the specific noise and vehicle assessed. It shall be modelled to be at source A (h = 1) and at source B (h = 2).

Aerodynamic noise is only relevant at high speeds above 200 km/h and therefore it should first be verified whether it is actually necessary for application purposes. If the rolling noise roughness and transfer functions are known, it can be extrapolated to higher speeds and a comparison can be made with existing high-speed data to check whether higher levels are produced by aerodynamic noise. If train speeds on a network are above 200 km/h but limited to 250 km/h, in some cases it may not be necessary to include aerodynamic noise, depending on the vehicle design.

The aerodynamic noise contribution is given as a function of speed:

$L_{W\mathrm{,0,}i}=L_{W\mathrm{,0,1,}i}\left(v_0\right)+{\alpha }_{\mathrm{1,}i}\times \lg \left(\frac{v}{v_0}\right)$	dB	For h = 1	(2.3.13)
$L_{W\mathrm{,0,}i}=L_{W\mathrm{,0,2,}i}\left(v_0\right)+{\alpha }_{\mathrm{2,}i}\times \lg \left(\frac{v}{v_0}\right)$	dB	For h = 2	(2.3.14)

where

• v ₀ is a speed at which aerodynamic noise is dominant and is fixed at 300 km/h

• L_W,0,1,i is a reference sound power determined from two or more measurement points, for sources at known source heights, for example the first bogie

• L_W,0,2,i is a reference sound power determined from two or more measurement points, for sources at known source heights, for example the pantograph recess heights

• α_1,i is a coefficient determined from two or more measurement points, for sources at known source heights, for example the first bogie

• α_2,i is a coefficient determined from two or more measurement points, for sources at known source heights, for example the pantograph recess heights.

The horizontal directivity ΔL_W,dir,hor,i in dB is given in the horizontal plane and by default can be assumed to be a dipole for rolling, impact (rail joints etc.), squeal, braking, fans and aerodynamic effects, given for each i-th frequency band by:

The vertical directivity ΔL_W,dir,ver,i in dB is given in the vertical plane for source A (h = 1), as a function of the centre band frequency f_c,i of each i-th frequency band, and for – π/2 < ψ < π/2 by:

${\mathrm{\Delta L}}_{\mathrm{W,dir,ver,i}}=\left(\left|\frac{40}{3}\times \left[\frac{2}{3}\times \sin \left(2\times \psi \right)-\sin \psi \right]\times \lg \left[\frac{f_{\mathrm{c,i}}+600}{200}\right]\right|\right)$

(2.3.16)

For source B (h = 2) for the aerodynamic effect:

ΔL_W,dir,ver,i = 0 elsewhere

Directivity ΔL_dir,ver,i is not considered for source B (h = 2) for other effects, as omni-directionality is assumed for these sources in this position.

In the case where the track section is on a bridge, it is necessary to consider the additional noise generated by the vibration of the bridge as a result of the excitation caused by the presence of the train. Because it is not simple to model the bridge emission as an additional source, given the complex shapes of bridges, an increase in the rolling noise is used to account for the bridge noise. The increase shall be modelled exclusively by adding a fixed increase in the noise sound power per each third octave band. The sound power of only the rolling noise is modified when considering the correction and the new L_{W,0,rolling–and–bridge,i} shall be used instead of L_{W,0,rolling-only,i} :

where C_bridge is a constant that depends on the bridge type, and L_{W,0,rolling–only,i} is the rolling noise sound power on the given bridge that depends only on the vehicle and track properties.

Various sources like depots, loading/unloading areas, stations, bells, station loudspeakers, etc. can be present and are associated with the railway noise. These sources are to be treated as industrial noise sources (fixed noise sources) and shall be modelled, if relevant, according to the following chapter for industrial noise.

The industrial sources are of very variable dimensions. They can be large industrial plants as well as small concentrated sources like small tools or operating machines used in factories. Therefore, it is necessary to use an appropriate modelling technique for the specific source under assessment. Depending on the dimensions and the way several single sources extend over an area, with each belonging to the same industrial site, these may be modelled as point sources, source lines or area sources. In practice, the calculations of the noise effect are always based on point sources, but several point sources can be used to represent a real complex source, which mainly extends over a line or an area.

The real sound sources are modelled by means of equivalent sound sources represented by one or more point sources so that the total sound power of the real source corresponds to the sum of the single sound powers attributed to the different point sources.

The general rules to be applied in defining the number of point sources to be used are:

• line or surface sources where the largest dimension is less than 1/2 of the distance between the source and the receiver can be modelled as single point sources,

• sources where the largest dimension is more than 1/2 of the distance between the source and the receiver should be modelled as a series of incoherent point sources in a line or as a series of incoherent point sources over an area, such that for each of these sources the condition of 1/2 is fulfilled. The distribution over an area can include vertical distribution of point sources,

• for sources where the largest dimensions in height are over 2 m or near the ground, special care should be administered to the height of the source. Doubling the number of sources, redistributing them only in the z-component, may not lead to a significantly better result for this source,

• in the case of any source, doubling the number of sources over the source area (in all dimensions) may not lead to a significantly better result.

The position of the equivalent sound sources cannot be fixed, given the large number of configurations that an industrial site can have. Best practices will normally apply.

The source directivity is strongly related to the position of the equivalent sound source next to nearby surfaces. Because the propagation method considers the reflection of the nearby surface as well its sound absorption, it is necessary to consider carefully the location of the nearby surfaces. In general, these two cases will always be distinguished:

• a source sound power and directivity is determined and given relative to a certain real source when this is in free field (excluding the terrain effect). This is in agreement with the definitions concerning the propagation, if it is assumed that there is no nearby surface less than 0,01 m from the source and surfaces at 0,01 m or more are included in the calculation of the propagation,

• a source sound power and directivity is determined and given relative to a certain real source when this is placed in a specific location and therefore the source sound power and directivity is in fact an ‘equivalent’ one, since it includes the modelling of the effect of the nearby surfaces. This is defined in ‘semi-free field’ according to the definitions concerning the propagation. In this case, the nearby surfaces modelled shall be excluded from the calculation of propagation.

The directivity shall be expressed in the calculation as a factor ΔL_W,dir,xyz (x, y, z) to be added to the sound power to obtain the right directional sound power of a reference sound source seen by the sound propagation in the direction given. The factor can be given as a function of the direction vector defined by (x,y,z) with $\sqrt{x^2+y^2+z^2}=1$. This directivity can also be expressed by means of other coordinate systems such as angular coordinate systems.

Real sources are described by a set of point sources or, in the case of railway traffic or road traffic, by incoherent source lines. The propagation method assumes that line or area sources have previously been split up to be represented by a series of equivalent point sources. This may have occurred as pre-processing of the source data, or may occur within the pathfinder component of the calculation software. The means by which this has occurred is outside the scope of the current methodology.

The method operates on a geometrical model consisting of a set of connected ground and obstacles surfaces. A vertical propagation path is deployed on one or more vertical planes with respect to the horizontal plane. For trajectories including reflections onto vertical surfaces not orthogonal to the incident plane, another vertical plane is subsequently considered including the reflected part of the propagation path. In these cases, where more vertical planes are used to describe the entire trajectory from the source to the receiver, the vertical planes are then flattened, like an unfolding Chinese screen.

The equivalent heights are obtained from the mean ground plane between the source and the receiver. This replaces the actual ground with a fictitious plane representing the mean profile of the land.

• 1

  Actual relief

• 2

  Mean plane

The equivalent height of a point is its orthogonal height in relation to the mean ground plane. The equivalent source height z_s and the equivalent receiver height z_r can therefore be defined. The distance between the source and receiver in projection over the mean ground plane is noted by d_p .

If the equivalent height of a point becomes negative, i.e. if the point is located below the mean ground plane, a null height is retained, and the equivalent point is then identical with its possible image.

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 (x_k, H_k ); k є {1,…,n}. This set of points defines a polyline, or equivalently, a sequence of straight segments H_k = a_kx + b_k, x є [x_k, x_{k + 1} ]; k є {1,…n}, where:

The mean plane is represented by the straight line Z = ax + b; x є [x ₁, x_n ], 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:

	$A=\frac{2}{3}\sum _{k=1}^{n-1}{a}_k\left(x_3^{k+1}-x_3^k\right)+\sum _{k=1}^{n-1}{b}_k\left(x_2^{k+1}-x_2^k\right)$	(2.5.3)
	$B=\sum _{k=1}^{n-1}{a}_k\left(x_2^{k+1}-x_2^k\right)+2\sum _{k=1}^{n-1}{b}_k\left(x_{k+1}-x_k\right)$

The coefficients of the straight line are given by:

	$a=\frac{3\left(2A-B\left(x_n+x_1\right)\right)}{{\left(x_n-x_1\right)}^3}$	(2.5.4)
	$b=\frac{2\left(x_3^n-x_3^1\right)}{{\left(x_n-x_1\right)}^4}B-\frac{3\left(x_n+x_1\right)}{{\left(x_n-x_1\right)}^3}A$

Where segments with x_{k + 1} = x_k shall be ignored when evaluating eq. 2.5.3.

Contributions from reflections are taken into account by the introduction of image sources as described further.

The term A_F represents the total attenuation along the propagation path in favourable conditions, and is broken down as follows:

where

• A_div is the attenuation due to geometrical divergence;

• A_atm is the attenuation due to atmospheric absorption;

• A_boundary,F is the attenuation due to the boundary of the propagation medium in favourable conditions. It may contain the following terms:

  • A_ground,F which is the attenuation due to the ground in favourable conditions;

  • A_dif,F which is the attenuation due to diffraction in favourable conditions.

For a given path and frequency band, the following two scenarios are possible:

• either A_ground,F is calculated with no diffraction (A_dif,F = 0 dB) and A_boundary,F = A_ground,F ;

• or A_dif,F is calculated. The ground effect is taken into account in the A_dif,F equation itself (A_ground,F = 0 dB). This therefore gives A_boundary,F = A_dif,F .

The procedure is strictly identical to the case of favourable conditions presented in the previous section.

The term A_H represents the total attenuation along the propagation path in homogeneous conditions and is broken down as follows:

where

• A_div is the attenuation due to geometrical divergence;

• Α_atm is the attenuation due to atmospheric absorption;

• A_boundary,H is the attenuation due to the boundary of the propagation medium in homogeneous conditions. It may contain the following terms:

  • Α_ground,H which is the attenuation due to the ground in homogeneous conditions;

  • A_dif,H which is the attenuation due to diffraction in homogeneous conditions.

For a given path and frequency band, the following two scenarios are possible:

• either Α_ground,H (A_dif,H = 0 dB) is calculated with no diffraction and A_boundary,H = Α_ground,H ;

• or A_dif,H (Α_ground,H = 0 dB) is calculated. The ground effect is taken into account in the A_dif,H equation itself. This therefore gives A_boundary,H = A_dif,H

Inside urban areas, a statistical approach to the calculation of the sound propagation behind the first line of buildings is also allowed, provided that such a method is duly documented, including relevant information on the quality of the method. This method may replace the calculation of the A_boundary,H and A_boundary,F by an approximation of the total attenuation for the direct path and all reflections. The calculation will be based on the average building density and the average height of all buildings in the area.

The total long-term sound level at the receiver for a frequency band is obtained by energy summing contributions from all N paths, all types included:

$L_{\mathrm{tot,LT}}=10\times \lg \left(\sum _n{10}^{\frac{L_{\mathrm{n,LT}}}{10}}\right)$

(2.5.10)

where

n is the index of the paths between S and R.

Taking reflections into account by means of image sources is described further. The percentage of occurrences of favourable conditions in the case of a path reflected on a vertical obstacle is taken to be identical to the occurrence of the direct path.

If S′ is the image source of S, then the occurrence p′ of the path (S′,R) is taken to be equal to the occurrence p of the path (S_i,R).

The total sound level in decibels A (dBA) is obtained by summing levels in each frequency band:

$L_{\mathrm{Aeq,LT}}=10\times \lg \sum _i{10}^{\left(L_{\mathrm{tot,LT,i}}+{\mathrm{AWC}}_{\mathrm{f,i}}\right)∕10}$

(2.5.11)

where i is the index of the frequency band. AWC is the A-weighting correction according to the international standard IEC 61672-1:2003.

This level L_Aeq,LT constitutes the final result, i.e. the long-term A-weighted sound pressure level at the receiver point on a specific reference time interval (e.g. day or evening, or night or a shorter time during day, evening or night).

The attenuation due to geometrical divergence, A_div, corresponds to a reduction in the sound level due to the propagation distance. For a point sound source in free field, the attenuation in dB is given by:

where d is the direct 3D slant distance between the source and the receiver.

The attenuation due to atmospheric absorption A_atm during propagation over a distance d is given in dB by the equation:

where

• d is the direct 3D slant distance between the source and the receiver in m;

• α_atm is the atmospheric attenuation coefficient in dB/km at the nominal centre frequency for each frequency band, in accordance with ISO 9613-1.

The values of the α_atm coefficient are given for a temperature of 15 °C, a relative humidity of 70 % and an atmospheric pressure of 101 325 Pa. They are calculated with the exact centre frequencies of the frequency band. These values comply with ISO 9613-1. Meteorological average over the long term shall be used if meteorological data is available.

The attenuation due to the ground effect is mainly the result of the interference between the reflected sound and the sound that is propagated directly from the source to the receiver. It is physically linked to the acoustic absorption of the ground above which the sound wave is propagated. However, it is also significantly dependent on atmospheric conditions during propagation, as ray bending modifies the height of the path above the ground and makes the ground effects and land located near the source more or less significant.

In case the propagation between the source and the receiver is affected by any obstacle in the propagation plane, the ground effect is calculated separately on the source and receiver side. In this case, z_s and z_r refer to the equivalent source and/or receiver position as indicated further where the calculation of the diffraction A_dif is presented.

The acoustic absorption properties of the ground are mainly linked to its porosity. Compact ground is generally reflective and porous ground is absorbent.

For operational calculation requirements, the acoustic absorption of a ground is represented by a dimensionless coefficient G, between 0 and 1. G is independent of the frequency. Table 2.5.a gives the G values for the ground outdoors. In general, the average of the coefficient G over a path takes values between 0 and 1.

G_path is defined as the fraction of absorbent ground present over the entire path covered.

When the source and receiver are close-by so that d_p ≤ 30(z_s + z_r ), the distinction between the type of ground located near the source and the type of ground located near the receiver is negligible. To take this comment into account, the ground factor G_path is therefore ultimately corrected as follows:

G′path =	$G_{\mathrm{path}}\frac{d_p}{30\left(z_s+z_r\right)}+G_s\left(1-\frac{d_p}{30\left(z_s+z_r\right)}\right)$	if dp ≤ 30(zs + zr )	(2.5.14)
	Gpath	otherwise

G may be linked to the flow resistivity.

The following two subsections on calculations in homogeneous and favourable conditions introduce the generic Ḡ_w and Ḡ_m notations for the absorption of the ground. Table 2.5.b gives the correspondence between these notations and the G_path and G′_path variables.

The attenuation due to the ground effect in homogeneous conditions is calculated according to the following equations:

if G_path ≠ 0

$A_{\mathrm{ground,H}}=\max \left(-10\times \lg \left[4\frac{k^2}{d_2^p}\left(z_2^s-\sqrt{\frac{2C_f}{k}}{z}_s+\frac{C_f}{k}\right)\left(z_2^r-\sqrt{\frac{2C_f}{k}}{z}_r+\frac{C_f}{k}\right)\right],A_{\mathrm{ground,H,min}}\right)$

(2.5.15)

where

fm is the nominal centre frequency of the frequency band considered, in Hz, c is the speed of the sound in the air, taken as equal to 340 m/s, and C_f is defined by:

$C_f=d_p\frac{1+3{\mathrm{wd}}_p{e}^{-\sqrt{{\mathrm{wd}}_p}}}{1+{\mathrm{wd}}_p}$

(2.5.16)

where the values of w are given by the equation below:

Ḡ_w may be equal to either G_path or G′_path depending on whether the ground effect is calculated with or without diffraction, and according to the nature of the ground under the source (real source or diffracted). This is specified in the following subsections and summarised in Table 2.5.b.

is the lower bound of A_ground,H .

For a path (S_i,R) in homogeneous conditions without diffraction:

• Ḡ_w = G′_path

• Ḡ_m = G′_path

With diffraction, refer to the section on diffraction for the definitions of Ḡ_w and Ḡ_m .

if G_path = 0: A_ground,H = – 3 dB

The term – 3(1 – Ḡ_m ) takes into account the fact that when the source and the receiver are far apart, the first reflection source side is no longer on the platform but on natural land.

The ground effect in favourable conditions is calculated with the equation of A_ground,H , provided that the following modifications are made:

• If G_path ≠ 0

  1. (a)

     In the equation of A_ground,H , the heights z_s and z_r are replaced by z_s + δ z_s + δ z_T and z_r + δ z_r + δ z_T respectively where

     	${\mathrm{\delta z}}_s=a_0{\left(\frac{z_s}{z_s+z_r}\right)}^2\frac{d_2^p}{2}$	(2.5.19)
     	${\mathrm{\delta z}}_r=a_0{\left(\frac{z_r}{z_s+z_r}\right)}^2\frac{d_2^p}{2}$

     a_o =2 × 10^–4 m^–1 is the reverse of the radius of curvature

     ${\mathrm{\delta z}}_T=6\times {10}^{-3}\frac{d_p}{z_s+z_r}$
  2. (b)

     The lower bound of A_ground,F depends on the geometry of the path:

     (2.5.20)

• If G_path = 0

  A_ground,F = A_ground,F,min

The height corrections δ z_s and δ z_r convey the effect of the sound ray bending. δ z_T accounts for the effect of the turbulence.

Ḡ_m may also be equal to either G_path or G′_path depending on whether the ground effect is calculated with or without diffraction, and according to the nature of the ground under the source (real source or diffracted). This is specified in the following subsections.

For a path (S_i,R) in favourable conditions without diffraction:

• Ḡ_w = G_path in equation (2.5.17);

• Ḡ_m = G′_path .

With diffraction, refer to the next section for the definitions of Ḡ_w and Ḡ_m .

As a general rule, the diffraction shall be studied at the top of each obstacle located on the propagation path. If the path passes ‘high enough’ over the diffraction edge, A_dif = 0 can be set and a direct view calculated, in particular by evaluating A_ground .

In practice, for each frequency band centre frequency, the path difference δ is compared with the quantity – λ/20. If an obstacle does not produce diffraction, this for instance being determined according to Rayleigh's criterion, there is no need to calculate A_dif for the frequency band considered. In other words, A_dif = 0 in this case. Otherwise, A_dif is calculated as described in the remainder of this part. This rule applies in both homogeneous and favourable conditions, for both single and multiple diffraction.

When, for a given frequency band, a calculation is made according to the procedure described in this section, A_ground is set as equal to 0 dB when calculating the total attenuation. The ground effect is taken into account directly in the general diffraction calculation equation.

The equations proposed here are used to process the diffraction on thin screens, thick screens, buildings, earth berms (natural or artificial), and by the edges of embankments, cuttings and viaducts.

When several diffracting obstacles are encountered on a propagation path, they are treated as a multiple diffraction by applying the procedure described in the following section on calculation of the path difference.

The procedures presented here are used to calculate the attenuations in both homogeneous conditions and favourable conditions. Ray bending is taken into account in the calculation of the path difference and to calculate the ground effects before and after diffraction.

Figure 2.5.c illustrates the general method of calculation of the attenuation due to diffraction. This method is based on breaking down the propagation path into two parts: the ‘source side’ path, located between the source and the diffraction point, and the ‘receiver side’ path, located between the diffraction point and the receiver.

The following are calculated:

• a ground effect, source side, Δ _ground(S,O)

• a ground effect, receiver side, Δ _ground(O,R)

• and three diffractions:

  • between the source S and the receiver R: Δ _dif(S,R)

  • between the image source S′ and R: Δ _dif(S′,R)

  • between S and the image receiver R′: Δ _dif(S,R′) .

• 1

  Source side

• 2

  Receiver side

where

• S is the source;

• R is the receiver;

• S′ is the image source in relation to the mean ground plane source side;

• R′ is the image receiver in relation to the mean ground plane receiver side;

• O is the diffraction point;

• z _s is the equivalent height of the source S in relation to the mean plane source side;

• z _o,s is the equivalent height of the diffraction point O in relation to the mean ground plane source side;

• z _r is the equivalent height of the receiver R in relation to the mean plane receiver side;

• z _o,r is the equivalent height of the diffraction point O in relation to the mean ground plane receiver side.

The irregularity of the ground between the source and the diffraction point, and between the diffraction point and the receiver, is taken into account by means of equivalent heights calculated in relation to the mean ground plane, source side first and receiver side second (two mean ground planes), according to the method described in the subsection on significant heights above the ground.

For pure diffraction, with no ground effects, the attenuation is given by:

Δdif =	$10C_h\times \lg \left(3+\frac{40}{\lambda }\mathrm{C″\delta }\right)$	if$\frac{40}{\lambda }\mathrm{C″\delta }\ge -2$	(2.5.21)
	0	otherwise

where

λ is the wavelength at the nominal centre frequency of the frequency band considered;

δ is the path difference between the diffracted path and the direct path (see next subsection on calculation of the path difference);

C″ is a coefficient used to take into account multiple diffractions:

C″ = 1 for a single diffraction.

For a multiple diffraction, if e is the total distance along the path, O1 to O2 + O2 to O3 + O3 to O4 from the ‘rubber band method’, (see Figures 2.5.d and 2.5.f) and if e exceeds 0,3 m (otherwise C″ = 1), this coefficient is defined by:

The values of Δ_dif shall be bound:

• if Δ _dif < 0: Δ _dif = 0 dB

• if Δ _dif > 25: Δ _dif = 25 dB for a diffraction on a horizontal edge and only on the term Δ_dif which figures in the calculation of A_dif . This upper bound shall not be applied in the Δ_dif terms that intervene in the calculation of Δ _ground , or for a diffraction on a vertical edge (lateral diffraction) in the case of industrial noise mapping.

The path difference δ is calculated in a vertical plane containing the source and the receiver. This is an approximation in relation to the Fermat principle. The approximation remains applicable here (source lines). The path difference δ is calculated as in the following Figures, based on the situations encountered.

In favourable conditions, it is considered that the three curved sound rays SO, OR, and SR have an identical radius of curvature Γ defined by:

The length of a sound ray curve MN is noted M̂N in favourable conditions. This length is equal to:

In principle, three scenarios should be considered in the calculation of the path difference in favourable conditions δ_F (see Figure 2.5.e). In practice, two equations are sufficient:

• if the straight sound ray SR is masked by the obstacle (1st and 2nd case in Figure 2.5.e):

  (2.5.26)

• if the straight sound ray SR is not masked by the obstacle (3rd case in Figure 2.5.e):

  (2.5.27)

where A is the intersection of the straight sound ray SR and the extension of the diffracting obstacle.

For the multiple diffractions in favourable conditions:

• determine the convex hull defined by the various potential diffraction edges;

• eliminate the diffraction edges which are not on the boundary of the convex hull;

• calculate δ_F based on the lengths of the curved sound ray, by breaking down the diffracted path into as many curved segments as necessary (see Figure 2.5.f)

  (2.5.28)

In the scenario presented in Figure 2.5.f, the path difference is:

The attenuation due to diffraction, taking the ground effects on the source side and receiver side into account, is calculated according to the following general equations:

$A_{\mathrm{dif}}={\Delta }_{\mathrm{dif}\left(\mathrm{S,R}\right)}+{\Delta }_{\mathrm{ground}\left(\mathrm{S,O}\right)}+{\Delta }_{\mathrm{ground}\left(O_n,R\right)}$

(2.5.30)

where

• Δ _{dif (S,R)} is the attenuation due to the diffraction between the source S and the receiver R

• Δ _ground(S,O) is the attenuation due to the ground effect on the source side, weighted by the diffraction on the source side; where it is understood that O = O₁ in case of multiple diffractions as in Figure 2.5.f

• Δ _ground(O,R) is the attenuation due to the ground effect on the receiver side, weighted by the diffraction on the receiver side (see the following subsection on calculation of the term Δ _ground(O,R) ).

where

• A_ground(S,O) is the attenuation due to the ground effect between the source S and the diffraction point O. This term is calculated as indicated in the previous subsection on calculations in homogeneous conditions and in the previous subsection on calculation in favourable conditions, with the following hypotheses:

  z_r = z_o,s ,

• G_path is calculated between S and O,

• In homogeneous conditions: Ḡ_w = G′_path in equation (2.5.17), Ḡ_m = G′_path in equation (2.5.18),

• In favourable conditions: Ḡ_w = G_path in equation (2.5.17), Ḡ_m = G′_path in equation (2.5.20),

• Δ _dif(S′,R) is the attenuation due to the diffraction between the image source S′ and R, calculated as in the previous subsection on pure diffraction,

• Δ _dif(S,R) is the attenuation due to the diffraction between S and R, calculated as in Subsection VI.4.4.b.

where

• A_{ground (O,R)} is the attenuation due to the ground effect between the diffraction point O and the receiver R. This term is calculated as indicated in the previous subsection on calculation in homogeneous conditions and in the previous subsection on calculation in favourable conditions, with the following hypotheses:

  z_s = z_o,r

• G_path is calculated between O and R.

The G′_path correction does not need to be taken into account here as the source considered is the diffraction point. Therefore, G_path shall indeed be used in the calculation of ground effects, including for the lower bound term of the equation which becomes – 3(1 – G_path ).

• In homogeneous conditions, Ḡ_w = G_path in equation (2.5.17) and Ḡ_m = G_path in equation (2.5.18);

• In favourable conditions, Ḡ_w = G_path in equation (2.5.17) and Ḡ_m = G_path in equation (2.5.20);

• Δ _dif(S,R′) is the attenuation due to the diffraction between S and the image receiver R′, calculated as in the previous section on pure diffraction;

• Δ _dif(S,R) is the attenuation due to the diffraction between S and R, calculated as in the previous subsection on pure diffraction.

Equation (2.5.21) may be used to calculate the diffractions on vertical edges (lateral diffractions) in case of industrial noise. If this is the case, A_dif = Δ _dif(S,R) is taken and the term A_ground is kept. In addition, A_atm and A_ground shall be calculated from the total length of the propagation path. A_div is still calculated from the direct distance d. Equations (2.5.8) and (2.5.6) respectively become:

$A_H=A_{\mathrm{div}}+A_{\mathrm{path}}^{\mathrm{atm}}+A_{\mathrm{path}}^{\mathrm{ground,H}}+{\Delta }_{\mathrm{dif,H}\left(\mathrm{S,R}\right)}$	(2.5.33)
$A_F=A_{\mathrm{div}}+A_{\mathrm{path}}^{\mathrm{atm}}+A_{\mathrm{path}}^{\mathrm{ground,F}}+{\Delta }_{\mathrm{dif,H}\left(\mathrm{S,R}\right)}$	(2.5.34)

Δ _dif is indeed used in homogeneous conditions in equation (2.5.34).

• AIP

  Aeronautical Information Publication

• Aircraft configuration

  The positions of slats, flaps and landing gear

• Aircraft movement

  An arrival, departure or other aircraft action that affects noise exposure around an aerodrome

• Aircraft noise and performance data

  Data describing the acoustic and performance characteristics of different aeroplanes types that are required by the modelling process. They include → NPD relationships and information that allows engine thrust/power to be calculated as a function of → flight configuration. The data are usually supplied by the aircraft manufacturer although when that is not possible it is sometimes obtained from other sources. When no data are available, it is usual to represent the aircraft concerned by adapting data for a suitably similar aircraft — this is referred to as substitution

• Altitude

  Height above mean sea level

• ANP database

  The Aircraft Noise and Performance database included in Appendix I

• A-weighted sound level, L_A

  Basic sound/noise level scale used for measuring environmental noise including that from aircraft and on which most noise contour metrics are based

• Backbone ground track

  A representative or nominal ground track which defines the centre of a swathe of tracks

• Baseline noise event level

  The noise event level read from an NPD database

• Brake release

  → Start of roll

• Corrected net thrust

  At a given power setting (e.g. EPR or N ₁) net thrust falls with air density and thus with increasing aircraft altitude; corrected net thrust is the value at sea level

• Cumulative sound/noise level

  A decibel measure of the noise received over a specified period of time, at a point near an airport, from aeroplane traffic using normal operating conditions and flight paths. It is calculated by accumulating in some way the event sound/noise levels occurring at that point

• Decibel sum or average
  Sometimes referred to elsewhere as ‘energy’ or ‘logarithmic’ (as opposed to arithmetic) values. Used when it is appropriate to sum or average the underlying energy-like quantities; e.g. $\mathrm{decibel\; sum}=10\times \lg \sum {10}^{L_i∕10}$
• Energy fraction, F

  Ratio of sound energy received from segment to energy received from infinite flight path

• Engine power setting

  Value of the → noise related power parameter used to determine noise emission from the NPD database

• Equivalent (continuous) sound level, L_eq

  A measure of long-term sound. The level of a hypothetical steady sound, which over a specified period of time, contains the same total energy as the actual variable sound

• Event sound/noise level

  A decibel measure of the finite quantity of sound (or noise) received from a passing aeroplane → sound exposure level

• Flight configuration

  = → Aircraft configuration + → Flight parameters

• Flight parameters

  Aircraft power setting, speed, bank angle and weight

• Flight path

  The path of an aeroplane through the air, defined in three dimensions, usually with reference to an origin at the start of take-off roll or at the landing threshold

• Flight path segment

  Part of an aircraft flight path represented for noise modelling purposes by a straight line of finite length

• Flight procedure

  The sequence of operational steps followed by the aircraft crew or flight management system: expressed as changes of flight configuration as a function of distance along the ground track

• Flight profile

  Variation of aeroplane height along the ground track (sometimes includes changes of → flight configuration too) — described by a set of → profile points

• Ground plane

  (Or Nominal Ground Plane) Horizontal ground surface through the aerodrome reference point on which the contours are normally calculated

• Ground speed

  Aircraft speed relative to a fixed point on the ground

• Ground track

  Vertical projection of the flight path onto the ground plane

• Height

  Vertical distance between aircraft and → ground plane

• Integrated sound level

  Otherwise termed → single event sound exposure level

• ISA

  International Standard Atmosphere — defined by ICAO. Defines variation of air temperature, pressure, and density with height above mean sea level. Used to normalise the results of aircraft design calculations and analysis of test data

• Lateral attenuation

  Excess attenuation of sound with distance attributable, directly or indirectly, to the presence of the ground surface. Significant at low angles of elevation (of the aircraft above the ground plane)

• Maximum noise/sound level

  The maximum sound level reached during an event

• Mean Sea Level, MSL

  The standard earth surface elevation to which the → ISA is referred

• Net thrust

  The propulsive force exerted by an engine on the airframe

• Noise

  Noise is defined as unwanted sound. But metrics such as A-weighted sound level (L_A ) and effective perceived noise level (EPNL) effectively convert sound levels into noise levels. Despite a consequent lack of rigour, the terms sound and noise are sometimes used interchangeably in this document, as elsewhere — especially in conjunction with the word level

• Noise contour

  A line of constant value of a cumulative aircraft noise level or index around an airport

• Noise impact

  The adverse effect(s) of noise on its recipients; importantly it is implied that noise metrics are indicators of noise impact

• Noise index

  A measure of long term, or cumulative sound which correlates with (i.e. is considered to be a predictor of) its effects on people. May take some account of factors in addition to the magnitude of sound (especially time of day). An example is day-evening-night level L_DEN

• Noise level

  A decibel measure of sound on a scale which indicates its loudness or noisiness. For environmental noise from aircraft, two scales are generally used: A-weighted sound level and Perceived Noise Level. These scales apply different weights to sound of different frequencies — to mimic human perception

• Noise metric

  An expression used to describe any measure of quantity of noise at a receiver position whether it be a single event or an accumulation of noise over extended time. There are two commonly used measures of single event noise: the maximum level reached during the event, or its sound exposure level, a measure of its total sound energy determined by time integration

• Noise-power-distance (NPD) relationships/data

  Noise event levels tabulated as a function of distance below an aeroplane in steady level flight at a reference speed in a reference atmosphere, for each of a number of → engine power settings. The data account for the effects of sound attenuation due to spherical wave spreading (inverse-square law) and atmospheric absorption. The distance is defined perpendicular to the aeroplane flight path and the aircraft wing-axis (i.e. vertically below the aircraft in non-banked flight)

• Noise-related power parameter

  Parameter that describes or indicates the propulsive effort generated by an aircraft engine to which acoustic power emission can logically be related; usually taken to be → corrected net thrust. Loosely termed ‘power’ or ‘power setting’ throughout the text

• Noise significance

  The contribution from a flight path segment is ‘noise significant’ if it affects the event noise level to an appreciable extent. Disregarding segments that are not noise-significant yields massive savings in computer processing

• Observer

  → Receiver

• Procedural steps

  Prescription for flying a profile — steps include changes of speed and/or altitude

• Profile point

  Height of flight path segment end point — in vertical plane above the ground track

• Receiver

  A recipient of noise that arrives from a source; principally at a point on or near the ground surface

• Reference atmosphere

  A tabulation of sound absorption rates used to standardise NPD data (see Appendix D)

• Reference day

  A set of atmospheric conditions on which ANP data are standardised

• Reference duration

  A nominal time interval used to standardise single event sound exposure level measurements; equal to 1 second in the case of → SEL

• Reference speed

  Aeroplane groundspeed to which NPD → SEL data are normalised

• SEL

  → Sound Exposure Level

• Single event sound exposure level

  The sound level an event would have if all its sound energy were compressed uniformly into a standard time interval known as the → reference duration

• Soft ground

  A ground surface that is acoustically ‘soft’, typically grassy, that surrounds most aerodromes. Acoustically hard, i.e. highly reflective, ground surfaces includes concrete and water. The noise contour methodology described herein applies to soft ground conditions

• Sound

  Energy transmitted through air by (longitudinal) wave motion which is sensed by the ear

• Sound attenuation

  The decrease in sound intensity with distance along a propagation path. For aircraft noise its causes include spherical wave spreading, atmospheric absorption and → lateral attenuation

• Sound exposure

  A measure of total sound energy immission over a period of time

• Sound Exposure Level, L_AE

  (Acronym SEL) A metric standardised in ISO 1996-1 or ISO 3891 = A-weighted single event sound exposure level referenced to 1 second

• Sound intensity

  The strength of sound immission at a point — related to acoustical energy (and indicated by measured sound levels)

• Sound level

  A measure of sound energy expressed in decibel units. Received sound is measured with or without ‘frequency weighting’; levels measured with a weighting are often termed → noise levels

• Stage/trip length

  Distance to first destination of departing aircraft; taken to be an indicator of aircraft weight

• Start of Roll, SOR

  The point on the runway from which a departing aircraft commences its take-off. Also termed ‘brake release’

• True airspeed

  Actual speed of aircraft relative to air (= groundspeed in still air)

• Weighted equivalent sound level, L_eq,W

  An modified version of L_eq in which different weights are assigned to noise occurring during different period of the day (usually day, evening and night)

• d

  Shortest distance from an observation point to a flight path segment

• d_p

  Perpendicular distance from an observation point to the flight path (slant distance or slant range)

• d_λ

  Scaled distance

• F_n

  Actual net thrust per engine

• F_n /δ

  Corrected net thrust per engine

• h

  Aircraft altitude (above MSL)

• L

  Event noise level (scale undefined)

• L(t)

  Sound level at time t (scale undefined)

• L_A, L_A(t)

  A-weighted sound pressure level (at time t) — measured on the slow sound level meter scale

• L_AE

  (SEL) Sound Exposure Level

• L_Amax

  Maximum value of L_A(t) during an event

• L_E

  Single event sound exposure level

• L_E∞

  Single event sound exposure level determined from NPD database

• L_EPN

  Effective Perceived Noise Level

• L_eq

  Equivalent (continuous) sound level

• L_max

  Maximum value of L(t) during an event

• L_max,seg

  Maximum level generated by a segment

• ℓ

  Perpendicular distance from an observation point to the ground track

• lg

  Logarithm to base 10

• N

  Number of segments or sub-segments

• NAT

  Number of events with L_max exceeding a specified threshold

• P

  Power parameter in NPD variable L(P,d)

• P_seg

  Power parameter relevant to a particular segment

• q

  Distance from start of segment to closest point of approach

• R

  Radius of turn

• S

  Standard deviation

• s

  Distance along ground track

• s_RWY

  Runway length

• t

  Time

• t_e

  Effective duration of single sound event

• t₀

  Reference time for integrated sound level

• V

  Groundspeed

• V_seg

  Equivalent segment groundspeed

• V_ref

  Reference groundspeed for which NPD data are defined

• x,y,z

  Local coordinates

• x′,y′,z′

  Aircraft coordinates

• X_ARP,Y_ARP,Z_ARP

  Position of aerodrome reference point in geographical coordinates

• z

  Height of aircraft above ground plane/aerodrome reference point

• α

  Parameter used for calculation of the finite segment correction D_F

• β

  Elevation angle of aircraft relative to ground plane

• ε

  Aircraft bank angle

• γ

  Climb/descent angle

• φ

  Depression angle (lateral directivity parameter)

• λ

  Total segment length

• ψ

  Angle between direction of aircraft movement and direction to observer

• ξ

  Aircraft heading, measured clockwise from magnetic north

• Λ(β,ℓ)

  Air-to-ground lateral attenuation

• Λ(β)

  Long range air-to-ground lateral attenuation

• Γ(ℓ)

  Lateral attenuation distance factor

• Δ

  Change in value of a quantity, or a correction (as indicated in the text)

• Δ _F

  Finite segment correction

• Δ _I

  Engine installation correction

• Δ _i

  Weighting for ith time of day period, dB

• Δ _rev

  Reverse thrust

• Δ _SOR

  Start of roll correction

• Δ _V

  Duration (speed) correction

• 1, 2

  Subscripts denoting start and end values of an interval or segment

• E

  Exposure

• i

  Aircraft type/category summation index

• j

  Ground track/subtrack summation index

• k

  Segment summation index

• max

  Maximum

• ref

  Reference value

• seg

  Segment specific value

• SOR

  Related to start of roll

• TO

  Takeoff

All input values affecting the emission level of a source, including the position of the source, shall be determined with at least the accuracy corresponding to an uncertainty of ± 2dB(A) in the emission level of the source (leaving all other parameters unchanged).

In the application of the method, the input data shall reflect the actual usage. In general there shall be no reliance on default input values or assumptions. Specifically, flight paths derived from radar data to derive the flight paths shall be used whenever they exist and is of sufficient quality. Default input values and assumptions are accepted, for example, to be used for modelled routes instead of radar derived flight paths, if the collection of real data is associated with disproportionately high costs.

Software used to perform the calculations shall prove compliance with the methods herewith described by means of certification of results against test cases.

• The aerodrome reference point (simply to locate the aerodrome in appropriate geographic coordinates). The reference point is set as the origin of the local Cartesian coordinate system used by the calculation procedure.

• The aerodrome reference altitude (= altitude of aerodrome reference point). This is the altitude of the nominal ground plane on which, in the absence of topography corrections, the noise contours are defined.

• Average meteorological parameters at or close to the aerodrome reference point (temperature, relative humidity, average windspeed and wind direction).

For each runway:

• Runway designation

• Runway reference point (centre of runway expressed in local coordinates)

• Runway length, direction and mean gradient

• Location of start-of-roll and landing threshold13.

Aircraft ground tracks shall be described by a series of coordinates in the (horizontal) ground-plane. The source of ground track data depends on whether relevant radar data are available or not. If they are, a reliable backbone track and suitable associated (dispersed) sub-tracks shall be established by statistical analysis of the data. If not, backbone tracks are usually constructed from appropriate procedural information, e.g. using standard instrument departure procedures from Aeronautical Information Publications. This conventional description includes the following information:

• Designation of the runway the track originates from

• Description of the track origin (start of roll, landing threshold)

• Length of segments (for turns, radius and change of direction).

This information is the minimum necessary to define the core (backbone) track. But average noise levels calculated on the assumption that aircraft follow the nominal routes exactly can be liable to localised errors of several decibels. Thus lateral dispersion shall be represented, and the following additional information is necessary:

• Width of the swathe (or other dispersion statistic) at each segment end

• Number of subtracks

• Distribution of movements perpendicular to the backbone track.

Air traffic data are

• the time period covered by the data and

• the number of movements (arrivals or departures) of each aircraft type on each flight track, subdivided by (1) time of day as appropriate for specified noise descriptors, (2) for departures, operating weights or stage lengths, and (3), if necessary, operating procedures.

Most noise descriptors require that events (i.e. aircraft movements) are defined as average daily values during specified periods of the day (e.g. day, evening and night) — see Sections 2.7.23 to 2.7.25.

The terrain around most airports is relatively flat. However this is not always the case and there may sometimes be a need to account for variations in terrain elevation relative to the airport reference elevation. The effect of terrain elevation can be especially important in the vicinity of approach tracks, where the aircraft is operating at relatively low altitudes.

Terrain elevation data are usually provided as a set of (x,y,z) coordinates for a rectangular grid of certain mesh-size. But the parameters of the elevation grid are likely to be different from those of the grid used for the noise computation. If so linear interpolation may be used to estimate the appropriate z-coordinates in the latter.

Comprehensive analysis of the effects of markedly non-level ground on sound propagation is complex and beyond the scope of this method. Moderate unevenness can be accounted for by assuming ‘pseudo-level’ ground; i.e. simply raising or lowering the level ground plane to the local ground elevation (relative to the reference ground plane) at each receiver point (see Section 2.7.4).

In many cases is not possible to model flight paths on the basis of radar data — because the necessary resources are not available or because the scenario is a future one for which there are no relevant radar data.

In the absence of radar data, or when its use is inappropriate, it is necessary to estimate the flight paths on the basis of operational guidance material, for example instructions given to flight crews via AIPs and aircraft operating manuals — referred to here as procedural steps. Advice on interpreting this material shall be sought from air traffic control authorities and the aircraft operators where necessary.

This coordinate is specific for each ground track and represents distance s measured along the track in the flight direction. For departure tracks s is measured from the start of roll, for approach tracks from the landing threshold. Thus s becomes negative in areas

• behind the start of roll for departures and

• before crossing the runway landing threshold for approaches.

Flight operational parameters such as height, speed and power setting are expressed as functions of s.

The aircraft-fixed Cartesian coordinate system (x′,y′,z′) has its origin at the actual aircraft location. The axis-system is defined by the climb-angle γ, the flight direction ξ and the bank-angle ε (see Figure 2.7.c).

A ground track, whether a backbone track or a dispersed sub-track, is defined by a series of (x,y) coordinates in the ground plane (e.g. from radar information) or by a sequence of vectoring commands describing straight segments and circular arcs (turns of defined radius r and change of heading Δξ).

For segmentation modelling, an arc is represented by a sequence of straight segments fitted to sub-arcs. Although they do not appear explicitly in the ground-track segments, the banking of aircraft during turns influences their definition. Appendix B4 explains how to calculate bank angles during a steady turn but of course these are not actually applied or removed instantaneously. How to handle the transitions between straight and turning flight, or between one turn and an immediately sequential one, is not prescribed. As a rule, the details, which are left to the user (see Section 2.7.11), are likely to have a negligible effect on the final contours; the requirement is mainly to avoid sharp discontinuities at the ends of the turn and this can be achieved simply, for example, by inserting short transition segments over which the bank angle changes linearly with distance. Only in the special case that a particular turn is likely to have a dominating effect on the final contours would it be necessary to model the dynamics of the transition more realistically, to relate bank angle to particular aircraft types and to adopt appropriate roll rates. Here it is sufficient to state that the end sub-arcs Δξ_trans in any turn are dictated by bank angle change requirements. The remainder of the arc with change of heading Δξ – 2 · Δξ_trans degrees is divided into n_sub sub-arcs according to the equation:

where int(x) is a function that returns the integer part of x. Then the change of heading Δξ_sub of each sub-arc is computed as

The parameters describing each flight profile segment at the start (suffix 1) and end (suffix 2) of the segment are:

• s₁, s₂

  distance along the ground track,

• z₁, z₂

  aeroplane height,

• V₁, V₂

  groundspeed,

• P₁, P₂

  noise-related power parameter (matching that for which the NPD-curves are defined), and

• ε₁, ε₂

  bank angle.

To build a flight profile from a set of procedural steps (flight path synthesis), segments are constructed in sequence to achieve required conditions at the end points. The end-point parameters for each segment become the start-point parameters for the next segment. In any segment calculation the parameters are known at the start; required conditions at the end are specified by the procedural step. The steps themselves are defined either by the ANP defaults or by the user (e.g. from aircraft flight manuals). The end conditions are usually height and speed; the profile building task is to determine the track distance covered in reaching those conditions. The undefined parameters are determined via flight performance calculations described in Appendix B.

If the ground track is straight, the profile points and associated flight parameters can be determined independently of the ground track (bank angle is always zero). However ground tracks are rarely straight; they usually incorporate turns and, to achieve best results, these have to be accounted for when determining the 2-dimensional flight profile, where necessary splitting profile segments at ground track nodes to inject changes of bank angle. As a rule the length of the next segment is unknown at the outset and it is calculated provisionally assuming no change of bank angle. If the provisional segment is then found to span one or more ground track nodes, the first being at s, i.e. s₁ < s < s₂ , the segment is truncated at s, calculating the parameters there by interpolation (see below). These become the end-point parameters of the current segment and the start-point parameters of a new segment — which still has the same target end conditions. If there is no intervening ground track node the provisional segment is confirmed.

If the effects of turns on the flight profile are to be disregarded, the straight flight, single segment solution is adopted although the bank angle information is retained for subsequent use.

Whether or not turn effects are fully modelled, each 3-dimensional flight path is generated by merging its 2-dimensional flight profile with its 2-dimensional ground track. The result is a sequence of coordinate sets (x,y,z), each being either a node of the segmented ground track, a node of the flight profile or both, the profile points being accompanied by the corresponding values of height z, ground speed V, bank angle ε and engine power P. For a track point (x,y) which lies between the end points of a flight profile segment, the flight parameters are interpolated as follows:

z = z1 + f · (z2 – z1)	(2.7.5)
$V=\sqrt{V_2^1+f\times \left(V_2^2-V_2^1\right)}$	(2.7.6)
ε = ε1 + f · (ε2 – ε1)	(2.7.7)
$P=\sqrt{P_2^1+f\times \left(P_2^2-P_2^1\right)}$	(2.7.8)

Where

When matching flight profile segments to radar data (flight path analysis) all end-point distances, heights, speeds and bank angles are determined directly from the data; only the power settings have to be calculated using the performance equations. As the ground track and flight profile coordinates can also be matched appropriately, this is usually quite straightforward.