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ANNEX I

NOISE INDICATORS

referred to in Article 5

1.   Definition of the day-evening-night level Lden

The day-evening-night level Lden in decibels (dB) is defined by the following formula:

in which:

in which:

and in which:

The height of the Lden assessment point depends on the application:

2.   Definition of the night-time noise indicator

The night-time noise indicator Lnight is the A-weighted long-term average sound level as defined in ISO 1996-2: 1987, determined over all the night periods of a year;

in which:

3.   Supplementary noise indicators

In some cases, in addition to Lden and Lnight, and where appropriate Lday and Levening, it may be advantageous to use special noise indicators and related limit values. Some examples are given below:

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ANNEX II

ASSESSMENT METHODS FOR THE NOISE INDICATORS

(Referred to in Article 6 of Directive 2002/49/EC)

1.   INTRODUCTION

The values of Lden and Lnight shall be determined at the assessment positions by computation, according to the method set out in Chapter 2 and the data described in Chapter 3. Measurements may be performed according to Chapter 4.

2.   COMMON NOISE ASSESSMENT METHODS

2.1.    General provisions — Road traffic, railway and industrial noise

2.1.1.    Indicators, frequency range and band definitions

Noise calculations shall be defined in ►C1  the frequency range from 63 Hz to 8 kHz octave bands ◄ . Frequency band results shall be provided at the corresponding frequency interval.

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Calculations are performed in octave bands for road traffic, railway traffic and industrial noise, except for the railway noise source sound power, which uses third octave bands. For road traffic, railway traffic and industrial noise, based on these octave band results, the A-weighted long-term average sound level for the day, evening and night period, as defined in Annex I and referred to in Article 5 of Directive 2002/49/EC, is computed by the method described in Sections 2.1.2, 2.2, 2.3, 2.4 and 2.5. For roads and railway traffic in agglomerations, the A-weighted long-term average sound level is determined by the contribution from road and railway segments therein, including major roads and major railways.

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where

Noise parameters:

Other physical parameters:

2.1.2.    Quality framework

Accuracy of input values

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).

Use of default values

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.

Quality of the software used for the calculations

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

2.2.    Road traffic noise

2.2.1.    Source description

Classification of vehicles

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].

Number and position of equivalent sound sources

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In this model, each vehicle (category 1, 2, 3, 4 and 5) is represented by one single point source radiating uniformly. 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.

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Figure [2.2.a]

Location of equivalent point source on light vehicles (category 1), heavy vehicles (categories 2 and 3) and two-wheelers (category 4)

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.

Sound power emission

General considerations

The sound power of the source is defined in the ‘semi-free field’, thus the sound power includes the effect of the reflection of the ground immediately under the modelled source where there are no disturbing objects in its immediate surroundings except for the reflection on the road surface not immediately under the modelled source.

Traffic flow

The noise emission of a traffic flow is represented by a source line characterised by its directional sound power per metre per frequency. This corresponds to the sum of the sound emission of the individual vehicles in the traffic flow, taking into account the time spent by the vehicles in the road section considered. The implementation of the individual vehicle in the flow requires the application of a traffic flow model.

If a steady traffic flow of Qm vehicles of category m per hour is assumed, with an average speed vm (in km/h), the directional sound power per metre in frequency band i of the source line LW′, eq,line,i,m is defined by:

where LW,i,m is the directional sound power of a single vehicle. LW′,m is expressed in dB (re. 10–12 W/m). These sound power levels are calculated for ►C1  each octave band i from 63 Hz to 8 kHz ◄ .

Traffic flow data Qm shall be expressed as yearly average per hour, per time period (day-evening-night), per vehicle class and per source line. For all categories, input traffic flow data derived from traffic counting or from traffic models shall be used.

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The speed vm is a representative speed per vehicle category: in most cases the lower of the maximum legal speed for the section of road and the maximum legal speed for the vehicle category.

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Individual vehicle

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In the traffic flow, all vehicles of category m are assumed to drive at the same speed, i.e. vm .

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A road vehicle is modelled by a set of mathematical equations representing the two main noise sources:

Aerodynamic noise is incorporated in the rolling noise source.

For light, medium and heavy motor vehicles (categories 1, 2 and 3), the total sound power corresponds to the energetic sum of the rolling and the propulsion noise. Thus, the total sound power level of the source lines m = 1, 2 or 3 is defined by:

where LWR,i,m is the sound power level for rolling noise and LWP,i,m is the sound power level for propulsion noise. This is valid on all speed ranges. For speeds less than 20 km/h it shall have the same sound power level as defined by the formula for vm = 20 km/h.

For two-wheelers (category 4), only propulsion noise is considered for the source:

This is valid on all speed ranges. For speeds less than 20 km/h it shall have the same sound power level as defined by the formula for vm = 20 km/h.

2.2.2.    Reference conditions

The source equations and coefficients are valid for the following reference conditions:

2.2.3.    Rolling noise

General equation

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

The coefficients AR,i,m and BR,i,m are given in octave bands for each vehicle category and for a reference speed vref = 70 km/h. ΔLWR,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:

ΔLWR,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.

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

ΔLWR,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.

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

Correction for studded tyres

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 ai and bi 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 Ts (in months) over the year. If Qstud,ratio is the average ratio of the total volume of light vehicles per hour equipped with studded tyres during the period Ts (in months), then the yearly average proportion of vehicles equipped with studded tyres ps is expressed by:

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:

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

Effect of air temperature on rolling noise correction

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 τref = 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 Km = 1 = 0,08 dB/°C for light vehicles (category 1) and Km = 2 = Km = 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.

2.2.4.    Propulsion noise

General equation

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:

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

ΔLWP,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:

ΔLWP,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.

ΔLWP,acc,i,m and ΔLWP,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.

Effect of road gradients

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 ΔLWP,grad,m which is a function of the slope s (in %), the vehicle speed vm (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:

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

2.2.5.    Effect of the acceleration and deceleration of vehicles

Before and after crossings with traffic lights and roundabouts a correction shall be applied for the effect of acceleration and deceleration as described below.

The correction terms for rolling noise, ΔLWR,acc,m,k , and for propulsion noise, ΔLWP,acc,m,k , are linear functions of the distance x (in m) of the point source to the nearest intersection of the respective source line with another source line. They are attributed to all octave bands equally:

The coefficients CR,m,k and CP,m,k depend on the kind of junction k (k = 1 for a crossing with traffic lights; k = 2 for a roundabout) and are given for each vehicle category. The correction includes the effect of change in speed when approaching or moving away from a crossing or a roundabout.

Note that at a distance |x| ≥ 100 m, ΔLWR,acc,m,k = ΔLWP,acc,m,k = 0.

2.2.6.    Effect of the type of road surface

General principles

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:

where

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.

Age effect on road surface noise properties

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.

2.3.    Railway noise

2.3.1.    Source description

Classification of vehicles

Definition of vehicle and train

For the purposes of this noise calculation method, a vehicle is defined as any single railway sub-unit of a train (typically a locomotive, a self-propelled coach, a hauled coach or a freight wagon) that can be moved independently and can be detached from the rest of the train. Some specific circumstances may occur for sub-units of a train that are a part of a non-detachable set, e.g. share one bogie between them. For the purpose of this calculation method, all these sub-units are grouped into a single vehicle.

For the purpose of this calculation method, a train consists of a series of coupled vehicles.

Table [2.3.a] defines a common language to describe the vehicle types included in the source database. It presents the relevant descriptors to be used to classify the vehicles in full. These descriptors correspond to properties of the vehicle, which affect the acoustic directional sound power per metre length of the equivalent source line modelled.

The number of vehicles for each type shall be determined on each of the track sections for each of the time periods to be used in the noise calculation. It shall be expressed as an average number of vehicles per hour, which is obtained by dividing the total number of vehicles travelling in a given time period by the duration in hours of this time period (e.g. 24 vehicles in 4 hours means 6 vehicles per hour). All vehicle types travelling on each track section shall be used.

Classification of tracks and support structure

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.

Number and position of the equivalent sound sources

Figure [2.3.a]

Equivalent noise sources position

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.

2.3.2.    Sound power emission

General equations

Individual vehicle

The model for railway traffic noise, analogously to road traffic noise, describes the noise sound power emission of a specific combination of vehicle type and track type which fulfils a series of requirements described in the vehicle and track classification, in terms of a set of sound power per each vehicle (LW,0).

Traffic flow

The noise emission of a traffic flow on each track shall be represented by a set of 2 source lines characterised by its directional sound power per metre per frequency band. This corresponds to the sum of the sound emissions due to the individual vehicles passing by in the traffic flow and, in the specific case of stationary vehicles, taking into account the time spent by the vehicles in the railway section under consideration.

The directional sound power per metre per frequency band, due to all the vehicles passing by each track section on the track type (j), is defined:

and is the energy sum of all contributions from all vehicles running on the specific j-th track section. These contributions are:

To calculate the directional sound power per metre (input to the propagation part) due to the average mix of traffic on the j-th track section, the following is used:

where

Tref

=

reference time period for which the average traffic is considered

X

=

total number of existing combinations of i, t, s, c, p for each j-th track section

t

=

index for vehicle types on the j-th track section

s

=

index for train speed: there are as many indexes as the number of different average train speeds on the j-th track section

c

=

index for running conditions: 1 (for constant speed), 2 (idling)

p

=

index for physical source types: 1 (for rolling and impact noise), 2 (curve squeal), 3 (traction noise), 4 (aerodynamic noise), 5 (additional effects)

LW′,eq,line,x

=

x-th directional sound power per metre for a source line of one combination of t, s, c, p on each j-th track section

If a steady flow of Q vehicles per hour is assumed, with an average speed v, on average at each moment in time there will be an equivalent number of Q/v vehicles per unit length of the railway section. The noise emission of the vehicle flow in terms of directional sound power per metre LW′,eq,line (expressed in dB/m (re. 10–12 W)) is integrated by:

where

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In the case of a stationary source, as during idling, it is assumed that the vehicle will remain for an overall time Tidle at a location within a track section with length L. Therefore, with Tref as the reference time period for the noise assessment (e.g. 12 hours, 4 hours, 8 hours), the directional sound power per unit length on that track section is defined by:

In general, directional sound power is obtained from each specific source as:

where

And where LW,0,dir,i(ψ,φ) shall, after being derived in 1/3 octave bands, be expressed in octave bands by energetically adding each pertaining 1/3 octave band together into the corresponding octave band.

Figure [2.3.b]

Geometrical definition

For the purpose of the calculations, the source strength is then specifically expressed in terms of directional sound power per 1 m length of track LW′,tot,dir,i to account for the directivity of the sources in their vertical and horizontal direction, by means of the additional corrections.

Several LW,0,dir,i (ψ,φ) are considered for each vehicle-track-speed-running condition combination:

A set of LW,0,dir,i (ψ,φ) are considered for each vehicle-track-speed-running condition combination, each track section, the heights corresponding to h = 1 and h = 2 and the directivity.

Rolling noise

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.

Wheel and rail roughness

Rolling noise is mainly excited by rail and wheel roughness in the wavelength range from 5-500 mm.

Definition

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
:

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, ►C1  and v is the train speed in m/s ◄ . 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 ►C1   A 3(λ) ◄ contact filter to take into account the filtering effect of the contact patch between the rail and the wheel, and is in dB:

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.

Vehicle, track and superstructure transfer function

Three speed-independent transfer functions, LH,TR,i LH,VEH,i and LH,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 LR,TOT,i as a function of the vehicle speed v, the track, vehicle and superstructure transfer functions LH,TR,i , LH,VEH,i and LH,VEH,SUP,i , and the total number of axles Na :

for h = 1:

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

Figure [2.3.c]

Scheme of the use of the different roughness and transfer function definitions

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 (crossings, switches and junctions)

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 LR,TOT + IMPACT,i shall be used in place of LR,TOT,i and it will then become:

LR,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 ►C1  and v is the s-th vehicle speed of the t-th vehicle type in m/s ◄ .

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:

where LR,IMPACT–SINGLE,i is the impact roughness level as given for a single impact and nl is the joint density.

The default impact roughness level is given for a joint density nl = 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 nl . 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 LW,0 of track, wheel/bogie and superstructure contribution are incremented by means of the LR,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 nl of 0,01 shall be used.

Squeal

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Curve squeal is a special source that is only relevant for curves and is therefore localised. Curve squeal is generally dependent on curvature, friction conditions, train speed, track-wheel geometry and dynamics. As it can be significant, an appropriate description is required. At locations where curve squeal occurs, generally in curves and turnouts of railway switches, suitable excess noise power spectra need to be added to the source power. The excess noise may be specific to each type of rolling stock, as certain wheel and bogie types may be significantly less prone to squeal than others. If measurements of the excess noise are available that take sufficiently the stochastic nature of squeal into account, these may be used.

If no appropriate measurements are available, a simple approach can be taken. In this approach, squeal noise shall be considered by adding the following excess values to the rolling noise sound power spectra for all frequencies.

where ltrack is the length of track along the curve and R is the curve radius.

The applicability of these sound power spectra or excess values shall normally be verified on-site, especially for trams and for locations where curves or turnouts are treated with measures against squeal.

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Traction noise

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 LW,0,const,i = LW,0,idling,i . Also, the LW,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 LW,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:

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

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:

where

Source directivity

The horizontal directivity ΔLW,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:

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Bridge noise is modelled at source A (h = 1), for which omni-directionality is assumed.

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The vertical directivity ΔLW,dir,ver,i in dB is given in the vertical plane for source A (h = 1), as a function of the centre band frequency fc,i of each i-th frequency band, and:

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

ΔLW,dir,ver,i = 0 elsewhere

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

2.3.3.    Additional effects

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Correction for structural radiation (bridges and viaducts)

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. The bridge noise is modelled as an additional source of which the sound power per vehicle is given by

where LH, bridge ,i is the bridge transfer function. The bridge noise LW,0, bridge ,i represents only the sound radiated by the bridge construction. The rolling noise from a vehicle on the bridge is calculated using (2.3.8) through (2.3.10), by choosing the track transfer function that corresponds to the track system that is present on the bridge. Barriers on the edges of the bridge are generally not taken into account.

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Correction for other railway-related noise sources

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.

2.4.    Industrial noise

2.4.1.    Source description

Classification of source types (point, line, area)

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.

Number and position of equivalent sound sources

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:

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.

Sound power emission

General

The following information constitutes the complete set of input data for sound propagation calculations with the methods to be used for noise mapping:

The point, line and area source sound power are required to be defined as:

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The working hours are an essential input for the calculation of noise levels. The working hours shall be given for the day, evening and night period and, if the propagation is using different meteorological classes defined during each of the day, night and evening periods, then a finer distribution of the working hours shall be given in sub-periods matching the distribution of meteorological classes. This information shall be based on a yearly average.

The correction for the working hours, to be added to the source sound power to define the corrected sound power that shall be used for calculations over each time period, CW in dB is calculated as follows:

where

For the more dominant sources, the yearly average working hours correction shall be estimated at least within 0,5 dB tolerance in order to achieve an acceptable accuracy (this is equivalent to an uncertainty of less than 10 % in the definition of the active period of the source).

Source directivity

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:

The directivity shall be expressed in the calculation as a factor ΔLW,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
. This directivity can also be expressed by means of other coordinate systems such as angular coordinate systems.

2.5.    Calculation of noise propagation for road, railway, industrial sources.

2.5.1.    Scope and applicability of the method

This document specifies a method for calculating the attenuation of noise during its outdoor propagation. Knowing the characteristics of the source, this method predicts the equivalent continuous sound pressure level at a receiver point corresponding to two particular types of atmospheric conditions:

The method of calculation described in this document applies to industrial infrastructures and land transport infrastructures. It therefore applies in particular to road and railway infrastructures. Aircraft transport is included in the scope of the method only for the noise produced during ground operations and excludes take-off and landing.

Industrial infrastructures that emit impulsive or strong tonal noises as described in ISO 1996-2:2007 do not fall within the scope of this method.

The method of calculation does not provide results in upward-refraction propagation conditions (negative vertical gradient of effective sound speed) but these conditions are approximated by homogeneous conditions when computing Lden.

To calculate the attenuation due to atmospheric absorption in the case of transport infrastructure, the temperature and humidity conditions are calculated according to ISO 9613-1:1996.

The method provides results per octave band, from 63 Hz to 8 000 Hz. The calculations are made for each of the centre frequencies.

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Objects sloping more than 15° in relation to the vertical are not considered as reflectors but taken into account in all other aspects of propagation, such as ground effects and diffraction.

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A single screen is calculated as a single diffraction calculation, two or more screens in a single path are treated as a subsequent set of single diffractions by applying the procedure described further.

2.5.2.    Definitions used

All distances, heights, dimensions and altitudes used in this document are expressed in metres (m).

The notation MN stands for the distance in 3 dimensions (3D) between the points M and N, measured according to a straight line joining these points.

The notation ^MN stands for the curved path length between the points M and N, in favourable conditions.

It is customary for real heights to be measured vertically in a direction perpendicular to the horizontal plane. Heights of points above the local ground are denoted h, absolute heights of points and absolute height of the ground are to be noted by the letter H.

To take into account the actual relief of the land along a propagation path, the notion of ‘equivalent height’ is introduced, to be noted by the letter z. This substitutes real heights in the ground effect equations.

The sound levels, noted by the capital letter L, are expressed in decibels (dB) per frequency band when index A is omitted. The sound levels in decibels dB(A) are given the index A.

The sum of the sound levels due to mutually incoherent sources is noted by the sign in accordance with the following definition:

2.5.3.    Geometrical considerations

Source segmentation

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.

Propagation paths

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.

Significant heights above the ground

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.

Figure 2.5.a

Equivalent heights in relation to the ground

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 zs and the equivalent receiver height zr can therefore be defined. The distance between the source and receiver in projection over the mean ground plane is noted by dp .

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.

Calculation of the mean plane

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:

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:

The coefficients of the straight line are given by:

Where segments with xk + 1 = xk shall be ignored when evaluating eq. 2.5.3.

Reflections by building façades and other vertical obstacles

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

2.5.4.    Sound propagation model

For a receiver R the calculations are made according to the following steps:

It should be noted that only the attenuations due to the ground effect (Aground ) and diffraction (Adif ) are affected by meteorological conditions.

2.5.5.    Calculation process

For a point source S of directional sound power Lw,0,dir and for a given frequency band, the equivalent continuous sound pressure level at a receiver point R in given atmospheric conditions is obtained according to the equations following below.

Sound level in favourable conditions (LF) for a path (S,R)

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

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where

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

Sound level in homogeneous conditions (LH) for a path (S,R)

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

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

where

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

Statistical approach inside urban areas for a path (S,R)

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 Aboundary,H and Aboundary,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.

Long-term sound level for a path (S,R)

The ‘long-term’ sound level along a path starting from a given point source is obtained from the logarithmic sum of the weighted sound energy in homogeneous conditions and the sound energy in favourable conditions.

These sound levels are weighted by the mean occurrence p of favourable conditions in the direction of the path (S,R):

NB: The occurrence values for p are expressed in percentages. So for example, if the occurrence value is 82 %, equation (2.5.9) would have p = 0,82.

Long-term sound level at point R for all paths

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:

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 (Si,R).

Long-term sound level at point R in decibels A (dBA)

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

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where i is the index of the frequency band. AWC is the A-weighting correction as follows:

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This level LAeq,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).

2.5.6.    Calculation of noise propagation for road, railway, industrial sources.

Geometrical divergence

The attenuation due to geometrical divergence, Adiv, 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.

Atmospheric absorption

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

where

The values of the αatm 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.

Ground effect

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, zs and zr refer to the equivalent source and/or receiver position as indicated further where the calculation of the diffraction Adif is presented.

Acoustic characterisation of ground

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.

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

When the source and receiver are close-by so that dp ≤ 30(zs + zr ), 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 Gpath is therefore ultimately corrected as follows:

where Gs is the ground factor of the source area. Gs = 0 for road platforms ( 5 ), slab tracks. Gs = 1 for rail tracks on ballast. There is no general answer in the case of industrial sources and plants.

G may be linked to the flow resistivity.

Figure 2.5.b

Determination of the ground coefficient Gpath over a propagation path

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The distances dn are determined by a 2D projection on the horizontal plane.

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The following two subsections on calculations in homogeneous and favourable conditions introduce the generic
w and
m notations for the absorption of the ground. Table 2.5.b gives the correspondence between these notations and the Gpath and G′path variables.

Calculations in homogeneous conditions

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

if Gpath ≠ 0

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 Cf is defined by:

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

w may be equal to either Gpath 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 Aground,H .

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

With diffraction, refer to the section on diffraction for the definitions of
w and
m .

if Gpath = 0: Aground,H = – 3 dB

The term – 3(1 –
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.

Calculation in favourable conditions

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

The height corrections δ zs and δ zr convey the effect of the sound ray bending. δ zT accounts for the effect of the turbulence.

m may also be equal to either Gpath 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 (Si,R) in favourable conditions without diffraction:

With diffraction, refer to the next section for the definitions of
w and
m .

Diffraction

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, Adif = 0 can be set and a direct view calculated, in particular by evaluating Aground .

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In practice, the following specifications are considered in the unique vertical plane containing both source and receiver (a flattened Chinese Screen in case of a path including reflections). The direct ray from source to receiver is a straight line under homogeneous propagation conditions and a curved line (arc with radius depending on the length of the straight ray) under favorable propagation conditions.

If the direct ray is not blocked, the edge D is sought which produces the largest path length difference δ (the smallest absolute value because these path length differences are negative). Diffraction is taken into account if:

This is the case, if δ is larger than λ/4 – δ*, where δ* is the path length difference calculated with this same edge D but related to the mirror source S* calculated with the mean ground plane at the source side and the mirror receiver R* calculated with the mean ground plane at the receiver side. To calculate δ* only the points S*, D and R* are taken into account – other edges blocking the path S*->D->R* are neglected.

For the above considerations, the wavelength λ is calculated using the nominal centre frequency and a speed of sound of 340 m/s.

If these two conditions are fulfilled, the edge D separates the source side from the receiver side, two separate mean ground planes are calculated, and A dif is calculated as described in the remainder of this part. Otherwise, no attenuation by diffraction is considered for this path, a common mean ground plane for the path S -> R is calculated, and A ground is calculated with no diffraction (A dif = 0 dB). This rule applies in both homogeneous and favourable conditions.

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When, for a given frequency band, a calculation is made according to the procedure described in this section, Aground 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.

General principles

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:

Figure 2.5.c

Geometry of a calculation of the attenuation due to diffraction

1

:

Source side

2

:

Receiver side

where

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.

Pure diffraction

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

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.

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For a multiple diffraction, if e is the total path length distance between first and last diffraction point (use curved rays in case of favourable conditions) and if e exceeds 0,3 m (otherwise C" = 1), this coefficient is defined by:

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The values of Δdif shall be bound:

Calculation of the path difference

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.

Homogeneous conditions

Figure 2.5.d

Calculation of the path difference in homogeneous conditions. O, O1 , and O2 are the diffraction points

Note: For each configuration, the expression of δ is given.

Favourable conditions

Figure 2.5.e

Calculation of the path difference in favourable conditions (single diffraction)

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In favourable conditions the three curved sound rays, , and have an identical radius of curvature Γ defined by:

Where d is defined by the 3D distance between source and receiver of the unfolded path.

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The length of a sound ray curve MN is noted ^MN 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 δF (see Figure 2.5.e). In practice, two equations are sufficient:

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:

Under favourable conditions, the propagation path in the vertical propagation plane always consists of segments of a circle whose radius is given by the 3D-distance between source and receiver, that is to say, all segments of a propagation path have the same radius of curvature. If the direct arc connecting source and receiver is blocked, the propagation path is defined as the shortest convex combination of arcs enveloping all obstacles. Convex in this context means that at each diffraction point, the outgoing ray segment is deflected downward with respect to the incoming ray segment.

Figure 2.5.f

Example of calculation of the path difference in favourable conditions, in the case of multiple diffractions

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

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Calculation of the attenuation Adif

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:

where

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Calculation of the term Δground(S,O)

where

In the special case where the source lies below the mean ground plane: Δ dif(S,R) = Δ dif(S',R) and Δ ground(S,O) = A ground(S,O)

Calculation of the term Δground(O,R)

where

In the special case where the receiver lies below the mean ground plane: Δ dif(S,R’) = Δ dif(S,R) and Δ ground ( O,R ) = A ground ( O,R )

Vertical Edge Scenarios

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, Adif = Δdif(S,R) is taken and the term Aground is kept. In addition, Aatm and Aground shall be calculated from the total length of the propagation path. Adiv is still calculated from the direct distance d. Equations (2.5.8) and (2.5.6) respectively become:

Δdif is indeed used in homogeneous conditions in equation (2.5.34).

Lateral diffraction is considered only in cases, where the following conditions are met:

If all these conditions are met, up to two laterally diffracted propagation paths are taken into account in addition to the diffracted propagation path in the vertical plane containing source and receiver. The lateral plane is defined as the plane that is perpendicular to the vertical plane and also contains source and receiver. The intersection areas with this lateral plane are constructed from all obstacles that are penetrated by the direct ray from source to receiver. In the lateral plane, the shortest convex connection between source and receiver, consisting of straight segments and encompassing these intersection areas, defines the vertical edges that are taken into account when the laterally diffracted propagation path is constructed.

To calculate ground attenuation for a laterally diffracted propagation path, the mean ground plane between the source and the receiver is calculated taking into account the ground profile vertically below the propagation path. If, in the projection onto a horizontal plane, a lateral propagation path cuts the projection of a building, this is taken into account in the calculation of Gpath (usually with G = 0) and in the calculation of the mean ground plane with the vertical height of the building.

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Reflections on vertical obstacles

Attenuation through absorption

The reflections on vertical obstacles are dealt with by means of image sources. Reflections on building façades and noise barriers are thus treated in this way.

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Surfaces of objects are only considered as reflectors if their slopes are less than 15° with respect to the vertical. Reflections are considered only for paths in the vertical propagation plane, that is to say, not for laterally diffracted paths. For the incident and reflected paths, and assuming the reflecting surface is to be vertical, the point of reflection (which lays on the reflecting object) is constructed using straight lines under homogeneous and curved lines under favourable propagation conditions. The height of the reflector, when measured through the point of reflection and viewed from the direction of the incident ray, shall be at least 0,5 m. After projection onto a horizontal plane, the width of the reflector when measured through the point of reflection and viewed from the direction of the incident ray, shall be at least 0,5 m.

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The obstacles where at least one dimension is less than 0,5 m shall be ignored in the reflection calculation, except for special configurations ( 6 ).

Note that reflections on the ground are not dealt with here. They are taken into account in the calculations of attenuation due to the boundary (ground, diffraction).

If LWS is the power level of the source S and αr the absorption coefficient of the surface of the obstacle as defined by the EN 1793-1:2013, then the power level of the image source S′ is equal to:

where 0 ≤ αr < 1

The propagation attenuations described above are then applied to this path (image source, receiver), as for a direct path.

Figure 2.5.g

Specular reflection on an obstacle dealt with by the image source method (S: source, S′: image source, R: receiver)

Attenuation through retrodiffraction

In the geometrical research of sound paths, during reflection on a vertical obstacle (barrier wall, building), the position of the impact of the ray in relation to the upper edge of this obstacle determines the more or less significant proportion of energy effectively reflected. This loss of acoustic energy when the ray undergoes a reflection is called attenuation through retrodiffraction.

In the case of potential multiple reflections between two vertical walls, at least the first reflection shall be considered.

In the case of a trench (see for example Figure 2.5.h), the attenuation through retrodiffraction shall be applied to each reflection on the retaining walls.

Figure 2.5.h

Sound ray reflected to the order of 4 in a track in a trench: actual cross-section (top), unfolded cross-section (bottom)

In this representation, the sound ray reaches the receiver ‘by successively passing through’ the retaining walls of the trench, which can therefore be compared to openings.

When calculating propagation through an opening, the sound field at the receiver is the sum of the direct field and the field diffracted by the edges of the opening. This diffracted field ensures the continuity of the transition between the clear area and the shadow area. When the ray approaches the edge of the opening, the direct field is attenuated. The calculation is identical to that of the attenuation by a barrier in the clear area.

The path difference δ′ associated with each retrodiffraction is the opposite of the path difference between S and R relatively at each upper edge O, and this in a view according to a deployed cross-section (see Figure 2.5.i).

Figure 2.5.i

The path difference for the second reflection

The ‘minus’ sign of equation (2.5.36) means that the receiver is considered here in the clear area.

Attenuation through retrodiffraction Δ retrodif is obtained by equation (2.5.37), which is similar to equation (2.5.21) with reworked notations.

This attenuation is applied to the direct ray each time it ‘passes through’ (reflects on) a wall or building. The power level of the image source S′ therefore becomes:

In complex propagation configurations, diffractions may exist between reflections, or between the receiver and the reflections. In this case, the retrodiffraction by the walls is estimated by considering the path between source and first diffraction point R′ (therefore considered as the receiver in equation (2.5.36)). This principle is illustrated in Figure 2.5.j.

Figure 2.5.j

The path difference in the presence of a diffraction: actual cross-section (top), unfolded cross-section (bottom)

In case of multiple reflections the reflections due to every single reflections are added.

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When there is a reflecting noise barrier or obstacle close to the railway track, the sound rays from the source are successively reflected off this obstacle and off the lateral face of the railway vehicle. In these conditions, the sound rays pass between the obstacle and railway vehicle body before diffraction from the top edge of the obstacle.

To take multiple reflections between railway vehicle and a nearby obstacle into account, the sound power of a single equivalent source is calculated. In this calculation, ground effects are ignored.

To derive the sound power of the equivalent source the following definitions apply:

The inner side of the obstacle has absorption coefficients α(f) per octave band. The railway vehicle body has an equivalent reflection coefficient Cref . Normally Cref is equal to 1. Only, in the case of open flat-bed freight wagons a value of 0 can be used. If dB >5hB or α(f)>0,8 no train barrier interaction is taken into account.

In this configuration, multiple reflections between the railway vehicle body and the obstacle can be calculated using image sources positioned at Sn (dn = -2n. dB, hn = hs), n=0,1,2,..N; as shown in the Figure 2.5.k.

Figure 2.5.k

The sound power of the equivalent source is expressed by:

Where the sound power of the partial sources is given by:

LW,n = LW + ΔLn

ΔLn= ΔLgeo,n + ΔLdif,n + ΔLabs,n + ΔLref,n + ΔLretrodif,n

With:

LW	the sound power of the real source

ΔLgeo,n

a correction term for spherical divergence

ΔLdif,n

a correction term for diffraction by the top of the obstacle

ΔLabs,n

a correction term for the absorption at the inner side of the obstacle

ΔLref,n

a correction term for reflection from the railway vehicle body

ΔLretrodif,n

a correction term for the finite height of the obstacle as a reflector

The correction for spherical divergence is given by

The correction for diffraction by the top of the obstacle is given by:

(2.5.42)

Where Dn is the attenuation due to diffraction, calculated by means of formula 2.5.21 where C'' = 1 , for the path linking source Sn to receiver R, taking into account diffraction at the top of the obstacle B:

The correction for absorption on the inner side of the obstacle is given by:

The correction for reflection from the railway vehicle body is given by:

The correction for the finite height of the reflecting obstacle is taken into account by means of retro-diffraction. The ray path corresponding to an image of order N > 0 will be reflected n times by the obstacle. In the cross section, these reflections take place at distances

di = – (2i-q)db, i = 1,2,..n Where Pi (d = di, h = hb ), i = 1,2,..n as the tops of these reflecting surfaces. At each of these points a correction term is calculated as:

Where Δ retrodif,n,i is calculated for a source at position Sn an obstacle top at Pi and a receiver at position R’. The position of the equivalent receiver R’ is given by R’=R if the receiver is above line of sight from Sn to B; otherwise the equivalent receiver position is taken on the line of sight vertically above the real receiver; namely:

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2.6.    General provisions — Aircraft noise

2.6.1.    Definitions and symbols

Some important terms are described here by the general meanings attributed to them in this document. The list is not exhaustive; only expressions and acronyms used frequently are included. Others are described where they first occur.

The mathematical symbols (listed after the terms) are the main ones used in equations in the main text. Other symbols used locally in both the text and the appendices are defined where they are used.

The reader is reminded periodically of the interchangeability of the words sound and noise in this document. Although the word noise has subjective connotations — it is usually defined by acousticians as ‘unwanted sound’ — in the field of aircraft noise control it is commonly taken to mean just sound — airborne energy transmitted by acoustic wave motion. The symbol → denotes cross references to other terms included in the list.

Terms

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, LA

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.

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, Leq

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 (LA ) 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 LDEN

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, LAE

(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, Leq,W

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

Symbols

d	Shortest distance from an observation point to a flight path segment

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

dλ	Scaled distance

Fn	Actual net thrust per engine

Fn /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)

LA, LA(t)

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

LAE	(SEL) Sound Exposure Level

LAmax

Maximum value of LA(t) during an event

LE	Single event sound exposure level

LE∞	Single event sound exposure level determined from NPD database

LEPN	Effective Perceived Noise Level

Leq	Equivalent (continuous) sound level

Lmax	Maximum value of L(t) during an event

Lmax,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 Lmax exceeding a specified threshold

P	Power parameter in NPD variable L(P,d)

Pseg	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

sRWY	Runway length

t

Time

te	Effective duration of single sound event

t 0	Reference time for integrated sound level

V	Groundspeed

Vseg	Equivalent segment groundspeed

Vref	Reference groundspeed for which NPD data are defined

x,y,z

Local coordinates

x′,y′,z′

Aircraft coordinates

XARP,YARP,ZARP

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 DF

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

Subscripts

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

2.6.2.    Quality framework

Accuracy of input values

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).

Use of default values

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.

Quality of the software used for the calculations

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

2.7.    Aircraft noise

2.7.1.    Aim and scope of document

Contour maps are used to indicate the extent and magnitude of aircraft noise impact around airports, that impact being indicated by values of a specified noise metric or index. A contour is a line along which the index value is constant. The index value aggregates in some way all the individual aircraft noise events that occur during some specified period of time, normally measured in days or months.

The noise at points on the ground from aircraft flying into and out of a nearby aerodrome depends on many factors. Principal among these are the types of aeroplane and their powerplant; the power, flap and airspeed management procedures used on the aeroplanes themselves; the distances from the points concerned to the various flight paths; and local topography and weather. Airport operations generally include different types of aeroplanes, various flight procedures and a range of operational weights.

Contours are generated by calculating surfaces of local noise index values mathematically. This document explains in detail how to calculate, at one observer point, the individual aircraft noise event levels, each for a specific aircraft flight or type of flight, that are subsequently averaged in some way, or accumulated, to yield index values at that point. The required surface of index values is generated merely by repeating the calculations as necessary for different aircraft movements — taking care to maximise efficiency by excluding events that are not ‘noise-significant’ (i.e. which do not contribute significantly to the total).

Where noise generating activities associated with airport operations do not contribute materially to the overall population exposure to aircraft noise and associated noise contours, they may be excluded. These activities include: helicopters, taxiing, engine testing and use of auxiliary power-units. This does not necessarily mean that their impact is insignificant and where these circumstances occur assessment of the sources can be undertaken as set out in paragraphs 2.7.21 and 2.7.22.

2.7.2.    Outline of the document

The noise contour generation process is illustrated in Figure 2.7.a. Contours are produced for various purposes and these tend to control the requirements for sources and pre-processing of input data. Contours that depict historical noise impact might be generated from actual records of aircraft operations — of movements, weights, radar-measured flight paths, etc. Contours used for future planning purposes of necessity rely more on forecasts — of traffic and flight tracks and the performance and noise characteristics of future aircraft.

Figure 2.7.a

The noise contour generation process

Whatever the source of flight data, each different aircraft movement, arrival or departure, is defined in terms of its flight path geometry and the noise emission from the aircraft as it follows that path (movements that are essentially the same in noise and flight path terms are included by simple multiplication). The noise emission depends on the characteristics of the aircraft — mainly on the power generated by its engines. The recommended methodology involves dividing the flight path into segments. Sections 2.7.3 to 2.7.6 outline the elements of the methodology and explain the principle of segmentation on which it is based; that the observed event noise level is an aggregation of contributions from all ‘noise-significant’ segments of the flight path, each of which can be calculated independently of the others. Sections 2.7.3 to 2.7.6 also outline the input data requirements for producing a set of noise contours. Detailed specifications for the operational data needed are set out in Appendix A.

How the flight path segments are calculated from pre-processed input data is described in Sections 2.7.7 to 2.7.13. This involves applications of aircraft flight performance analysis, equations for which are detailed in Appendix B. Flight paths are subject to significant variability — aircraft following any route are dispersed across a swathe due to the effects of differences in atmospheric conditions, aircraft weights and operating procedures, air traffic control constraints, etc. This is taken into account by describing each flight path statistically — as a central or ‘backbone’ path which is accompanied by a set of dispersed paths. This too is explained in Sections 2.7.7 to 2.7.13 with reference to additional information in Appendix C.

Sections 2.7.14 to 2.7.19 set out the steps to be followed in calculating the noise level of one single event — the noise generated at a point on the ground by one aircraft movement. Appendix D deals with the re-calculation of NPD-data for non-reference conditions. Appendix E explains the acoustic dipole source used in the model to define sound radiation from flight path segments of finite length.

Applications of the modelling relationships described in Chapters 3 and 4 require, apart from the relevant flight paths, appropriate noise and performance data for the aircraft in question.

Determining the event level for a single aircraft movement at a single observer point is the core calculation. It has to be repeated for all aircraft movements at each of a prescribed array of points covering the expected extent of the required noise contours. At each point the event levels are aggregated or averaged in some way to arrive at a ‘cumulative level’ or noise index value. This part of the process is described in Sections 2.7.20 and 2.7.23 to 2.7.25.

Sections 2.7.26 to 2.7.28 summarise the options and requirement for fitting noise contours to arrays of noise index values. They provide guidance on contour generation and post-processing.

2.7.3.    The concept of segmentation

For any specific aircraft, the database contains baseline Noise-Power-Distance (NPD) relationships. These define, for steady straight flight at a reference speed in specified reference atmospheric conditions and in a specified flight configuration, the received sound event levels, both maximum and time integrated, directly beneath the aircraft ( 7 ) as a function of distance. For noise modelling purposes, the all-important propulsive power is represented by a noise-related power parameter; the parameter generally used is corrected net thrust. Baseline event levels determined from the database are adjusted to account for, firstly, differences between actual (i.e. modelled) and reference atmospheric conditions and (in the case of sound exposure levels) aircraft speed and, secondly, for receiver points that are not directly beneath the aircraft, differences between downwards and laterally radiated noise. This latter difference is due to lateral directivity (engine installation effects) and lateral attenuation. But the event levels so adjusted still apply only to the total noise from the aircraft in steady level flight.

Segmentation is the process by which the recommended noise contour model adapts the infinite path NPD and lateral data to calculate the noise reaching a receiver from a non-uniform flight path, i.e. one along which the aircraft flight configuration varies. For the purposes of calculating the event sound level of an aircraft movement, the flight path is represented by a set of contiguous straight-line segments, each of which can be regarded as a finite part of an infinite path for which an NPD and the lateral adjustments are known. The maximum level of the event is simply the greatest of the individual segment values. The time integrated level of the whole noise event is calculated by summing the noise received from a sufficient number of segments, i.e. those which make a significant contribution to the total event noise.

The method for estimating how much noise one finite segment contributes to the integrated event level is a purely empirical one. The energy fraction F — the segment noise expressed as a proportion of the total infinite path noise — is described by a relatively simple expression which allows for the longitudinal directivity of aircraft noise and the receiver's ‘view’ of the segment. One reason why a simple empirical method is generally adequate is that, as a rule, most of the noise comes from the nearest, usually, adjacent segment — for which the closest point of approach (CPA) to the receiver lies within the segment (not at one of its ends). This means that estimates of the noise from non-adjacent segments can be increasingly approximate as they get further away from the receiver without compromising the accuracy significantly.

2.7.4.    Flight paths: Tracks and profiles

In the modelling context, a flight path (or trajectory) is a full description of the motion of the aircraft in space and time ( 8 ). Together with the propulsive thrust (or other noise related power parameter) this is the information required to calculate the noise generated. The ground track is the vertical projection of the flight path on level ground. This is combined with the vertical flight profile to construct the 3-D flight path. Segmentation modelling requires that the flight path of every different aircraft movement is described by a series of contiguous straight segments. The manner in which the segmentation is performed is dictated by a need to balance accuracy and efficiency — it is necessary to approximate the real curved flight path sufficiently closely while minimising the computational burden and data requirements. Each segment has to be defined by the geometrical coordinates of its end points and the associated speed and engine power parameters of the aircraft (on which sound emission depends). Flight paths and engine power may be determined in various ways, the main ones involving (a) synthesis from a series of procedural steps and (b) analysis of measured flight profile data.

Synthesis of the flight path (a) requires knowledge of (or assumptions for) ground tracks and their lateral dispersions, aircraft weight, speed, flap and thrust-management procedures, airport elevation, and wind and air temperature. Equations for calculating the flight profile from the required propulsion and aerodynamic parameters are given in Appendix B. Each equation contains coefficients (and/or constants) which are based on empirical data for each specific aircraft type. The aerodynamic-performance equations in Appendix B permit the consideration of any reasonable combination of aircraft operational weight and flight procedure, including operations at different takeoff gross weights.

Analysis of measured data (b), e.g. from flight data recorders, radar or other aircraft tracking equipment, involves ‘reverse engineering’, effectively a reversal of the synthesis process (a). Instead of estimating the aircraft and powerplant states at the ends of the flight segments by integrating the effects of the thrust and aerodynamic forces acting on the airframe, the forces are estimated by differentiating the changes of height and speed of the airframe. Procedures for processing the flight path information are described in Section 2.7.12.

In an ultimate noise modelling application, each individual flight could, theoretically, be represented independently; this would guarantee accurate accounting for the spatial dispersion of flight paths — which can be very significant. But to keep data preparation and computer time within reasonable bounds it is normal practice to represent flight path swathes by a small number of laterally displaced ‘subtracks’. (Vertical dispersion is usually represented satisfactorily by accounting for the effects of varying aircraft weights on the vertical profiles.)

▼M6

2.7.5.    Aircraft noise and performance

The ANP database provided in Appendix I contains aircraft and engine performance coefficients, departure and approach profiles as well as NPD relationships for a substantial proportion of civil aircraft operating from European Union airports. For aircraft types or variants for which data are not currently listed, they can best be represented by data for other, normally similar, aircrafts that are listed.

This data was derived to calculate noise contours for an average or representative fleet and traffic mix at an airport. It may not be appropriate to predict absolute noise levels of an individual aircraft model and is not suitable to compare the noise performance and characteristics of specific aircraft types, models or a specific fleet of aircraft. Instead, to determine which aircraft types, models or specific fleet of aircrafts are the noisiest contributors, the noise certificates shall be looked at.

The ANP database includes one or several default take-off and landing profiles for each aircraft type listed. The applicability of these profiles to the airport under consideration shall be examined, and either the fixed-point profiles or the procedural steps that best represent the flight operations at this airport shall be determined.

▼M2

2.7.6.    Airport and aircraft operations

Case-specific data from which to calculate the noise contours for a particular airport scenario includes the following.

General airport data

Runway data

For each runway:

Ground track data

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:

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:

Air traffic data

Air traffic data are

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.

Topographical data

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).

Reference conditions

The international aircraft noise and performance (ANP) data are normalised to standard reference conditions that are widely used for airport noise studies (see Appendix D).

Reference conditions for NPD data

(1)	Atmospheric pressure : 101,325 kPa (1 013,25 mb)

(2)	Atmospheric absorption : Attenuation rates listed in Table D-1 of Appendix D

(3)	Precipitation : None

(4)	Wind Speed : Less than 8 m/s (15 knots)

(5)	Groundspeed : 160 knots

(6)	Local terrain : Flat, soft ground free of large structures or other reflecting objects within several kilometres of aircraft ground tracks.

Standardised aircraft sound measurements are made 1,2 m above the ground surface. However no special account of this is necessary as, for modelling purposes, it may be assumed that event levels are relatively insensitive to receiver height ( 10 ).

Comparisons of estimated and measured airport noise levels indicate that the NPD data can be assumed applicable when the near surface average conditions lie within the following envelope:

This envelope is believed to encompass conditions encountered at most of the world's major airports. Appendix D provides a method for converting NPD data to average local conditions which fall outside it, but, in extreme cases, it is suggested that the relevant aeroplane manufacturers be consulted.

Reference conditions for aeroplane aerodynamic and engine data

(1)	Runway Elevation : Mean sea level

(2)	Air temperature : 15 °C

(3)	Takeoff gross weight : As defined as a function of stage length in the ANP database

(4)	Landing gross weight : 90 percent of maximum landing gross weight

(5)	Engines supplying thrust : All

Although ANP aerodynamic and engine data are based on these conditions, they can be used as tabulated for non-reference runway elevations and average air temperatures in ECAC states without significantly affecting the accuracy of the calculated contours of cumulative average sound level. (see Appendix B.)

The ANP database tabulates aerodynamic data for the takeoff and landing gross weights noted in items 3 and 4 above. Although, for cumulative noise calculations, the aerodynamic data themselves need not be adjusted for other gross weights, calculation of the takeoff and climbout flight profiles, using the procedures described in Appendix B, shall be based on the appropriate operational takeoff gross weights.

2.7.7.    Description of the flight path

The noise model requires that each different aircraft movement is described by its three-dimensional flight path and the varying engine power and speed along it. As a rule, one modelled movement represents a subset of the total airport traffic, e.g. a number of (assumed) identical movements, with the same aircraft type, weight and operating procedure, on a single ground track. That track may itself be one of several dispersed ‘sub-tracks’ used to model what is really a swathe of tracks following one designated route. The ground track swathes, the vertical profiles and the aircraft operational parameters are all determined from the input scenario data — in conjunction with aircraft data from the ANP database.

The noise-power-distance data (in the ANP database) define noise from aircraft traversing idealised horizontal flight paths of infinite length at constant speed and power. To adapt this data to terminal area flight paths that are characterised by frequent changes of power and velocity, every path is broken into finite straight-line segments; the noise contributions from each of these are subsequently summed at the observer position.

2.7.8.    Relationships between flight path and flight configuration

The three-dimensional flight path of an aircraft movement determines the geometrical aspects of sound radiation and propagation between aircraft and observer. At a particular aircraft weight and in particular atmospheric conditions, the flight path is governed entirely by the sequence of power, flap and altitude changes that are applied by the pilot (or automatic flight management system) in order to follow routes and maintain heights and speeds specified by ATC — in accordance with the aircraft operator's standard operating procedures. These instructions and actions divide the flight path into distinct phases which form natural segments. In the horizontal plane they involve straight legs, specified as a distance to the next turn, and turns, defined by radius and change of heading. In the vertical plane, segments are defined by the time and/or distance taken to achieve required changes of forward speed and/or height at specified power and flap settings. The corresponding vertical coordinates are often referred to as profile points.

For noise modelling, flight path information is generated either by synthesis from a set of procedural steps (i.e. those followed by the pilot) or by analysis of radar data — physical measurements of actual flight paths flown. Whatever method is used, both horizontal and vertical shapes of the flight path, are reduced to segmented forms. Its horizontal shape (i.e. its 2-dimensional projection on the ground) is the ground track defined by the inbound or outbound routeing. Its vertical shape, given by the profile points, and the associated flight parameters speed, bank angle and power setting, together define the flight profile which depends on the flight procedure that is normally prescribed by the aircraft manufacturer and/or the operator. The flight path is constructed by merging the 2-D flight profile with the 2-D ground track to form a sequence of 3-D flight path segments.

It should be remembered that, for a given set of procedural steps, the profile depends on the ground track; e.g. at the same thrust and speed the aircraft climb rate is less in turns than in straight flight. Although this guidance explains how to take this dependency into account, it has to be acknowledged that doing so would normally involve a very large computing overhead and users may prefer to assume that, for noise modelling purposes, the flight profile and ground track can be treated as independent entities; i.e. that the climb profile is unaffected by any turns. However, it is important to determine changes of bank angle that turns require as this has an important bearing on the directionality of sound emission.

The noise received from a flight path segment depends on the geometry of the segment in relation to the observer and the aircraft flight configuration. But these are interrelated — a change in one causes a change in the other and it is necessary to ensure that, at all points on the path, the configuration of the aircraft is consistent with its motion along the path.

In a flight path synthesis, i.e. when constructing a flight path from a set of ‘procedural steps’ that describe the pilot's selections of engine power, flap angle, and acceleration/vertical speed, it is the motion that has to be calculated. In a flight path analysis, the reverse is the case: the engine power settings have to be estimated from the observed motion of the aeroplane — as determined from radar data, or sometimes, in special studies, from aircraft flight recorder data (although in the latter case engine power is usually part of the data). In either case, the coordinates and flight parameters at all segment end points have to be fed into the noise calculation.

Appendix B presents the equations that relate the forces acting on an aircraft and its motion and explains how they are solved to define the properties of the segments that make up the flight paths. The different kinds of segments (and the sections of Appendix B that cover them) are take-off ground roll (B5), climb at constant speed (B6), power cutback (B7), accelerating climb and flap retraction (B8), accelerating climb after flap retraction (B9), descent and deceleration (B10) and final landing approach (B11).

Inevitably, practical modelling involves varying degrees of simplification — the requirement for this depends on the nature of the application, the significance of the results and the resources available. A general simplifying assumption, even in the most elaborate applications, is that when accounting for flight track dispersion, the flight profiles and configurations on all the sub-tracks are the same as those on the backbone track. As at least 6 subtracks are to be used (see Section 2.7.11) this reduces computations massively for an extremely small penalty in fidelity.

2.7.9.    Sources of flight path data

Radar data

Although aircraft flight data recorders can yield very high quality data, this is difficult to obtain for noise modelling purposes and radar data shall be regarded as the most readily accessible source of information on actual flight paths flown at airports ( 11 ). As it is usually available from airport noise and flight path monitoring systems, it is now used increasingly for noise modelling purposes.

Secondary surveillance radar presents the flight path of an aircraft as a sequence of positional coordinates at intervals equal to the period of rotation of the radar scanner, typically about 4 seconds. The position of the aircraft over the ground is determined in polar coordinates — range and azimuth — from the reflected radar return (although the monitoring system normally transforms these to Cartesian coordinates); its height ( 12 ) is measured by the aeroplane's own altimeter and transmitted to the ATC computer by a radar-triggered transponder. But inherent positional errors due to radio interference and limited data resolution are significant (although of no consequence for the intended air traffic control purposes). Thus, if the flight path of a specific aircraft movement is required, it is necessary to smooth the data using an appropriate curve-fitting technique. However, for noise modelling purposes the usual requirement is for a statistical description of a swathe of flight paths; e.g. for all movements on a route or for just those of a specific aircraft type. Here the measurement errors associated with the relevant statistics can be reduced to insignificance by the averaging processes.

Procedural steps

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.

2.7.10.    Coordinate systems

The local coordinate system

The local coordinate system (x,y,z) is a Cartesian one and has its origin (0,0,0) at the aerodrome reference point (XARP,YARP,ZARP ), where ZARP is the airport reference altitude and z = 0 defines the nominal ground plane on which contours are usually calculated. The aircraft heading ξ in the xy-plane is measured clockwise from magnetic north (see Figure 2.7.b). All observer locations, the basic calculation grid and the noise contour points are expressed in local coordinates ( 13 ).

Figure 2.7.b

Local coordinate system (x,y,z) and ground-track fixed coordinate s

The ground-track fixed coordinate system

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

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

The aircraft coordinate system

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).

Figure 2.7.c

Aircraft fixed coordinate system (x′,y′,z′)

Accounting for topography

In cases where topography has to be taken into account (see Section 2.7.6), the aircraft height coordinate z has to be replaced by z′= z – zo (where zo is the z-coordinate of the observer location O) when estimating the propagation distance d. The geometry between aircraft and observer is shown in Figure 2.7.d. For the definitions of d and ℓ see Sections 2.7.14 to 2.7.19 ( 14 ).

Figure 2.7.d

Ground elevation along (left) and lateral (right) to ground track

(The nominal ground plane z = 0 passes through the aerodrome reference point. O is the observer location.)

2.7.11.    Ground Tracks

Backbone tracks

The backbone track defines the centre of the swathe of tracks followed by aircraft using a particular routeing. For the purposes of aircraft noise modelling it is defined either (i) by prescriptive operational data such as the instructions given to pilots in AIPs, or (ii) by statistical analysis of radar data as explained in Section 2.7.9 — when this is available and appropriate to the needs of the modelling study. Constructing the track from operational instructions is normally quite straightforward as these prescribe a sequence of legs which are either straight — defined by length and heading, or circular arcs defined by turn rate and change of heading; see Figure 2.7.e for an illustration.

Figure 2.7.e

Ground track geometry in terms of turns and straight segments

Fitting a backbone track to radar data is more complex, firstly because actual turns are made at a varying rate and secondly because its line is obscured by the scatter of the data. As explained, formalised procedures have not yet been developed and it is common practice to match segments, straight and curved, to the average positions calculated from cross-sections of radar tracks at intervals along the route. Computer algorithms to perform this task are likely to be developed in future but, for the present, it is for the modeller to decide how to use available data to best advantage. A major factor is that the aircraft speed and turn radius dictate the angle of bank and, as will be seen in Section 2.7.19, non-symmetries of sound radiation around the flight path govern noise on the ground, as well as the position of the flight path itself.

Theoretically, seamless transition from straight flight to fixed radius turn would require an instantaneous application of bank angle ε, which is physically impossible. In reality it takes a finite time for the bank angle to reach the value required to maintain a specified speed and turn radius r, during which the turn radius tightens from infinity to r. For modelling purposes the radius transition can be disregarded and the bank angle assumed to increase steadily from zero (or other initial value) to ε at the start of the turn and to be the next value of ε at the end of the turn ( 15 ).

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Lateral track dispersion

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Where possible, definitions of lateral dispersion and representative sub-tracks shall be based on relevant past experience from the study airport; normally via an analysis of radar data samples. The first step is to group the data by route. Departure tracks are characterised by substantial lateral dispersion which, for accurate modelling, has to be taken into account. Arrival routes normally coalesce into a very narrow swathe about the final approach path and it is usually sufficient to represent all arrivals by a single track. But if the approach swathes are wide within the region of the noise contours they might need to be represented by sub-tracks in the same way as departure routes.

It is common practice to treat the data for a single route as a sample from a single population; i.e. to be represented by one backbone track and one set of dispersed subtracks. However, if inspection indicates that the data for different categories of aircraft or operations differ significantly (e.g. should large and small aircraft have substantially different turn radii), further subdivision of the data into different swathes may be desirable. For each swathe, the lateral track dispersions are determined as a function of distance from the origin; movements then being apportioned between a backbone track and a suitable number of dispersed sub-tracks on the basis of the distribution statistics.

As it is normally unwise to disregard the effects of track dispersion, in the absence of measured swathe data a nominal lateral spread across and perpendicular to the backbone track shall be defined by a conventional distribution function. Calculated values of noise indices are not particularly sensitive to the precise shape of the lateral distribution: the Normal (Gaussian) Distribution provides an adequate description of many radar-measured swathes.

Typically a 7-point discrete approximation is used (i.e. representing the lateral dispersion by 6 subtracks equally spaced around the backbone track). The spacing of the subtracks depends on the standard deviation of the lateral dispersion function.

For normally distributed tracks with a standard deviation S, 98,8 % of the tracks are located within a corridor with boundaries located at ± 2,5 · S. Table 2.7.a gives the spacing of the six subtracks and the percentage of the total movements assigned to each. Appendix C gives values for other numbers of subtracks.

The standard deviation S is a function of the coordinate s along the backbone-track. It can be specified — together with the description of the backbone-track — in the flight track data sheet shown in Appendix A3. In the absence of any indicators of the standard deviation — e.g. from radar data describing comparable flight tracks — the following values are recommended:

For practical reasons, S(s) is assumed to be zero between the start of roll and s = 2 700 m or s = 3 300 m depending on the amount of turn. Routes involving more than one turn shall be treated as per equation (2.7.2). For arrivals, lateral dispersion can be neglected within 6 000 m of touchdown.

2.7.12.    Flight profiles

The flight profile is a description of the aircraft motion in the vertical plane above the ground track, in terms of its position, speed, bank angle and engine power setting. One of the most important tasks facing the model user is that of defining aircraft flight profiles that adequately meet the requirements of the modelling application — efficiently, without consuming excessive time and resources. Naturally, to achieve high accuracy, the profiles have to reflect closely the aircraft operations they are intended to represent. This requires reliable information on the atmospheric conditions, aircraft types and variants, operating weights and the operating procedures — the variations of thrust and flap settings and the trade-offs between changes of height and speed — all appropriately averaged over the time period(s) of interest. Often such detailed information are not available but this is not necessarily an obstacle; even if they are, the modeller has to exercise judgement to balance the accuracy and detail of the input information with the needs for, and uses of, the contour outputs.

The synthesis of flight profiles from ‘procedural steps’ obtained from the ANP database or from aircraft operators is described in Section 2.7.13 and Appendix B. That process, usually the only recourse open to the modeller when no radar data are available, yields both the flight path geometry and the associated speed and thrust variations. It would normally be assumed that all (alike) aircraft in a swathe, whether assigned to the backbone or the dispersed subtracks, follow the backbone track profile.

Beyond the ANP database, which provides default information on procedural steps, the aircraft operators are the best source of reliable information, i.e. the procedures they use and the typical weights flown. For individual flights, the ‘gold standard’ source is the aircraft flight data recorder (FDR) from which all relevant information can be obtained. But even if such data are available, the pre-processing task is formidable. Thus, and in keeping with the necessary modelling economies, the normal practical solution is to make educated assumptions about mean weights and operating procedures.

Caution must be exercised before adopting default procedural steps provided in the ANP database (customarily assumed when actual procedures are not known). These are standardised procedures that are widely followed but which may or may not be used by operators in particular cases. A major factor is the definition of take-off (and sometimes climb) engine thrust that can depend to an extent on prevailing circumstances. In particular, it is common practice to reduce thrust levels during departure (from maximum available) in order to extend engine life. Appendix B gives guidance on representing typical practice; this will generally produce more realistic contours than a full thrust assumption. However, if, for example, runways are short and/or average air temperatures are high, full thrust is likely to be a more realistic assumption.

When modelling actual scenarios, improved accuracy can be achieved by using radar data to supplement or replace this nominal information. Flight profiles can be determined from radar data in a similar way to the lateral backbone tracks — but only after segregating the traffic by aircraft type and variant and sometimes by weight or stage length (but not by dispersion) — to yield for each sub-group a mean profile of height and speed against ground distance travelled. Again, when merging with the ground tracks subsequently, this single profile is normally assigned to the backbone and subtracks alike.

Knowing the aircraft weight, the variation of speed and propulsive thrust can be calculated via step-by-step solution of the equations of motion. Before doing so it is helpful to pre-process the data to minimise the effects of radar errors which can make acceleration estimates unreliable. The first step in each case is to redefine the profile by fitting straight line segments to represent the relevant stages of flight; with each segment being appropriately classified; i.e. as a ground roll, constant speed climb or descent, thrust cutback, or acceleration/deceleration with or without flap change. The aircraft weight and atmospheric state are also required inputs.

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An aircraft noise source should be entered at a minimum height of 1,0m (3,3ft) above the aerodrome level, or above the terrain elevation levels of the runway, as relevant.

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Section 2.7.11 makes it clear that special provision has to be made to account for the lateral dispersion of flight tracks about the nominal or backbone routeings. Radar data samples are characterised by similar dispersions of flight paths in the vertical plane. However it is not usual practice to model vertical dispersion as an independent variable; it arises mainly due to differences in aircraft weights and operating procedures that are taken into account when pre-processing traffic input data.

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2.7.13.    Construction of flight path segments

Each flight path has to be defined by a set of segment coordinates (nodes) and flight parameters. The starting point is to determine the co-ordinates of the ground track segments. The flight profile is then calculated, remembering that for a given set of procedural steps, the profile depends on the ground track; e.g. at the same thrust and speed the aircraft climb rate is less in turns than in straight flight. Sub-segmentation is then undertaken for the aircraft on the runway (takeoff or landing ground roll), and for the aircraft near to the runway (initial climb or final approach). Airborne segments with significantly different speeds at their start and end points should then be sub-segmented. The two-dimensional co-ordinates of the ground track ( 16 ) segments are determined and merged with the two-dimensional flight profile to construct the three-dimensional flight path segments. Finally, any flight path points that are too close together are removed.

Flight profile

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, ε 2

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, namely 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 co-ordinate 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:

where

Note that whilst z and ε are assumed to vary linearly with distance, V and P are assumed to vary linearly with time (namely constant acceleration ( 17 )).

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.

Takeoff ground roll

When taking off, as an aircraft accelerates between the point of brake release (alternatively termed Start-of-Roll SOR) and the point of lift-off, speed changes dramatically over a distance of 1 500 to 2 500  m, from zero to between around 80 and 100 m/s.

The takeoff roll is thus divided into segments with variable lengths over each of which the aircraft speed changes by specific increment ΔV of no more than 10 m/s (about 20 kt). Although it actually varies during the takeoff roll, an assumption of constant acceleration is adequate for this purpose. In this case, for the takeoff phase, V1 is initial speed, V2 is the takeoff speed, nTO is the number of takeoff segment and sTO is the equivalent takeoff distance. For equivalent takeoff distance sTO (see Appendix B) and takeoff speed V1 and takeoff speed VTO the number nTO of segments for the ground roll is

and hence the change of velocity along a segment is

and the time Δt on each segment is (constant acceleration assumed)

The length sTO,k of segment k (1 ≤ k ≤ nTO) of the takeoff roll is then:

Example: For a takeoff distance sTO  = 1 600  m, V1 = 0m/s and V2 = 75 m/s, this yields nTO  = 8 segments with lengths ranging from 25 to 375 metres (see Figure 2.7.g):

Figure 2.7.g
Segmentation of a takeoff roll (example for 8 segments)

Similarly to the speed changes, the aircraft thrust changes over each segment by a constant increment ΔP, calculated as

where PTO and P init respectively designate the aircraft thrust at the point of lift-off and the aircraft thrust at the start of takeoff roll.

The use of this constant thrust increment (instead of using the quadratic form equation 2.7.6) aims at being consistent with the linear relationship between thrust and speed in the case of jet-engine aircraft.

Important note: The above equations and example implicitly assume that the initial speed of the aircraft at the start of the takeoff phase is zero. This corresponds to the common situation where the aircraft starts to roll and accelerate from the brake release point. However, there are also situations where the aircraft may start to accelerate from its taxiing speed, without stopping at the runway threshold. In that case of non-zero initial speed Vinit the following ‘generalised’ equations should be used in replacement of equations 2.7.8, 2.7.9. 2.7.10 and 2.7.11.

In this case, for the takeoff phase, V1  is initial speed Vinit , V2  is the takeoff speed VTO , n is the number of takeoff segment nTO , s is the equivalent takeoff distance sTO and sk  is the length sTO,k  of segment k (1[Symbol]k[Symbol]n).

The landing ground roll

Although the landing ground roll is essentially a reversal of the takeoff ground roll, special account has to be taken of

In contrast to the takeoff roll distance, which is derived from aircraft performance parameters, the stop distance sstop (namely the distance from touchdown to the point where the aircraft leaves the runway) is not purely aircraft specific. Although a minimum stop distance can be estimated from aircraft mass and performance (and available reverse thrust), the actual stop distance depends also on the location of the taxiways, on the traffic situation, and on airport-specific regulations on the use of reverse thrust.

The use of reverse thrust is not a standard procedure – it is only applied if the needed deceleration cannot be achieved by the use of the wheel brakes. (Reverse thrust can be exceptionally disturbing as a rapid change of engine power from idle to reverse settings produces a sudden burst of noise.)

However, most runways are used for departures as well as for landings so that reverse thrust has a very small effect on the noise contours since the total sound energy in the vicinity of the runway is dominated by the noise produced from takeoff operations. Reverse thrust contributions to contours may only be significant when runway use is limited to landing operations.

Physically, reverse thrust noise is a very complex process but because of its relatively minor significance to air noise contours it can be modelled simplistically – the rapid change in engine power being taken into account by suitable segmentation.

It is clear that modelling the landing ground roll is less straightforward than for takeoff roll noise. The following simplified modelling assumptions are recommended for general use, when no detailed information is available (see Figure 2.7.h.1).