EN 14531-1:2015

SLOVENSKI STANDARD
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Railway applications - Methods for calculation of stopping and slowing distances and
immobilisation braking - Part 1: General algorithms utilizing mean value calculation for
train sets or single vehicles
Bahnanwendungen - Verfahren zur Berechnung der Anhalte- und
Verzögerungsbremswege und der Feststellbremsung - Teil 1: Grundlagen
Applications ferroviaires - Méthodes de calcul des distances d'arrêt, de ralentissement et
d'immobilisation - Partie 1: Algorithmes généraux utilisant des valeurs moyennes pour
des compositions de trains ou véhicules isolés
Ta slovenski standard je istoveten z: EN 14531-1:2015
ICS:
45.060.01 Železniška vozila na splošno Railway rolling stock in
general
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN 14531-1
EUROPEAN STANDARD
NORME EUROPÉENNE
December 2015
EUROPÄISCHE NORM
ICS 45.060.01 Supersedes EN 14531-1:2005
English Version
Railway applications - Methods for calculation of stopping
and slowing distances and immobilization braking - Part 1:
General algorithms utilizing mean value calculation for
train sets or single vehicles
Applications ferroviaires - Méthodes de calcul des Bahnanwendungen - Verfahren zur Berechnung der
distances d'arrêt, de ralentissement et Anhalte- und Verzögerungsbremswege und der
d'immobilisation - Partie 1 : Algorithmes généraux Feststellbremsung - Teil 1: Allgemeine Algorithmen für
utilisant le calcul par la valeur moyenne pour des Einzelfahrzeuge und Fahrzeugverbände unter
rames ou des véhicules isolés Berücksichtigung von Durchschnittswerten
This European Standard was approved by CEN on 27 June 2015.

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-CENELEC 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-CENELEC 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, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2015 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 14531-1:2015 E
worldwide for CEN national Members.

Contents Page
European foreword . 4
Introduction . 4
1 Scope . 6
2 Normative references . 6
3 Definitions, symbols and abbreviations . 6
3.1 Terms and definitions . 6
3.2 Symbols and indices . 8
4 Stopping and slowing distances calculation . 11
4.1 General . 11
4.2 Accuracy of input values . 11
4.3 General characteristics . 11
4.3.1 Train formation . 11
4.3.2 Characteristics of a train . 12
4.4 Brake equipment type characteristics . 14
4.4.1 General . 14
4.4.2 Tread braking . 15
4.4.3 Disc braking . 15
4.4.4 Forces of friction brake (tread brake) equipment . 16
4.4.5 Forces of friction brake (disc brake) equipment. 21
4.4.6 Mean dynamic coefficient of friction ( m ) tread and disc brakes . 25
m
4.4.7 Brake forces of other brake equipment types . 25
4.4.8 Time characteristics . 34
4.4.9 Blending concept . 37
4.4.10 Sharing, proportioning of the brake forces - achieved forces . 38
4.5 Initial and operating characteristics . 38
4.5.1 Gradient of the track . 38
4.5.2 Initial speed . 39
4.5.3 Coefficient of adhesion . 39
4.5.4 Level of the brake demand . 40
4.5.5 Quantity of each brake equipment type available . 40
4.5.6 Calculation in degraded conditions . 40
4.6 Total decelerating force at train level . 40
4.7 External forces . 41
4.7.1 Gradient . 41
4.7.2 Wind force on the train . 41
4.7.3 Train resistance . 41
4.8 Stopping and slowing distance calculation based on mean values . 42
4.8.1 General . 42
4.8.2 Mean braking force with respect to the distance . 42
4.8.3 Equivalent deceleration (a ) based on mean forces . 42
e
4.8.4 Mean decelerations supplied by each braking force ( a ) . 43
i
4.8.5 Equivalent free run distance (s ) . 43
4.8.6 Stopping and slowing distance on level track (s) . 44
4.8.7 Stopping and slowing distance on a gradient (s ) . 44
grad
4.8.8 Other specific formulae for the calculation of stopping distance . 45
4.9 Supplementary dynamic calculations . 45
4.9.1 General . 45
4.9.2 Mass to be braked (m ) . 46
B
4.9.3 Braking energy . 46
4.9.4 Maximum braking power of each brake equipment type . 48
4.9.5 Maximum specific power flux for each type of friction brake . 48
4.10 Specific expressions of braking performance . 49
4.10.1 General . 49
4.10.2 Braked weight percentage (λ) . 49
4.10.3 Braked weight . 49
4.10.4 Braking ratio . 49
4.10.5 Equivalent brake force . 49
5 Immobilization brake calculation . 49
5.1 General . 49
5.2 General characteristics . 49
5.3 Static coefficient of friction . 50
5.4 Train and operating characteristics . 50
5.5 Immobilization force provided by equipment type . 50
5.5.1 General . 50
5.5.2 Force of a screw hand brake (Tread brake) . 51
5.5.3 Force of a screw hand brake (Disc brake) . 51
5.5.4 Force of a tread brake unit . 51
5.5.5 Force of a disc brake unit arrangement . 52
5.5.6 Force of a permanent magnetic track brake . 52
5.6 Immobilization force for each axle. 53
5.7 Total immobilization force per train . 53
5.8 Immobilization safety factor . 54
5.9 Coefficient of adhesion required by each braked axle . 54
5.10 Maximum achievable gradient . 55
Annex A (informative) Workflow of stopping and slowing distance calculation method . 56
Annex B (informative) Workflow of immobilization calculations . 58
Annex C (informative) Brake equipment type example calculations . 59
Annex D (informative) Train stopping distance and immobilization brake calculation
example . 71
D.1 General . 71
D.2 Train stopping calculations . 72
D.3 Train stopping calculations on a gradient . 74
D.4 Train immobilization (parking) brake calculations . 74
Annex E (informative) Development of the formula for the mean brake force with respect to
the braking distance . 76
Annex F (informative) Slowing or stopping distance calculation using alternative method of
equivalent response time calculation as French Railway requirements in particular
for trains operating in 'G' position . 77
Annex ZA (informative) Relationship between this European Standard and the Essential
Requirements of EU Directive 2008/57/EC . 79
Bibliography . 82
European foreword
This document (EN 14531-1:2015) 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 June 2016, and conflicting national standards shall be
withdrawn at the latest by June 2016.
This document supersedes EN 14531-1:2005.
This document has been prepared under a mandate given to CEN 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 series of European standards EN 14531, Railway applications — Methods for calculation of stopping
and slowing distances and immobilization braking consists of:
— Part 1: General algorithms utilizing mean value calculation for train sets or single vehicles;
— Part 2: Step-by-step calculations for train sets or single vehicles.
The two parts are interrelated and should be considered together when conducting the step-by-step
calculation of stopping and slowing distances.
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.
According to the CEN/CENELEC Internal Regulations, the national standards organisations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
Introduction
This European Standard describes a common calculation method for railway applications. It describes
the general algorithms utilizing mean value calculation for use in the design and validation of brake
equipment and braking performance for all types of train sets and single vehicles. In addition the
algorithms provide a means of comparing the results of other braking performance calculation
methods.
EN 14531 was originally planned to have six parts covering the calculation methodology to be used
when conducting calculations relating to the braking performance of various types of railway vehicles
under the heading EN 14531, Railway applications – Methods for calculation of stopping, slowing
distances and immobilization braking. The six parts were as follows:
— Part 1: General algorithms
— Part 2: Application to single freight wagon
— Part 3: Application to mass transit (LRV's and D- and E- MU's)
— Part 4: Application to single passengers coach
— Part 5: Application to locomotive
— Part 6: Application to high speed trains
EN 14531-1 was originally published in 2005 followed by EN 14531-6 which was published in 2009.
Following the above it was decided that a common methodology could be used for Parts 2 to 5 and this
should be contained under a revised version of Part 1 with a title of Railway applications — Methods for
calculation of stopping and slowing distances and immobilisation braking — Part 1: General algorithms
utilizing mean value calculation for train sets or single vehicles while revising Part 6 to be Part 2 with the
title of Railway applications - Methods for calculation of stopping and slowing distances and
immobilization braking - Part 2: Step by step calculations for train sets or single vehicles.
EN 14531-1:2005 and EN 14531-6:2009 are referenced in the current technical specifications for
interoperability (TSIs) (Freight wagons and locomotive and passenger rolling stock (RST)). The tables
of the Annex ZA give the equivalence of the TSI referenced clauses of the original EN 14531 series to the
clauses of this issue of EN 14531-1 and EN 14531-2.
1 Scope
This European Standard describes general algorithms for the brake performance calculations to be used
for all types of train sets, units or single vehicles, including high speed, locomotive and passenger
coaches, conventional vehicles and wagons.
This European Standard does not specify the performance requirements. It enables the estimation
and/or comparison by calculation of the various aspects of the performance: stopping or slowing
distances, dissipated energy, power, force calculations and immobilization braking.
If it is required to validate, verify or assess braking performance it is recommended that a more detailed
calculation is performed in accordance with EN 14531-2, i.e. a step by step calculation.
This European Standard contains generic examples of the calculation of brake forces for individual
brake equipment types and calculation of stopping distance and immobilization braking relevant to a
train (see Annexes C and D).
2 Normative references
The following referenced documents, in whole or in part, are normatively referenced in this document
and are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
EN 14067-4, Railway applications - Aerodynamics - Part 4: Requirements and test procedures for
aerodynamics on open track
EN 14478, Railway applications - Braking - Generic vocabulary
EN 14531-2, Railway applications – Methods for calculation of stopping and slowing distances and
immobilisation braking – Part 2: Step by step calculations for trains or single vehicles
prEN 15328, Railway applications - Braking - Brake pads
EN 16452, Railway applications – Braking – Brake blocks
EN 15663, Railway applications - Definition of vehicle reference masses
3 Terms, definitions, symbols and indices
3.1 Terms and definitions
For the purpose of this document, the terms and definitions given in EN 14478 and EN 14531-2 and the
following apply.
3.1.1
static mass per axle
mass measured by weighing at the wheel-rail interface, or estimated from design evaluation, of each
axle in a stationary condition for each operating condition required
3.1.2
static mass of the train
summation of all the static mass values per entity
Note 1 to entry: E.g. per axle, for each operating condition.
3.1.3
equivalent rotating mass
linear conversion of the moment of inertia due to rotating parts coupled to the wheelsets during
braking into an equivalent additional static mass
Note 1 to entry: This includes brake discs, gear wheels etc.
3.1.4
brake equipment type
group of equipment that provide braking force
Note 1 to entry: When brake equipment is used on one part of the train under certain conditions and used on
another part of the same train under other conditions, two different brake equipment types shall be considered.
3.1.5
tread brake unit/disc brake unit
functional unit from which brake force is delivered, typically consisting of a brake cylinder, slack
adjuster portion and all associated component parts
Note 1 to entry: Sometimes referred to as tread/disc brake actuator.
3.1.6
isolated brake equipment
equipment not considered in the calculation due to assumed isolation
Note 1 to entry: E.g. brake equipment of a bogie.
3.1.7
active brake equipment
equipment considered to be operational in the calculation of a specific brake equipment type
3.1.8
mean value calculation
calculation method in which the values used for each active brake equipment type are a mean value
based on speed, force or distance as applicable for a particular speed range
3.1.9
decelerating force
force resulting from summation of all forces acting contrary to the direction of movement when
considering a train
Note 1 to entry: Each operational brake equipment type produces its own decelerating force which when added
to the additional external forces opposing motion results in the total decelerating force of the train.
Note 2 to entry: For the purpose of this standard a decelerating force is considered as a positive value, therefore
accelerating force is considered as a negative value.
3.1.10
braking force
force produced by the active brake equipment types to brake the train
Note 1 to entry: It does not include external forces which contribute to the overall decelerating force of the
vehicle or train.
3.1.11
external forces
forces typically including rolling resistance, gradient, head wind etc
3.1.12
entity
group or item considered in a calculation
Note 1 to entry: E.g. train, vehicle, bogie, axle, wheel.
3.2 Symbols and indices
For the purposes of this document, the general symbols given in Table 1 and indices given in Table 2
apply.
NOTE Specific symbols and indices are defined in the relevant clauses.
Table 1 — Symbols
Symbol Definition Unit
area
m
A
a deceleration
m / s
area of a friction surface swept by the friction elements
m
A
s
braked weight
T
B
m
wheel diameter
D
force N
F
braking force related to the rail
N
F
B
downhill force on the train N
F
g
standard acceleration of free fall = 9,80665 m/s (see: ISO 80000-3)
g m / s
n
gradient (rising gradient is positive; e.g. for a gradient of 5 ‰, i = 0,005) -
i
cylinder ratio -
i
c
rigging ratio -
i
rig
transmission ratio -
i
tra
inertia due to rotation of masses

J kg ⋅ m
m
mass kg
n
quantity -
power W
P
p pressure Pa
m
r radius
m
s distance
safety factor -
S
s
time
t
τ
coefficient of adhesion -
v speed
m / s
J
energy
W
energy per unit area J
W
S
m
braked weight percentage -
λ
m
coefficient of friction -
η
efficiency -
Table 2 — General indices
Indices Term
AMG attraction force for a magnetic track

ap application point
ax axle
a available
B braking force
BEC braking force for an eddy current brake
BED electro-dynamic braking force
BFR fluid retarder braking force
BMG braking force for a magnetic track brake
b block or pad
bog bogie
C cylinder
act unit/actuator
cha characteristic
Bd braking force demanded
disc disc
dyn dynamic
e equivalent
ent entity
ext external
fin final state
H hand brake
i brake equipment type
j range or step
im immobilization, parking, holding
ind independent of adhesion
nt internal
inst instantaneous
max maximum
min minimum
mot motor
MG magnetic track brake
n normal direction
R response
Ra train resistance to motion
req required
rig rigging
rot rotating
R1 return spring
R2 regulator
S spring
st static
T tangential direction
tot total
tra transmission
wind wind
0 initial state
1, 2, 3, 4 –- etc. intermediate state

4 Stopping and slowing distances calculation

4.1 General
The principle of the algorithm flow is presented in Annex A, Figure A.1.
In general the formulae contained in this clause are used in the first instance when considering constant
brake forces with respect to speed.
In the second instance the formulae may be used as a mean value calculation when considering a non
constant speed dependent brake force which is transformed to a mean brake force value. This mean
value of brake force is considered as a fully developed force without considering the response time and
results in the same braking distance as if calculated using the speed dependent brake force. See
Annex E.
The algorithms in this standard use mean values, however if it is necessary to use instantaneous values
and algorithms using finite time steps then EN 14531-2 shall be used.
4.2 Accuracy of input values
The accuracy of the calculation described here depends directly on the accuracy of the input data.
The accuracy of the input data values shall be relevant to the purpose of the calculation and shall be
traceable as to how these values were established e.g. engineer's estimation, test results,
manufacturer’s data etc. Supporting calculations or test reports (or extracts of these documents) should
be attached with the performance calculation where applicable.
Representative curves of the performance of a type of brake equipment e.g. electro dynamic brake, can
be determined by numerical or practical methods. The values can be given as a table.
4.3 General characteristics
4.3.1 Train formation
The brake system design parameters necessary to conduct the calculation shall be defined at the level of
an entity e.g. an axle, bogie or a vehicle.
Calculations shall be performed for each brake equipment type. In so doing, the brake force
contributions from each of the brake equipment types (e.g. disc brakes, tread brakes, electrodynamic
brakes) shall be taken into consideration. All of the various types of brake equipment applied to one
entity shall be identified and accounted for in the calculation.
The parameters which are typically used to define train formation include but are not limited to:
— quantity of motor axles;
— quantity of trailer axles;
— quantity of braked axles for each adhesion dependent brake equipment type;
— quantity of non-adhesion dependent brake equipment type.
NOTE 1 When there are several brake equipment types, it is preferable to identify each type (for example by
means of a number: type 1, type 2, etc.).
A train can consist of one or more units or vehicles. For the purpose of this document, no distinction is
made between unit and vehicle, therefore the term vehicle is used.
NOTE 2 'Unit' is used in the same sense as described in the technical specification for interoperability (TSI)
relating to the rolling stock sub-system – 'Locomotives and Passenger rolling stock' of the Trans-European
conventional rail system.
When the brake equipment types fitted to the train are used under different circumstances, e.g. load
level, speed range, brake demand etc. each condition or state of the brake shall be considered together
with the resultant effect on brake force.
4.3.2 Characteristics of a train
4.3.2.1 Train mass
EN 15663 shall be used to provide a common set of reference masses on which the assessment of loads
and performance evaluation can be based; it also describes how each is to be derived.
4.3.2.2 Static mass of the train, or axle ( m )
st
The static mass of the train and/or the static mass of the axle (as defined in 3.1) shall be used to
establish the brake force required or the adhesion requirements respectively, for each operating
condition required e.g. operational mass in working order, as defined in EN 15663.
When there are different 'static masses per axle values' e.g. due to different vehicle arrangements or
axle mounted equipment, the static mass shall be calculated for each axle.
It may be required to assess the effect of the position of a vehicle type in a train e.g. with respect to the
adhesion required.
4.3.2.3 Equivalent rotating mass ( m )
rot
The equivalent rotating mass shall be calculated using a theoretical approach or established as a result
of tests, using test conditions similar to the expected operating conditions.
The wheel size applicable to the rotating mass shall be identified. Any value of equivalent rotating mass,
identified by a % of static mass, is normally calculated using the assumed static mass of each vehicle
within the train.
When there are different 'rotating masses per axle' e.g. a mix of trailer and motor axles, the rotating
mass shall be calculated for each type.
It may be required to assess the effect of the position of a vehicle type in a train e.g. with respect to the
adhesion required.
If an inertia value (J) due to the rotating masses is known, rather than the equivalent mass of the
rotating parts, then the associated wheel diameter shall be defined, this diameter is normally the new
wheel diameter. The formula for the calculation of equivalent rotating mass using inertia is shown
below:
4 ⋅ J
m = (1)
rot
D
where:
equivalent rotating mass, in kg
m
rot
Inertia
J
wheel diameter, in m
D
m
dyn
4.3.2.4 Dynamic mass ( )
Dependent on the calculation being conducted the dynamic mass is the sum of the static mass and the
equivalent rotating mass for the entity being considered e.g. axle, bogie, vehicle etc.
m = (m + m ) (2)
dyn ∑ st rot
where:
dynamic mass, in kg
m
dyn
static mass, in kg
m
st
rotating mass, in kg
m
rot
4.3.2.5 Wheel diameter
The wheel diameter is measured on the nominal rolling circle.
NOTE The wheel diameter used in the emergency brake calculation is usually that which gives the lowest
deceleration e.g. in the case of disc brakes, this would normally be the maximum wheel diameter.
τ
req
When checking the required adhesion the wheel diameter used shall be the size which generates
the maximum adhesion demand e.g. in the case of disc brakes, this would normally be the minimum
wheel diameter.
If the train is equipped with different sizes of wheels (by design not due to wear) each size of wheel
shall be identified in the train composition.
4.3.2.6 Mean train resistance
The train resistance is a component of the train decelerating force provided by the structure of the
train, referred to as resistance to motion in EN 14067-4. This however uses instantaneous values. The
running resistance formula considers straight and level tracks, zero wind conditions, in open air and at
constant speed, The characteristic of train resistance can be by analogy to a similar existing train, or
based on a specific calculation or test. When the values are established as a result of tests, the test
conditions shall be similar to the expected operating conditions.
As an approximation or first calculation the following mean mathematical formula derived from the
instantaneous formula in EN 14067-4 shall be used:
2 2
v +⋅vv + v
0 0 fin fin
F Ra= A+ ⋅⋅B + ⋅Cv⋅ + v (3)
( )
0 fin
vv+
0 fin
where:
mean value of the train resistance force, in N
F Ra
initial speed of the train, in m/s
v
final speed of the train, in m/s
v
fin
characteristic coefficient of the train independent of speed considered as C in EN 14067-
A
4, in N
characteristic coefficient of the train proportional to the speed considered as C in
B
N
m/s
EN 14067-4, in
characteristic coefficient of aerodynamic train resistance considered as C in EN 14067-
C
N
(m/s)
4, in
The above mathematical units should be used for the calculations purpose; however the speed can be
expressed usually in km/h and the train resistance in N or kN.
NOTE A , B , and C coefficients are function of various parameters, e.g. mass, train length. Values for A , B ,
and C can be obtained using the test method given in EN 14067-4.
When conducting brake performance calculations as a first estimation, designers may ignore train
resistance if they also ignore the rotating masses, until these particular values are available.
For the application of other mathematical units, the coefficients of the formula shall be adapted
accordingly.
4.4 Brake equipment type characteristics
4.4.1 General
This part of the standard identifies how to calculate the braking force generated by each brake
equipment type related to the rail.
When the same brake equipment is used on one part of the train under certain conditions and used on
another part of the same train under other conditions (e.g. different pressure/force conditions) two
different brake equipment types shall be assumed and considered in the formulae.
The following sub clauses consider the braking force generated by various brake equipment types. If
other brake equipment types are used e.g. new or novel types, then alternative methods of brake force
calculation should be adopted.
The following is a description of brake equipment types currently in use:
a) Adhesion dependent (wheel to rail)
1) Friction brake
i) Tread brake equipment type
ii) Disc brake equipment type
2) Screw hand brake
i) Tread brake equipment type
ii) Disc brake equipment type
3) Electro-dynamic brake equipment type
4) Fluid retarder brake equipment type
b) Adhesion independent
1) Eddy current brake equipment type
2) Magnetic track brake equipment type
When using the following formulae to calculate the brake force for the different brake equipment types
(i) and possible arrangements of this equipment e.g. a clasp brake arrangement of a tread brake, the
number of arrangements fitted per entity shall be considered. As applicable, factors have been
identified in each of the formulae and are shown in the examples given.
For tread and disc brake equipment types typically a pressure applied brake cylinder is used. However,
a spring applied brake cylinder may be used. For the calculation of the output force (F ) the formula
c
shall consider the following with reference to Figure 1:
i
C
a) The internal ratio/factor of the cylinder ( ) is normally one except for a design with an internal
cylinder ratio. The sign of the ratio/factor when considered in the calculation formula is dependent
on the type of brake equipment i.e. for pressure applied brake equipment it is a positive value and
for spring applied brake equipment it is negative value.
F
S ,C
b) The cylinder spring force ( ) in a pressure applied brake cylinder operates to release the brake
F
S ,C
force (cylinder piston return) and is therefore a negative value. For a spring applied brake
operates as a braking force and is therefore a positive value.

Figure 1 — Basic principle of a pressure applied (left) and spring applied (right) cylinder
Subclauses 4.4.2 and 4.4.3 consider the formulae for a representative tread brake unit and disc brake
unit with an arrangement as shown in the corresponding figures. Different designs of tread and disc
brake units may have the component parts arranged differently and the formulae may be changed to
represent the physical arrangement and its effect on the force calculation.
4.4.2 Tread braking
The braking effect is caused by the friction of the brake blocks to the wheel treads; the resulting heat
needs to be dissipated through the brake blocks and the wheels.
The brake cylinder force is transferred to the brake blocks with the relevant degrees of efficiency
(cylinder, rigging and brake lever efficiency). Additionally, design-specific spring forces also shall be
overcome (e.g. cylinder spring, slack adjuster spring).
Calculation of the braking force is directly derived from the defined mechanical functional chain. It is
based on a computation of forces only, taking into consideration rigging ratios and degrees of efficiency
from a mathematical point of view.
The braking force is independent of the wheel diameter.
4.4.3 Disc braking
The braking effect is caused by the friction of the brake pad to the brake disc the resultant heat being
dissipated by the brake pad and disc.
The brake cylinder force is transferred to the brake pads with the relevant degrees of efficiency
(cylinder, rigging and brake caliper efficiency); additionally design-specific spring forces also shall be
overcome (e.g. cylinder spring, slack adjuster spring).
Calculation of the braking force is directly derived from the defined mechanical functional chain. It is
based on a computation of forces only, taking into consideration rigging (caliper lever) ratios and
degrees of efficiency from a mathematical point of view.
The braking force is dependent on the wheel diameter.
4.4.4 Forces of friction brake (tread brake) equipment
4.4.4.1 Tread brake unit
The brake equipment of a tread brake unit acts on one brake block configuration per cylinder as shown
in Figure 2, this shows a representative arrangement of a pressure applied tread brake unit. The
principle is the same for a spring applied design but the values for internal brake unit spring force and
the internal ratio of a cylinder are reversed.

Figure 2 — Representative tread brake unit
The braking force characteristic of a tread brake unit can be expressed by:
Cylinder output force
F= p⋅ Ai⋅⋅η+ F (4)
c c c c c s,c
Force on the application point
F= Fi⋅⋅η + F (5)
n c rig rig,dyn s,rig
Mean braking force per brake unit
FF`.= m
(6)
B,act n µ
Pressure per application point
F
n
p = (7)
ap
A
b
where:
brake cylinder pressure, in Pa

p
C
brake cylinder piston area, in m
A
C
internal brake cylinder efficiency

η
C
internal brake cylinder ratio/factor
i
C
sum of internal brake actuator spring forces, in N

F
S,C
rigging efficiency in dynamic condition
η
rig,dyn
rigging ratio
i
rig
rigging spring force normally used as a rigging return spring, therefore a negative value,
F
S,rig
in N
mean friction coefficient of brake block
m
µ
total area of the friction surface per application point, in m

A
b
NOTE With reference to rigging efficiencies, ratios and return springs, for tread brake units these can be
wholly contained in the unit itself.
4.4.4.2 Tread brake
The brake equipment of a tread brake acts on an arrangement with several blocks per cylinder as
shown in Figure 3 (a typical clasp brake arrangement). However, this is also applicable to a pusher
brake arrangement with one application point per wheel.
The force generated by the brake cylinder is typically transmitted to the main brake rods via the central
brake linkage and then on to the brake shoes via the slack adjuster and the brake levers.

NOTE Dashed lines represent additional tread brake arrangements, if applicable.
Figure 3 — Typical tread brake arrangement
The braking force characteristic of a tread brake arrangement can be expressed by:
Output cylinder force
F = p ⋅ A ⋅i ⋅η + F (8)
C C C C C S,C
Total force on the application points
F = (F ⋅i + F )⋅i ⋅η (9)
b C rig S,R R R
With the ratios
i = l / l (10)
rig a b
and
i = n ⋅ n ⋅i (11)
R ax ap rig,ax
with
i = l / l (12)
rig,ax a,ax b,ax
Mean brake force per complete tread brake ar
...