Energy Technology SP Report 2014:34

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### Speed Railway Applications in Sweden

**Summary **

A new noise assessment method was proposed, which is for evaluating noise impact along high-speed railway lines and for estimating noise mitigation measures where required. The method was prepared in a way that it can easily be further expanded to cover conventional trains as well as low speed or idling situations.

As the Nord2000 model has already been chosen as the propagation module of the new method, in this report only the source module and the calculation module are described. In fact these two modules have impact on each other: calculating maximum noise level of train passages requires a classification based on train types, while a dB-value description of noise mitigation measures benefits the desired noise calculation. In the report the most typical issue addressed is classification. It is found that a classification based on vehicle types is noise mitigation measure oriented, which is neither convenient for noise calculation nor proper for high-speed applications. Thus, “a classification of noise calculation oriented” was considered. Based on this understanding, a train classification based on noise emission strength was proposed. Moreover, noise mitigation measures are integrated and described by a single parameter, additional noise reduction, which shall be given either in total level or in spectrum.

For a source model an important part is source data. At this time (and in Sweden) there are no real source data available for high-speed railway noise. A set of default source data was then worked out based on the source data of X2 trains together with the TSI requirement on noise. This set of default source data is thought enough good for estimating noise impact along high-speed lines, based on two reasons: (1) As for X2 trains the rolling noise and the aerodynamic noise become comparable at about 370 km/h which is the same as for typical TGV trains; this suggests that the ratio between the two noise components is the same or comparable for the two train types. (2) Many TGV trains just fulfil the TSI requirement on noise. Therefore, although X2 trains are found too noisy, by adding on proper noise reduction (6 dB) useful default source data have been obtained.

Not only the mathematical equations for calculating desired acoustic quantities have been formulated, the necessary numerical formulations have also been provided that aims at benefiting a quick IT-implementation of the new method.

**Key words: Noise assessment method, high-speed railway noise, source model, **

classification

**SP Sveriges Tekniska Forskningsinstitut **

SP Technical Research Institute of Sweden
**SP Report 2014:34 **

ISBN 978-91-86622-18-3 ISSN 0284-5172

**Content **

**Summary **

**3**

**Content **

**4**

**Preface **

**6**

**1**

**Introduction **

**7**

1.1 List of symbols 8
**2**

**Basic source model **

**11**

2.1 General 11

2.2 Source line and source position 11

2.2.1 Lateral source position 12

2.2.2 Source height 12

2.3 Classifications of trains/vehicles, tracks and driving conditions 17

2.4 Directional sound power levels 23

2.4.1 Directivity 23

2.4.2 Sound power levels 26

2.4.2.1 Rolling noise and the indirect roughness method 26

2.4.2.2 Aerodynamic noise 30

2.4.2.3 Other noise types 31

2.4.2.4 Default source data for high-speed railway noise 31

2.5 Tunnel openings 32

2.5.1 General 34

2.5.2 Values of a 35

2.5.3 Calculation procedure 36

2.6 Noise mitigation measures 37

2.6.1 Acoustic grinding 37

2.6.2 Reduction of the wheel component of noise 37

2.6.3 Reduction of the track component of noise 38

2.6.4 Shielding measures 38

2.6.4.1 Trackside barriers 38

2.6.5 Reduction of aerodynamic noise 39

2.7 Source data 39

**3**

**Determination of railway noise impact **

**41**

3.1 Propagation attenuation 41

3.2 Source line description 42

3.3 *Instantaneous sound pressure level Lp* 43

3.4 *Leq,T* and SEL of a single train passage 44

3.5 *Leq,T* of railway traffic noise 47

3.6 *Standard noise indicators Lden and Lnight* 47

3.7 Consideration of vertical directivity 48

3.8 *The maximum level LAFmax* 48

3.8.1 An empirical approach for estimating

*L*

_{AF}_{max}49

3.9 Indoor noise impact levels 49

3.10 Steps of calculation process 52

**4**

**Future work **

**55**

4.1 Further improvement of the noise assessment method 55

4.2 Data collection 55

4.2.1 Collection of the representative source data 55

4.2.2 Specifying noise mitigation measures and the representative

noise reductions 56

**Reference **

**57**

**Annex A **

**The transfer function between L**

**The transfer function between L**

**W**** and L**

**and L**

**eq,Tp****59**

**Annex B **

**Source data for X2 rolling noise **

**63**

**Annex C **

**Default noise source data for high-speed railway **

**systems **

**65**

**Annex D **

**Default noise source data for high-speed railway **

**Preface **

This project is funded by the Swedish Transport Administration (Trafikverket), with
the framework contract number (ramavtal kontraktsnummer) TRV 2011/51717A and
**the order number (avropsavtal beställningsnummer) 2541. **

The Nord2000 source model and the CNOSSOS-Harmonoise source model for railway noise have been referred to.

Kjell Strömmer (Trafikverket) provides his constructive comments on façade noise reduction.

All the above direct or indirect supports are gratefully acknowledged. Borås 2014-08-10

.

**1 **

**Introduction **

The Swedish Transport Administration (Trafikverket) is now requiring a new noise assessment method for evaluating noise impact from high-speed railway lines (up to 320 km/h) and for estimating noise mitigation measures where required, because the current method used in Sweden is not applicable for the purpose [1]. SP Acoustics was consulted and a three-month long project was launched for preparing the new method. The project is divided into two parts. In the first part (Etapp A) three typical noise assessment methods in EU (Nord2000, CNOSSOS-Harmonoise, NMPB2008) have been reviewed [2]; this review provides a solid basis for the Swedish Transport Administration to choose the most suitable parts of these methods for building up a new Swedish noise assessment method. In the second part (Etapp B) the focus is put on preparing a new source module for high-speed railway noise, because the Nord2000 model has already been chosen as the propagation module of the new method. The calculations of desired acoustic quantities will also be formulated; and in fact they have an impact on building up a source module. For example, in order to calculate maximum noise level of train passages, a classification based on train types instead of on vehicle types is favoured.

In general, a noise assessment method consists of three parts: a propagation module which is for handling sound propagation under different conditions, a source module which is for specifying the noise sources and the source positions and determining the directional sound powers, and a calculation module which is for calculating desired acoustic quantities as well as estimating noise mitigation measures where required. As has been mentioned, in this report only the source module and the calculation module will be described.

Railway noise has multiple sub-sources, either localized ones such as locomotive
traction noise or pantograph noise, or the ones distributed along the whole train such
as rolling noise or aerodynamic noise around the bogies. Thus, railway noise will be
described by source lines and/or point sources, with directional sound power levels
*specified. A source line consists of a line of incoherent point sources, differing from *
*a line source which consists of a line of coherent point sources. And, source positions *
are specified by representative lateral positions and heights, referring to the physical
origins.

For being able to accurately specify directional sound power levels for each noise
source, trains, tracks and driving conditions are classified. A classification shall aim
at helping with accurate noise calculations, while not increasing the burden in source
data collection. Therefore, a classification of noise calculation oriented is favoured.
*Desired calculation quantities are the European standard noise indicators Lden* and

*Lnight, the common noise indicators for case studies Lp, Leq,T and SEL, the special *

*Swedish noise indicator LAFmax*, as well as the required indoor noise level of traffic

*noise, Leq,indoor*. The frequency range is one-third octave bands of the centre

The new noise assessment method have been prepared in the way that it has a focus on high-speed railway applications (because of the short project time); however, it can be easily further expanded (in near future) to cover conventional speed (< 200 km/h) and low speed (< 50 km/h) as well as idling situations.

The source module will be described in Section 2 and the calculation module will be described in Section 3. And, in last section, possible future works will be discussed.

**1.1 **

**List of symbols **

*excess*

*A* excess attenuation

###

*f*

*A*_{1} level difference between the average vibration at the measurement
point and the railhead

###

*f*

*A*2 level difference between the vibration displacement at the contact
point on the railhead and the combined effective roughness

###

*f*

*A*4 level difference between the vibration at the contact point and the
vibration of the railhead averaged over the wheel passage interval

*tun*

*A* the cross section of a tunnel portal

*c * speed of sound in air

###

*v*

*C*

*speed-dependent correction for façade sound reduction*

_{aero}*CF * contact filter

*D(f) * track decay rate

* f * 1/3 octave band centre frequency
max

*AF*

*L*

maximum sound pressure level using frequency weighting A and
time weighting F
###

*f*

*L _{a,}_{contact}* equivalent vertical rail acceleration level at the contact point

###

*f*

*L _{a,}_{head}* equivalent vertical rail acceleration level at the railhead over the
measurement position

###

*f*

*L*

*a,meas*equivalent vertical rail acceleration level at the measurement position

*day*

*L* yearly averaged day time

*L*

_{eq}*den*

*L*

yearly averaged day-evening-night weighted *L*

_{eq}*evening*

*L* yearly averaged evening-weighted

*L*

_{eq}*eq*

*L*

(*L*

*,*

_{eq}*)*

_{T}*equivalent continuous sound pressure level (over time interval T)*

*f*
*T*
*eq*

*L*

_{,}

*L*

_{eq}_{,}

*under favourable weather condition*

_{T}*h*
*T*
*eq*

*L*

_{,}

*L*

_{eq}_{,}

*under homogenous weather condition*

_{T}*cvkm*
*T*
*eq*

*L*

_{,}the contribution to

*L*

_{eq}_{,}

_{T}*from source type k of source height m of*

*train type c at speed v*

*km*
*T*
*eq*

*L*

_{,}the contribution to

*L*

_{eq}_{,}

_{T}*from source type k of source height m*

*u*
*T*
*eq*

*L*

_{,}

*L*

*,*

_{eq}*under unfavourable weather condition*

_{T}*indoor*
*eq*

*p*

*T*
*eq*

*L*

_{,}

*L*

*over the time interval defined in Figure A1 in Annex A.*

_{eq}*tot*
*H*

*L*

_{,}the total transfer function of rolling noise

*veh*
*H*

*L*

_{,}the vehicle transfer function of rolling noise, 1 axle per meter

*tr*
*H*

*L*

_{,}the track transfer function of rolling noise, 1 axle per meter

*night*

*L*

yearly averaged night-weighed *L*

_{eq}*CE*

*L*

C-weighted sound exposure level of a train passing by a tunnel portal
*p*

*L*

instantaneous sound pressure level
*pF*
*L*
*F*
*T*
*eq*
*L* _{,}
, with

*T*

*= 1/8 second*

_{F}*km*

*p*

*L*

_{,}the contribution to

*L*

_{p}*from source type k of source height m*

*tot*
*p*

*L*

_{,}instantaneous sound pressure level of total rolling noise

*RE*

*L*

sound exposure level for micro-pressure wave
*r*
*r*

*L*

_{,}rail roughness level

*w*
*r*

*L*

_{,}wheel roughness level

*tot*
*r*

*L*

_{,}total roughness level

*W*

*L*

sound power level
*o*
*a*
*W*

*L* , er sound power level of aerodynamic noise

*i*
*W*

*L*

*sound power level of ith*unit of a train

###

*m*

*L*

*i*

_{W}### 1

*sound power level per meter train emitted from ith*unit of a train

###

*1m*

### ,

### 0

###

*L*

*i*the omni-directional component of

_{W}*L*

*i*

_{W}###

### 1

*m*

*wagon*

*L*

wagon length
###

*f*

*Lx,contact* vibration displacement at the contact point

*M = v/c * the Mach number

*axle*

*N*

number of axles per wagon
*f*

*p* yearly averaged occurrence probability for favourable weather
condition

*h*

*p*

yearly averaged occurrence probability for homogeneous weather
condition
*u*

*p*

yearly averaged occurrence probability for unfavourable weather
condition
*SEL * sound exposure level

*Tx* the time length for the measurement illustrated in Figure 2.8.

*t * time

*v * train speed

*W * tunnel width

*T*

*W*

sound power radiated from a tunnel opening
*a*

*L*

###

the propagation effect of air absorption,*d*

*L*

###

*v*

*L*

_{façade}

###

###

### 30

###

*C*

_{aero}###

*v*

, speed-dependent façade sound reduction for high-
speed railway noise
*r*

*L*

the propagation effect of obstacle dimensions and surface

properties when calculating a contribution from sound reflected by an obstacle.

*s*

*L*

###

the propagation effect of scattering zones,*t*

*L*

###

the propagation effect of the terrain (ground and barriers),*MPW*

*p*

###

disturbance of micro-pressure wave###

*ji*

*L*

###

###

the directional component of*L*

*i*

_{W}###

### 1

*m*

### )

### (

###

*x*

*L*

###

horizontal directivity for source x where x can be rail, track, wheel, bogie, pantograph### )

### (

###

*y*

*vertical*

*L*

###

*vertical directivity for source or source component y where y can be*

*R (which is for rolling noise), or, bogie/pantograph component of *

aerodynamic noise

###

wavelength###

horizontal angle*j*

###

the horizontal angle of a train centre*ji*

###

*the horizontal angle of ith*unit of a train

###

vertical angle*C*

###

receptance of the contact stiffness*R*

###

rail receptance*W*

###

wheel receptance solid angle which depends on the geometry of the portal and the surroundings

*tot*

**2 **

**Basic source model **

**2.1 **

**General **

A source model for railway noise should specify the important noise types, the representative source positions, the directional sound power levels, and make classifications of vehicle/train types, track types and driving conditions as well as define the related calculation procedures.

Railway noise has multiple sources. The three main noise types are: traction noise (emitted from traction motors, cooling fans, gears and auxiliary equipment), rolling noise (through wheel-rail contact interaction) and aerodynamic noise (due to vortex shedding from wheels and pantographs, flow separations at train nose and tail, flow disturbances at edges and cavities). And, there are also other noise types like impact noise (at joints, points and switches, or due to out-of-round wheels), bridge noise, viaduct vibration noise, curve squeal noise, braking noise and braking squeal noise, noise from auxiliary equipment, etc. These noise sources are distributed over the height and length of the train, with directional sound powers of different strengths. A source model for railway noise should be capable to properly describe these features. After more than 40 years research effort, railway noise has now been well understood and its most important component, rolling noise, can be properly predicted [3]. At high speed, the other noise type, aerodynamic noise, needs to be considered. For this noise type, theoretical modelling of it is still limited to a few simple configurations [3]; it will thus be handled in an empirical method [4-5]. Theoretical research on impact noise and curve squeal noise can be thought quite successful. However, for traction noise and other noise types the source descriptions of them are mainly based on measurements.

Within this project, the focus is put on making a source model for high-speed railway noise. At high speed traction noise is negligible (while cooling fan noise may have some effect on the total noise level [18]); and, on a high-speed line, other noise types such as curve squeal noise or impact noise are as believed irrelevant. For some high-speed lines noise emission from viaduct vibration may be relevant; while the most important noise types are always rolling noise and aerodynamic noise.

The source model prepared in this project follows the main line of the Harmonoise source model for railway noise, while revised where necessary. The frequency range is one-third octave bands of the centre frequencies between 25 Hz and 10 kHz.

**2.2 **

**Source line and source position **

A source line, differing from a line source which is modelled as a line of coherent point sources, is defined as a line of incoherent point sources. For rolling noise, roughness on two wheels’ running surfaces are incoherent; for aerodynamic noise, flow disturbances at two cavities as well as vortex shedding from two bogies are incoherent. Thus, the concept of source line removes possible confusions in source modelling.

**2.2.1 **

**Lateral source position **

For strategic noise mapping, it is acceptable to put all source lines at the centre of the track. However, for detailed case studies exact source locations may be required, e.g. to study the shielding effect of near-track low noise barriers. Therefore, the nearest rail was chosen as the lateral position for all the source lines/point sources, although for pantograph noise this position may be slightly worse than the centre of the track.

**2.2.2 **

**Source height **

In the Nord2000 model, the default source heights for railway rolling noise are 0.01 m, 0.35 m and 0.7 m (above the railhead; the same hereafter), which are comparable to the somehow simplified choice made in the Harmonoise model: 0 and 0.5 m. (Note: In the Nord2000 calculation software, a source or receiver height less than 0.01 m will be treated as 0.01 m to avoid possible numerical difficulty.) However, in CNOSSOS-EU, only one source height of 0.5 m was specified for rolling noise; this choice is thought questionable as discussed in the following.

The source height around the railhead is for rail/track contribution and the source height of 0.5 m is for wheels’ contribution. In the Nord2000 model the two default source heights, 0.35 m and 0.7 m, are for wheels’ contribution. According to the measurement study showed in [6], see Figure 2.1, it seems that one height (0.5 m) or the two heights (0.35 m and 0.7 m) are the same good for describing wheels’ contribution. Considering that by reducing one source height will save quite a lot calculation time, the simplification made in the Harmonoise model is favoured.

**Figure 2.1. Vibration distribution across the wheel (Figure 6 in [6]). **

A balance between accuracy and calculation time is important; calculation errors should be controlled following the required accuracy. Accordingly, one is limited to make simplifications in a source model; each simplification should be evaluated, through benchmark calculations or measurements.

(a)

(b)

**Figure 2.2. (a) The representative terrain profile (2D) for a railway track and the **

*surrounding, the two source heights (0.01 m and 0.5 m above the railhead), and the *
*three typical receiving positions (7.5m/1.2m, 25m/3.5m, 100m/2m). (b) Difference in *
*excess attenuations for the two source heights 0.01 m and 0.5 m. *

0 10 20 30 40 50 60 70 80 90 100 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 distance to track (m) h e ig h t w .r .t . ra il w a y b e d ( m ) hs: 0.01 m hs: 0.5 m hr: 1.2 m hr: 3.5 m hr: 2 m terrain 101 102 103 104 -10 -8 -6 -4 -2 0 2 4 6 8 10 excess(hs = 0.01 m) - excess(hs = 0.5 m) dB dr/hr = 7.5m/1.2m dr/hr = 25m/3.5m dr/hr = 100m/2m

(a)

(b)

**Figure 2.3. (a) The terrain profile is similar as that in Figure 2.2 while a near-track **

*low noise barrier (1 m to the rail and 0.7 m over the railhead) is added; the two *
*standard receiving positions (7.5m/1.2m, 25m/3.5m). (b) Difference in excess *
*attenuations for the two source heights 0.01 m and 0.5 m. *

0 5 10 15 20 25 -1 0 1 2 3 4 distance to track (m) h e ig h t w .r .t . ra il w a y b e d ( m ) hs: 0.01 m hs: 0.5 m hr: 1.2 m hr: 3.5 m terrain 101 102 103 104 -8 -6 -4 -2 0 2 4 6 8 10 excess(hs = 0.01 m) - excess(hs = 0.5 m) dB dr/hr = 7.5m/1.2m dr/hr = 25m/3.5m

(a)

(b)

**Figure 2.4. (a) The terrain profile is similar as that in Figure 2.2 while a noise **

*barrier (6 m from the rail and 4 m over the railhead) is added; one receiving position *
*100m/2m. (b) Difference in excess attenuations for the two source heights 0.01 m and *
*0.5 m. *

In Figures 2.2 - 2.4, the difference in excess attenuations in sound propagation from each of the two source heights, 0.01 m and 0.5 m, to typical receiving positions was

0 10 20 30 40 50 60 70 80 90 100 -1 0 1 2 3 4 5 6 distance to track (m) h e ig h t w .r .t . ra il w a y b e d ( m ) hs: 0.01 m hs: 0.5 m hr: 2 m terrain 101 102 103 104 -8 -6 -4 -2 0 2 4 excess(hs = 0.01 m) - excess(hs = 0.5 m) dB dr/hr = 100m/2m

shown, for several representative situations. Based on these calculation results, we
conclude that it is NOT proper to use 0.5 m source height for rail/track noise. In other
words, two representative source heights are necessary and enough for describing
rolling noise: 0.01 m for rail/track contribution and 0.5 m for wheels’ contribution.
Detailed source distribution along the whole train is usually not considered (in noise
mappings), although the pantograph and the train head/locomotive are often
point-source like. As for pantograph, its point-source data can be given as per meter train if only
equivalent noise impact or total noise exposure is concerned. However, for some case
studies, detailed source distribution needs to be considered. This issue will be
*discussed in detail when formulating how to calculate LAFmax*.

For aerodynamic noise, 0.5 m source height is for the noise components around bogie areas including cooling fan noise, 4 m height for the roof component and 5 m for the pantograph. In the CNOSSOS source model for railway noise, only two source heights of 0.5 m and 4 m were chosen. Considering that pantograph noise is often more important than other roof components of the aerodynamic noise [18, 22], in this new source model 5 m instead of 4 m is chosen as the second source height for aerodynamic noise.

For traction noise, engine exhausts for diesel powered vehicles are often located at a roof height of 4 m above the railhead; louvers and cooling outlets can be at various heights about 2 ~ 3 m; gear transmission and electric motors are usually at the axle height of 0.5 m.

The positions of railway noise sources have been specified in Table 2.1.

**Table 2.1 Source positions **

Lateral position: the rail nearest to the receiver Vertical position (above the railhead):

**Noise type ** **Source height (m) ** **Explanation **

Aerodynamic 0.5 for the components around bogie areas

5 for pantograph or other roof components

Rolling 0.01 for rail/track component

0.5 for wheel component

Traction 0.5 for electric motors, gear transmission

3 for louvers and cooling outlets

4 for engine exhaust

Impact noise has its source heights the same as those for rolling noise. Curve squeal, braking squeal and braking noise have a source height of 0.5 m. For bridge noise, the source heights are those for rolling noise plus the vertical expansion of the bridge. For viaducts, the representative source height(s) is currently not clear; the centre of the noise emission area could be an option.

For high-speed railway noise, three source heights of 0.01 m, 0.5 m and 5 m have been proposed for noise calculations. And, an extra source height will be considered if viaduct vibration noise contributes.

**2.3 **

**Classifications of trains/vehicles, tracks and **

**driving conditions **

*A vehicle is defined as any single railway subunit of a train that can be moved *

*independently and can be detached from the rest of the train. Typically, a vehicle can *

be a locomotive, a self-propelled coach, a hauled coach or a freight wagon. Some units of a train, that are a part of a non-detachable set e.g. share one bogie between them, are grouped into a single vehicle according to the definition.

A train consists of a series of coupled vehicles.

A classification of train/vehicle types in a noise source model is mainly based on those important parameters which have significant effects on the noise emission. Some parameters are related to roughness level (e.g. brake type or normally maintained rail) while the others will affect the response of a vehicle or a track to a roughness-induced excitation (this response is described by respective transfer function). For aerodynamic noise, there are currently no any parameters specified. (Note: By “high speed vehicle” it indicates that aerodynamic noise needs to be considered; however, not all types of high-speed trains have the same aerodynamic and acoustic characteristics.) Within this project, it was considered that a classification should help with noise calculation while not increase the burden in source data collection. Accordingly, a classification of noise calculation oriented is expected.

Let us take the CNOSSOS-Harmonoise classification for railway vehicles [7], shown in Figure 2.5, as the starting point for this discussion. If choosing vehicle type “high speed vehicle”, we will find that other three descriptors become not necessary or less relevant: modern high-speed vehicles all have disc brakes, all have the same number of axles (?) and all do not need (or, are not practical to have) extra wheel measure (?). (The question mark “?” indicates that the author believes so while not 100% sure.) In fact, it is not proper for high speed trains to make a classification based on vehicle types because the design of the train nose and train tail, as well as the design of inter-coach spacing is important for good streamline behaviour of the train. Moreover, aerodynamic noise around a bogie depends not directly on the train speed but the mean flow velocity at the bogie which in turn depends on the train speed and the distance between the bogie and the train nose. A measurement of flow velocity made in Japan showed that at the middle of fifth car (118.9 m from the train nose) the mean flow velocity decreases to 42% of the train speed [8]. Thus, it is understood as that aerodynamic noise around pantograph, train nose and train tail can be considered as local noise sources while aerodynamic noise around bogies depends also on the train length and the bogies’ positions relative to the train nose. Therefore, for high-speed trains, a classification based on train types is favoured because if a train has been disassembled into individual vehicles the aerodynamic noise could not be properly defined.

A classification based on vehicle types can distinguish a locomotive from coaches, concerned with traction noise and possible difference in rolling noise. However, for specifying traction noise it has no problem to merge locomotive types into train types, such as a train with “diesel loco” or “electric loco” or “self-propelled”. What left in a vehicle classification is to distinguish a locomotive from a coach based on

their rolling noise emission. In general, a locomotive may have larger wheels and traction wheels may be rougher than trailer wheels. In other words, a locomotive may emit rolling noise a few dB more than a coach vehicle does. However, this is not always true even for passenger trains: some coach vehicles can emit rolling noise more than the locomotive does. Considering a noise mapping, it is usually the mean roughness level of a train that will be specified. Accordingly, if difference in roughness levels between coach wheels is not specified, then it does not always make a sense to distinguish locomotive rolling noise from the coaches’. Moreover, when necessary (e.g. for detailed case studies) one can specify a roughness distribution along a train. Thus, it has no problem, for a classification based on train types, to distinguish locomotive rolling noise from the coaches’.

In Sweden, maximum value of AF-weighted sound pressure level of train pass-by
*noise, LAFmax, is an important noise indicator. Obviously, for calculating LAFmax*, a

classification based on train types is favored. It seems that a classification based on vehicle types is noise mitigation oriented, which is neither convenient for noise calculation nor proper for high-speed applications.

Thus, put all these discussions together, we like to conclude that a classification based on train types is better than based on vehicle types, not only for handling high-speed railway noise but also for detailed case studies.

Moreover, passenger trains can have different wheel types (with a straight or curved web) and different wheel sizes. These two parameters should be considered in classification because they are important in determining the vehicle transfer function. These two parameters may be merged into some other parameter. And, if considering noise emission strength, not all high-speed train types are necessary to be distinguished; those train types which behave acoustically the same or comparable shall be put into the same category. For example, some TGV train types and some ICE train types may be put into one category if they behave acoustically the same. This is to say, a train classification may not intend to point out the differences between train types but focus on their acoustic characteristics, or simply, their noise emission strengths. Of course the relevant noise source data shall be obtained from validated field measurements, or based on manufacturer’s product specification (the acoustical part) if the relevant information is provided.

Being noise calculation oriented, for high-speed applications, a train classification based on noise emission strength becomes very simple, as shown in Table 2.2-1. The descriptor “wheel measure” (see Figure 2.5) is more relevant for noise reduction than for noise prediction, because a train with some kind of wheel measure may not be quieter than another train which has no wheel measures. The vehicle/train transfer function depends mainly on the wheel type and wheel size; wheel skirts and wheel dampers will provide a few dB effect. Therefore, a train type, e.g. passenger trains, may need to be further divided into several categories based on their vehicle transfer functions and/or wheel roughness levels. Under a train type, to apply some wheel measure(s) may change the train from one category to another quieter one.

For conventional trains, a train classification shall be made based on train types including the traction manner and the wheel size(s). Passenger trains may need being further divided into three categories according to the noise emission strength (taking

the TSI requirement on noise as the reference): normal, low and high. For freight trains, there will also be three groups: normal, high and very high. The train classification of conventional systems was presented in Table 2.2-2.

Driving conditions are used for specifying traction noise, for specifying curve squeal noise when a sharp curve is relevant, and for specifying brake squeal noise when braking to (nearly) stop. Except cooling fan noise which may at high speed still have some influence on the total noise level [18], traction noise is only relevant at low speed including idling. And, for high-speed lines, a sharp curve is irrelevant. Thus, driving conditions are classified following these considerations, as shown in Table 2.4.

For freight trains, wagons with different brake types shall be distinguished because the wheels’ roughness levels can differ much. However, without pre-provided information, what a brake type a freight wagon has is not predicable. For a strategic noise mapping which is based on statistics the information on the ratio of a brake type in use is useful. However, for predicting pass-by noise of a specified freight train, one needs to know which wagons are equipped with what brake type - in general such information is not available. Accordingly, this descriptor, brake type, is applicable when considering noise measure while not fully practical when making noise prediction.

A general classification of railway track types [7], see Figure 2.6, looks complicated. It can be divided into two categories, conventional railway tracks and high-speed railway tracks. For the latter track classification is likely to be very simple: for high-speed railways descriptors 3-6 are not or less relevant; only two descriptors are relevant: track base and railhead roughness. And, options for descriptor 2 reduces to two: normally maintained and other situations. (Note: Some French experience [18] may suggest that for high-speed lines a very smooth rail running surface shall not be expected.) The classification of tracks was presented in Table 2.3, which includes track classification for conventional systems.

**Table 2.2-1. Classification of high-speed train types **

**Digit ** **1 ** **Note **

**Descriptor ** Train category *

Type N trains just fulfils the TSI noise requirement: 92 dB(A) at the standard receiving position 25 m/3.5 m, with 1 dB tolerance.

**_{ Type Q trains shall be at least }
3 dB(A) quieter than type N
trains.

**Explanation of the descriptor ** Based on noise

emission level
**Codes allowed **
**N* **
Normal
**Q** **
Quiet
**O **
Other

**Table 2.2-2. Classification of conventional-speed (< 200 km/h) train types **

**Digit ** **1 ** **2 ** **3 ** **4 **

**Descriptor ** **Train type ** **Train category ** **Brake type ** **Wheel measure **

**Explanation of **
**the descriptor **
A letter that
describe the
train type
according to the
noise emission
level LW
A letter that
describe the
brake type
A letter that
describe the
noise reduction
measure type
Possible codes
**pm **
passenger trains
with
self-propelled
coaches
**N **

fulfil the TSI
noise
requirement (for
coaches*) with
1 dB tolerance
**c **
cast-iron block
**n **
no measure
**pe **
passenger trains
with electric
loco
**L **
at least 3 dB
quieter than
category N
**k **
composite or
sinter metal
block
**d **
dampers
**pd** **
passenger trains
with diesel loco

**H **
2~5 dB more
noisy than
category N
**n **
non-tread brake,
like disc, drum,
magnetic
**o **
other
**c **
city tram or
light metro
**VH **
>= 6 dB more
noisy than
category N
**a **
any generic
freight train
**o **
other (e.g.
maintenance
train etc.)
*

A correction for train length is expected. **

To separate passenger train types by pm, pe and pd is for general engineering applications. As traction noise is often negligible above certain speed e.g. 80 km/h, these three train types may be merged into one type “p”.

**Table 2.3. Classification of railway track types **

Conventional railway tracks: shown in Figure 2.6 while may suffer revisions when necessary

High-speed railway tracks:

**Digit ** **1 ** **2 **

**Descriptor ** Track base Railhead roughness

**Explanation of the descriptor ** Type of track base Indicator for

roughness
**Codes allowed **
**B **
Ballast
**N **
Normally maintained
**S* **
Slab
**O **
Others
**V **
Viaduct
**T **
Tunnel
**O **
**Other (bridge …) **
*

: A slab track is 5 dB+ more noisy than a conventional ballasted track [28].

**Table 2.4. Classification of driving conditions **

**Descriptor ** **Speed range ** **Category ** **Specification **

Possible codes

High speed (> 200 km/h) - irrelevant

Conventional speed 1 on a sharp curve

2 the others Low speed (< 50 km/h) including idling 1 on a sharp curve 2 accelerating 3 cruising or decelerating 4 braking to (nearly) stop

**Figure 2.5. The CNOSSOS-Harmonoise classification for railway vehicles [7]. **

*(Note: According to the definition of a vehicle, for descriptor 2 parameter value 1 is *
*not proper.) *

**Figure 2.6. The CNOSSOS-Harmonoise classification for railway track types [7]. **

**2.4 **

**Directional sound power levels **

**2.4.1 **

**Directivity **

Based on the work presented in [10], in general, directivity of railway noise has two components: the directional effect originated in source emission and the directional effect due to the motion of the source (the Doppler Effect). In ref. [10] the former directional effect was named “source term” in the formulation and the latter named “motion term”.

The angles are defined in Figure 2.7. As two source heights have been specified for each noise type (of rolling noise and aerodynamic noise), the respective horizontal and vertical directivity functions are specified as given by Eqs. (2-1) – (2-7).

**Figure 2.7. Definition of angles: **

###

*is a horizontal angle in the x-y plane and*

*relative to the y-z plane; *

*is a vertical angle in the y-z plane;*

###

'*is a vertical angle*

*in a vertical plane containing the receiver and the source (or the centre of the source*

*line); both *

*and*

###

'*are relative to the x-y plane.*

The horizontal directivities for rolling noise are:

)] sin( * 1 lg[ 20 )] cos( * 6 . 0 4 . 0 lg[ 10 ) ( wheel

###

###

*M*

###

*L* (2-1)

### Hz

### 400

### )],

### sin(

### *

### 1

### lg[

### 20

### )

### (

### Hz

### 400

### )],

### sin(

### *

### 1

### lg[

### 20

### )]

### (

### cos

### *

### 999

### .

### 0

### 001

### .

### 0

### lg[

### 10

### )

### (

track 2 rail###

###

###

###

###

###

###

###

###

###

###

*f*

*M*

*L*

*f*

*M*

*L*

###

###

###

###

###

(2-2)*where M = v/c is the Mach number, v is the train speed and lg denotes for log*10.

The horizontal directivities for aerodynamic noise are:

###

### 10

### *

### lg

###

### 0

### .

### 006

###

### 1

### 0

### .

### 006

###

### *

### cos

2###

###

### 40

### *

### lg

###

### 1

### *

### sin

###

###

pantograph###

###

*M*

###

*L*

*A*

###

###

###

###

###

###

(2-3)###

###

###

###

###

###

###

###

###

###

###

) 10*lg0.03 0.97*cos /2 40*lg1 *sin ( 2 bogie*M*

*LA* (2-4)

However, for low frequency components (estimated

*f*

###

### 250

Hz), there is###

###

###

###

###

, 250 ) 40*lg1 *sin ( bogie*f*

*Hz*

*M*

*LA* (2-4’)

The vertical directivities for aerodynamic noise are:

### )]

### 2

### /

### cos(

### *

### 6

### .

### 0

### 4

### .

### 0

### lg[

### 10

### )

### (

###

###

###

###

###

###

###

*pantograph*

*vertical*

*L*

(2-5)
### Source

### Receiver 2 Receiver 1

### 0

### )

### (

###

###

*bogie*

###

*vertical*

*L*

(2-6)
As has been discussed in [10], the vertical directivities of wheel and rail noise can be described as

###

*L*

###

###

###

### 10

### lg[

### 0

### .

### 4

###

### 0

### .

### 6

### *

### cos(

###

### )]

. However, the vertical directivity of total rolling noise depends also on the shielding effect of the train body and/or wheel skirts, as well as the near track noise barriers where they present. As these shielding effect varies with train type (and even with track section where near-track noise barriers present), a general vertical directivity function for total rolling noise was not specified because of lack of such data.In ref. [7], a vertical directivity function was proposed for total rolling noise

###

###

###

###

###

###

###

###

###

###

###

###

_{}

###

###

### 200

### 600

### lg

### *

### sin

### 2

### sin

### 3

### 2

### *

### 3

### 40

### )

### (

*f*

*L*

*R*

_{vertical}###

###

###

(2-7)Note: In equations from (2-1) to (2-6) there is not a normalisation constant, considering the non-directional part of the sound power level data is determined at (equivalently)

###

###

### 0

angular position.Remarks: In the CNOSSOS source model for railway noise [7] the directivity functions proposed therein differ from the directivity functions given by Eqs. (2-1) - (2-6), in two aspects,

The CNOSSOS directivity proposal considers only the source term, not the directional part of the Doppler Effect which is important at high speed for aerodynamic noise sources;

The CNOSSOS directivity proposal (source term only) differs from the source term proposed in [10].

For other noise types, the directivities have been proposed as [10]: Traction noise: neglected

Impact noise: the same as that for rolling noise Braking noise: the same as that for wheel noise

Curve squeal noise, braking squeal noise: the same as that for wheel noise (while a further study of the issue is required)

Bridge noise: neglected

Super structure vibration: neglected

**2.4.2 **

**Sound power levels **

**2.4.2.1 **

**Rolling noise and the indirect roughness method **

An engineering method to collect raw source data of railway rolling noise was
proposed in [11-12]. The method is named the indirect roughness method, which was
**developed during the European project MetaRail (Methodologies and Actions for **
Rail Noise and Vibration Control) [11] and validated during the European project

**STAIRRS (Strategies and Tools to Assess and Implement noise Reducing measures **

for Railway Systems) [12]. Briefly, the indirect roughness method separates pass-by
*sound pressure spectra (not power spectra) into total effective roughness of the *
*wheels and the rail and total transfer function of the vehicle and the track. (Note: By *
“effective roughness” means the rail roughness plus the wheel roughness plus the
*effect of the contact filter.) The total effective roughness (in wave-length domain) *
and total transfer function (in frequency domain) are given as 1/3 octave band
spectra. The separation is accurate within

###

3 dB per 1/3 octave band. Combination of the total effective roughness, the total transfer function and the axles per meter gives an estimation of the pass-by sound pressure spectra, which is accurate within###

1 dB(A).The total effective roughness is derived from the vertical rail vibration measured during a pass-by. The total vibro-acoustic transfer function is determined using the derived total effective roughness and the measured sound pressure from the pass-by. The accuracy of the indirect roughness method has been analysed theoretically and by verification measurements, which showed a maximum systematic error of

###

3 dB per 1/3 octave band in a frequency range from 100 to 3150 Hz. This frequency range directly restricts the wavelength range in which roughness levels can be obtained at a certain speed. For example, at a train speed of 100 km/h, the wavelength range is limited between 0.278 m and 0.009 m (*v*

###

*f*

###

).Rolling noise consists of wheel vibration noise and track/rail vibration noise. When rolling noise dominates in railway noise (usually true for train speed range between 50 km/h and 200 km/h)，the total equivalent sound pressure level

*L*

_{p}_{,}

*during a train pass-by can be determined by*

_{tot}###

###

_{}

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

*f*

*v*

*L*

*f*

*L*

*L*

*N*

*f*

*L*

_{H}_{tot}

_{r}_{tot}*wagon*

*axle*

*tot*

*p*,

### 10

### lg

, , (2-8) where###

*f*

*L*

*the equivalent total sound pressure level (for a specified pass-by time period) that is due to rolling noise and in 1/3 octave band*

_{p,}_{tot}###

*f*

*L*

_{H ,}_{tot}*L*

_{H}_{,}

_{tot}###

*f*

###

*L*

_{H}_{,}

_{veh}###

*f*

###

*L*

_{H}_{,}

_{tr}###

*f*

, the total transfer function in 1/3
octave band
###

*v*

*f*

###

*L*

_{r}_{,}

_{tot}### /

*L*

_{r}_{,}

_{tot}###

*v*

### /

*f*

###

###

*L*

_{r}_{,}

_{w}###

*v*

### /

*f*

###

###

*L*

_{r}_{,}

_{r}###

*v*

### /

*f*

###

###

*CF*

, the total roughness
level in 1/3 octave band
###

*f*

*L*

*vehicle transfer function, 1 axle per meter*

_{H ,}_{veh}###

*f*

*L*

*track transfer function, 1 axle per meter*

_{H ,}_{tr}###

*v*

*f*

###

*L*

_{r}_{,}

_{w}### /

wheel roughness level###

*v*

*f*

###

*L*

_{r}_{,}

_{r}### /

rail roughness level*CF * the contact filter

*axle*

*N*

number of axles per wagon
*wagon*

*L*

wagon length
*f*

1/3 octave band centre frequencies
*v* train speed (m/s)

The key part of the method is to determine the total effective roughness. This quantity is to be determined as

###

*f*

*L*

###

*f*

*A*

###

*f*

*A*

###

*f*

*A*

###

*f*

###

*f*

*L*

_{r}_{,}

_{tot}###

_{a}_{,}

_{meas}###

_{1}

###

_{2}

###

_{4}

###

### 40

### lg

### 2

###

(2-9)where

###

*f*

*L*

*1/3 octave band level of equivalent vertical rail acceleration*

_{a,}_{meas}###

*f*

*A*1 the level difference between the average vibration at the
measurement point and the railhead:

###

*f*

*L*

###

*f*

*L*

###

*f*

*A*

_{1}

###

_{a}_{,}

_{meas}###

_{a}_{,}

*(2-10)*

_{head}Often one can take *A*1

###

*f*0.

###

*f*

*A*2 the level difference between the vibration displacement at the contact
point on the railhead and the combined effective roughness:

###

*f*

*L*

###

*f*

*L*

###

*f*

*A*

2 ###

*x*,

*contact*

###

*r*,

*tot*(2-11)

###

###

###

###

###

###

###

###

###

###

###

*C*

*W*

*R*

*R*

*A*

###

###

###

###

### lg

### 20

2 (2-12) where*R*

###

rail receptance*W*

###

wheel receptance*C*

###

receptance of the contact stiffnessThe spectrum *A*_{2}** is determined for a range of parameter values using the TWINS **

*software [14]. The pad stiffness is shown to be the most influential parameter. In the *
frequency range from 100 to 3150 Hz inclusive, the spectrum *A*_{2} can be determined
to an accuracy of

###

3 dB for application to conventional wheels (given in Table 2.5), provided that the rail pad stiffness can be allocated to one of the three categories, as listed in Table 2.6.###

*f*

*A*4 the level difference between the vibration at the contact point and the
vibration of the railhead averaged over the wheel passage interval

###

*f*

*L*

###

*f*

*L*

###

*f*

*A*

4 ###

*a*,

*head*

###

*a*,

*contact*(2-13)

###

2###

*f*

lg

40 =

*L*

_{a}_{,}

_{contact}###

*f*

###

*L*

_{x}_{,}

_{contact}###

*f*

, to convert from acceleration to
displacement

The conversion spectrum *A*_{4}* depends on the spatial vibration decay D of the track *
[11]:

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

###

686 , 8 , , 4### 1

### 686

### ,

### 8

### lg

### 10

*x*

*vDT*

*x*

*contact*

*a*

*head*

*a*

*e*

*vDT*

*f*

*L*

*f*

*L*

*f*

*A*

(2-14)
*where v is the train speed and Tx* the time length for the measurement illustrated in

*Figure 2.8. The frequency dependent decay per meter, D(f), depends on the track *
characteristics (mainly the rail pads). As the stiffness and damping of the rubber rail
pad depends on lifetime, temperature, pre-load and the loading history, this quantity
varies during the track lifetime, and even can vary during a train passage.

**Figure 2.8. **Vertical acceleration measurement during four wheel passages (Figure 3.1 in *[12]). *

*The spatial vibration decay of the track, D(f), which is used in determining the *
conversion spectra of *A*_{2} and *A*_{4}, can be measured according to the standard method
shown in [15], or using a simplified method proposed in [16].

By measuring two quantities,

1. the pass-by time history of

*L*

_{p,}_{tot}###

*f*

at 7.5m from the centre of the track and
1.2m above the railhead and
2. the pass-by time history of the vertical rail acceleration in 1/3 octave bands,

###

*f*

*L*

*(measured at the centre of and under the rail),*

_{a,}_{meas}the total roughness can be determined using Eq. (2-9), and then the total transfer function can be determined using Eq. (2-8).

With the total roughness and total transfer function determined,

*L*

*p,tot*

###

*f*

at a given
train speed can be determined. However, the source data shall be the sound power
level, not a sound pressure level at a given receiving position. This issue was
addressed during the Harmonoise project and was solved during the Imagine project.
*In ref. [17] a practical method was proposed to transfer a measured Leq,Tp* to the

*corresponding sound power level LW,* as shown in Annex A. With this proposal the

**Table 2.5. **Spectra A_{2}** for three categories of rail pad stiffness [12] **

**Table 2.6. **Proposed ranges of pad stiffness

** Soft pad ** **Medium pad ** ** Stiff pad **

Biblock sleepers

###

400 MN/m 400 – 800 MN/m###

800 MN/mMonoblock sleepers

###

800 MN/m###

800 MN/m -Wooden sleepers all - -

In ref. [4] the source data for the rolling noise component of X2 trains had been worked out using the indirect roughness method. These source data, with a certain adjustment by referring to the ratio of the CNOSSOS-Harmonoise default track and vehicle transfer functions [7], are presented in Annex B.

**2.4.2.2 **

**Aerodynamic noise **

As theoretical modelling of railway aerodynamic noise is still limited to a few simple configurations [3], this noise type will be handled using an empirical method proposed in [4-5]. Briefly, one should measure train pass-by noise at a typical high speed (

*v*

_{0}

###

### 250

km/h). As the rolling noise component of the pass-by noise can be accurately predicted using the theoretical model TWINS [14], or the engineering method “the indirect roughness method” which was described in 2.4.2.1, thecontribution of the aerodynamic noise at this typical speed can be obtained by
subtracting the rolling noise contribution from the measured total. With the
pantograph noise measured independently, or, estimated by referring to a typical
known data, the source data of the aerodynamic noise for this speed, *LW*_{,}*a*_{er}*o*

###

*f, v*

_{0}

###

,can be obtained by applying the respective tabular values given in Annex A.

The source data of aerodynamic noise at other speeds can then be obtained by applying the spectrum shift,

*f*

###

*f*

_{0}

### *

*v*

### /

*v*

_{0}, and the speed dependence of the noise sound level, in the way [5]

###

, * , 60log 0 10 0 0 er , er , *v*

*v*

*v*

*v*

*v*

*f*

*L*

*v*

*f*

*LW*

*a*

*o*

*W*

*a*

*o*,

*f*

###

### 250

Hz (2-15)###

, * , 40log 0 10 0 0 er , er , *v*

*v*

*v*

*v*

*v*

*f*

*L*

*v*

*f*

*L*

_{W}

_{a}

_{o}

_{W}

_{a}*,*

_{o}*f*

###

### 250

Hz (2-16)Note: Equations (2-15) and (2-16) could be revised to have a smooth transition from the speed index 6 to 4.

**2.4.2.3 **

**Other noise types **

Source data for cooling fan noise is currently not available.

Source data for other non-high-speed noise types have not been handled within this project because of the short of time.

**2.4.2.4 **

**Default source data for high-speed railway noise **

There are currently no high speed trains in Sweden, neither high speed lines. For evaluating noise impact from high-speed lines, a set of default source data was then worked out.

As many TGV trains fulfil the TSI requirement on noise [18], it would be good to take the source data for TGV trains as the default one. However, unfortunately, such TGV source data are currently not available. Thus, the source data for X2 trains are considered. It was found that X2 trains have a transition speed around 370 km/h [4-5], which is nearly the same as for TGV trains [3]. This feature implies that a set of default source data based on X2 train type can be made the same good as the TGV source data. (Note: At the transition speed, the sound power of the aerodynamic noise becomes the same as that of the rolling noise.)

The noise level of X2 trains are about 6 dB(A) over the TSI noise limits. Thus, by reducing 6 dB, a set of default source data for high speed railway noise was obtained as shown in Annex C.

**2.5 **

**Tunnel openings **

Among the existing European noise assessment methods only the Nord2000 method provides a description on handling tunnel opening noise [19]. However, the method described in [19] is based on the Japanese work [24] and is for road vehicle noise. For high-speed railway applications, strong micro-pressure waves (MPW) emitted from the portal of a long tunnel (sonic boom incidents which are clearly audible up to about 1 km distance) are the most serious problem [30-32], which differ much from the tunnel opening noise for road vehicles.

**Figure 2.9. Measured C-weighted sound pressure level as a function of time for an **

*ICE 3 –type train with 300 km/h at Euerwang southern portal at a distance of 65 m *
*(next public road) in front of the tunnel (Fig. 5 in [31]). The first high peak is caused *
*by the sonic boom. *

A clearly audible MPW was reported before only for the Shinkansan-lines in Japan
[31,33]. At regular traffic of European high-speed lines this phenomenon did not
*show up in the past due to the use of ballasted track (its absorption effect mitigates *

*the impact) and the specifications for length and cross section of the tunnels. In *

December 2005 prior to the opening of the new high-speed line
Nuremberg-Ingolstadt in Germany, sonic boom occurred at the tunnels Euerwang and Irlahüll
*(which both are more than 7 km long and have a double slab track) when the test *
trains ICE S or ICE 3 entered the tunnels at the opposite entrance with speeds up to
330 km/h [31].

To compare micro-pressure sound and train pass-by noise, the adjusted sound
*exposure level LRE* is defined as

*dB*
*L*
*for*
*L*
*L*
*dB*
*L*
*for*
*L*
*L*
*CE*
*CE*
*RE*
*CE*
*CE*
*RE*
100
,
11
1.18
100
,
93
2
(2-17)

where C-weighting takes the contribution at low frequencies of micro-pressure wave
*effects into account. LRE* for the MPW at public places in the immediate vicinity of

the tunnel entrances (Note: a better wording seems portals/exits, not entrances) can
*be compared to LCE* of the train pass-by measured at the same locations. (Note: The

train pass-by noise is delayed by more than one minute with respect to the occurrence of the sonic boom for a 7 km long tunnel and a train running at a speed of 300 km/h [31], as shown in Figure 2.9.)

One example of recorded sonic booms is presented in Figure 2.10. The third-octave spectra are characterised by strong contributions below 125 Hz including infra-sound below 20 Hz. For the original tunnel without using absorbers the pronounced sound pressure levels above 250 Hz were recorded, which corresponds to a hearing impression as sharp and bright bang [31].

Only the whole tunnel equipped with track absorbers reduction up to 9 dB in the low frequency range were obtained, which leads to a clear reduction of the micro-wave sound effect: only weakly audible and experienced as a dull dump. And, after this successful countermeasure, the effect of the MPW including a correction level of 8 dB(A) for impulsive noise contributes only 0.4 dB(A) at day time and 0.1 dB(A) at night time [31].

**Figure 2.10. Third octave band spectra of the sound pressure level for an ICE 3-type **

*train with 300 km/h at a distance of 50 m to Euerwang southern portal. * *without *

*absorbers; * * partly equipped with absorbers; * *fully equipped with *

*absorbers (Fig. 6 in [31]). *

In ref. [30] a prediction formula for MPW disturbance *p _{MPW}* in the far field is
proposed as

###

_{}

###

_{}

###

_{}

_{}

###

_{}

_{}

###

_{}

_{}

_{}

*p*

*t*

*d*

*T*

*T*

*k*

*d*

*t*

*p*

*T*

*k*

*t*

*p*

*s*

*s*

*c*

*A*

*c*

*s*

*t*

*p*

*t*

*t*

*tun*

*MPW*' 0 2 2 2 2 2 ' 0 2 1 2 1 ' 0 4 exp 4 exp 2 1 2 (2-18)

*where t is for time, s for the axial distance from the portal, c for the speed of sound in *
air, *A _{tun}* for the cross section of the tunnel portal, for the solid angle which
depends on the geometry of the portal and the surroundings,

*p*'

*p*/

*t*,

*T*1 1.4

*r*/

*c*

*with r the (hydraulic) tunnel radius, T*_{2} *r*/*c*, *k*_{1} 1/

###

4 *T*

_{1}

###

and*k*

_{2}11/

###

50 *T*

_{2}

###

. For the case shown in [30] it was found that*s*0 8 (the origin where the axial

*distance s is measured) together with a solid angle of *5/4. This formula has
been evaluated and concluded as that it is satisfactory [30].

In the rest of this sub-section the method proposed in [19] to handle tunnel noise is presented. The method is based on Japanese work on road vehicle noise [24]. It is not clear at this time if the method can properly handle the railway tunnel noise directly after the micro-pressure wave (see Figure 2.9), because the ratio between the cross sections of the vehicles and the tunnel opening can be different for road and for railway applications. Thus, the method will probably suffer revision in near future.

**2.5.1 **

**General **

Tunnel openings are regarded as special sound sources. Each train passing through a
*tunnel yields a certain sound energy level, L*J, through the tunnel opening. This
energy depends on the total sound power level of the train and its speed, but it also
depends on the sound propagation properties inside the tunnel.

*At a certain moment a single train car is positioned inside the tunnel at the distance x *
from the tunnel mouth. For a stationary car, consider its sound power radiating
*through the tunnel opening to be W*T. In a short time interval *t the corresponding *
energy *E through the opening will be W*T*t. The time interval can be estimated by *
*x/v, **x and v being the driving distance and the speed respectively during the time *
*t. Positioning it at subsequent equidistant positions can simulate the pass through of *

the car through the tunnel and thus the total radiated energy through the tunnel opening can be calculated. By summing over all cars and the engine the corresponding level for the train is obtained.

*It can be shown [24] that the sound power W*T radiating through the tunnel opening
due to a stationary sound source in the tunnel, is:

)
)
(
1
(
2
)
,
(
2
2
*ax*
*r*
*ax*
*W*
*x*
*a*
*WT*
(2-19)

*W is the total sound power, in watts, of the source, x is the distance, in m, of the *

*sound source from the tunnel mouth, r is the radius, in m, of the tunnel (in case of a *
*semi-circular cross section), a is a parameter regarding the sound absorption inside *
the tunnel (0 * a * 1).

For a tunnel with a rectangular cross section, the sound power is [24]:

2
2
2
4
1
)
)(
(
tan
)
,
(
*ax*
*h*
*w*
*x*
*h*
*w*
*W*
*x*
*a*
*W*
*T*
*T*
*T*