Railway applications - Aerodynamics - Part 5: Requirements and test procedures for aerodynamics in tunnels

This European Standard applies to the aerodynamic loading caused by trains running in a tunnel

Bahnanwendungen - Aerodynamik - Teil 5: Anforderungen und Prüfverfahren für Aerodynamik im Tunnel

Diese Europäische Norm gilt für die aerodynamischen Belastungen, die Züge bei der Fahrt durch einen Tunnel verursachen.

Applications ferroviaires - Aérodynamique - Partie 5: Exigences et procédures d'essai pour l'aérodynamique en tunnel

La présente norme européenne traite des sollicitations aérodynamiques des trains circulant dans un tunnel.

Železniške naprave - Aerodinamika - 5. del: Zahteve in preskusni postopki pri aerodinamiki v predorih

Ta evropski standard velja za aerodinamično obremenitev, ki jo povzročajo vlaki med vožnjo skozi tunel.

General Information

Status
Withdrawn
Publication Date
02-Nov-2010
Current Stage
9960 - Withdrawal effective - Withdrawal
Completion Date
22-Dec-2021

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2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Železniške naprave - Aerodinamika - 5. del: Zahteve in preskusni postopki pri aerodinamiki v predorihBahnanwendungen - Aerodynamik - Teil 5: Anforderungen und Prüfverfahren für Aerodynamik im TunnelApplications ferroviaires - Aérodynamique - Partie 5: Exigences et procédures d'essai pour l'aérodynamique en tunnelRailway applications - Aerodynamics - Part 5: Requirements and test procedures for aerodynamics in tunnels93.060Gradnja predorovTunnel construction45.060.01Železniška vozila na splošnoRailway rolling stock in generalICS:Ta slovenski standard je istoveten z:EN 14067-5:2006+A1:2010SIST EN 14067-5:2007+A1:2010en,fr,de01-december-2010SIST EN 14067-5:2007+A1:2010SLOVENSKI

STANDARD
SIST EN 14067-5:2007+A1:2010
EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM
EN 14067-5:2006+A1
November 2010 ICS 45.060.01; 93.060 Supersedes EN 14067-5:2006English Version

Railway applications - Aerodynamics - Part 5: Requirements and test procedures for aerodynamics in tunnels

Applications ferroviaires - Aérodynamique - Partie 5: Exigences et procédures d'essai pour l'aérodynamique en tunnel

Bahnanwendungen - Aerodynamik - Teil 5: Anforderungen und Prüfverfahren für Aerodynamik im Tunnel This European Standard was approved by CEN on 30 June 2006 and includes Amendment 1 approved by CEN on 28 September 2010.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN Management Centre or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre:
Avenue Marnix 17,

B-1000 Brussels © 2010 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN 14067-5:2006+A1:2010: ESIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 2 Contents Page Foreword ..............................................................................................................................................................41Scope ......................................................................................................................................................52Normative references ............................................................................................................................53Terms, definitions, symbols and abbreviations .................................................................................54Methodologies for quantifying the pressure changes in order to meet the medical health criterion ...................................................................................................................................................54.1General ....................................................................................................................................................54.2Train-tunnel-pressure signature ..........................................................................................................54.3Maximum pressure changes ................................................................................................................85Pressure loading on unsealed crossing trains ................................................................................ 106Pressure loading on sealed trains in tunnels .................................................................................. 126.1General ................................................................................................................................................. 126.2Single train case ................................................................................................................................. 136.3Two train case ..................................................................................................................................... 15Annex A (informative)

Predictive equations ................................................................................................ 20Annex B (informative)

Pressure comfort criteria ........................................................................................ 28Annex C (informative)

Micro-pressure wave ............................................................................................... 29Annex ZA (informative)

!!!!Relationship between this European Standard and the Essential Requirements of EU Directive 2008/57/EC of the European Parliament and of the Council of 17 June 2008 on the interoperability of the rail system within the Community (Recast)"""" .......................................................................................................................................... 32Bibliography ..................................................................................................................................................... 35 Figure 1 — Train-tunnel-pressure signature at a fixed position in a tunnel (detail) ....................................6Figure 2 — Train-tunnel-pressure signature at an exterior position just behind the nose of the train .........................................................................................................................................................7Figure 3 — External pressure drop due to the head passage of a crossing train .................................... 10Figure 4 — Internal pressure evolution inside an unsealed vehicle due to the head passage of a crossing train ...................................................................................................................................... 10Figure 5 — Pressure differences on an unsealed vehicle due to the head passage of a crossing train ...................................................................................................................................................... 11Figure 6 — Typical measured maximum forces on a freight wagon door during the head passage of a crossing train ............................................................................................................................... 12Figure 7 — Pressure difference on a well sealed train in two successive tunnels .................................. 13Figure 8 — External pressure histories at different speeds in two successive tunnels .......................... 14Figure 9 — Influence of tunnel length on maximum external pressure variation ..................................... 14Figure 10 — Influence of the relative entry time ∆∆∆∆t1,2 on maximum absolute values of pressure differences for a particular situation ................................................................................................ 15SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 3 Figure 11 — Example scenario for train crossings during 1,5 h of scheduled traffic on a high speed line with 6 trains in circulation passing 6 tunnels which cover 10 % of the line length .................................................................................................................................................... 17Figure 12 — Effect of time schedule variation on the number of train crossings in tunnels for a particular train ..................................................................................................................................... 18Figure 13 — Calculated pressure trace and resulting pressure loadings above 500 Pa (arrowed) ........ 19Figure 14 — Pressure loadings for two different crossing frequency scenarios ...................................... 19Figure A.1 — Calculation of a train-tunnel-pressure signature ................................................................... 21Figure A.2 — Solutions Xfr of Equation (A.13) for different values of frhζζζ+= ...................................... 23Figure A.3 — Solution Xt of Equation (A.18) for different values of ζζζζ1 ==== ζζζζh ++++ ζζζζfr ++++ ζζζζt with ζζζζE ==== 0,5 ............. 25Figure A.4 — Aerodynamic drag coefficient .................................................................................................. 27Figure C.1 — Wave generation, propagation and radiation ......................................................................... 29Figure C.2 — Steepening in concrete slab tunnels ...................................................................................... 30Figure C.3 — Radiation of micro pressure wave........................................................................................... 31 SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 4 Foreword This document (EN 14067-5:2006+A1:2010) has been prepared by Technical Committee CEN/TC 256 “Railway applications”, the secretariat of which is held by DIN. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by May 2011, and conflicting national standards shall be withdrawn at the latest by May 2011. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights. This document includes Amendment 1, approved by CEN on 2010-09-28. This document supersedes EN 14067-5:2006. The start and finish of text introduced or altered by amendment is indicated in the text by tags ! ". !This document has been prepared under a mandate given to CEN/CENELEC/ETSI by the European Commission and the European Free Trade Association, and supports essential requirements of EU Directive 2008/57/EC. For relationship with EU Directive 2008/57/EC, see informative Annex ZA, which is an integral part of this document." This European Standard is part of the series "Railway applications — Aerodynamics" which consists of the following parts:  Part 1: Symbols and units  Part 2: Aerodynamics on open track  Part 3: Aerodynamics in tunnels  Part 4: Requirements and test procedures for aerodynamics on open track  Part 5: Requirements and test procedures for aerodynamics in tunnels  Part 6: Cross wind effects on railway operation According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom. SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 5 1 Scope This European Standard applies to the aerodynamic loading caused by trains running in a tunnel. 2 Normative references The following referenced document is indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. EN 14067-1:2003, Railway applications — Aerodynamics — Part 1: Symbols and units 3 Terms, definitions, symbols and abbreviations For the purposes of this document, the terms, definitions, symbols and abbreviations given in

EN 14067-1:2003 and the following apply. NOTE Additional definitions, symbols and abbreviations are explained in the text. 3.1 tunnel closed structure enveloping track(s) with a length of more than 20 m 4 Methodologies for quantifying the pressure changes in order to meet the medical health criterion 4.1 General The relevant pressure changes caused by trains running in a tunnel may be measured at full-scale, estimated from approximating equations (see Annex A), predicted using validated numerical methods or measured using moving model tests. The determination of the pressure variations in order to meet the medical safety pressure limits may be undertaken in the same way. Full-scale test data may be the basis for train and tunnel acceptance and homologation. Each single train/tunnel combination is described by a train-tunnel-pressure signature. 4.2 Train-tunnel-pressure signature 4.2.1 General The static pressure in the tunnel as shown in Figure 1 develops as follows when a train enters the tunnel:  there is a sharp first increase in pressure ∆pN caused by the entry of the nose of the train into the tunnel;  there is a second increase in pressure ∆pfr due to friction effects caused by the entry of the main part of the train into the tunnel;  there is then a drop in pressure ∆pT caused by the entry of the tail of the train in the tunnel;  there is a sharp drop in pressure ∆pHP caused by the passing of the train head at the measurement position in the tunnel. SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 6 Real measurements of pressure may differ from the idealised signature shown in Figure 1, for instance if the train cross sectional area varies along the train. In such a case special consideration shall be given to determining the individual ∆p values. All ∆p values are to be considered as absolute values.

Figure 1 — Train-tunnel-pressure signature at a fixed position in a tunnel (detail) The following methods are suitable for characterising the aerodynamic quality of a train in a tunnel. The train-tunnel-pressure signature can be derived from calculations or measurements at a fixed position in a tunnel, i.e. the four pressure changes ∆pN, ∆pfr, ∆pT and ∆pHP at a given point in the tunnel (see 4.2.2). 4.2.2 Full scale measurement of ∆∆∆∆pN, ∆∆∆∆pfr, ∆∆∆∆pT and ∆∆∆∆pHP at a fixed location in the tunnel The tunnel should have constant cross section, no airshafts and no residual pressures waves. Ideally there should be no initial air flow in the tunnel. However, if there is, its influence on the measurements should be checked. Pressures are measured using transducers in the tunnel. These should be calibrated prior to use over the expected pressure range, typically ± 4 kPa. The measurement error should be less than 1 %. The speed of the train shall be known within an accuracy of 1 % and should be constant during the entry into the tunnel within 1 %. Data should be sampled at a rate of at least 5 vtr/LN Hz, with anti-aliasing filters with a cut-off frequency of one quarter of the sampling rate. In order to obtain precise values of ∆pN, ∆pfr, ∆pT and ∆pHP for a fully developed wave pattern, it is necessary to ensure the following conditions when the train speed vtr and the length of the train Ltr are given:  the distance xp between the entrance portal and the measuring position is 1trtrpxvccLx∆+−= (1) where the additional distance ∆x1 ensures a good temporal separation of the individual pressure variations and ideally should be about 100 m. The measuring system should be installed at xp to avoid wave damping effects;  the minimum tunnel length is SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 7 1trtrpmintu,2LvcLxL∆++= if ∆pHP is not needed (2) 1trpmintu,12LvcxL∆++= if ∆pHP is needed (3) where the additional length ∆L1 ensures a good temporal separation of the individual pressure variations and ideally should be about 150 m. 4.2.3 Full scale measurements of ∆∆∆∆pN,o, ∆∆∆∆pfr,o and ∆∆∆∆pT,o on the exterior of the train If it is not possible to carry out measurements at fixed locations in a tunnel, ∆pN, ∆ptr and ∆pT can be approximated by measurements of ∆pN,o, ∆pfr,o and ∆pT,o on the exterior of the train. If needed, ∆pHP can be derived either from predictive formulae or assumed to be equal to ∆pN,o. The tunnel shall have constant cross section, no airshafts and no residual pressures waves. Ideally there should be no initial air flow in the tunnel. However, if there is, its influence on the measurements should be checked. Pressures are measured using transducers on the exterior of the train. These should be calibrated prior to use over the expected pressure range, typically ± 4 kPa. The measurement error should be less than 1 %. The speed of the train shall be known within an accuracy of 1 % and should be constant during the entry into the tunnel within 1 %. Data should be sampled at a rate of at least 5 vtr/LN Hz, with anti-aliasing filters with a cut-off frequency of one quarter of the sampling rate.

Figure 2 — Train-tunnel-pressure signature at an exterior position just behind the nose of the train To get the whole friction pressure rise ∆pfr it is necessary to measure the pressures on the outside of the train just behind the nose at a position where the full cross section is reached. The minimum tunnel length Ltu,min is SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 8 2trtrtrtrmintu,2LvcvcvcLL∆+−+= (4) where the additional length ∆L2 ensures a good temporal separation of the individual pressure variations and ideally should be about 200 m. As the tunnel length reduces the amplitude of the first reflection of the head wave ∆pN,o by friction, the tunnel should not be much longer than Ltu,min. 4.2.4 Predictive formulae for ∆∆∆∆pN, ∆∆∆∆pfr, ∆∆∆∆pT and ∆∆∆∆pHP Estimates for ∆pN, ∆pfr, ∆pT and ∆pHP can be made using the equations given in Annex A, A.2 and A.3. For tunnels with varying cross section the smallest cross section shall be considered. 4.2.5 Assessment of ∆∆∆∆pN, ∆∆∆∆pfr, ∆∆∆∆pT and ∆∆∆∆pHP by numerical simulation Calculations can be done with validated numerical methods. Tunnel length and measurement position shall be derived from Equations (1), (2) and (3). 4.2.6 Reduced scale measurement of ∆∆∆∆pN, ∆∆∆∆pfr, ∆∆∆∆pT and ∆∆∆∆pHP at a fixed location in the tunnel Models of the test train should be constructed which accurately represent the train head and tail, and have a good representation of the bogies, intercar gaps and train exterior surface features (e.g. roughness, shape). The test models shall be at scale 1/25 or larger for the test train to ensure that Reynolds number effects are minimised. It is essential that the full-scale train Mach number is respected. With scaled tunnel and train models, the pressure waves in the tunnel will reproduce those at full-scale, except that the time base will be decreased by model scale. For instance, in a 1/25 scale test, all the pressure waves will occur on a time base 25 times faster than at full-scale. In most cases it is not practicable to use models which represent the full scale train length. A train model consisting of the leading and end cars, with two intermediate coaches is a minimum for this purpose. The frictional part of the pressure signature for these reduced length models reproduces the full pressure rise, as long as the full scale length is accounted for by extrapolation. The use of shorter train models will produce conservative values for ∆pT and ∆pHP. The tunnel model shall be rigid and very well sealed onto the test rig bed to ensure that no reduction of pressure wave amplitude occurs. The minimum tunnel length and measurement position shall respect the dimensions given in 4.2.2 scaled by the model scale. Pressures are measured using transducers in the tunnel. These should be calibrated prior to use over the expected pressure range, typically ± 4 kPa. The measurement error should be less than 1 %. The speed of the train shall be known within an accuracy of 1 % and should be constant during the entry into the tunnel within 1 %. Data should be sampled at a rate of at least 5 vtr/LN,model Hz, with anti-aliasing filters with a cut-off frequency of one quarter of the sampling rate. 4.3 Maximum pressure changes The maximum pressure change (peak-to-peak) ∆pmax under worst case conditions (e.g. critical tunnel length, critical crossing or parallel running, critical location) are given by the following equations. At a fixed location in a tunnel for a 2 train situation: HPTfrNmax2222ppppp∆+∆+∆+∆=∆ (5) SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 9 (crossing or parallel running)

At a fixed location in a tunnel for a 1 train situation: HPTfrNmaxppppp∆+∆+∆+∆=∆ (6) Onboard a train in a 2 train crossing situation: altHPTfrNmax222pppppp∆+∆+∆+∆+∆=∆ (7) Onboard a train in a 1 train situation:

altTfrNmaxppppp∆+∆+∆+∆=∆ (8) where hgp∆=∆0altρ (9) is the natural pressure variation due to the difference in altitude where ρ0 = 1,225 kg/m³

∆h is the difference between maximum and minimum altitudes in the tunnel. The maximum pressure variations are useful information for comparison with TSI and national pressure limits and for load estimates. SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 10 5 Pressure loading on unsealed crossing trains When the head of a train passes another train a pressure drop occurs, which travels with the relative speed of the trains (see Figure 3). A pressure increase happens when the tail passes. The gradient of these pressure changes may be much steeper than the gradients of the train induced pressure waves. Due to this steepness these pressure changes may lead to the loading of unsealed vehicles.

Key 1 external pressure at the front 2 external pressure in the middle 3 external pressure at the rear Figure 3 — External pressure drop due to the head passage of a crossing train When the head of the opposing train passes the front of the unsealed vehicle the internal pressure starts to decrease too. As the information about the pressure drop travels with the speed of sound inside the vehicle, the internal pressure is nearly independent of the location inside the vehicle (see Figure 4).

Key 1 internal pressure at the front 2 internal pressure in the middle 3 internal pressure at the rear Figure 4 — Internal pressure evolution inside an unsealed vehicle due to the head passage of a crossing train SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 11 Figure 5 shows the differences between internal and external pressure at locations at the front, in the middle and at the rear of an unsealed vehicle during the head passage of a crossing train. At the front, both external and internal pressure drops start at the same time. Due to the steeper gradient of the external pressure drop the pressure difference effects a load from the inside to the outside which may be important for doors opening to the outside. In the middle of the unsealed vehicle, the drop of the internal pressure starts earlier than the external pressure drop which has a steeper gradient. This firstly leads to a pressure difference directed from the outside to the inside which then changes its direction. At the rear end of the unsealed vehicle the drop of the internal pressure starts earlier than the external pressure drop. The resulting pressure difference effects a load from the outside to the inside which may be important for vehicles covered with canvas, e.g. swap bodies.

Key 1 pressure difference at the front 2 pressure difference in the middle 3 pressure difference at the rear Figure 5 — Pressure differences on an unsealed vehicle due to the head passage of a crossing train The time the nose of the crossing train takes to travel along a vehicle is tr,2tr,1vehvvLt+=∆ (10) where Lveh

is the length of the vehicle. This means in the case of a moving vehicle that the time for the nose passing becomes shorter. The resulting mechanical forces may be higher, because of lateral accelerations, three-dimensional and inertial effects, as shown in Figure 6. SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 12
Key Fmax
maximum measured force on the door ∆pd,max

maximum difference between internal and external pressure NOTE Each point represents a different passing train speed vtr,2. Figure 6 — Typical measured maximum forces on a freight wagon door during the head passage of a crossing train 6 Pressure loading on sealed trains in tunnels 6.1 General The pressure variations caused by traffic in tunnels shall be considered in the construction of sealed trains. Both the single train case and the train crossing situation shall be considered. The train has to withstand all the loads occurring during its life cycle. The differences between external and internal pressures lead to the loading of car bodies, windows, gangway bellows, doors etc. Depending on the degree of sealing of the vehicle, the pressure variations outside the train cause pressure variations inside the train. If the train is perfectly sealed (pi = 0), the differential pressure is equal to the external pressure. If the train is completely unsealed (pi = pe), the differential pressure is equal

to 0. For partially sealed trains, the differential pressure may be higher than the external pressure (see

Figure 7). This effect shall be taken into account. SIST EN 14067-5:2007+A1:2010
EN 14067-5:2006+A1:2010 (E) 13

Key 1 single train transit 2 critical crossing with two trains pe external pressure pi internal pressure pd pressure difference between external and internal pressure Figure 7 — Pressure difference on a well sealed train in two successive tunnels The information given in Clause 6 is one approach which may be used to deal with the pressure loading. 6.2 Single train case 6.2.1 General The usual operational situation is the single train case, even when the tunnel has two tracks. The loads due to the pressure variations in this case generally lead to the fatigue endurance design case. The pressure on the outside of the train surface depends on the train speed, train and tunnel cross section and position along the train etc. Measurements and/or calculations of the pressure differences for the single train case should be carried out for all situations expected during operation. All significant positive and negative pressure loads required for the stress calculation should be collected. Different operating speeds should be considered since the load spectra induced by single train events may differ as shown in Figure 8. The maximum external pressure variation also depends on the tunnel length (see Figure 9). The critical tunnel length Ltu,crit which leads to the largest negative pressure in the single train situation is approximately +≈trtrtrcrittu,14vcvcLL (11) SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 14

Figure 8 — External pressure histories at different speeds in two successive tunnels

Figure 9 — Influence of tunnel length on maximum external pressure variation 6.2.2 Number of single train tunnel transits The total number of single train passages during the train’s lifetime can be approximated as StrdpySnTnN××= (12) where Ttr is the duration of life of the train in years; ndpy is the number of operating days per year; nS is the number of single train tunnel transits per day. SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 15 6.3 Two train case 6.3.1 General The two train case can be crossing trains, successive trains and parallel trains. Current operational experience shows that successive and parallel trains are rarer cases than crossing trains and yield lower pressure loadings on the trains and therefore are covered by the crossing case. The train crossing situation in tunnels usually occurs less often than the single train tunnel transit. In the majority of cases the pressure amplitudes are higher compared to the single train situation. The pressure amplitudes are strongly dependent on the relative entry time of the trains in the tunnel. Figure 10 shows the maximum absolute values of pressure differences as a function of the relative entry time of two identical trains running with the same speed. The situation when the opposing train has left the tunnel before the second train enters may also lead to higher pressure peaks than the single train case.

Key p

absolute values of pressure difference ∆t1,2 relative entry time of train 1 and train 2, in s 1 opposing train has left the tunnel before train 1 enters the tunnel (virtual crossing) 2 both trains are inside the tunnel 3 opposing train enters the tunnel after train 1 has left the tunnel (single train case) 4 p – p0 < 0 5 p – p0 > 0 Figure 10 — Influence of the relative entry time ∆∆∆∆t1,2 on maximum absolute values of pressure differences for a particular situation

SIST EN 14067-5:2007+A1:2010

EN 14067-5:2006+A1:2010 (E) 16 For each tunnel‚ numerical simulations (or measurements) with different relative entry times ∆te should be carried out considering the following time interval: trtrtuetrtrtuvLLtvLLn+<∆<+−; n < 3 (depending on the pressure wave damping of the tunnel) (13) with suitable time steps sufficient to capture the peaks: ∆t ≤ Ltu/(5c). The critical tunnel length Ltu,crit which leads to the maximum negative pressure peak in the two train crossing situation may be obtained semi-empirically and is approximately +≈tr,2tr,2tr,1tr,1crittu,2vLvLcL (14) If operational information required for precise calculation is not available in sufficient detail or an approximation is required, the missing information may be replaced by:  the combination of train speed, train length, tunnel length and tunnel cross section which leads to the highest pressure amplitude;  a

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