Prediction of High-Speed Train Noise on Swedish Tracks

Prediction of high-speed train noise on Swedish tracks

Xuetao Zhang

SP Technical Research Institute of Sweden of Institute Research Technical SP

Energy Technology

SP Report 2010:75 2

Prediction of high-speed train noise on Swedish tracks

Xuetao Zhang

Abstract

Aiming at applying the Nord2000 propagation model to predict high speed train noise in Sweden, the noise emission data of X2 trains has been studied. By using the Imagine source model for rolling noise (i.e. the roughness-transfer-function method), it becomes possible to empirically estimate the aerodynamic noise based on the collected inclusive noise emission data. The sound power level per meter train has been determined for each noise type/component (i.e. the rail/track and wheel radiation and the aerodynamic noise) and for the speed range of interest (150-300 km/h). The calculation method is described and the horizontal directivity for each noise type/component is provided.

Key words: X2 train noise, high speed train noise, aerodynamic noise, pantograph noise, aero-noise around bogie area, sound power level, horizontal directivity, roughness and transfer function

SP Sveriges Tekniska Forskningsinstitut SP Technical Research Institute of Sweden

SP Report 2010:75 ISBN 978-91-86622-18-3 ISSN 0284-5172 Borås 2010

Contents

Abstract 3

Contents 4

Preface 5

Summary 6

1 Introduction 7

2 X2 train noise and the model prediction 8

3 Method to determine input data 16 3.1 Rolling noise 16 3.2 Aerodynamic noise 16

4 Input data for prediction of X2 train noise 18 4.1 Estimation of X2 train pantograph noise 18 4.2 Revised model prediction of X2 train noise 20 4.3 Input data 26

5 Discussion 32

Reference 33

Annex A Methods to determine the sound power level of a traffic noise source 34 A.1 Determination of L from the L of a train pass by 34 WA Aeq,Tp

A.2 To determine LWA from the SEL of a train pass by 39

A.3 To calculate the LpF max of a train pass by 39

Annex B The horizontal directivity of railway noise 41 B.1 Directivity function 41 B.2 Normalization 42

Annex C Input data for higher speeds 44

Preface

This project is founded by the Swedish Transport Administration (Trafikverket), with the contract nr TRV 2010/57212.

Dr. Hans Jonasson provides his valuable comments.

The cover picture is provided by Bombardier.

All the above supports are gratefully acknowledged.

Borås 2010-09-30

Xuetao Zhang

Summary

The Imagine model has successfully been applied on Swedish X2 trains to predict rolling noise. By subtracting this predicted rolling noise contribution from the collected total noise emission data, it becomes possible to estimate the contribution of the aerodynamic noise from the bogie areas as well as from the pantograph(s). Thus, a complete model of the noise emission of X2 trains at high speed was elaborated capable of predicting the overall noise level in one-third octave frequency bands of interest within the speed range 150-300 km/h. The model assumes certain roughness levels and transfer functions but it can later be used to incorporate new values on these parameters.

1 Introduction

In this project, the input data, the sound power level per meter of the X2 train type, will be worked out. The relevant methods will also be described.

In traffic noise engineering, the quantities of sound pressure level ( L p ), (for a certain time interval T) the equivalent (continuous) sound pressure level ( Leq, T ), the sound exposure level (SEL), the maximum sound pressure level using time-weighting F

( L pF max ) and the corresponding sound power level ( LW ) are frequently used. The first four quantities can be measured directly, whereas the sound power level can in principle be derived from one of these measured quantities.

As proposed by the European Harmonoise project, the sound power level is to be used in describing the noise emission of rail bound vehicles. Therefore, the method to determine the sound power level using one of the measured quantities is described in Annex A. In Annex B, the relevant horizontal directivity is provided. Moreover, in the model calculations, the sound propagation is handled using the Nord2000 propagation model, which was proved during the European Harmonoise project to be accurate, in particular for cases little affected by meteorological conditions.

Aiming at estimating noise impact from high speed trains on Swedish tracks, the noise emission data of X2 trains was studied as shown in section 2. The measured SEL data of X2 trains presented in SP Rapport 1994:25, the SEL values predicted by using the Nord2000 source model and by using the Imagine source model are compared.

Based on the positive results shown in section 2, the way to work out the input data was then proposed in section 3 and the input data was given in section 4. Some detailed discussion was presented in section 5.

2 X2 train noise and the model prediction

Presently, the X2 train is, together with the Arlanda Express X3 train, the existing high speed train type in Sweden, which can reach 200 km/h. In the near future, the Gröna Tåg (Green Train), developed based on the Regina train type, is expected to achieve a top service speed of 250 km/h [1].

In this section, SEL values of the noise emission data of X2 trains have been studied.

SEL values of X2 trains are calculated using the method shown in Annex A. The different input data, the sound power level per meter of the train type, for a given speed and on a track equipped with BV50 rail, for the Imagine source model (based on the description of roughness and transfer function) and for the Nord2000 source model (based on the measured data presented in SP Rapport 1994:25), have been tested respectively. The resulted SEL values were presented in Fig. 1(a) and 1(b).

For single values of the A-weighted SEL levels, the Imagine-source-model results show the speed dependence of 20,9*log10(v), compared with 24*log10(v) showing by the Nord2000-source-model results. (The corresponding speed exponent of the sound power level is then 30,9 for the Imagine results and 34 for the Nord2000 results.) The Imagine-source-model results are for the rolling noise only, whereas the Nord2000-source-model results are for the inclusive noise emission. Except for low and middle frequencies where noise types other than rolling noise have a strong influence, the Imagine-source-model results are in general about 0,5-1 dB higher than the Nord2000-source-model results (Fig. 3). This small difference is not critical and can easily be explained by the difference between the real and assumed roughness levels. Moreover, as in the Nord2000-source-model the contribution of the aerodynamic noise is included, then the resulted SEL values are of a speed dependence higher than that when considering rolling noise only.

In Fig. 2, the collected SEL data presented in SP Rapport 1994:25 [2] are shown. Comparing Fig. 1(a) and Fig. 2, it is clear that the Imagine source model correctly describes the shift of the peak level of rolling noise in frequency domain when train speed varies. This feature is important when working in spectrum for estimating aero-noise contribution. Since rolling noise is not important below about 500 Hz, it is obvious that other noise types need to properly be dealt with in order to have a good noise prediction not only in the single value of the total A-weighted noise exposure level but also in its spectrum components. For high speed trains, the low-frequency noise components are mainly contributed by aerodynamic noise.

In Fig. 3, the predicted SEL values by using the two source models were compared with the collected SEL data of the noise emission from X2 trains. It can be seen that, the Imagine source model and the Nord2000 source model agree well for rolling noise. Moreover, it seems that aerodynamic noise is important up to 500 Hz below 200 km/h, whereas it will also influence 1 kHz or even higher when above 200 km/h.

SEL for X2 trains, predicted by the Imagine model

100

60 dB 50 100 km/h (92,7 dBA) 150 km/h (96,6 dBA) 40 200 km/h (99,6 dBA) 250 km/h (101,8 dBA) 30 300 km/h (103,4 dBA) 350 km/h (104,4 dBA) 20 400 km/h (105,3 dBA)

2 3 4 10 10 10 Frequence (Hz) (a)

SEL for X2 trains, predicted by the Nord2000 model

100

60 dB 50 100 km/h (92,1 dBA) 150 km/h (95,9 dBA) 40 200 km/h (98,8 dBA) 250 km/h (101,3 dBA) 30 300 km/h (103,3 dBA) 350 km/h (105,2 dBA) 20 400 km/h (106,8 dBA)

2 3 4 10 10 10 Frequence (Hz) (b)

Fig. 1. The SEL values (the A-weighting is included) of the noise emission from X2 trains at representative speeds, in one-third octave bands of 25-10000 Hz, predicted (a) by using the Imagine source model (rolling noise only) and (b) by using the Nord2000 source model (including all noise types).

SEL data for X2 trains, SP Rapport 1994:25

70 km/h (90,1 dB) 130 km/h (95,4 dB) 80 140 km/h (94,7 dB) 160 km/h (97,2 dB) 170 km/h (97,6 dB) 75 180 km/h (98,8 dB) 190 km/h (98,2 dB) 200 km/h (98,4 dB) 70 2 3 10 10 Frequence (Hz) (a)

SEL data for X2 trains, SP Rapport 1994:25

80 210 km/h (98,9 dB) 220 km/h (98,6 dB) 230 km/h (100,2 dB) 240 km/h (99,3 dB) 75 250 km/h (101,1 dB) 260 km/h (102,2 dB) 270 km/h (103,2 dB) 70 2 3 10 10 Frequence (Hz) (b)

Fig. 2. The SEL data of the noise emission from X2 trains in octave bands of 63-4000 Hz, SP Rapport 1994:25.

85 Imagine 95,1 dBA 80 Nord2000 94,5 dBA SP-1994 95,4 dBA 75 2 3 10 10 130 km/h

85 Imagine 95,9 dBA 80 Nord2000 95,2 dBA SP-1994 94,7 dBA 75 2 3 10 10 140 km/h

85 Imagine 97,4 dBA 80 Nord2000 96,5 dBA SP-1994 97,2 dBA 75 2 3 10 10 160 km/h

(a)

Fig. 3. The comparison of the SEL values of the noise emission from X2 trains, between the Imagine-source-model prediction, the Nord2000-source-model prediction and the SP-1994 data [2]. (a) For train speed 130, 140 and 160 km/h.

SEL for X2 trains 95

85 Imagine 97,9 dBA 80 Nord2000 97,2 dBA SP-1994 97,6 dBA 75 2 3 10 10 170 km/h

85 Imagine 98,7 dBA 80 Nord2000 97,7 dBA SP-1994 98,8 dBA 75 2 3 10 10 180 km/h

85 Imagine 99,2 dBA 80 Nord2000 98,3 dBA SP-1994 98,2 dBA 75 2 3 10 10 190 km/h

(b)

Fig. 3. (continued) (b) For train speed 170–190 km/h.

85 Imagine 99,8 dBA Nord2000 98,8 dBA 80 SP-1994 98,4 dBA 75 2 3 10 10 200 km/h SEL for X2 trains

85 Imagine 100,2 dBA Nord2000 99,4 dBA 80 SP-1994 98,9 dBA 75 2 3 10 10 210 km/h

85 Imagine 100,8 dBA Nord2000 99,9 dBA 80 SP-1994 98,6 dBA 75 2 3 10 10 220 km/h

(c)

Fig. 3. (continued) (c) For train speed 200–220 km/h.

100 95 90 85 Imagine 101,3 dBA Nord2000 100,3 dBA 80 SP-1994 100,2 dBA 75 2 3 10 10 230 km/h

100 95 90 85 Imagine 101,7 dBA Nord2000 100,8 dBA 80 SP-1994 99,3 dBA 75 2 3 10 10 240 km/h SEL for X2 trains 100 95 90 85 Imagine 102,1 dBA Nord2000 101,3 dBA 80 SP-1994 101,1 dBA 75 2 3 10 10 250 km/h

(d)

Fig. 3. (continued) (d) For train speed 230–250 km/h.

100

85 Imagine 102,3 dBA 80 Nord2000 101,7 dBA SP-1994 102,2 dBA 75 2 3 10 10 260 km/h

100

85 Imagine 102,7 dBA 80 Nord2000 102,1 dBA SP-1994 103,2 dBA 75 2 3 10 10 270 km/h

(e)

Fig. 3. (continued) (e) For train speed 260 and 270 km/h.

3 Method to determine input data

For high speed trains, the important noise types are rolling noise and aerodynamic noise, in normal situations. (The other situations can be, for example, on a bridge or under braking.) This is to say, traction noise including engine/motor noise and cooling fan noise will be neglected when analyzing noise emission data of high speed trains [3,4].

3.1 Rolling noise

Based on the positive results presented in section 2, it seems clear that the Imagine source model works well in predicting rolling noise. The model automatically holds the speed exponent of the noise-emission sound power by applying the roughness and transfer functions of the corresponding train-track system. (Thus, for different train-track systems and roughness spectra, the speed exponent of rolling noise can differ by a little.)

As has been shown in Fig. 3, the Imagine-source-model results are in general about 0,5-1 dB higher than the SP-1994 data. As in the Imagine-source-model calculations the roughness level is based on the SP data collected during 2004 and 2005 [5], about 10 years later than when the SP-1994 data were collected [2], the two sets of noise emission data are then likely corresponding to different roughness levels although the difference is small. Thus, to make a compromise between the two sets of noise emission data, the roughness level used in the Imagine-source-model will be adjusted by a little: 1 dB is reduced for wave length components 2,5-6,3 cm; 0,5 dB is raised for wave length components 12,5-20 cm.

Wheel roughness depends on, at a large extent, which brake type has been used. However, for a new type of high speed trains, the average wheel roughness level cannot be known for sure before roughness measurement has been carried out. Without this information, the average roughness level of a similar wheel type can be used. Moreover, if the information on the wheel running surface is available, an averaged wheel roughness level can be estimated.

As for transfer functions, if no special noise reduction measure is applied (such as using rail and/or wheel dampers), track transfer function can be estimated according to the rail type, sleeper type and the rail pad, whereas vehicle transfer function is mainly determined by the wheel size. In general, the larger the wheel size, the higher the vehicle transfer function.

A softer rail pad will lead to a lower track decay rate then a higher total rail radiation level. However, a softer rail pad will also lead to a lower growth rate for the rail roughness. Thus, for a long-term view of rail noise emission, a softer rail pad is believed to be a better choice.

3.2 Aerodynamic noise

When train speed increases, aerodynamic noise will become an important noise component at low and middle frequencies. Aerodynamic noise can be important even

at higher frequencies if train speed further increases. Presently, there is no reliable theoretical method to handle this noise type. Thus, an empirical method has to be considered.

Fig. 4. Typical one-third octave band data of TGV train noise, from the trailing coaches [6].

A possible way to work out an empirical model of aerodynamic noise for X2 trains is to study the SEL data presented in [2], also shown in Figs. 2 and 3. However, there are some drawbacks: this Swedish SEL data of the noise emission from X2 trains was given only in the octave bands of 63–4000 Hz.

Fortunately, one can find French data of TGV trains in literature, given in the one- third octave bands of 50-5000 Hz, as shown in Fig. 4 [6]. By referring to this data, the aerodynamic component of X2 train noises can be estimated in the one-third octave bands.

4 Input data for prediction of X2 train noise

In section 4.1, first, the sound power level of X2 train pantograph noise will be estimated, by referring to the pantograph noise data of Japanese Shinkansen 300 series [7] also compared the TGV pantograph noise data [8]. This estimation, although mainly focusing on the tonal feature of the noise, is necessary for separating the pantograph noise from the aero-sound around bogie areas. Then, in section 4.2, a combined model was made which consists of the Imagine source model for rolling noise and the empirical model for aerodynamic noise. The SEL values predicted by the combined model well fit the SP-1994 data of the SEL values for X2 trains [2]. Based on this good result, it is believed that the input data are properly made. (While, the estimation for the pantograph noise may be rough.) Then in section 4.3, the input data, the sound power level per meter of the X2 train type, is given in the tabular values for each sub-source. The relevant directivity is provided in Annex B.

4.1 Estimation of X2 train pantograph noise

Railway aerodynamic noise has two important components: one is due to the vortex shedding from the pantograph and the other is the scattered fluid sound out from the bogie areas. As the former has a source height of 5 m above the railhead and the latter a source height of about 0,5 m, it is necessary to separate these two sub- sources.

Pantograph noise 120

110

100

70 dB 60

40 Shinkansen 300, 300 km/h (106,0 dBA) French-TGV, 280 km/h (108,6 dBA) 30 Total-aero for X2, 270 km/h (109,1 dBA)

20 2 3 4 10 10 10 Frequency (Hz)

Fig. 5. Comparing with the estimated total sound power level of X2 train aerodynamic noise at 270 km/h, for modeling X2 train pantograph noise, the pantograph noise of Japanese Shinkansen 300 series measured in the wind tunnel [7] seems more suitable than the TGV pantograph noise which is extracted from field measurement [8].

The total sound power of X2 train aerodynamic noise is obtained through subtracting the sound power of rolling noise from the measured total. Next, for separating the sound powers of the two aerodynamic components, one of them needs to be estimated. Since a few data for pantograph noise can be found in literature, while no data are available for the aerodynamic noise around bogie areas, the X2 train pantograph noise is to be estimated.

As no data available for X2 train pantograph noise, the pantograph noise of Japanese Shinkansen 300 series measured in the wind tunnel is referred to as shown in Fig. 5, also comparing the TGV pantograph noise data [7,8]. Obviously, for modeling X2 train pantograph noise, the Japanese data is more suitable to refer to. Thus, by keeping the tonal feature also adjusting the level to fit the total level of the aerodynamic noise, the X2 train pantograph noise is estimated, as shown in Fig. 6. The sound power level of aerodynamic component around bogie areas, obtained by subtracting the pantograph noise component from the total, is also shown in Fig. 6, which is about 3 dB stronger than the pantograph noise.

Pantograph noise 105

100

Shinkansen 300, 300 km/h (106,0 dBA) 70 Total-aero for X2, 270 km/h (109,1 dBA) dB Estimated X2-panto, 270 km/h (104,2 dBA) 65 Estimated X2-bogie, 270 km/h (107,4 dBA)

60 2 3 4 10 10 10 Frequency (Hz)

Fig. 6. The sound power levels of the aero-components of X2 train noise at 270 km/h: the estimated total aerodynamic noise, the pantograph noise (of tonal feature) and the aerodynamic component around bogie areas, referring to the pantograph noise of Japanese Shinkansen 300 series [7].

For railway aerodynamic noise, the spectrum shall shift with train speed. This effect is handled according to

f  f *v / v (1) 0 0

Due to this spectrum shift, the equivalent speed dependence (speed exponent) of this noise type becomes different from what is used in the modeling formulation. For instance, for X2 train type, in the sound power description the speed exponent for the aero-noise around bogie areas is chosen to be 40 for 25-250 Hz and 60 for 315- 10 000 Hz, whilst for the pantograph noise the speed exponent of 60 is used for all frequencies. Then, equivalent speed exponent of the dB(A) level becomes 66 for the aero-noise around bogie areas, 71,3 for the pantograph noise and 67,5 for the total.

4.2 Revised model prediction of X2 train noise

The revised model prediction was presented in Fig. 7, whereas, in Fig. 8, the model prediction was compared with the measured data. As can be seen, in general, the combined model, the Imagine source model for rolling noise and the empirical model for aerodynamic noise, works well.

100

80 dB 70

60 100 km/h (92,1 dBA) 150 km/h (96,1 dBA) 200 km/h (99,2 dBA) 50 250 km/h (101,7 dBA) 300 km/h (103,8 dBA) 350 km/h (105,7 dBA) 40 400 km/h (107,7 dBA)

2 3 4 10 10 10 Frequence (Hz)

Fig. 7. The SEL values (the A-weighting is included) of the noise emission from X2 trains at representative speeds, in one-third octave bands of 25-10000 Hz, predicted by the combined method (the Imagine source model for rolling noise and the empirical model for aerodynamic noise). The speed exponent for the A-weighted SEL is: 25,9*lg(v).

100

80 Combined model 94,4 dBA SP-1994 95,4 dBA 70 2 3 10 10 130 km/h

100

80 Combined model 95,3 dBA SP-1994 94,7 dBA 70 2 3 10 10 140 km/h

100

80 Combined model 96,8 dBA SP-1994 97,2 dBA 70 2 3 10 10 160 km/h

Fig. 8. The comparison of the SEL values of the noise emission from X2 trains, between the model prediction, “Combined model”, and the SP-1994 data [2]. (a) For speeds 130, 140 and 160 km/h.

100

80 Combined model 97,3 dBA SP-1994 97,6 dBA 70 2 3 10 10 170 km/h

100

80 Combined model 98,1 dBA SP-1994 98,8 dBA 70 2 3 10 10 180 km/h

100

80 Combined model 98,7 dBA SP-1994 98,2 dBA 70 2 3 10 10 190 km/h

Fig. 8. (continued) (b) For speeds 170–190 km/h.

100

80 Combined model 99,2 dBA SP-1994 98,4 dBA 70 2 3 10 10 200 km/h SEL for X2 trains 100

80 Combined model 99,6 dBA SP-1994 98,9 dBA 70 2 3 10 10 210 km/h

100

80 Combined model 100,3 dBA SP-1994 98,6 dBA 70 2 3 10 10 220 km/h

Fig. 8. (continued) (c) For speeds 200–220 km/h.

110 Combined model 100,8 dBA SP-1994 100,2 dBA 100

80 2 3 10 10 230 km/h

110 Combined model 101,2 dBA SP-1994 99,3 dBA 100

80 2 3 10 10 240 km/h

110 Combined model 101,7 dBA SP-1994 101,1 dBA 100

80 2 3 10 10 250 km/h

Fig. 8. (continued) (d) For speeds 230–250 km/h.

110 Combined model 102,0 dBA SP-1994 102,2 dBA 100

80 2 3 10 10 260 km/h

110 Combined model 102,5 dBA SP-1994 103,2 dBA 100

80 2 3 10 10 270 km/h

100 Combined model 89,2 dBA SP-1994 90,1 dBA 95

70 2 3 10 10 70 km/h

Fig. 8. (continued) (e) For speeds 260,270 and 70 km/h.

The TEL values predicted by the combined method (the Imagine source mode for rolling noise and the empirical model for aerodynamic noise) were listed in Table 4.1, for the representative speeds. The TSI-requirement [9] was also listed.

Table 4.1. The transit exposure level TEL at 25m from the track centre line. Speed (km/h)

250 300 320 350 The model prediction (dBA) – at an ordinary track 96,1 98,9 100,0 101,6

TSI-requirement (dBA) for existing design – at a 90 93 94 - reference track

To properly understand the predicted and TSI-required TEL values, it should be aware that the TSI required TEL values are for a rolling stock running on a reference track, where the rail roughness level can be much lower than that of an ordinary track. In Table 4.1, 6 dB difference between the model predicted and TSI required TELs at the three representative speeds probably originates from the difference in rail roughness levels. In other words, when verifying a rolling stock, a reference track should be used.

4.3 Input data

For the speed range of interest (150-300 km/h) and for each noise source component (rail/track radiation, wheel radiation, aerodynamic-noise around bogie areas and pantograph noise), the sound power levels per meter of the X2 train type in one-third octave bands of 25-10000 Hz, LWA 1m,0, as the input data, are given in the Tables 4.2–4.5.

It should be understood that these noise emission data are based on the average rail and wheel roughness level. In railway engineering application, when real roughness level differs from the model value, the real sound power level will differ from these input data.

As no better information is available, the sound power level of X2 train pantograph noise was estimated by referring to the pantograph noise data of Japanese Shinkansen 300 series [7], by holding the tonal feature and by adjusting the level to fit the total SEL data [2]. This estimation of the sound power level data should be used with caution. For some cases, for example when predicting the noise impact of high speed train behind high barriers, an accurate description of the pantograph noise is required.

The horizontal directivity is provided in Annex B.

As traction noise is irrelevant for high speed train noise, it has not been considered in this report. When it is needed, the noise sound power level of traction noise should be worked out in a separate way. Therefore, the input data provided in the following

tables may not be suitable for noise prediction at low speed where traction noise can be important, even for X2 trains.

Table 4.2. Sound power level per meter train of rail/track radiation (0 above railhead in source height), for X2 train Speed (km/h) Freq. (Hz) 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 25 65,9 66,2 66,5 66,7 67,0 67,2 67,4 67,6 67,8 68,0 68,2 68,3 68,5 68,7 68,8 69,0 31,5 68,9 69,2 69,3 69,6 69,8 70,1 70,3 70,5 70,7 70,9 71,1 71,2 71,4 71,6 71,7 71,9 40 71,4 71,7 72,0 72,2 72,5 72,7 72,8 73,0 73,2 73,4 73,6 73,8 73,9 74,1 74,3 74,4 50 73,0 73,3 73,6 73,8 74,1 74,3 74,5 74,7 74,9 75,1 75,3 75,3 75,5 75,7 75,9 76,0 63 75,3 75,5 75,7 76,0 76,2 76,5 76,7 76,9 77,1 77,3 77,5 77,6 77,8 78,0 78,1 78,3 80 78,8 79,1 79,3 79,6 79,9 80,1 80,2 80,4 80,6 80,8 81,0 81,2 81,3 81,5 81,7 81,8 100 82,2 82,5 82,8 83,0 83,3 83,5 83,7 83,9 84,1 84,3 84,5 84,6 84,7 84,9 85,1 85,2 125 81,5 82,3 82,7 83,4 83,7 83,9 84,1 84,3 84,5 84,7 84,9 85,0 85,2 85,4 85,5 85,7 160 80,7 81,2 81,6 82,0 82,6 83,2 83,6 84,1 84,7 84,9 85,1 85,2 85,4 85,5 85,7 85,9 200 81,6 82,0 82,4 82,7 83,2 83,6 83,8 84,2 84,6 85,1 85,6 85,8 86,2 86,7 87,1 87,2 250 83,4 83,4 83,3 83,3 83,6 84,0 84,2 84,5 84,9 85,2 85,5 85,7 86,0 86,3 86,7 87,1 315 87,1 87,0 87,0 86,9 86,8 86,8 86,7 86,7 86,8 87,0 87,3 87,5 87,8 88,0 88,3 88,5 400 86,3 86,7 87,0 87,4 87,3 87,2 87,2 87,2 87,1 87,1 87,0 87,0 87,0 86,9 86,9 87,2 500 89,0 88,7 88,4 88,1 88,4 88,7 89,0 89,3 89,4 89,4 89,3 89,3 89,3 89,2 89,2 89,1 630 92,5 91,6 91,1 90,3 89,9 89,6 89,4 89,1 89,0 89,3 89,6 89,8 90,0 90,3 90,3 90,3 800 95,5 95,4 95,3 95,2 94,5 93,8 93,4 92,8 92,1 91,9 91,7 91,4 91,3 91,1 91,0 91,2 1000 95,3 95,9 96,4 96,9 96,8 96,7 96,7 96,6 96,3 95,7 95,1 94,9 94,4 93,9 93,4 93,2 1250 92,6 93,6 94,2 95,1 95,6 96,0 96,4 96,8 97,0 96,9 96,9 96,8 96,8 96,7 96,3 95,8 1600 89,0 89,9 90,5 91,4 92,2 93,0 93,4 94,1 94,8 95,2 95,5 95,9 96,2 96,5 96,8 96,7 2000 88,6 89,6 90,5 91,5 92,3 93,0 93,5 94,1 94,8 95,5 96,1 96,3 96,9 97,4 97,9 98,3 2500 81,5 83,5 85,2 87,0 88,0 88,8 89,5 90,2 91,0 91,6 92,1 92,5 93,0 93,6 94,1 94,6 3150 75,5 77,1 77,9 79,4 81,1 82,7 84,0 85,5 86,8 87,5 88,1 88,7 89,3 89,9 90,5 91,0 4000 69,9 71,4 72,7 74,1 75,5 76,8 77,3 78,5 79,7 81,0 82,3 83,5 84,5 85,7 86,7 87,3 5000 69,3 70,4 71,4 72,4 73,7 74,9 75,9 77,0 78,2 79,3 80,3 80,6 81,5 82,5 83,4 84,5 6300 69,4 70,0 70,4 71,0 72,0 72,9 73,6 74,4 75,3 76,4 77,3 78,1 79,0 79,9 80,8 81,7 8000 70,5 71,0 71,4 71,9 72,5 73,0 73,3 73,7 74,2 75,0 75,7 76,4 76,9 77,6 78,3 79,1 10000 71,5 72,0 72,5 73,1 73,6 74,0 74,3 74,7 75,1 75,6 76,0 76,1 76,5 76,9 77,3 77,9 A-weighted 101,0 101,4 101,8 102,4 102,6 102,8 103,0 103,4 103,6 103,8 103,9 104,1 104,3 104,5 104,7 104,9

The speed exponent is: 12,9*lg(v) (dBA).

Table 4.3. Sound power level per meter train of wheel radiation (0,5 m in source height), for X2 train Speed (km/h) Freq. (Hz) 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 25 40,9 41,2 41,5 41,7 42,0 42,2 42,4 42,6 42,8 43,0 43,2 43,3 43,5 43,7 43,8 44,0 31,5 41,9 42,2 42,3 42,6 42,8 43,1 43,3 43,5 43,7 43,9 44,1 44,2 44,4 44,6 44,7 44,9 40 44,9 45,2 45,5 45,7 46,0 46,2 46,3 46,5 46,7 46,9 47,1 47,3 47,4 47,6 47,8 47,9 50 48,0 48,3 48,6 48,8 49,1 49,3 49,5 49,7 49,9 50,1 50,3 50,3 50,5 50,7 50,9 51,0 63 51,9 52,1 52,3 52,6 52,8 53,1 53,3 53,5 53,7 53,9 54,1 54,2 54,4 54,6 54,7 54,9 80 56,9 57,2 57,4 57,7 58,0 58,2 58,3 58,5 58,7 58,9 59,1 59,3 59,4 59,6 59,8 59,9 100 62,2 62,5 62,8 63,0 63,3 63,5 63,7 63,9 64,1 64,3 64,5 64,6 64,7 64,9 65,1 65,2 125 63,1 63,9 64,3 65,0 65,3 65,5 65,7 65,9 66,1 66,3 66,5 66,6 66,8 67,0 67,1 67,3 160 63,9 64,4 64,8 65,2 65,8 66,4 66,8 67,3 67,9 68,1 68,3 68,4 68,6 68,7 68,9 69,1 200 66,5 66,9 67,3 67,6 68,1 68,5 68,7 69,1 69,5 70,0 70,5 70,7 71,1 71,6 72,0 72,1 250 71,2 71,2 71,1 71,1 71,4 71,8 72,0 72,3 72,7 73,0 73,3 73,5 73,8 74,1 74,5 74,9 315 83,1 83,0 83,0 82,9 82,8 82,8 82,7 82,7 82,8 83,0 83,3 83,5 83,8 84,0 84,3 84,5 400 79,9 80,3 80,6 81,0 80,9 80,8 80,8 80,8 80,7 80,7 80,6 80,6 80,6 80,5 80,5 80,8 500 80,4 80,1 79,8 79,5 79,8 80,1 80,4 80,7 80,8 80,8 80,7 80,7 80,7 80,6 80,6 80,5 630 87,7 86,8 86,3 85,5 85,1 84,8 84,6 84,3 84,2 84,5 84,8 85,0 85,2 85,5 85,5 85,5 800 90,0 89,9 89,8 89,7 89,0 88,3 87,9 87,3 86,6 86,4 86,2 85,9 85,8 85,6 85,5 85,7 1000 97,0 97,6 98,1 98,6 98,5 98,4 98,4 98,3 98,0 97,4 96,8 96,6 96,1 95,6 95,1 94,9 1250 94,7 95,7 96,3 97,2 97,7 98,1 98,5 98,9 99,1 99,0 99,0 98,9 98,9 98,8 98,4 97,9 1600 96,7 97,6 98,2 99,1 99,9 100,7 101,1 101,8 102,5 102,9 103,2 103,6 103,9 104,2 104,5 104,4 2000 98,2 99,2 100,1 101,1 101,9 102,6 103,1 103,7 104,4 105,1 105,7 105,9 106,5 107,0 107,5 107,9 2500 95,9 97,9 99,6 101,4 102,4 103,2 103,9 104,6 105,4 106,0 106,5 106,9 107,4 108,0 108,5 109,0 3150 93,4 95,0 95,8 97,3 99,0 100,6 101,9 103,4 104,7 105,4 106,0 106,6 107,2 107,8 108,4 108,9 4000 86,3 87,8 89,1 90,5 91,9 93,2 93,7 94,9 96,1 97,4 98,7 99,9 100,9 102,1 103,1 103,7 5000 86,0 87,1 88,1 89,1 90,4 91,6 92,6 93,7 94,9 96,0 97,0 97,3 98,2 99,2 100,1 101,2 6300 84,4 85,0 85,4 86,0 87,0 87,9 88,6 89,4 90,3 91,4 92,3 93,1 94,0 94,9 95,8 96,7 8000 84,0 84,5 84,9 85,4 86,0 86,5 86,8 87,2 87,7 88,5 89,2 89,9 90,4 91,1 91,8 92,6 10000 83,5 84,0 84,5 85,1 85,6 86,0 86,3 86,7 87,1 87,6 88,0 88,1 88,5 88,9 89,3 89,9 A-weighted 105,3 106,4 107,3 108,5 109,3 110,1 110,7 111,5 112,3 112,9 113,4 113,8 114,4 114,9 115,4 115,9

The speed exponent is: 35*lg(v) (dBA). (The speed exponent for rolling noise is: 31,6*lg(v) (dBA).)

Table 4.4. Sound power level per meter train of aerodynamic noise around the bogie areas (0,5 m in source height), for X2 train Speed (km/h) Freq. (Hz) 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 25 86,6 87,7 88,7 90,6 92,1 93,4 94,9 96,4 98,0 99,4 100,6 101,9 103,3 104,2 105,0 105,9 31,5 88,6 88,8 88,8 89,7 90,6 91,4 92,2 93,4 94,7 96,0 96,9 98,0 99,1 100,4 101,6 102,8 40 90,3 91,1 91,8 92,2 92,4 92,7 92,8 93,1 93,8 94,4 95,1 95,6 96,2 97,2 98,2 99,2 50 91,0 91,7 92,3 92,9 93,4 94,0 94,4 95,0 95,5 95,9 96,2 96,4 96,4 97,0 97,5 98,0 63 88,9 91,1 93,2 93,7 94,1 94,5 94,8 95,1 95,4 95,5 95,6 95,6 95,4 97,4 98,3 98,9 80 86,5 87,6 88,6 90,4 92,3 93,8 95,2 95,9 96,0 96,0 95,9 95,7 95,1 94,4 93,2 90,6 100 87,1 87,8 88,5 89,4 90,3 91,0 91,8 92,8 94,2 95,3 96,0 96,4 95,6 94,5 92,3 83,1 125 87,6 88,7 89,7 90,2 90,8 91,3 91,7 92,4 93,0 93,6 94,1 94,6 94,9 95,8 96,2 96,1 160 88,5 89,1 89,5 90,3 91,2 92,1 92,9 93,5 93,9 94,2 94,6 94,9 95,1 95,5 95,8 96,1 200 88,4 89,7 91,0 91,5 91,8 92,2 92,5 93,0 93,7 94,4 95,0 95,7 96,3 96,5 96,7 96,9 250 88,5 89,1 89,7 90,9 92,0 92,9 93,7 94,0 94,2 94,4 94,7 94,8 94,9 95,5 96,0 96,5 315 84,3 85,7 86,8 87,7 88,5 89,2 89,6 90,6 91,8 92,8 93,8 94,6 95,2 96,1 97,1 97,9 400 84,2 86,2 88,2 89,4 90,5 91,6 92,5 93,4 94,1 94,7 95,3 95,7 95,9 96,9 97,8 98,7 500 83,2 84,5 85,8 88,5 90,5 92,0 93,6 94,8 95,6 96,5 97,4 98,2 98,9 99,5 100,0 100,5 630 83,5 85,2 86,7 88,1 89,3 90,4 91,3 93,2 95,0 96,6 97,8 99,1 100,2 101,0 101,7 102,4 800 83,5 85,2 86,7 88,2 89,7 91,0 92,3 93,4 94,5 95,4 96,3 97,1 97,7 99,5 101,0 102,3 1000 82,9 84,9 86,8 88,3 89,7 91,0 92,2 93,4 94,6 95,8 96,8 97,9 98,8 99,7 100,5 101,2 1250 78,4 82,1 85,5 87,4 89,1 90,7 92,3 93,5 94,7 95,8 96,8 97,8 98,7 99,7 100,7 101,6 1600 73,8 75,8 77,9 81,0 84,2 87,1 90,0 92,3 93,8 95,1 96,4 97,6 98,8 99,8 100,7 101,6 2000 71,6 73,9 76,2 78,2 80,1 81,7 83,3 85,4 88,1 90,7 92,9 95,2 97,5 98,7 99,8 100,9 2500 68,7 71,2 73,6 75,9 77,9 79,7 81,6 83,3 84,8 86,2 87,5 88,8 90,0 92,3 94,5 96,5 3150 65,8 68,2 70,6 72,9 75,0 76,9 78,8 80,7 82,4 84,1 85,4 86,9 88,4 89,7 90,8 92,0 4000 62,9 65,1 67,5 69,8 71,9 73,8 75,7 77,6 79,3 81,0 82,5 84,0 85,5 87,0 88,4 89,7 5000 59,9 62,4 64,8 67,1 69,2 70,9 72,9 74,7 76,5 78,2 79,6 81,1 82,6 84,1 85,5 86,8 6300 57,4 59,6 61,8 64,0 66,2 68,1 70,1 71,9 73,7 75,3 76,7 78,2 79,7 81,2 82,6 83,9 8000 55,5 57,5 59,6 61,6 63,5 65,3 67,0 68,7 70,5 72,2 73,7 75,3 76,8 78,2 79,6 80,9 10000 54,5 56,2 57,8 61,3 62,7 64,0 65,3 68,5 69,6 70,8 71,8 72,8 73,8 77,7 78,6 79,5 A-weighted 90,5 92,3 94,1 95,7 97,3 98,7 100,1 101,5 102,8 104,0 105,1 106,3 107,4 108,5 109,5 110,4

The speed exponent is: 66*lg(v) (dBA).

Table 4.5. Sound power level per meter train of pantograph noise (5 m in source height), for X2 train Speed (km/h) Freq. (Hz) 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 25 73,7 75,9 77,9 80,2 82,2 83,9 85,7 87,6 89,5 91,2 92,7 94,4 96,0 97,3 98,5 99,7 31,5 78,9 77,8 76,0 78,0 79,9 81,6 83,3 85,1 86,7 88,3 89,6 91,1 92,5 94,1 95,5 96,9 40 85,2 86,7 88,0 86,7 85,2 84,5 83,1 82,8 84,4 85,9 87,3 88,7 90,0 91,4 92,7 94,0 50 86,2 87,6 88,9 90,1 91,3 92,5 93,5 93,2 91,8 90,7 90,3 89,2 88,0 89,3 90,5 91,7 63 82,3 86,1 89,9 91,2 92,3 93,5 94,5 95,5 96,5 97,4 98,4 99,2 100,0 98,9 97,9 96,9 80 78,2 80,0 81,9 85,0 88,4 91,3 94,4 96,6 97,5 98,4 99,4 100,2 101,0 101,8 102,5 103,3 100 78,5 79,7 81,0 82,7 84,4 85,8 87,3 89,4 92,2 94,8 97,1 99,6 102,0 102,8 103,5 104,3 125 80,0 81,2 82,4 83,5 84,5 85,6 86,5 87,9 89,2 90,4 91,6 92,8 94,0 96,3 98,5 100,6 160 82,4 83,4 84,2 85,1 86,2 87,2 88,2 89,0 89,9 90,7 91,5 92,3 93,0 94,1 95,2 96,2 200 81,6 84,1 86,8 87,7 88,4 89,3 89,9 90,5 91,4 92,2 93,0 93,8 94,5 95,2 95,9 96,5 250 78,1 80,6 83,1 85,6 88,0 89,9 92,1 93,3 93,8 94,4 95,1 95,6 96,0 96,7 97,4 98,0 315 78,5 79,4 80,0 82,2 84,4 86,3 88,3 90,3 92,3 94,1 95,6 97,3 99,0 99,4 99,9 100,3 400 82,5 83,3 83,6 84,1 84,7 85,4 85,9 86,9 88,7 90,4 91,9 93,5 95,0 96,6 98,2 99,7 500 83,1 85,6 87,8 88,1 88,4 89,1 89,4 89,7 90,2 90,6 91,3 91,6 92,0 93,5 94,9 96,2 630 80,0 82,5 84,9 87,2 89,4 91,3 93,3 93,9 94,2 94,4 95,1 95,3 95,5 95,8 96,2 96,5 800 77,1 79,3 81,7 84,0 86,2 88,1 90,0 91,9 93,7 95,4 96,9 98,5 100,0 100,2 100,4 100,6 1000 74,1 76,6 79,1 81,3 83,5 85,1 87,0 88,9 90,7 92,4 93,9 95,5 97,0 98,5 99,9 101,2 1250 70,6 73,4 76,1 78,3 80,5 82,4 84,4 86,3 88,0 89,3 90,9 92,5 94,0 95,5 96,9 98,2 1600 66,3 68,9 71,6 74,2 76,6 78,7 80,9 82,9 84,7 86,4 87,9 89,5 91,0 92,5 93,9 95,2 2000 62,6 65,1 67,8 70,4 72,7 74,7 76,9 79,0 81,0 82,9 84,6 86,3 88,0 89,5 90,9 92,2 2500 58,6 61,4 64,1 66,6 69,0 70,9 73,1 75,2 77,1 79,0 80,6 82,3 84,0 85,6 87,2 88,7 3150 54,6 57,2 59,9 62,5 64,9 67,0 69,2 71,3 73,3 75,1 76,6 78,3 80,0 81,6 83,2 84,7 4000 50,6 53,1 55,8 58,4 60,7 62,7 64,9 67,0 69,0 70,9 72,6 74,3 76,0 77,6 79,2 80,7 5000 46,6 49,4 52,1 54,6 57,0 58,9 61,1 63,2 65,1 67,0 68,6 70,3 72,0 73,6 75,2 76,7 6300 43,6 45,8 47,9 50,5 52,9 55,0 57,2 59,3 61,3 63,1 64,6 66,3 68,0 69,6 71,2 72,7 8000 41,7 43,6 45,8 47,8 49,7 51,5 53,2 55,0 57,0 58,9 60,6 62,3 64,0 65,6 67,2 68,7 10000 40,7 42,4 44,0 47,4 48,8 50,2 51,5 54,7 55,8 56,9 58,0 59,0 60,0 64,9 65,9 66,7 A-weighted 85,6 87,7 89,8 91,4 93,1 94,7 96,4 97,7 99,0 100,2 101,5 102,9 104,2 105,1 106,1 107,1 The speed exponent is: 71,3*lg(v) (dBA). (Note: when using this sound power per meter train of pantograph noise, a correction term shall be applied: -

10 *lgltrain /168.)

5 Discussion

Input data for the X2 train type have been worked out based on the Imagine source model for rolling noise and the empirical model for the aerodynamic noise described in section 4. These input data are presented in Tables 4.2-4.5. The relevant directivity is provided in Annex B. As have been shown in Fig. 8, using these input data, the Nord2000 propagation model can properly predict X2 train noise in the one-third octave bands within the speed range of interest (150-300 km/h).

However, these input data should be used with caution, because

 The total roughness, including rail and wheel roughness, can differ between train types and track sites.  The vehicle transfer function can differ depending on wheel size, damping and screening.  The aerodynamic noise depends much on the surface details of the train type.

The basic model described in section 4 can be adjusted to take these variations into account.

As pantograph noise can, both in level and in spectrum, vary with train type and speed, the estimation of the sound power level of X2 train pantograph noise, provided in Table 4.5, should be used with caution. Especially when predicting the noise impact of high speed train behind high barriers, in case an accurate description of X2 pantograph noise may need to be worked out.

Reference

[1] www.gronataget.se . [2] Clara Göransson and Tomas Ström, Externt buller från svenska tågtyper – Nya indata till den nordiska beräkningsmodellen, SP rapport 1994:25. [3] Xuetao Zhang, Railway Traction noise – the state of the art, HAR12TR-030530-SP01 (Harmonoise technical report). [4] C. Czolbe and M. Hwcht, Noise reduction measures at freight train locomotives “Blue Tiger”, the 9th International Workshop on Railway Noise, Munich, Germany, September 4-8, 2007. [5] Xuetao Zhang, To determine the Swedish inputs for using the Harmonoise model of railway noise, report ETa6140-6:3, December 2005. [6] C. Mellet, F. Létourneaux, F. Poisson, C. Talotte, High speed train noise emission: Latest investigation of the aerodynamic/rolling noise contribution, Journal of Sound and Vibration 293 (2006) 535–546. [7] Private communication with Takehisa Takaishi at Japanese Railway Technical Research Institute, October 2010. [8] C. Charbonnel, Definition of a simple model of sources for the TGV-R, HAR12TR- 021206-SNCF01 (the Harmonoise technical report). [9] European Commission: Technical Specifications for Interoperability relating to the rolling stock subsystem, COM (2002) 1952, Annex. [10] ISO 3744:1994: Acoustics – Determination of sound power levels of noise sources using sound pressure – Engineering method in an essentially free filed over a reflecting plane. [11] Xuetao Zhang, To evaluate the sound power level L using the L of a train WA Aeq, Tp pass-by – A possible way to simplify the measurement procedure, IMA6TR-040415-SP06 (The IMAGINE Technical Report). [12] Xuetao Zhang, A practical method to determine the sound power of railway rolling noise using one-microphone recordings, ForumAcusticum 2005, 29 Aug. – 2 Sept., Budapest, paper 579_0. [13] Xuetao Zhang, Directivity of Railway Rolling Noise, Noise and Vibration Mitigation for Rail Transportation Systems, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Volume 99, ©2008 Springer-Verlag Berlin Heidelberg. [14] J. F. Hamet and M. Bérengier, Acoustical characteristics of porous pavements: A new phenomenological model, Internoise 93, Leuven, Belgium, 641-646 (1993). [15] M. E. Delany and E. N. Bazley, Acoustical properties of fibrous absorbent materials, Applied Acoustics 3, 309-322 (1970). [16] Xuetao Zhang, The Directivity of Railway Noise at Different Speeds, Journal of Sound and Vibration 329 (2010) 5273–5288. [17] Xuetao Zhang, Applicable Directivity Description of Railway Noise Sources, PhD thesis, Chalmers University of Technology (2010). [18] A. Johansson, Out-of-round railway wheels – assessment of wheel tread irregularities in train traffic, Journal of Sound and Vibration 293 (2006) 795–806.

Annex A Methods to determine the sound power level of a traffic noise source

For a stationary sound source, an engineering method to determine the sound power level using measured distributed sound pressure levels is given in ISO 3744 [10]. According to this method, a measurement surface is defined, which encloses the source and terminates on the reflecting plane or planes. The measurement points are located on this hypothetical surface. Obviously, for handling a moving sound source like a train, this method is not suitable and will then not be considered.

In traffic noise engineering, the equivalent sound pressure level, Leq, T , or the sound exposure level, SEL, for a specified time interval is often measured. The maximum sound pressure level using time-weighting F, L pF max , is also used in Sweden. In practice, it is not straight forward to determine the sound power level of a traffic noise source from one of these measured quantities, because the directivity (of a traffic noise source) and the excess attenuation (the ground absorption and reflection together with meteorological effects on sound propagation) are complicated issues to handle.

During the European IMAGINE project, a practical method to determine the sound power level from the L of a train pass by was proposed [11,12]. This method Aeq, Tp will be described in section A1.

The method to determine the sound power level from the SEL is derived and presented in section A2.

The can be calculated under certain assumptions, which is discussed in section A3.

L L A.1 Determination of WA from the Aeq,Tp of a train pass by

As described in ISO 3095:2005, one of the standard receiver positions when measuring railway rolling noise is 7,5 m from the centre line of the track concerned and 1,2 m above the railhead. The A-weighted equivalent (continuous) sound pressure level, measured in the specified time interval T p (as shown in Figs. A1 and A2), should be determined using the formula

t T / 2  1 0 p p 2 t  L  10 lg A dt dB (A-1) Aeq,Tp   2  Tp p0  t0 Tp / 2  where:

L the A-weighted equivalent continuous sound pressure level for the Aeq,Tp

time period T p ;

Tp  L / v the specified measurement time interval, which is centred at t0 , where L is the train length and v the (constant) train speed; the instantaneous time moment when the distance between the train centre and the receiver is the shortest (for a straight track);

pA t the A-weighted instantaneous sound pressure;

p0  20 Pa the reference sound pressure.

To determine the sound power level LWA from the , one normally assumes that the sound power of rolling noise is (approximately) uniformly distributed along the train. Thus, without losing generality, one can divide the whole train into N ( 1) sections of equal-length of l0  1 m , and treat each source section as a point sub- source. Then, each sub-source will contribute to the total sound power level by

si LWA  LWA 1m10 lgl0   LWA 1m,010 lgl0  Li , (A-2)

where LWA 1m is the sound power level produced by 1 meter long source element and LWA 1m,0 for its omni-directional component. For simplicity, let us first consider only one source height. To the received pass-by noise, the contribution of a sub-source si of a length l0  1 m is then calculated as [11,12] (see Fig. A2)

t T / 2 t T / 2  0 p   0 p (LW ,i  Aexcess,i ) /10   1 L (s ,t) /10   1 10  Lsi  10 lg 10 pAeq i dt  10 lg dvt Aeq,Tp      2  Tp Tp v 4 r t  t0 Tp / 2   t0 Tp / 2 i  .

i ,max   l   L 1m A  /10   10 lg 0 10 lg 10 WA excess i d     i  4 dTp v   i ,min  (A-3)

Then the total L is given by pAeq,Tp

N N si  LpAeq,T /10  L  Lsi  10 lg 10 p  . (A-4) Aeq,Tp  pAeq,Tp  i1  i1 

Inserting Eq. (A-2) into Eq. (A-4), one obtains

 i,max  s  l L  A  /10  L i  L 1m,010 lg 0 10 i excess i d . (A-5) Aeq,Tp WA   i  4 dTp v  i,min 

t0  Tp / 2 t0 t0  Tp / 2

v L (train) d = 7,5m

Receiver

Fig. A1. The time interval of T p .

i,min i,max

Fig.A2. The trace of a sub-source during the tine interval T p .

Using the relationship Tp v  Nl0  ltrain , it becomes

 i,max  s  l L  A  /10  L i  L 1m,010 lg 0 10 i excess i d . (A-6) Aeq,Tp WA   i  4 dltrain  i,min 

Combining Eqs. (A-4) and (A-6), there will be

N N   i,max  s  l L  A  /10  L  L i  L 1m,010 lg 0 10 i excess i d  Aeq,Tp  pAeq,Tp  WA   i  i1 i1  4 dltrain     i,min 

 N i,max   1 L A  /10   L 1m,0 10 lg l 10 lg 10 i excess i d WA    train     i  4 dNltrain i1  i,min 

 L 1m,0 A WA line, propagation(Tp ) (A-7) where

 N i,max   1 L  A  /10  A  10 lg 10 i excess i d . (A-8) line, propagation(Tp )    i  4 dN i1  i,min 

It has been shown that, at this short distance, the horizontal directivity of rolling noise has non-important effect on L [13]. Therefore, taking L   0 is pAeq,Tp   acceptable when doing the integration. Moreover, it is not difficult to find a measurement site of a simple terrain, for which the Nord2000 propagation model can properly handle the excess attenuation.

Thus, A gives the average propagation attenuation of the line source line, propagation(Tp ) of length Tp v  Nl0  ltrain . As has been shown, the pre-calculated tabular values of the spectrum of this quantity given in Table A1 can be used for most applications [11,12].

The tabular values presented in Table A1 are calculated based on Eq. (A-8), and averaged over 10 typical terrains, which are described in the following.

Fig.A3. A representative terrain for a railway.

A representative terrain shape for a railway is shown in Fig. A3, which consists of three sections. (1) The first section is for a ballast railway bed that is flat and about 2m wide (from the outmost rail to the edge of the ballast bed). Its ground impedance is chosen to be 3000 Pas/m 2 , and will be handled by the Hamet impedance model [14]. (2) The second section is a transit section between the railway bed and the ground beside it, which in many cases will be a slope but sometimes can also be flat. A height h and a slope of 30 degrees and the ground impedance of 200 kPas/m are

used to describe this section. Five typical values are chosen for h: 0, 0,5m, 1m, 1,5m, and 2m; then a case of h < 0 is not considered which implies that it is not favorable to be used for such power determination. (3) The last section is for the ground beside the railway, which is (roughly) flat and has its ground impedance being 200 or 200.000 kPas/m 2 . For the second and the third sections the Delany and Bazley impedance model [15] will be applied. The third section can (in many cases) begin with a shallow ditch, which is neglected in the model calculation.

It has been shown that, using the tabular values given in Table A1, Eq, (A-7) will determine L with an error less than 0,5 dB [11,12]. Aeq,Tp

Eqs. (A-7) and (A-8) indicate that, by using , one can determine the sound power level (per meter length) of rolling noise in the way

L 1m,0  L  A . (A-9) WA Aeq,Tp line, propagation(Tp )

Table A1 The pre-calculated third-octave bands values (25 ~ 10000 Hz) of A [11,12]. line, propagation(Tp ) Source height (m) (above railhead) Freq. (Hz) 0 0,5 2 3 4 25 -8,8 -9,1 -9,8 -10,2 -10,7 31,5 -8,7 -9,1 -10,0 -10,6 -11,3 40 -8,8 -9,2 -10,5 -11,4 -12,3 50 -8,9 -9,5 -11,3 -12,6 -13,9 63 -9,6 -10,6 -13,1 -14,7 -15,7 80 -11,6 -13,4 -15,4 -16,0 -15,9 100 -13,7 -15,0 -15,3 -15,5 -14,3 125 -12,6 -13,2 -15,3 -15,0 -13,7 160 -11,3 -13,4 -15,4 -14,0 -14,1 200 -11,2 -13,9 -15,1 -13,9 -13,3 250 -11,7 -15,7 -14,3 -13,9 -13,1 315 -13,6 -15,3 -13,9 -13,6 -12,8 400 -12,2 -15,9 -13,9 -13,4 -13,2 500 -13,7 -16,5 -13,9 -14,0 -13,2 630 -13,4 -15,2 -13,7 -13,4 -13,4 800 -14,8 -15,2 -14,1 -13,7 -13,3 1000 -15,2 -15,4 -13,7 -13,6 -13,4 1250 -15,6 -14,3 -13,9 -13,8 -13,5 1600 -15,0 -14,6 -14,0 -13,8 -13,6 2000 -15,6 -15,1 -14,1 -13,9 -13,7 2500 -15,3 -14,8 -14,1 -14,1 -13,8 3150 -15,3 -14,8 -14,3 -14,2 -14,0 4000 -14,8 -15,1 -14,5 -14,4 -14,2 5000 -14,8 -15,5 -14,8 -14,6 -14,5 6300 -15,0 -15,7 -15,1 -15,0 -14,9 8000 -15,8 -16,3 -15,6 -15,5 -15,4 10000 -16,1 -16,8 -16,3 -16,2 -16,2

A.2 To determine LWA from the SEL of a train pass by

Considering a time interval T  Tp centred at t0 (see Fig. A1), Eq. (A-5) can be used to describe the corresponding equivalent sound pressure level when replacing

T p by T ,

 l i,max  si  0 Li Aexcess i /10  LAeq,T  LWA 1m,010 lg 10 di  . (A-10) 4 dTv   i,min 

The SEL value of the passing-by train is given by

N si SEL   LAeq,T 10 lg(T) . (A-11) i1

When T  Tp , all the sub-sources will equally contribute. Then, we have

l max   train   L Aexcess  /10  SEL  LWA 1m,010 lg  10 lg 10 d , (A-12) 4 dv    min 

where max and min are the limit angles of the integration, which are approximately the same for all source elements while differing from those defined in Fig.A2. As is shown in [13,16], the horizontal directivity of railway rolling noise is speed dependent and can be described when the track and vehicle transfer functions are known. If the last term in Eq. (A-12) can be pre-calculated, then the sound power level of the train pass by, when the rolling noise is predominant, is given by

max   L Aexcess  /10  LWA 1m,010 lgltrain  SEL 10 lg4 dv10 lg 10 d .    min  (A-13)

Once again, it has been assumed that the sound power of rolling noise is uniformly distributed along the train.

A.3 To calculate the LpF max of a train pass by

If the sound power level distributed along a train is known, one can calculate the

LpF max of a pass by of the train type. For a line source with its two ends located at 1 and  N , the sound pressure level of the line source at a receiver can numerically be calculated as [17]

N  LW i 10 lg 4 d Aexcessi /10  Lp  10 lg10 i  . (A-14)  i1 

Assuming that the sound power is uniformly distributed along the train and the horizontal directivity is not important, the maximum level shall occur when the train centre is (nearly) located in front of the receiver. Since the angular position of the i-th source element, i , will be known when the train length and the location of the train centre are given, L pF max is then given by

Nl N  0   1 Li Aexcess i /10  LpF max  LWA 1m,010 lg  10 lg 10 i  . 4 d   N i1  (A-15)

However, as the noise sound power is often not uniformly distributed along the train (e.g. powered wheels are often rougher than trailer wheels [18]), one needs to calculate Lp levels in a several angle positions of the train in order to find LpF max . Moreover, for a distant receiver, the noise sound power distribution along the train becomes less important in calculating .

Annex B The horizontal directivity of railway noise

B.1 Directivity function

Here provided are the horizontal directivities of railway rolling noise and aerodynamic noise, including the Doppler effect. The horizontal directivity functions of the noise components are given in Table B1 [16],.

Table B1. The horizontal directivities [13]. Source type Horizontal directivity function (source height)

Rolling noise

 20lg[1 M *sin()], for the contribution of the sleeper rail/track vibration (for frequency components below the decoupling (0) frequency, e.g. < 400 Hz). 10 lg[0.001  0.999 *cos2 ()]  20 lg[1 M *sin()] , for the contribution from the rail vibration (for the other frequency components, e.g. 400 Hz and above). wheel 10lg[0.4  0.6*cos()] 20lg[1 M *sin()] (0,5 m)

Aerodynamic noise

pantograph 10 *lg0.006  1 0.006*cos2  40 *lg1 M *sin (5 m) bogie area 10 *lgC  1 C *cos2   / 2 40 *lg1 M *sin, (0,5 m) 1 1 where C1 is taken as 0,03.

Note: M is the Mach number and the horizontal angle,  , is shown in Fig. B1. takes a positive value when a train approaches and a negative value when it runs away.

Receiver 2 z

' Source  

 x v 

Receiver 1

Fig. B1. The definition of angles:  is a horizontal angle in the x-y plane and relative to the y-axis;  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).

B.2 Normalization

By Eq. (A-9) or Eq. (A-13) in Annex A, what has been determined is the omni- directional component, LWA 1m,0, of the sound power level (per meter train). The sound power level also has a directional component as given below

L 1m  L 1m,0  L  , (B-1) WA   WA     where L equals to one of the directivity functions given in Table B1, may or may not plus a corresponding normalization constant. (Caution: if one adds a normalization constant to , then he/she should also subtract the same constant from the LWA 1m,0.)

When is normalized in the way

1  / 2 10 L /10 d  1, (B-2)    / 2 then becomes the normalized sound power level (per meter train) and the normalized horizontal directivity.

Les us denote a directivity function given in Table B1 as L0 , one can obtain its normalization factor by

 / 2 1 L  /10 10 0 d  C . (B-3)   0  / 2 Then, the normalized directivity function is given by

L  L0 10 lgC0 . (B-4)

The horizontal directivity functions given in Table B1 depend on noise type also the train speed, so does its normalization factor. The values of the normalization factor for the specified noise types at the speeds of interest are given in Table B2.

Table B2. The normalization factor of the horizontal directivities given in Table B1. Source type V (source height – above the railhead) (km/h) sleeper rail wheel aero-bogie pantograph radiation radiation radiation area (5 m) (0) (0) (0,5 m) (0,5 m) 150 1,01 0,50 0,50 0,57 0,52 160 1,01 0,50 0,50 0,58 0,52 170 1,02 0,50 0,50 0,59 0,52 180 1,02 0,50 0,50 0,60 0,53 190 1,03 0,50 0,50 0,61 0,53 200 1,03 0,51 0,51 0,62 0,53 210 1,03 0,51 0,51 0,63 0,54 220 1,04 0,51 0,51 0,64 0,54 230 1,04 0,51 0,51 0,66 0,55 240 1,05 0,51 0,51 0,67 0,55 250 1,05 0,51 0,51 0,69 0,55 260 1,06 0,51 0,51 0,70 0,56 270 1,07 0,51 0,51 0,72 0,57 280 1,07 0,52 0,52 0,74 0,57 290 1,08 0,52 0,52 0,76 0,58 300 1,09 0,52 0,52 0,78 0,58

Annex C Input data for higher speeds

Similar as the input data given in Section 4.3, the input data given in this appendix (in Tables C.1 – C.4) are the noise emission sound power level per meter train for X2 train type, for the extended speed range 310-350 km/h.

As the measured noise emission data are only up to 270 km/h, uncertainty of the input data in this extended speed range becomes greater.

Table C.1. Sound power level per meter train of rail/track radiation (0 above railhead in source height), for X2 train Speed (km/h) Frequency (Hz) 310 320 330 340 350 25 69,1 69,3 69,3 69,5 69,6 31,5 72,0 72,2 72,3 72,4 72,5 40 74,6 74,7 74,8 75,0 75,1 50 76,2 76,3 76,4 76,6 76,7 63 78,4 78,6 78,6 78,7 78,9 80 82,0 82,1 82,2 82,4 82,5 100 85,4 85,5 85,6 85,8 85,9 125 85,8 86,0 86,0 86,2 86,3 160 86,0 86,2 86,2 86,4 86,5 200 87,4 87,5 87,6 87,8 87,9 250 87,5 87,8 87,9 88,3 88,6 315 88,8 89,0 89,1 89,4 89,6 400 87,4 87,6 87,7 87,9 88,1 500 89,1 89,1 89,1 89,0 89,0 630 90,2 90,2 90,2 90,1 90,1 800 91,4 91,6 91,7 91,9 92,1 1000 93,0 92,9 92,7 92,6 92,4 1250 95,4 94,9 94,8 94,4 94,0 1600 96,6 96,6 96,6 96,5 96,4 2000 98,6 98,8 99,1 99,3 99,6 2500 95,1 95,6 95,7 96,1 96,6 3150 91,4 91,8 92,1 92,5 92,9 4000 87,9 88,4 88,8 89,2 89,7 5000 85,6 86,5 87,3 88,2 89,2 6300 82,5 83,3 83,3 84,1 84,8 8000 79,9 80,6 81,2 81,9 82,6 10000 78,5 79,1 79,5 80,0 80,6 A-weighted 105,0 105,1 105,3 105,4 105,6

Table C.2. Sound power level per meter train of wheel radiation (0,5 m in source height), for X2 train Speed (km/h) Frequency (Hz) 310 320 330 340 350 25 44,1 44,3 44,3 44,5 44,6 31,5 45,0 45,2 45,3 45,4 45,5 40 48,1 48,2 48,3 48,5 48,6 50 51,2 51,3 51,4 51,6 51,7 63 55,0 55,2 55,2 55,3 55,5 80 60,1 60,2 60,3 60,5 60,6 100 65,4 65,5 65,6 65,8 65,9 125 67,4 67,6 67,6 67,8 67,9 160 69,2 69,4 69,4 69,6 69,7 200 72,3 72,4 72,5 72,7 72,8 250 75,3 75,6 75,7 76,1 76,4 315 84,8 85,0 85,1 85,4 85,6 400 81,0 81,2 81,3 81,5 81,7 500 80,5 80,5 80,5 80,4 80,4 630 85,4 85,4 85,4 85,3 85,3 800 85,9 86,1 86,2 86,4 86,6 1000 94,7 94,6 94,4 94,3 94,1 1250 97,5 97,0 96,9 96,5 96,1 1600 104,3 104,3 104,3 104,2 104,1 2000 108,2 108,4 108,7 108,9 109,2 2500 109,5 110,0 110,1 110,5 111,0 3150 109,3 109,7 110,0 110,4 110,8 4000 104,3 104,8 105,2 105,6 106,1 5000 102,3 103,2 104,0 104,9 105,9 6300 97,5 98,3 98,3 99,1 99,8 8000 93,4 94,1 94,7 95,4 96,1 10000 90,5 91,1 91,5 92,0 92,6 A-weighted 116,3 116,7 116,9 117,3 117,7

Table C.3. Sound power level per meter train of aerodynamic noise around the bogie areas (0,5 m in source height), for X2 train Speed (km/h) Frequency (Hz) 310 320 330 340 350 25 106,6 107,4 108,1 108,8 109,5 31,5 103,6 104,7 105,7 106,7 107,4 40 99,8 100,7 101,6 102,4 103,4 50 98,4 98,8 99,2 99,6 100,4 63 99,3 99,7 99,9 100,0 100,4 80 83,6 92,6 95,8 97,9 91,9 100 92,3 96,0 98,4 100,1 101,4 125 95,0 87,0 97,2 101,5 102,8 160 96,3 96,4 96,4 96,3 95,8 200 97,0 97,1 97,2 97,2 97,1 250 96,9 97,4 97,8 98,1 98,1 315 98,7 99,5 100,2 100,9 101,9 400 99,5 100,2 100,8 101,3 101,9 500 101,0 101,4 101,6 101,9 102,7 630 103,1 103,7 104,3 104,9 105,4 800 103,2 104,3 105,3 106,2 106,9 1000 102,0 102,6 103,1 103,9 105,3 1250 102,5 103,3 104,1 104,8 105,5 1600 102,4 103,3 104,0 104,8 105,5 2000 101,9 102,9 103,9 104,8 105,6 2500 98,2 100,1 102,0 103,6 104,5 3150 93,0 94,0 95,0 96,0 97,8 4000 90,7 91,9 93,1 94,3 95,3 5000 88,0 89,2 90,5 91,7 92,8 6300 85,0 86,2 87,4 88,6 89,8 8000 82,0 83,2 84,4 85,7 86,8 10000 80,4 81,2 82,0 85,7 86,5 A-weighted 111,3 112,2 113,1 114,0 114,8

Table C.4. Sound power level per meter train of pantograph noise (5 m in source height), for X2 train Speed (km/h) Frequency (Hz) 310 320 330 340 350 25 100,8 101,9 103,0 104,1 105,1 31,5 98,1 99,4 100,7 102,0 103,0 40 94,9 96,1 97,3 98,4 99,6 50 92,8 93,9 95,0 96,1 97,2 63 96,8 95,9 95,0 94,0 95,0 80 104,1 104,8 105,4 106,0 105,6 100 105,0 105,7 106,3 107,0 107,6 125 102,4 104,4 106,4 108,0 108,6 160 97,1 98,1 99,0 99,9 101,2 200 97,2 97,8 98,4 99,0 99,9 250 98,7 99,3 99,9 100,5 101,0 315 100,9 101,3 101,7 102,0 102,6 400 100,7 102,1 103,5 104,8 105,5 500 97,4 98,7 99,9 101,1 102,5 630 97,1 97,4 97,7 98,0 99,2 800 101,2 101,4 101,5 101,7 101,9 1000 102,4 103,7 104,9 105,8 106,0 1250 99,4 100,7 101,9 103,1 104,3 1600 96,1 97,3 98,6 99,8 100,9 2000 93,4 94,7 95,9 97,1 98,3 2500 90,0 91,4 92,8 94,1 95,3 3150 85,9 87,3 88,6 90,0 91,3 4000 81,7 83,1 84,5 85,8 87,2 5000 78,0 79,4 80,8 82,1 83,5 6300 73,9 75,3 76,6 78,0 79,3 8000 69,7 71,1 72,5 74,0 75,2 10000 67,6 68,4 69,2 74,0 74,8 A-weighted 108,0 109,1 110,1 111,1 111,8

(Note: when using this sound power per meter train of pantograph noise, a correction term shall be applied: -10 *lgltrain /168.)

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