ISO 23373:2024

International
Standard
ISO 23373
First edition
Heavy commercial vehicles
2024-05
and buses — Vehicle dynamics
simulation and validation — Tyre
model for lateral estimation
of heavy vehicle combinations
operated at dry paved road surface
Véhicules utilitaires lourds et bus — Simulation et validation de
la dynamique du véhicule — Modèle de pneu pour l'estimation
latérale des combinaisons de véhicules lourds exploités sur une
surface de route pavée sèche
Reference number
© ISO 2024
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ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Tyre model formulae . 4
4.1 Steady-state calculation .4
4.2 Transient properties . .5
4.3 Standard values of the model parameters .5
Bibliography . 7

iii
Foreword
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iv
Introduction
This document describes a generic tyre model intended for lateral stability performance estimations of
commercial vehicle combinations operated at dry paved road surface.
Even though the recommended use is limited to moderate excitation levels, non-linear components of truck
tyres are included to not underestimate risk levels, especially when it comes to loads with high centres of
gravity. Hence the standard model calculates the lateral force from vertical force and slip angle input with a
non-linear formula.
The tyre model in this document is inspired by a trigonometric formula for calculating steady-state lateral
or longitudinal force under pure slip conditions, often referred to as the Magic Formula. This formula was
introduced by HB Pacejka and colleagues in the 1980s.
The standard tyre model is however less complex compared to many tyre models based on the Magic
Formula, for example, by neglecting the influence of camber inclination, asymmetry and combined
longitudinal slip and sideslip. There are five characterizing parameters in the tyre model that describe the
steady state properties of the tyre, and two parameters that describe its transient properties.

v
International Standard ISO 23373:2024(en)
Heavy commercial vehicles and buses — Vehicle dynamics
simulation and validation — Tyre model for lateral
estimation of heavy vehicle combinations operated at dry
paved road surface
1 Scope
This document specifies a generic tyre model and model parameters for calculating lateral tyre forces, for
use in lateral stability simulations of heavy commercial vehicle combinations with test cases according
to ISO 14791. This tyre model is parameterized by easily understandable characteristics which can be
estimated from tyre measurement data. If tyre data is not available, the parameters proposed in this
document can be used.
One typical application area of this document is the comparing and ranking of various vehicle combination
configurations with respect to on-road lateral and roll stability. Such an assessment is usually performed
at close to constant speed levels typical for public roads, usually higher than 40 km/h. The tyre model,
however, can be useful for both high- and low-speed manoeuvring.
This tyre model is relevant for representing the lateral performance of tyres on a vehicle combination when
the longitudinal forces are insignificant, typically less than 10 % of the peak longitudinal friction utilization.
The tyre model can be used for normal forces ranging from zero to twice the nominal normal force of the
tyre. This tyre model has been developed for moderate lateral slip conditions; it is important that the model
is used with care for scenarios where tyre slip angle exceeds 15°.
This tyre model is suitable for vehicle models operating in the yaw and roll plane which naturally include
vertical load transfer between the wheels during manoeuvring. The tyre model can also be used in models
with less complexity such as pure yaw plane models.
This document applies to heavy vehicles, including commercial vehicles, commercial vehicle combinations,
buses and articulated buses as defined in ISO 3833 (trucks and trailers with a maximum weight above 3,5
tonnes and buses and articulated buses with a maximum weight above 5 tonnes, according to ECE and EC
vehicle classification, categories M3, N2, N3, O3 and O4).
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 3833, Road vehicles — Types — Terms and definitions
ISO 8855, Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary
ISO 15037-2, Road vehicles — Vehicle dynamics test methods — Part 2: General conditions for heavy vehicles
and buses
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3833, ISO 8855, ISO 15037-2 and
the following apply.
...