# ETCS braking curves

The speedometer of the driver's cab display (DMI) around 190 while braking is in progress m before the end of the travel permit ( End of Movement Authority , EOA)

The calculation and monitoring of braking curves is an essential part of the European train control system European Train Control System ( ETCS ).

The main task of ETCS is to ensure that a train does not exceed the permitted speed and that it can be brought to a stop in front of a possible danger point at any time . For this purpose, the current speed is compared at any time with the permissible speed calculated for the current position, which is determined using braking curves. The monitoring takes place with a family of braking curves.

The braking curve calculation is based on a mathematical model of the braking system (braking model), which describes the kinematic behavior of a train in the event of service or rapid braking and which meets the operational requirements. The essential basis for this are the speed-dependent instantaneous decelerations stored on the vehicle, which can either be determined from the braking power (expressed in braking hundredths ) or through tests. Furthermore, the calculation on the ETCS vehicle computer (EVC) u. a. Train data, route data (e.g. gradient and adhesion conditions ) as well as safety goals specified by the railway infrastructure company . Using data from the ETCS driving permit and odometry , the distance to an operationally significant point (e.g. braking target point) can be determined and train- and situation-specific braking curves can be calculated.

The ETCS braking curve calculation is mainly described in Chapter 3 of the ETCS system requirements specification (subset 026).

## Braking curves

Braking curves of different trains (example without ETCS)

When braking curves all curves are called, which are of a train for monitoring the movement profile available. They simulate the speed curve over the route. Here to stopping distances as well as deceleration distances are calculated (for speed reductions) (for braking to a stop).

For guidance and monitoring, ETCS uses a set of braking curves and a point:

• The emergency braking flow curve ( Emergency Brake Deceleration Curve , EBD) is defined by a rapid braking with a guaranteed, safe deceleration (AEB) to the Supervised Location (SVL). The EBD describes the speed curve of the train according to the developed braking force. The safe deceleration includes all safety margins and takes into account the longitudinal slope of the route. The safety margins, which are also summarized under the term braking distance safety, serve to compensate for fluctuations in braking force, mass and (in particular) the coefficient of adhesion from the nominal values. Rapid braking can lead to increased wear and tear on the braking system and reduced comfort for travelers.
• The emergency braking input curve ( Emergency Brake intervention Curve , EBI) corresponds to the EBD with an additional upstream brake assembly time (TEB). If the EBI is exceeded, rapid braking is initiated and the braking force is built up. To do this, the main air line , if present, is vented. After the braking force has built up, the EBD follows.
• The optional service brake flow curve ( Service Brake Deceleration Curve , SBD) is a full braking defined (with delay ASB). Since unsafe brakes may also be taken into account in its calculation, it can have a greater delay than the EBD.
• The optional service brake input curve ( Service Brake intervention Curve , SBI) corresponding to the SBD in consideration of the brake assembly time. A distinction is made between two variants: The SBI1 is derived from the SBD, the SBI2 from the EBD. Insofar as the route and vehicle permit the use of the SBI, it serves to avoid rapid braking and at the stop in front of the regular stopping area.
• The warning curve ( Warning Curve , W) is the braking curve, beyond which the driver is warned audibly. It serves as the final piece of information for the driver that an intervention by the system is imminent.
• The target curve ( Permitted Speed , P) describes the target speed without braking development time. In the active target speed monitoring it is the minimum of the maximum permissible vehicle and route speed and is displayed to the driver as the permissible speed. If possible, it should not be exceeded by the driver.
• The information ( indication curve , I) describes the curve at which the driver should switch off the tractive effort and initiate braking in order to follow the permitted speed curve. The curve is only available in target speed monitoring .
• The indication point (IP) informs the driver of an approach to the location to initiate braking. The function corresponds to the indicator light G of the line control .

The use of the two service brake curves (SBI / SBD) is permitted as standard according to the ETCS specification, but can be suppressed by the infrastructure operator using a national value (Q_NVSBTSMPERM). If they are not used, the W, P and I curves shift towards the EBI curve, combined with an increase in capacity.Are the SBI curves active, the more restrictive of the two is as intervention function ( First Line of intervention , floi), respectively. If the SBI curves are suppressed, the EBI acts as a FLOI. The warning and target curves are in front of the FLOI at fixed time intervals.

Optional one can Guidance Curve (GUI) (partly to German guide curve ) are defined, with the great and not wear realizable braking delays are to be avoided to meet the target curve. The GUI enables the driver to brake comfortably, with low wear and tear, and in an energy-saving manner. For example, it is possible to define braking delays that can be implemented purely electrically and thus wear-free. It is comparable to the LZB target curve used in Germany . Their use must be explicitly permitted by the route ( RBC ). In this way, the infrastructure operator can avoid possible negative capacity effects of the GUI. The corresponding national value ( Q_NVGUIPERM ) is set to "No" by default. If the guidance curve is activated, the driver is shown the minimum of the permitted speed and the speed of the guidance curve . The calculation of the GUI is based on the normal service brake, which is relatively freely definable by the vehicle operator . Longitudinal slopes are also taken into account when calculating the GUI.

Depending on their function, ETCS braking curves can be divided into sequence curves (P, GUI, SBD, EBD), intervention curves (SBI, EBI) and information curves (I, W).

### ATO

In the case of automated driving (ATO), the achievable driving curve is close to the emergency braking curve; all other service braking curves are dispensed with. The ATO requirements specification available as a draft provides that the ATO on- board unit avoids braking interventions by ETCS using Supervised Speed ​​Envelope Management (SSEM). These should not be exceeded in the case of target speed or release speed monitoring . When monitoring the target speed , only compliance with the emergency brake application curve (EBI) is decisive; the warning tones when the target curve (P) and the warning curve (W) are exceeded are suppressed.

### Influencing factors

The following data provided by the route are included in the braking curve calculation: speed restrictions, longitudinal inclines, braking prohibition zones, currentless sections, areas with reduced adhesion, speed and distance specifications and national values .

The longitudinal slope is included in the calculation of the EBD, SBD and GUI. It is modeled as a deceleration value ( A_gradient ), with gradients with an additional deceleration of less than 0.01 m / s² per per mille, whereas downhill gradients reduce the braking deceleration by less than 0.01 m / s² per per mille. The larger the rotating masses of the train, the smaller the influence on the deceleration.

## Representation in the driver's cab display (DMI)

Speedometer disc in the driver's cab display in the ceiling speed monitoring

In the driver's cab display (Driver Machine Interface, DMI), the driver is shown the permitted speed at all times.

If there is no need to change to a lower speed, the vehicle is in Ceiling Speed ​​Monitoring (CSM). ETCS only monitors compliance with the permitted speed; target braking is not required. If target braking to a lower speed or to a stop is necessary, Target Speed ​​Monitoring (TSM) becomes active. The driver is made acoustically and visually aware of the necessary upcoming braking. The speedometer needle turns yellow, a vertical bar shows the distance to the target point, a yellow segment of a circle on the speedometer disc shows the distance between the permitted speed according to the indication curve and the target speed.

ETCS can manage several braking target points. Only the most relevant target point (“Most Relevant Displayed Target”, MRDT) is shown to the driver.

## National values

Eleven national values , which are specified by the infrastructure operator, affect the braking curve calculation and thus lead to different ETCS braking curves from country to country with otherwise the same boundary conditions.

While different and not publicly accessible methods have so far been used to determine safe braking deceleration from country to country, these should be determined uniformly for ETCS. In an expert group of the International Union of Railways (UIC), corresponding, standardizing approaches were developed. When defining the individual parameters used, there is still room for interpretation, which is interpreted differently by different experts.

## Brake models

ETCS models the rapid or full braking application curve in two stages:

• The brake build-up time , known as the equivalent brake development time , begins with the triggering of an emergency or full brake application. In this phase the braking effect is zero. It ends at the moment when 95 percent of the maximum braking force has been built up. (The time for switching off the tractive effort is not taken into account . This occurs before braking is initiated.)
• The subsequent braking time is based on the maximum braking force built up. It is modeled as a step function of the braking deceleration as a function of the speed.

To simplify matters, the ETCS brake model assumes a phase without and a further phase with fully built-up braking force, while the actual build-up of the braking force takes place continuously.

In order to calculate braking curves, ETCS needs knowledge of the nominal braking capacity of a train, which today is mainly described with braking percentages . The determination of ETCS braking curves is described in UIC leaflet 544-1. It can be based on the UIC brake model (brake hundredths) or from tests. In ETCS, these approaches are referred to as the conversion model or gamma model . Both methods are described in the leaflet.

To ensure sufficient safety, the route transmits correction factors to the train as well as the release of optional functions of the braking curve calculation. A distinction is made between correction factors of the vehicle and those of the infrastructure. While the correction factors of the vehicle are defined by the railway company and are responsible for those of the infrastructure, those of the infrastructure are determined by the railway infrastructure company and are responsible and transmitted from the infrastructure to the vehicle.

The corresponding safety margins can either be specified globally by the infrastructure company or defined for each train using two correction factors.

### Conversion model

With the conversion model developed by UIC (also UIC General Brake Model for ERTMS / ETCS ), braking percentages can be converted into the braking delays and braking build-up times required by ETCS. It is also referred to as the lambda model , based on the symbol lambda , which stands for brake hundredths .

The path is calculated that is required to reduce the speed from the initial braking speed to the target speed on a dry track on the level. Hidden safety margins are not included, nor are possible failures of parts of the braking system. In addition to the braking percentage, the type of train ( passenger or freight train ), the train length and the braking position (G or P) are included.

The model has been tested and can be used for a maximum of 900 m long passenger trains and a maximum of 1500 m long freight trains. It applies to speeds of up to 220 km / h, longitudinal inclines of up to ± 8 percent and 30 to 250 braking hundredths.

The stopping and decelerating values ​​supplied by the model correspond to the mean values ​​measured in tests. The instantaneous delays provided by the model do not necessarily reflect the actual physical characteristics of the trains or individual vehicles. It is therefore a theoretical variable which, together with the predefined brake development time, ensures reliable calculation of stopping distances.

The statistical spread of the actually realized braking distances is countered with correction factors which are transmitted as national values. They are based on a risk analysis and the security goal of the respective system.

### Gamma model

With the gamma model, the braking capacity is defined directly via braking delays and braking build-up times. The conversion from brake hundredths, as in the conversion model , is not necessary. In French, gamma stands for delay .

The safe braking deceleration A_brake_safe is calculated in the gamma model from the nominal rapid braking deceleration A_brake_emerency , multiplied by the correction factors for dry rails and that for wet rails. The braking performance is determined on the basis of UIC Leaflet 544-1 in driving tests from various initial braking speeds and under various conditions. These include u. a. dry rail and friction elements, as straight and level a route as possible and defined load conditions. The vehicle manufacturer is responsible for calculating these safety factors.

Up to seven delay levels can be defined.

#### Correction factors

##### For dry rails

The correction factor Kdry_rst ensures that the vehicle safely achieves the specified, guaranteed braking deceleration on a dry track. The factor describes possible vehicle-related deviations from the deceleration of the train under normal conditions (dry rails). It depends on the speed, the characteristics of the braking system and the level of confidence required by the route (M_NVEBCL). It should be determined for all speed levels and confidence levels (EBCL). The factor can be differentiated according to speeds and the level of confidence dictated by the route. means that no deviations from the nominal conditions are to be expected. ${\ displaystyle Kdry \ _rst = 1}$

There is no standardized procedure for the Kdry_rst calculation. In principle, vehicle manufacturers have a free choice for determining the parameter, as long as the values ​​can be determined for different confidence levels. One possible approach was suggested by the UIC working group B126.15, and based on this, the European Railway Agency developed a case study based on the Monte Carlo simulation.

As a rule, the Monte Carlo method is therefore used as a general numerical method for describing the failure behavior of technical systems. For this purpose, various factors that have an influence on the performance of the entire brake system are modeled and underpinned with occurrence probabilities and statistical distributions . In addition to the individual components, the architecture of the braking system must also be modeled. As part of the Monte Carlo simulation, many ( ) different states of the brake system to be examined are simulated and the resulting deviations from the nominal braking capacity are examined. From the resulting statistical distributions, the correction factors Kdry_rst are determined for different confidence levels in such a way that the probability of a correction factor is greater than or equal to Kdry_rst and the required confidence level (EBCL). ${\ displaystyle 10 ^ {10}}$

country EBCL value
Germany 3 ( Level 1 LS )
7 ( Level 2 ) (99.99999%)
Finland 8 (99.999999%)
Luxembourg 9 (99.9999999%)
New South Wales 9 (99.9999999%)
Netherlands (full supervision in the conventional network) 9 (99.9999999%)
Netherlands 4 (99.99%)
Norway 8 (99.999999%)
Switzerland
Level 1
Level 2 (Baseline 3)

1 (90%)
5 (99.999%)
Czech Republic not yet defined

The emergency brake confidence level ( EBCL ) to be complied with specified by the route describes the permissible probability that the danger point will be exceeded. The parameter M_NVEBCL is defined on the infrastructure side and transferred from the route to the vehicle. It describes the probability with which a vehicle will achieve the safe braking deceleration on dry rails. The number of wagons / units of the train, the control of the brakes (bogie or wagon selective), the probability of a failure of the traction cut-off or the quality of the brake linings (probability of batch errors that lead to a reduced coefficient of friction ) can influence the value . . The standard value according to the ETCS specification is 9 (99.9999999%).

Typical Kdry_rst values ​​for traction vehicles in the Netherlands are between 0.70 (worst case for EBCL 8) and 0.88 (best case for EBCL 4). For the 423 series , provisional values ​​of 0.694 (for EBCL 7) and 0.89 (for EBCL 3) are given.

In the case of multiple traction, some vehicle operators differentiate between Kdry_rst values ​​according to train length. Longer trains tend to achieve higher Kdry_rst values, since the probability that several critical components fail at the same time is much lower than the already low probability of a single failure.

The ETCS specification does not make any statements about the accuracy of Kdry_rst values. While individual ETCS suppliers round Kdry_rst values ​​down to a full 0.05, others can map the values ​​to an accuracy of 0.001.

Brake systems of (new) rail vehicles can be specifically optimized for particularly high Kdry_rst values.

##### For wet rails

The correction factor Kwet_rst describes the safety factor for wet rails, which in practice is less than one and is determined from braking tests for anti-skid protection . It describes how the braking deceleration is reduced under poor adhesion conditions .

The loss of braking force due to the influence of moisture on the coefficient of friction is determined by bench tests. These are carried out in accordance with the EN 15595 standard.

The larger the value of M_NVADAH , the shorter the braking distance.

In Germany, the value M_NVAVADH is set to 1, which means that the safe rapid braking deceleration for dry and wet rails is identical. Separate provisions apply to train travel in areas with reduced static friction. Among other things, train drivers must adapt their speed and driving style to the rail conditions and report areas with reduced static friction to the dispatcher.

## history

### Early ETCS braking curves

In 1994 the European Rail Research Institute presented a proposal for the uniform brake evaluation of high-speed trains by means of braking decelerations (instead of braking percentages and braked weight). This laid the foundations for the later gamma model.

Version 3.01 of the ETCS specification presented in 1996 provided for a braking curve model that consisted of seven curves: an Emergency Brake Intervention curve , a Service Brake Intervention curve , a Warning curve , a Permitted curve , a Traction Cut-off curve , a Predicted curve and a movement authority request curve . While the function of the first four corresponds to its current function, the predicted curve should calculate the speed and position of the train "in the near future" using the driver's control in order to request the driver to brake or to support him. Upon reaching the movement authority request curve , the train should request a new movement authority . The consideration of longitudinal inclinations and release speeds were also already included in the ETCS specification. When the traction cut-off curve is reached, the traction should be switched off by ETCS.

Several special braking curves were programmed on the Swiss ETCS Level 2 pilot route Zofingen – Sempach , which was equipped according to preliminary specifications from 1998 and put into operation in April 2002.

For the radio train control (FZB) initially planned on the high-speed route Cologne – Rhine / Main , the Institute for Rail Vehicles and Mechanical Railway Systems at the University of Hanover (ISB) and the Department for Brake Operation, Regulations, Brake Force Generation (BT 21) of the Research and Technology Center of Deutsche Bahn (DB) designed new braking curves in Minden at the end of the 1990s.

In contrast to the braking curves used up to then for the line control (LZB), the braking decelerations should no longer be assumed to be constant over the entire braking distance. Longitudinal inclinations should be better taken into account, braking with less wear and more feedback should be enabled and an unnecessarily large gap between the setpoint and monitoring speed should be avoided. The new braking curves were modeled as a speed-dependent function of the instantaneous deceleration, with which different deceleration values ​​could be specified for different speed ranges. Furthermore, the gradient of the route was realistically taken into account, so that uphill sections shortened the braking distance. Based on this, a set of six braking curves was formed for FZB operation:

• The emergency brake input curve ( emergency brake intervention curve , EBIC ) should trigger a forced rapid deceleration. It should be formed from the rapid braking capacity of the train, taking into account the required braking distance safety and taking into account the braking force development phase. It was the only one of the intended braking curves that was considered to be safety-relevant, since its foot point ends at the supervised location (SL) at the end of the slip path . In contrast, all other braking curves should have their base point at the end of the driving permit ( End of Authority , EOA).
• The full brake application curve ( [full] service brake intervention curve , SBIC ) should launch automatically on the brakes, if it has not already been initiated by the driver, thus preventing the initiation of the EBIC. In your calculation, the full braking deceleration should include the full braking development time. If a sufficient distance to the EBIC has not been achieved, the curve should be shifted accordingly to achieve this. The use of magnetic rail brakes should therefore be avoided for reasons of comfort and wear.
• The curve for tension shutdown ( traction cut-off curve , TCO ) should traction switch off in time to traction freedom in reaching the SBIC sure. For this purpose, the TCO should be derived from the SBIC, in that the necessary path for traction shutdown should be placed upstream of the SBIC for each point.
• The required braking curve ( permitted curve , PER ) should serve the normal course of the braking operation and the driver are displayed as a target speed. Previously announced braking should take place along this curve after the braking force has built up. Your calculation should be based on defined instantaneous delays.
• The warning curve ( warning curve , WRN ) should trigger a visual and audible prompt to initiate an emergency braking to prevent kick-off of the EBIC. It should be in a freely definable time lead to the target braking curve . There should be sufficient early warning time between WRN and SBIC in order to give the driver enough reaction time to initiate an emergency stop in front of the SBIC. If this had not been the case, the WRN and the PER coupled to it should be shifted accordingly.
• The advance notice curve ( pre-indication curve , PIC ) should serve as a visual and audible announcement for the upcoming braking. For this purpose, it should be derived from the PER with a time constant. The longitudinal slope should also be taken into account.

The braking curves were checked for practicality with the ICE V in spring 1998 . You have proven to be drivable for the driver. Among other things, different time intervals between the braking curves were tested, including a. a time difference of 8 s between PIC and PER was recommended. In order to compile the required vehicle-specific data, a corresponding new brake evaluation procedure was in work at DB at the end of the 1990s.

While the high-speed line Cologne – Rhine / Main was ultimately equipped with a further developed LZB ( LZB L72 CE-II ) due to foreseeable delays in the ETCS specification , the work for the braking curve model of the FZB ultimately formed a decisive basis for ETCS.

The further developed LZB braking curves were compared in 1997 with those of ETCS. The ETCS braking curves consistently did not exceed the LZB braking curves.

### Inadequate braking curves of the baseline 2

The braking curve calculation up to baseline 2 (including SRS 2.3.0 ) could not meet the railways' expectations regarding capacity and service braking processes, the corresponding braking curves were not considered to be practical. SRS 2.3.0 did not yet contain a guaranteed uniform braking curve calculation and contained some requirements that led to severe restrictions on the line performance compared to previous train control systems. The driver was given "too much comfort".

The definition of braking curves in Baseline 2 was considered to be insufficiently standardized across Europe at the end of the 2000s.

The insufficient consideration of braking curves in Baseline 2 left infrastructure and vehicle operators room for deviations. This led to a number of special solutions that differed from the TSI. For each individual route, the security margins of the respective infrastructure operator were stored on the vehicle device. It was not planned to transmit these values ​​via the air interface.

### Development of the baseline 3 braking curves

Due to the inadequacies of the baseline 2 braking curves, a working group (B126.5) was set up which was initially based at ERRI and later at UIC and worked closely with the ERTMS Users Group . Track and simulator tests were carried out to optimize the braking curves. In autumn 2005 the optimized braking curves on the ETCS pilot route of the ÖBB, between Parndorf and Zurndorf, were driven with a passenger and a freight train. The train drivers were thus able to drive down to the set speed (Permitted Speed), unexpected emergency braking operations did not occur.

Work on the conversion model began around 2001. The mathematical model was first developed on the basis of theoretical principles and then calibrated and refined using the results of actual braking tests. This resulted in a fundamental revision of document 97E881, which was introduced into ERA's change control process .

At the end of 2006 there were still three open points regarding the new braking curve definition, for which simulator tests were to be carried out in autumn 2007. The result was a final specification of the ETCS braking curves. The "comfort" for the driver has been reduced to a minimum. With the safety-relevant braking curve (EBI / EBD) unchanged, the upstream non-safety-relevant curves were changed. Compared to the baseline 2 braking curves, the distance between the warning and intervention curve has been reduced to an operationally acceptable minimum. The original approach that after crossing the warning curve an intervention (FLOI) could have been prevented by initiating braking was rejected because of the large distance between the warning and intervention curve and the resulting reduced route performance. Instead, the driver is now only given the option of intensifying an already initiated braking by quickly increasing the braking force.

If, for example , a braking time of 132 s was planned for a passenger train with 210 braking hundredths in 6 per thousand gradient from 200 km / h to a stop (without SBI, 50 m slip distance) , this value could be reduced to 82 s according to SRS 2.2.2 .

2006 in addition to the up to now used braking curves (EBD, SBD, EBI, SBI, warning and target curve and Guidance Curve) still were curve for switching off the traction ( traction cut-off curve TCO) provided. The TCO should switch off the traction by ETCS when the warning curve is exceeded . This should also prevent the train from being forced to stop before the EOA in the event of a short or zero slip path (distance between EOA and SvL). In addition to the curves were beyond even a brake advance notice ( Pre indication ). This should inform the driver that he is approaching a route section in which braking is to be initiated in order to reach a destination. This involved switching from ceiling speed monitoring to target speed monitoring .

With Baseline 3 , the UIC's conversion model was introduced and the braking curve algorithm was revised in order to achieve greater route performance than with Baseline 2.

The contents of version 7A of document 97E881 were incorporated into the draft of the first Baseline 3 specification (SRS 3.0.0) published in December 2008.

### Further development

Representation of the pre-indication braking curve, which was omitted with SRS version 3.6.0 and which preceded the indication curve.

In simulations of the ETCS-L2 equipment of the LGV Sud-Est (Paris-Lyon), the pre-indication was reached very often, with correspondingly frequent information to the driver. In the uphill sections, the speed of the trains was well below the permissible speed. This led to a long time lag between pre-indication and indication, in which an updated travel permit was usually transmitted so that the train did not enter target speed monitoring. Other railways also reported unnecessary disruptions. With the transition from Baseline 3 MR1 ( SRS 3.4.0 ) to Baseline 3 Release 2 ( SRS 3.6.0 ), the pre-indication location has therefore been omitted. The approval of the Railway Interoperability & Safety Committee for SRS 3.5.0 was given under the condition that the pre-indication still contained in version 3.5.0 should be omitted.

In early 2020, the International Union of Railways published the standard IRS 50544-3. This defines the requirements for quick brake valves for trains that use the lambda brake model under ETCS. The brake development time of this brake model had previously been determined using the driver brake model D2 from Knorr-Bremse . The new standard document defines requirements and test procedures so that the ETCS braking distances are adhered to even when other brake valves are used.

### outlook

The UIC working group B126.15 is working on standardizing the safety margins for ETCS (status: 2006). To do this, u. a. a universally accepted security goal. Until then, safety margins must be mapped as national correction factors.

For the European Railway Agency, the further development of the ETCS braking curve model, through further optimization and weighing of operational and safety aspects, is a potential "game changer" for ETCS. Various suggestions for optimization are available. (Status: 2015)

The Swiss Federal Office of Transport sees a need for action with ETCS braking curves in order to achieve the capacity targets pursued with ETCS (status: 2019).

There is potential for improvement in the current ETCS specification ( baseline 3 M2 ) when braking down to speed bumps and when changing longitudinal inclines under the train.

It is also proposed that the current braking deceleration of trains already braking be taken into account when calculating the braking curve. This does not lead to a shortening of the braking distances, but increases the control latitude for the driver or ATO during the braking process.

In order to optimize the gamma model, sensitivity analyzes of traction and braking torques (loads, coefficients of friction) are proposed as well as improved assumptions for input parameters based on observations of traction during operation and the use of physical friction models to identify the dispersion of braking torques.

## Capacity effects

Compared to train control systems such as Eurosignum , which offer no braking curve monitoring, no monitoring of impermissible approaches against "stop" signals and no speed monitoring, ETCS also offers a safety advantage with its braking curve monitoring. In countries with variable distant signal distances, for example Austria, the flexible ETCS braking curves with their option to take into account the actual distance to the main signal offer a higher level of safety compared to conventional train control systems with rigid braking curves.

ETCS braking curves can be more restrictive (flatter) than braking curves of previous national train control systems, which have been optimized for the respective boundary conditions, and thus lead to longer headway times.

A comparison of the braking curves of LZB (for ICE 3), TVM (for TGV ) and ETCS (for TGV) in 2006 showed ETCS braking curves that were slightly flatter than those of the LZB and were comparable to those of the TVM. When ETCS was introduced in Luxembourg , ETCS braking curves proved to be consistently flatter than those of conventional control and safety technology. This led to the laying of additional infill balises.

In ETCS operation, the approach travel time begins at the indication point. The course of the braking curves is therefore dependent on the performance of the brakes installed in the vehicles. With decreasing performance, the braking curves become flatter and braking must take place earlier. This must be taken into account when planning time-dependent route elements, such as level crossings and traffic warning systems . With the introduction of ETCS in Germany, for example, the switch-on sections of signal-covered level crossings must be brought forward, based on the train with the longest expected braking distance, in order to ensure a timely extension of the travel permit (after the level crossing has been secured). This is the only way to ensure that the driver of a poorly braking train still has sufficient reaction time to stop the train without emergency braking if the level crossing is disturbed. In order to optimize the blocking times, direct control of the level crossing safety systems by ETCS is proposed, with rail contacts as a fall-back level.

In Switzerland, the introduction of ETCS led to flatter braking curves in order to be able to take decisions and risks previously borne by the driver with additional safety reserves. The capacitive improvements hoped for through ETCS Level 2 did not occur due to the continuous, SIL-4 -safe monitoring, due to the flatter braking curves. During the commissioning of an ETCS section at Giubiasco (Switzerland) at the end of May 2018, the speeds for freight trains had to be reduced in the area of ​​an ETCS entrance on a slope. This is due to larger safety margins. The Association of Swiss Locomotive Drivers and Candidates criticizes the fact that train headways with ETCS Level 2 are longer than optical external signals and that automated driving (ATO) and ETCS Level 3 are required to achieve shorter headway times.

For ETCS Level 1 Limited Supervision in Germany, the correction factors for the route were chosen so that PZB braking curves were simulated and the travel time and capacity of a route roughly correspond to those of the PZB.

ETCS entrances should be avoided in areas in which braking regularly occurs (e.g. nodes) in order to avoid forced braking due to different braking curves of the two train control systems involved. If the ETCS braking curve is flatter than that of the conventional train control system, an undesired braking curve jump can occur when entering the ETCS with a subsequent signal showing "Halt".

In front of points at which speeds have to be reduced, “traffic jams” can occur, i. H. longer headway times come. The length of the braking distance is derived in the area of ​​the speed threshold from the higher, original speed. However, in order to actually cover this braking distance, the train needs significantly more time due to the braking to the lower speed than if it had continued to travel at a constant (higher) speed. The greater the speed reduction, the greater the occupancy. To compensate for the effect, train sequence sections can be shortened.

When using the gamma model, optimizations in the braking system can lead to shorter headway times, for example through optimized control of the brake, with which the probability of failure of the brakes on a single wagon or bogie is reduced.

An investigation into the introduction of ETCS at the Stuttgart S-Bahn recommends for the ETCS equipment of the traction vehicles according to SRS 3.6.0 (thus without pre-indication braking curve), a gamma braking model and automated driving operation (ATO) in order to achieve the largest possible To achieve efficiency. Even with the conversion model, braking from 60 km / h must take place 14 s later than with conventional Ks signaling (start of the approach driving time 29 s instead of 43 s before the end of the driving permit). With the training and experience of train drivers and the use of ATO, the use of the brakes can be further delayed and performance can be further increased. Nonetheless, flat braking curves in the case of a signal showing "stop" at the end of the platform lead to the recommendation to place an additional block indicator at a short distance of up to 100 m after the " exit signal " . At the beginning of 2020, the potential of optimized ETCS braking curves for the minimum headway time on the main S-Bahn line was estimated at around ten seconds.

During an investigation into the introduction of ETCS on the main route Vienna , restrictive ETCS braking curves resulted in an increase in headway times compared to conventional control and safety technology.

The guidance curve reduces brake wear, but leads to longer travel times and reduced performance of the infrastructure.

Compared to the braking curves of the polyline control, a thesis presented in 2019 for ETCS Level 2 (with lambda braking model) generally sees somewhat flatter braking curves. ETCS braking curves are somewhat less restrictive in the upper speed range, whereas the ETCS target curve is flatter in the speed range below approx. 60 km / h. The constant deceleration assumed for LZB braking curves over the entire speed range is limited by the decreasing braking power at higher speeds. The place of the brake announcement takes place in ETCS Level 2 usually much later than with LZB.

In the digital node Stuttgart , however, due to optimization, steeper braking curves are expected compared to the LZB. To optimize the braking curve, the use of gamma models and the variation of the confidence level (EBCL) according to operating conditions is suggested.

By exhausting the possibilities when modeling braking curves (taking into account the respective safety requirements) of locomotives, economies of scale can occur without additional costs as the ETCS equipment progresses .

## literature

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