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

ISO 4138:2012 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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31-May-2012
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9092 - International Standard to be revised
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INTERNATIONAL ISO
STANDARD 4138
Fourth edition
2012-06-01
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 4138:2012(E)
ISO 2012
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ISO 4138:2012(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2012

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,

electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO’s

member body in the country of the requester.
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Published in Switzerland
ii © ISO 2012 – All rights reserved
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ISO 4138:2012(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 ..................................................................................................................................................... 3

8.1 Warm-up ................................................................................................................................................................. 3

8.2 Initial driving condition ...................................................................................................................................... 3

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

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

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

8.6 Method 3 — Constant speed ............................................................................................................................ 5

9 Data analysis ........................................................................................................................................................ 6

9.1 General ................................................................................................................................................................... 6

9.2 Lateral acceleration ............................................................................................................................................ 6

9.3 Path radius ............................................................................................................................................................ 7

10 Data evaluation and presentation of results ................................................................................................ 7

10.1 General ................................................................................................................................................................... 7

10.2 Plotted results (see also Annex A) .................................................................................................................... 7

10.3 Evaluation of characteristic values ................................................................................................................ 8

Annex A (normative) Presentation of results ............................................................................................................12

Annex B (normative) Determination of overall (static) steering ratio ................................................................17

Annex C (informative) General information — Theoretical basis for the test methods ................................18

Bibliography .....................................................................................................................................................................19

© ISO 2012 – All rights reserved iii
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ISO 4138:2012(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.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. Draft International Standards

adopted by the technical committees are circulated to the member bodies for voting. Publication as an

International Standard requires approval by at least 75 % of the member bodies casting a vote.

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.

ISO 4138 was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee SC 9, Vehicle

dynamics and road-holding ability.

This fourth edition cancels and replaces the third edition (ISO 4138:2004), which has been technically revised.

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ISO 4138:2012(E)
Introduction

The main purpose of this International Standard 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 must necessarily involve 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

require proven correlation between test results and accident statistics.
© ISO 2012 – All rights reserved v
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INTERNATIONAL STANDARD ISO 4138:2012(E)
Passenger cars — Steady-state circular driving behaviour —
Open-loop test methods
1 Scope

This International Standard 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 referenced documents are indispensable for the application of this document. For dated

references, only the edition cited applies. For undated references, the latest edition of the referenced document

(including any amendments) applies.
ISO 3833:1977, Road vehicles — Types — Terms and definitions

ISO 8855:2011, Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary

ISO 15037-1:2006, 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.

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.

Each method is presented with two variations and differs in requirements for testing space, driver skill

and instrumentation. Methods 1 and 3 depend upon 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.
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ISO 4138:2012(E)
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
Measured or
Test method Constant Varied
calculated
Constant radius Radius Speed Steering-wheel angle
Constant steering-wheel angle Steering-wheel angle Speed Radius
Constant speed with discrete turn radii Speed Radius Steering-wheel angle
Constant speed with discrete steering-
Speed Steering-wheel angle Radius
wheel angles

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 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 .
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 could require the measurement of additional variables

(yaw velocity, vehicle roll angle or sideslip angle) for use in the computation.
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ISO 4138:2012(E)
The following variables should also be measured:
— yaw velocity, ddψ t ;
— 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 15037-1:2006, 4.2.
6.3 Data processing
The provisions given in ISO 15037-1:2006, 4.3, 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 could 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 15037-1:2006, Clause 5. General data on the test vehicle shall

be recorded as specified in ISO 15037-1:2006, 5.4.1. 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 15037-1:2006, Annex A).

8 Test procedure
8.1 Warm-up
The warm-up shall be carried out in accordance with ISO 15037-1:2006, 6.1.
8.2 Initial driving condition

The conditions shall be in accordance with 15037-1:2006, 6.2.1 and 6.2.3, and with 8.3 to 8.6 as follows,

according to which method and variation is used.
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ISO 4138:2012(E)
8.3 General test description

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

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 15037-1:2006, Annex B). At a minimum, data shall be taken at increments of lateral

acceleration no larger than 0,5 m/s .

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.

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.

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ISO 4138:2012(E)
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 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.

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 Except that in this this procedure the steering-wheel angle is maintained and the speed varied, it 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

2 2

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.
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ISO 4138:2012(E)

The standard test speed is 100 km/h. 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

and hold them constant or mechanically fixed within ± 1° for 3 s after the measured vehicle motion variables

reach steady-state. Control the throttle 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.
8.6.2.2 With discrete turn radii

Drive the vehicle onto the circle at the pre-selected speed. After attaining steady-state, the steering wheel and

throttle position shall be held constant for at least 3 s.
8.6.2.3 With discrete steering-wheel angles

With the vehicle being driven at the pre-selected speed, apply a steering input and hold it constant for at least

3 s after the measured vehicle motion variables reach steady-state. Control the throttle in order to maintain

constant speed throughout the run.

NOTE It is possible to use the constant-speed test method with discrete steering-wheel angles to extract transient

response measures comparable to those obtained from the step input method of ISO 7401, if the steering input is applied

in accordance with ISO 7401:2011, 10.1. However, since ISO 7401:2011, 10.1 requires a fixed throttle position versus the

controlled throttle position of the constant-speed test method, the resulting measured transient response might not be

identical to that obtained from ISO 7401:2011, 10.2.
9 Data analysis
9.1 General

The steady-state values for all measured variables shall be established as their average values during any time

interval of 1 to 3 s during which steady-state is maintained. For each selected time interval, the limitations on

path radius, steer angle, speed, rate of increase of lateral acceleration and/or throttle position specified in the

description of the test procedure being followed shall be observed. In addition, for each selected time interval

the standard deviation of lateral acceleration shall not exceed 5 % of its mean value.

9.2 Lateral acceleration

Theoretically, steady-state characteristics should be determined as functions of centripetal acceleration,

which is measured perpendicular to the path. Traditionally, these characteristics have been expressed as

functions of lateral acceleration, which is measured perpendicular to the intermediate x-axis. At steady-state,

lateral acceleration and centripetal acceleration differ only by the cosine of the sideslip angle. In most cases,

the vehicle sideslip angle is small, so lateral acceleration may generally be considered equal to centripetal

acceleration. Where large values of vehicle sideslip angle are observed, or where greater accuracy is desired,

centripetal acceleration may be corrected to obtain lateral acceleration.
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ISO 4138:2012(E)

Steady-state centripetal acceleration may be obtained by any one of the following three methods.

a) The product of yaw velocity and horizontal velocity:
b) The square of the horizontal velocity, divided by the path radius:
c) The product of the square of the yaw velocity and the path radius:
dψ 
 
 

The method used to determine lateral acceleration shall be noted in the test report.

9.3 Path radius

For the constant steering-wheel angle test method, path radius R (defined in ISO 8855:2011, 5.3.3) may be

computed at steady-state from longitudinal velocity, corrected for sideslip angle, divided by yaw velocity and

corrected for vehicle roll angle.
10 Data evaluation and presentation of results
10.1 General

General data on the test vehicle shall be presented on a summary form using the general data test report

presented in ISO 15037-1:2006, Annex A. The general test conditions shall be presented using the test

conditions test report presented in ISO 15037-1:2006, Annex B.
10.2 Plotted results (see also Annex A)

Measured data shall be plotted directly against lateral acceleration on figures as follows:

a) steering-wheel angle data points for the constant-radius and constant-speed test methods in Figure A.1;

b) path radius data points for the constant steering-wheel angle test method in Figure A.2;

c) sideslip angle data points, if measured, in Figure A.3;
d) vehicle roll angle data points, if measured, in Figure A.4;
e) steering-wheel torque data points, if measured, in Figure A.5.

Curves may be fitted to the plotted points, either freehand or using one of the many mathematical routines

available. The method of curve fitting should be stated. This is particularly recommended where the process

involves fitting smooth curves to experimental data for the purpose of evaluating the gradients. The type of

curve and the method of fitting will influence the results obtained.

NOTE Within the context of this International Standard it is not possible to recommend any one way as better

than any other.
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ISO 4138:2012(E)
10.3 Evaluation of characteristic values
10.3.1 General
There are a number of ways to further process the data presented here. These
...

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