Passenger cars — Steady-state circular driving behaviour — Open-loop test methods

This document specifies open-loop test methods for determining the steady-state circular driving behaviour of passenger cars as defined in ISO 3833 and of light trucks, such behaviour being one of the factors comprising vehicle dynamics and road-holding properties. The open-loop manoeuvres included in these methods are not representative of real driving conditions, but are nevertheless useful for obtaining measures of vehicle steady-state behaviour resulting from several specific types of control inputs under closely controlled test conditions. This document specifies open-loop test methods for determining the steady-state circular driving behaviour of passenger cars as defined in ISO 3833 and of light trucks, such behaviour being one of the factors comprising vehicle dynamics and road-holding properties. The open-loop manoeuvres included in these methods are not representative of real driving conditions, but are nevertheless useful for obtaining measures of vehicle steady-state behaviour resulting from several specific types of control inputs under closely controlled test conditions.

Voitures particulières — Tenue de route en régime permanent sur trajectoire circulaire — Méthodes d'essai en boucle ouverte

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Publication Date
19-Sep-2021
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6060 - International Standard published
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20-Sep-2021
Completion Date
20-Sep-2021
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INTERNATIONAL ISO
STANDARD 4138
Fifth edition
2021-09
Passenger cars — Steady-state circular
driving behaviour — Open-loop test
methods
Voitures particulières — Tenue de route en régime permanent sur
trajectoire circulaire — Méthodes d'essai en boucle ouverte
Reference number
ISO 4138:2021(E)
ISO 2021
---------------------- Page: 1 ----------------------
ISO 4138:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 4138:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Principle ........................................................................................................................................................................................................................ 1

4.1 Test methods ............................................................................................................................................................................................. 1

4.2 Equivalence of test methods ....................................................................................................................................................... 2

5 Variables ....................................................................................................................................................................................................................... 2

5.1 Reference system .................................................................................................................................................................................. 2

5.2 Measurement ............................................................................................................................................................................................ 2

6 Measuring equipment ..................................................................................................................................................................................... 3

6.1 Description ................................................................................................................................................................................................. 3

6.2 Transducer installation.................................................................................................................................................................... 3

6.3 Data processing ...................................................................................................................................................................................... 3

7 Test conditions ....................................................................................................................................................................................................... 3

8 Test procedure ........................................................................................................................................................................................................ 4

8.1 Warm-up....................................................................................................................................................................................................... 4

8.2 Initial driving condition .................................................................................................................................................................. 4

8.3 General test description .................................................................................................................................................................. 4

8.4 Method 1 — Constant radius ...................................................................................................................................................... 4

8.4.1 Description .................. .................................................... ...................................................................................................... 4

8.4.2 Procedure ............................................................................................................................................................................... 5

8.5 Method 2 — Constant steering-wheel angle ................................................................................................................. 5

8.5.1 Description .................. .................................................... ...................................................................................................... 5

8.5.2 Procedure ............................................................................................................................................................................... 5

8.6 Method 3 — Constant speed ....................................................................................................................................................... 6

8.6.1 Description .................. .................................................... ...................................................................................................... 6

8.6.2 Procedure ............................................................................................................................................................................... 6

9 Data analysis ............................................................................................................................................................................................................. 7

9.1 General ........................................................................................................................................................................................................... 7

9.2 Lateral acceleration ............................................................................................................................................................................ 7

9.3 Path radius .................................................................................................................................................................................................. 8

10 Data evaluation and presentation of results ........................................................................................................................... 8

10.1 General ........................................................................................................................................................................................................... 8

10.2 Plotted results (see also Annex A) ......................................................................................................................................... 8

10.3 E valuation of characteristic values ........................................................................................................................................ 8

10.3.1 General...................................................................................................................................................................................... 8

10.3.2 Evaluation of gradients — Differentiation................................................................................................. 9

10.3.3 Normalization of results — Comparison of results from different vehicles ..............10

10.3.4 Normalized steady-state properties ............................................................................................................11

Annex A (normative) Presentation of results...........................................................................................................................................13

Annex B (normative) Determination of overall (static) steering ratio ..........................................................................19

Annex C (informative) General information — Theoretical basis for the test methods ..............................20

Bibliography .............................................................................................................................................................................................................................21

© ISO 2021 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 4138:2021(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/

iso/ foreword .html.

This document was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee SC 33,

Vehicle dynamics and chassis components.

This fifth edition cancels and replaces the fourth edition (ISO 4138:2012), which has been technically

revised.
The main changes compared to the previous edition are as follows:
— editorial changes,

— a third variation of the constant speed test method was added. This variation involves slowly

increasing the steering-wheel angle.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2021 – All rights reserved
---------------------- Page: 4 ----------------------
ISO 4138:2021(E)
Introduction

The main purpose of this document is to provide repeatable and discriminatory test results.

The dynamic behaviour of a road vehicle is a very important aspect of active vehicle safety. Any given

vehicle, together with its driver and the prevailing environment, constitutes a closed-loop system that

is unique. The task of evaluating the dynamic behaviour is, therefore, very difficult since the significant

interactions of these driver–vehicle–environment elements are each complex in themselves. A complete

and accurate description of the behaviour of the road vehicle involves information obtained from a

number of different tests.

Since this test method quantifies only one small part of the complete vehicle handling characteristics,

the results of these tests can only be considered significant for a correspondingly small part of the

overall dynamic behaviour.

Moreover, insufficient knowledge is available concerning the relationship between overall vehicle

dynamic properties and accident avoidance. A substantial amount of work is necessary to acquire

sufficient and reliable data on the correlation between accident avoidance and vehicle dynamic

properties in general and the results of these tests in particular. Consequently, any application of this

test method for regulation purposes will need proven correlation between test results and accident

statistics.
© ISO 2021 – All rights reserved v
---------------------- Page: 5 ----------------------
INTERNATIONAL STANDARD ISO 4138:2021(E)
Passenger cars — Steady-state circular driving behaviour
— Open-loop test methods
1 Scope

This document specifies open-loop test methods for determining the steady-state circular driving

behaviour of passenger cars as defined in ISO 3833 and of light trucks, such behaviour being one of the

factors comprising vehicle dynamics and road-holding properties. The open-loop manoeuvres included

in these methods are not representative of real driving conditions, but are nevertheless useful for

obtaining measures of vehicle steady-state behaviour resulting from several specific types of control

inputs under closely controlled test conditions.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements 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.

ISO 8855, Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary

ISO 15037-1:2019, Road vehicles — Vehicle dynamics test methods — Part 1: General conditions for

passenger cars
3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 8855 and the following apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
low-speed path radius

radius of the circular path transcribed by the origin of the vehicle axis system when the vehicle is

operated at constant speed with a given fixed steering-wheel angle and with approximately zero lateral

acceleration
4 Principle
4.1 Test methods
Three test methods are specified:
— method 1, the constant-radius test method;
— method 2, the constant steering-wheel angle test method;
— method 3, the constant-speed test method.

Methods 1 and 2 are presented with two variations and method 3 with three variations. The methods

differ in requirements for testing space, driver skill and instrumentation. Methods 1 and 3 depend upon

© ISO 2021 – All rights reserved 1
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ISO 4138:2021(E)

the path-keeping ability of the driver to minimize instrumentation requirements. Method 2 uses fixed

steering-wheel angle and calculates path radius from measures of inertial instruments.

4.2 Equivalence of test methods

The nature of any stable steady-state is independent of the method by which it is achieved. Therefore, to

obtain a desired set of steady-state equilibrium conditions of speed, steering-wheel angle and turning

radius, it is possible to hold any one of them constant, vary the second and measure the third. Thus,

either a constant-radius test method (in which speed is varied and steering-wheel angle is measured),

a constant steering-wheel angle test method (in which speed is varied and radius is calculated from

variables of vehicle motion) or a constant-speed test method (in which radius is varied and steering-

wheel angle is either measured or varied and the radius calculated from variables of vehicle motion)

may be used. The conditions that are to be held constant, varied and measured or calculated are

summarized in Table 1.
Table 1 — Test conditions
Test Measured or
Constant Variable Variation
method calculated
With discrete test speeds
Steering wheel
1 Radius Speed
angle
With continuous speed increase
Steer- With discrete test speeds
2 ing-wheel Speed Radius
With continuous speed increase
angle
Steering-wheel
Radius With discrete turn radii
angle
3 Speed
With discrete steering-wheel angles
Steering wheel
Radius
angle
With slowly increasing steering-wheel angle

All three test methods will produce equivalent steady-state results, provided they span the same

combination of speed–steer–radius steady-state conditions. Moreover, in principle, an equivalent to any

of the methods can be obtained by cross plotting a series of results from one to produce the results

from another.

EXAMPLE Taking points at constant speed from a series of constant-radius tests run on different turn radii.

In practice, however, results obtained from tests conducted with different combinations of speed, steer

and radius may differ due to differences in road-load throttle, aerodynamics, tyre slip and inclination

angles at different steering angles, etc. Also, the steering system is nonlinear in many vehicles and does

not have a fixed overall steering ratio. Gradients obtained using one method at a given steady-state

equilibrium condition can differ from those obtained using another and, whereas in one method lateral

acceleration is controlled by changing speed, in another it is controlled by changing the steering-wheel

angle. Practical considerations such as available size of the test area, tyre heating during long test runs

and failure to maintain true steady-state also tend to affect test results.
5 Variables
5.1 Reference system
The provisions given in ISO 15037-1 apply.
5.2 Measurement
Measure the following variables:
a) longitudinal velocity, v .
2 © ISO 2021 – All rights reserved
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ISO 4138:2021(E)
b) lateral acceleration, a ;
c) steering-wheel angle, δ .

Alternatively, lateral acceleration may be determined from other motion variables (see 9.2).

NOTE The method chosen to determine lateral acceleration can require the measurement of additional

variables (yaw velocity, vehicle roll angle or sideslip angle) for use in the computation.

The following variables should also be measured:
— yaw velocity, dψ/dt;
— sideslip angle, β and/or lateral velocity, v ;
— longitudinal acceleration, a ;
— vehicle roll angle, φ ;
— steering-wheel torque, M .
The front steer angle, δ , and rear steer angle, δ , may also be measured.
F R
6 Measuring equipment
6.1 Description

The variables selected for test purposes shall be measured using appropriate transducers and the

data recorded on a multi-channel recording system having a time base. Typical operating ranges and

recommended maximum errors of the transducer and recording system are given in ISO 15037-1 and

Table 2.
6.2 Transducer installation
The transducer installation shall be in accordance with ISO 15037-1:2019, 5.2.
6.3 Data processing
The provisions given in ISO 15037-1:2019, 5.3, apply.

Table 2 — Variables, their typical operating ranges and recommended maximum errors

Recommended maximum error of the
Variable Typical operating range
combined transducer/recorder system
Front-steer angle ±20° ±0,2°
Rear-steer angle ±10° ±0,1°

NOTE Increased measurement accuracy can be desirable for computation of some of the characteristic values given in

10.3.
7 Test conditions

Test conditions shall be in accordance with ISO 15037-1:2019, Clause 6. General data on the test vehicle

shall be recorded as specified in ISO 15037-1:2019, 6.4.1. In addition, the tyre type, tyre brand, any

special equipment on the test vehicle, any deviation in type or operating condition of components from

the manufacturer’s specification, the odometer reading at the beginning and end of the test, and any

other condition that could affect test results shall be recorded on the test report for general data (see

ISO 15037-1:2019, Annex A).
© ISO 2021 – All rights reserved 3
---------------------- Page: 8 ----------------------
ISO 4138:2021(E)
8 Test procedure
8.1 Warm-up
The warm-up shall be carried out in accordance with ISO 15037-1:2019, 7.1.
8.2 Initial driving condition

The conditions shall be in accordance with ISO 15037-1:2019, 7.2.1 and 7.2.3, and with 8.3 to 8.6 as

follows, according to which method and variation is used.
8.3 General test description

All necessary variables shall be recorded throughout the manoeuvre. Data shall be taken for both left

and right turns. A minimum of three repetitions is recommended.

For tests utilizing discrete increments of speed, radius or steering-wheel angle, all of the test data may

be taken in one turning direction followed by all the data in the other turning direction, as experience

has shown that this minimizes data scatter. However, to obtain more even tyre wear and reduced tyre

heating, data may be taken in alternating turning directions at each test speed/radius/steering-wheel

angle.

The method chosen shall be noted on the test report, in the section on test-method-specific data for test

conditions (see ISO 15037-1:2019, Annex B). At a minimum, data shall be taken at increments of lateral

acceleration no larger than 0,5 m/s . Annex C provides general information for the test methods.

NOTE Where data vary rapidly with changes in lateral acceleration, it can be useful to decrease the speed/

radius/steering-wheel angle increments.

The test should be repeated several times so that the results can be examined for repeatability and

averaged.

Caution should be exercised during testing so that tyre heating is minimized as much as possible. Tyre

heating is a particular concern for test methods using continuous speed increase, with attendant long

periods of data acquisition, and for all test methods at high levels of lateral acceleration. The tyres

should be cooled to normal operating temperatures between test runs.
8.4 Method 1 — Constant radius
8.4.1 Description

This test method requires driving the test vehicle at several speeds over a circular path of known

radius. The standard radius of the path shall be 100 m, but larger and smaller radii may be used, with

40 m as the recommended lower value and 30 m as the minimum.

The directional-control response characteristics are determined from data obtained while driving the

vehicle at successively higher speeds on the constant-radius path. This procedure can be conducted in a

relatively small area. The procedure can be adapted to existing test track facilities by selecting a circle

or path of appropriate radius. A constant-radius (in plane) road will often suffice for a test facility.

The constant-radius test exists in two variations. In the first, the vehicle is driven on the circular path

at discrete constant speeds. Data are taken when steady-state is attained. The test can be run on any

level constant-radius path of sufficient length to attain and hold on-radius steady-state for at least a

3 s measurement period. In the second, the vehicle remains on the circle with a continuous, slow speed

increase, during which data are taken.
4 © ISO 2021 – All rights reserved
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ISO 4138:2021(E)
8.4.2 Procedure
8.4.2.1 General

First drive the vehicle on the desired circular path at the lowest possible speed. Record data with the

steering-wheel and throttle positions fixed, so that the approximate Ackermann steer angle can be

recorded.
Then drive the vehicle at the next speed at which data are to be taken.

Increase the level of the lateral acceleration and take data until it is no longer possible to maintain

steady-state conditions.
8.4.2.2 With discrete test speeds

Drive the vehicle onto the circle at each test speed. After attaining steady-state, in which the desired

path radius is held within ± 0,5 m, the steering wheel and throttle positions shall be held constant for

at least 3 s.
8.4.2.3 With continuous speed increase

Steadily increase the speed and record data continuously for as long as the vehicle remains on the

desired circular path within ± 0,5 m. The maximum rate of increase of lateral acceleration should be

2 2

0,1 m/s /s. The maximum permissible rate of increase of lateral acceleration shall be 0,2 m/s /s.

8.5 Method 2 — Constant steering-wheel angle
8.5.1 Description

This test method requires driving the test vehicle at several speeds with a single selected steering-

wheel angle that is held fixed. The path radius is determined by computation: from horizontal velocity

and yaw velocity, or from horizontal velocity and lateral acceleration. The test exists in two variations:

a series of discrete test runs, or a single continuous test run. In the first, the steering-wheel angle is

applied with the vehicle travelling at discrete speeds, and is maintained until steady-state conditions

are reached. In the second, the steering-wheel angle is held fixed while speed is increased continuously

at a slow rate, up to the limit of control.

The standard steering-wheel angle shall provide a low-speed path radius of 30 m. Other radii may be

used, with 20 m as the minimum. For testing to the limit of control with the standard initial condition,

the path radius can increase to 100 m or more.
8.5.2 Procedure
8.5.2.1 General

First drive the vehicle at the lowest possible speed to establish the steering-wheel angle for the selected

low-speed path radius.

Then drive the vehicle at successively higher speeds, with the steering-wheel angle held constant or

mechanically fixed within ± 1° of the selected steering-wheel angle. Run the test through the desired

range of lateral acceleration, or until the limits of test space, vehicle speed or vehicle stability are

reached.
© ISO 2021 – All rights reserved 5
---------------------- Page: 10 ----------------------
ISO 4138:2021(E)
8.5.2.2 With discrete test speeds

At each selected speed, the steering wheel shall be turned to the pre-selected steering-wheel angle

and maintained until steady-state conditions, including speed and throttle, are attained. The steering-

wheel angle and throttle position shall be held constant for at least 3 s.

NOTE With the exception that in this procedure the steering-wheel angle is maintained and the speed is

varied, this procedure and the procedure given in 8.5.2.3 are the same.
8.5.2.3 With continuous speed increase

The steering-wheel angle shall be held constant or mechanically fixed at the pre-selected steering-

wheel angle while the vehicle speed is steadily increased. The maximum rate of increase of lateral

acceleration is 0,1 m/s /s. The maximum permissible rate of increase of lateral acceleration shall be

0,2 m/s /s.
8.6 Method 3 — Constant speed
8.6.1 Description

This test method requires driving the test vehicle at one speed on circular paths of different radii,

utilizing a range of steering-wheel angles. The directional-control response characteristics are

determined from data plotted against lateral acceleration. This test method could require large test

areas, depending on the combination of speed and lateral acceleration. The discrete turn radii method

requires a number of marked circles or circular segments with different radii, sufficient in number

to provide 0,5 m/s lateral acceleration increments at the selected speed. An adjustable steering stop

should be used, for maintaining constant steering-wheel angles when using the discrete steering-wheel

angle method.

The standard test speed is 100 km/h for discrete turn radii and wheel angles and 80 km/h for a

slowly increasing steering wheel angle. If higher or lower speeds are selected, they shall be in 20 km/h

increments.
8.6.2 Procedure
8.6.2.1 General

From an initial constant-speed driving condition, apply steering inputs of successively increasing

magnitude Control the throttle smoothly in order to maintain constant speed within 3 % throughout

the test run. Run the test through the desired range of lateral acceleration, or until the limits of test

space, vehicle speed or vehicle stability are reached.

NOTE To avoid rapid changes in throttle inputs, it is possible to choose to keep the throttle con

...

INTERNATIONAL ISO
STANDARD 4138
Fifth edition
Passenger cars — Steady-state circular
driving behaviour — Open-loop test
methods
Voitures particulières — Tenue de route en régime permanent sur
trajectoire circulaire — Méthodes d'essai en boucle ouverte
PROOF/ÉPREUVE
Reference number
ISO 4138:2021(E)
ISO 2021
---------------------- Page: 1 ----------------------
ISO 4138:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii PROOF/ÉPREUVE © ISO 2021 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 4138:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Principle ........................................................................................................................................................................................................................ 1

4.1 Test methods ............................................................................................................................................................................................. 1

4.2 Equivalence of test methods ....................................................................................................................................................... 2

5 Variables ....................................................................................................................................................................................................................... 2

5.1 Reference system .................................................................................................................................................................................. 2

5.2 Measurement ............................................................................................................................................................................................ 2

6 Measuring equipment ..................................................................................................................................................................................... 3

6.1 Description ................................................................................................................................................................................................. 3

6.2 Transducer installation.................................................................................................................................................................... 3

6.3 Data processing ...................................................................................................................................................................................... 3

7 Test conditions ....................................................................................................................................................................................................... 3

8 Test procedure ........................................................................................................................................................................................................ 4

8.1 Warm-up....................................................................................................................................................................................................... 4

8.2 Initial driving condition .................................................................................................................................................................. 4

8.3 General test description .................................................................................................................................................................. 4

8.4 Method 1 — Constant radius ...................................................................................................................................................... 4

8.4.1 Description .................. .................................................... ...................................................................................................... 4

8.4.2 Procedure ............................................................................................................................................................................... 5

8.5 Method 2 — Constant steering-wheel angle ................................................................................................................. 5

8.5.1 Description .................. .................................................... ...................................................................................................... 5

8.5.2 Procedure ............................................................................................................................................................................... 5

8.6 Method 3 — Constant speed ....................................................................................................................................................... 6

8.6.1 Description .................. .................................................... ...................................................................................................... 6

8.6.2 Procedure ............................................................................................................................................................................... 6

9 Data analysis ............................................................................................................................................................................................................. 7

9.1 General ........................................................................................................................................................................................................... 7

9.2 Lateral acceleration ............................................................................................................................................................................ 7

9.3 Path radius .................................................................................................................................................................................................. 8

10 Data evaluation and presentation of results ........................................................................................................................... 8

10.1 General ........................................................................................................................................................................................................... 8

10.2 Plotted results (see also Annex A) ......................................................................................................................................... 8

10.3 E valuation of characteristic values ........................................................................................................................................ 8

10.3.1 General...................................................................................................................................................................................... 8

10.3.2 Evaluation of gradients — Differentiation................................................................................................. 9

10.3.3 Normalization of results — Comparison of results from different vehicles ..............10

10.3.4 Normalized steady-state properties ............................................................................................................11

Annex A (normative) Presentation of results...........................................................................................................................................13

Annex B (normative) Determination of overall (static) steering ratio ..........................................................................19

Annex C (informative) General information — Theoretical basis for the test methods ..............................20

Bibliography .............................................................................................................................................................................................................................21

© ISO 2021 – All rights reserved PROOF/ÉPREUVE iii
---------------------- Page: 3 ----------------------
ISO 4138:2021(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/

iso/ foreword .html.

This document was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee SC 33,

Vehicle dynamics and chassis components.

This fifth edition cancels and replaces the fourth edition (ISO 4138:2012), which has been technically

revised.
The main changes compared to the previous edition are as follows:
— editorial changes,

— a third variation of the constant speed test method was added. This variation involves slowly

increasing the steering-wheel angle.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/ members .html.
iv PROOF/ÉPREUVE © ISO 2021 – All rights reserved
---------------------- Page: 4 ----------------------
ISO 4138:2021(E)
Introduction

The main purpose of this document is to provide repeatable and discriminatory test results.

The dynamic behaviour of a road vehicle is a very important aspect of active vehicle safety. Any given

vehicle, together with its driver and the prevailing environment, constitutes a closed-loop system that

is unique. The task of evaluating the dynamic behaviour is, therefore, very difficult since the significant

interactions of these driver–vehicle–environment elements are each complex in themselves. A complete

and accurate description of the behaviour of the road vehicle involves information obtained from a

number of different tests.

Since this test method quantifies only one small part of the complete vehicle handling characteristics,

the results of these tests can only be considered significant for a correspondingly small part of the

overall dynamic behaviour.

Moreover, insufficient knowledge is available concerning the relationship between overall vehicle

dynamic properties and accident avoidance. A substantial amount of work is necessary to acquire

sufficient and reliable data on the correlation between accident avoidance and vehicle dynamic

properties in general and the results of these tests in particular. Consequently, any application of this

test method for regulation purposes will need proven correlation between test results and accident

statistics.
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INTERNATIONAL STANDARD ISO 4138:2021(E)
Passenger cars — Steady-state circular driving behaviour
— Open-loop test methods
1 Scope

This document specifies open-loop test methods for determining the steady-state circular driving

behaviour of passenger cars as defined in ISO 3833 and of light trucks, such behaviour being one of the

factors comprising vehicle dynamics and road-holding properties. The open-loop manoeuvres included

in these methods are not representative of real driving conditions, but are nevertheless useful for

obtaining measures of vehicle steady-state behaviour resulting from several specific types of control

inputs under closely controlled test conditions.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements 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.

ISO 8855, Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary

ISO 15037-1:2019, Road vehicles — Vehicle dynamics test methods — Part 1: General conditions for

passenger cars
3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 8855 and the following apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
low-speed path radius

radius of the circular path transcribed by the origin of the vehicle axis system when the vehicle is

operated at constant speed with a given fixed steering-wheel angle and with approximately zero lateral

acceleration
4 Principle
4.1 Test methods
Three test methods are specified:
— method 1, the constant-radius test method;
— method 2, the constant steering-wheel angle test method;
— method 3, the constant-speed test method.

Methods 1 and 2 are presented with two variations and method 3 with three variations. The methods

differ in requirements for testing space, driver skill and instrumentation. Methods 1 and 3 depend upon

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ISO 4138:2021(E)

the path-keeping ability of the driver to minimize instrumentation requirements. Method 2 uses fixed

steering-wheel angle and calculates path radius from measures of inertial instruments.

4.2 Equivalence of test methods

The nature of any stable steady-state is independent of the method by which it is achieved. Therefore, to

obtain a desired set of steady-state equilibrium conditions of speed, steering-wheel angle and turning

radius, it is possible to hold any one of them constant, vary the second and measure the third. Thus,

either a constant-radius test method (in which speed is varied and steering-wheel angle is measured),

a constant steering-wheel angle test method (in which speed is varied and radius is calculated from

variables of vehicle motion) or a constant-speed test method (in which radius is varied and steering-

wheel angle is either measured or varied and the radius calculated from variables of vehicle motion)

may be used. The conditions that are to be held constant, varied and measured or calculated are

summarized in Table 1.
Table 1 — Test conditions
Test Measured or
Constant Variable Variation
method calculated
With discrete test speeds
Steering wheel
1 Radius Speed
angle
With continuous speed increase
Steer- With discrete test speeds
2 ing-wheel Speed Radius
With continuous speed increase
angle
Steering-wheel
Radius With discrete turn radii
angle
3 Speed
With discrete steering-wheel angles
Steering wheel
Radius
angle
With slowly increasing steering-wheel angle

All three test methods will produce equivalent steady-state results, provided they span the same

combination of speed–steer–radius steady-state conditions. Moreover, in principle, an equivalent to any

of the methods can be obtained by cross plotting a series of results from one to produce the results

from another.

EXAMPLE Taking points at constant speed from a series of constant-radius tests run on different turn radii.

In practice, however, results obtained from tests conducted with different combinations of speed, steer

and radius may differ due to differences in road-load throttle, aerodynamics, tyre slip and inclination

angles at different steering angles, etc. Also, the steering system is nonlinear in many vehicles and does

not have a fixed overall steering ratio. Gradients obtained using one method at a given steady-state

equilibrium condition can differ from those obtained using another and, whereas in one method lateral

acceleration is controlled by changing speed, in another it is controlled by changing the steering-wheel

angle. Practical considerations such as available size of the test area, tyre heating during long test runs

and failure to maintain true steady-state also tend to affect test results.
5 Variables
5.1 Reference system
The provisions given in ISO 15037-1 apply.
5.2 Measurement
Measure the following variables:
a) longitudinal velocity, v .
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ISO 4138:2021(E)
b) lateral acceleration, a ;
c) steering-wheel angle, δ .

Alternatively, lateral acceleration may be determined from other motion variables (see 9.2).

NOTE The method chosen to determine lateral acceleration can require the measurement of additional

variables (yaw velocity, vehicle roll angle or sideslip angle) for use in the computation.

The following variables should also be measured:
— yaw velocity, dψ/dt;
— sideslip angle, β and/or lateral velocity, v ;
— longitudinal acceleration, a ;
— vehicle roll angle, φ ;
— steering-wheel torque, M .
The front steer angle, δ , and rear steer angle, δ , may also be measured.
F R
6 Measuring equipment
6.1 Description

The variables selected for test purposes shall be measured using appropriate transducers and the

data recorded on a multi-channel recording system having a time base. Typical operating ranges and

recommended maximum errors of the transducer and recording system are given in ISO 15037-1 and

Table 2.
6.2 Transducer installation
The transducer installation shall be in accordance with ISO 15037-1:2019, 5.2.
6.3 Data processing
The provisions given in ISO 15037-1:2019, 5.3, apply.

Table 2 — Variables, their typical operating ranges and recommended maximum errors

Recommended maximum error of the
Variable Typical operating range
combined transducer/recorder system
Front-steer angle ±20° ±0,2°
Rear-steer angle ±10° ±0,1°

NOTE Increased measurement accuracy can be desirable for computation of some of the characteristic values given in

10.3.
7 Test conditions

Test conditions shall be in accordance with ISO 15037-1:2019, Clause 6. General data on the test vehicle

shall be recorded as specified in ISO 15037-1:2019, 6.4.1. In addition, the tyre type, tyre brand, any

special equipment on the test vehicle, any deviation in type or operating condition of components from

the manufacturer’s specification, the odometer reading at the beginning and end of the test, and any

other condition that could affect test results shall be recorded on the test report for general data (see

ISO 15037-1:2019, Annex A).
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8 Test procedure
8.1 Warm-up
The warm-up shall be carried out in accordance with ISO 15037-1:2019, 7.1.
8.2 Initial driving condition

The conditions shall be in accordance with ISO 15037-1:2019, 7.2.1 and 7.2.3, and with 8.3 to 8.6 as

follows, according to which method and variation is used.
8.3 General test description

All necessary variables shall be recorded throughout the manoeuvre. Data shall be taken for both left

and right turns. A minimum of three repetitions is recommended.

For tests utilizing discrete increments of speed, radius or steering-wheel angle, all of the test data may

be taken in one turning direction followed by all the data in the other turning direction, as experience

has shown that this minimizes data scatter. However, to obtain more even tyre wear and reduced tyre

heating, data may be taken in alternating turning directions at each test speed/radius/steering-wheel

angle.

The method chosen shall be noted on the test report, in the section on test-method-specific data for test

conditions (see ISO 15037-1:2019, Annex B). At a minimum, data shall be taken at increments of lateral

acceleration no larger than 0,5 m/s . Annex C provides general information for the test methods.

NOTE Where data vary rapidly with changes in lateral acceleration, it can be useful to decrease the speed/

radius/steering-wheel angle increments.

The test should be repeated several times so that the results can be examined for repeatability and

averaged.

Caution should be exercised during testing so that tyre heating is minimized as much as possible. Tyre

heating is a particular concern for test methods using continuous speed increase, with attendant long

periods of data acquisition, and for all test methods at high levels of lateral acceleration. The tyres

should be cooled to normal operating temperatures between test runs.
8.4 Method 1 — Constant radius
8.4.1 Description

This test method requires driving the test vehicle at several speeds over a circular path of known

radius. The standard radius of the path shall be 100 m, but larger and smaller radii may be used, with

40 m as the recommended lower value and 30 m as the minimum.

The directional-control response characteristics are determined from data obtained while driving the

vehicle at successively higher speeds on the constant-radius path. This procedure can be conducted in a

relatively small area. The procedure can be adapted to existing test track facilities by selecting a circle

or path of appropriate radius. A constant-radius (in plane) road will often suffice for a test facility.

The constant-radius test exists in two variations. In the first, the vehicle is driven on the circular path

at discrete constant speeds. Data are taken when steady-state is attained. The test can be run on any

level constant-radius path of sufficient length to attain and hold on-radius steady-state for at least a

3 s measurement period. In the second, the vehicle remains on the circle with a continuous, slow speed

increase, during which data are taken.
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8.4.2 Procedure
8.4.2.1 General

First drive the vehicle on the desired circular path at the lowest possible speed. Record data with the

steering-wheel and throttle positions fixed, so that the approximate Ackermann steer angle can be

recorded.
Then drive the vehicle at the next speed at which data are to be taken.

Increase the level of the lateral acceleration and take data until it is no longer possible to maintain

steady-state conditions.
8.4.2.2 With discrete test speeds

Drive the vehicle onto the circle at each test speed. After attaining steady-state, in which the desired

path radius is held within ± 0,5 m, the steering wheel and throttle positions shall be held constant for

at least 3 s.
8.4.2.3 With continuous speed increase

Steadily increase the speed and record data continuously for as long as the vehicle remains on the

desired circular path within ± 0,5 m. The maximum rate of increase of lateral acceleration should be

2 2

0,1 m/s /s. The maximum permissible rate of increase of lateral acceleration shall be 0,2 m/s /s.

8.5 Method 2 — Constant steering-wheel angle
8.5.1 Description

This test method requires driving the test vehicle at several speeds with a single selected steering-

wheel angle that is held fixed. The path radius is determined by computation: from horizontal velocity

and yaw velocity, or from horizontal velocity and lateral acceleration. The test exists in two variations:

a series of discrete test runs, or a single continuous test run. In the first, the steering-wheel angle is

applied with the vehicle travelling at discrete speeds, and is maintained until steady-state conditions

are reached. In the second, the steering-wheel angle is held fixed while speed is increased continuously

at a slow rate, up to the limit of control.

The standard steering-wheel angle shall provide a low-speed path radius of 30 m. Other radii may be

used, with 20 m as the minimum. For testing to the limit of control with the standard initial condition,

the path radius can increase to 100 m or more.
8.5.2 Procedure
8.5.2.1 General

First drive the vehicle at the lowest possible speed to establish the steering-wheel angle for the selected

low-speed path radius.

Then drive the vehicle at successively higher speeds, with the steering-wheel angle held constant or

mechanically fixed within ± 1° of the selected steering-wheel angle. Run the test through the desired

range of lateral acceleration, or until the limits of test space, vehicle speed or vehicle stability are

reached.
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8.5.2.2 With discrete test speeds

At each selected speed, the steering wheel shall be turned to the pre-selected steering-wheel angle

and maintained until steady-state conditions, including speed and throttle, are attained. The steering-

wheel angle and throttle position shall be held constant for at least 3 s.

NOTE With the exception that in this procedure the steering-wheel angle is maintained and the speed is

varied, this procedure and the procedure given in 8.5.2.3 are the same.
8.5.2.3 With continuous speed increase

The steering-wheel angle shall be held constant or mechanically fixed at the pre-selected steering-

wheel angle while the vehicle speed is steadily increased. The maximum rate of increase of lateral

acceleration is 0,1 m/s /s. The maximum permissible rate of increase of lateral acceleration shall be

0,2 m/s /s.
8.6 Method 3 — Constant speed
8.6.1 Description

This test method requires driving the test vehicle at one speed on circular paths of different radii,

utilizing a range of steering-wheel angles. The directional-control response characteristics are

determined from data plotted against lateral acceleration. This test method could require large test

areas, depending on the combination of speed and lateral acceleration. The discrete turn radii method

requires a number of marked circles or circular segments with different radii, sufficient in number

to provide 0,5 m/s lateral acceleration increments at the selected speed. An adjustable steering stop

should be used, for maintaining constant steering-wheel angles when using the discrete steering-wheel

angle method.

The standard test speed is 100 km/h for discrete turn radii and wheel angles and 80 km/h for a

slowly increasing steering wheel angle. If higher or lower speeds are selected, they shall be in 20 km/h

increments.
8.6.2 Procedure
8.6.2.1 General

From an initial constant-speed driving condition, apply steering inputs of successively increasing

magnitude Control the throttle smoothly in order to maintain constant speed within 3 % throughout

the test run. Run the test through the desired range of lateral acceleration, or until the limits of test

space, vehicle speed or vehic
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