ISO 9043:2008

• Abstract:

  ISO 9043:2008 specifies a measuring method for determining the moments of inertia of the moped and of the moped/rider combination. It applies to two-wheeled mopeds. Other measuring methods can be used if it is demonstrated that the results are equivalent. Measurement results obtained exclusively by the method described in ISO 9043:2008 cannot be used for an evaluation of vehicle stability because they deal with only one aspect of this very complex phenomenon.

• Status: Published
• Publication Date: 20-Feb-2008
• ICS: 43.140 - Motorcycles and mopeds
• Technical Committee: ISO/TC 22/SC 38 - Motorcycles and mopeds
• Drafting Committee: ISO/TC 22/SC 38 - Motorcycles and mopeds
• Current Stage: 9093 - International Standard confirmed
• Start Date: 18-Oct-2023
• Completion Date: 29-Aug-2026

• Revises: ISO 9043:1991 - Mopeds — Measurement method for moments of inertia
• Effective Date: 15-Apr-2008

Overview

ISO 9043:2008 - "Mopeds - Measurement method for moments of inertia" defines a standardized laboratory method to determine the moments of inertia of two-wheeled mopeds and moped/rider combinations. The standard describes measurement conditions, required instruments, and step-by-step procedures to obtain roll, pitch and yaw moments of inertia using pendulum methods. It is intended for engineers, test laboratories and manufacturers who need repeatable inertia data for dynamic modelling, design and validation. Note: results from ISO 9043:2008 alone do not constitute a full vehicle-stability evaluation.

Key topics and technical requirements

• Scope and limitations
  • Applies to two-wheeled mopeds and moped/rider combinations.
  • Other methods are acceptable if equivalence can be demonstrated.
  • Measurement output addresses only one aspect of vehicle stability.
• Measurement conditions
  • Moped prepared per manual (fuel, lubricants, tyre pressure), clean and undamaged.
  • Suspension fixed; front wheel aligned with the longitudinal axis.
  • Rider simulated by a 73.4 kg test dummy (49 CFR Part 572 Subpart B) or equivalent human per protocol.
• Instruments and accuracy
  • Precision square level, steel tape, weighing stands (0.1 kg accuracy), stopwatch (0.01 s), rigid lightweight platform, knife edges and balancing weights.
• Measurement procedures
  • Centre of gravity located according to ISO 8705 before inertia tests.
  • Roll and pitch moments: measured by the physical-pendulum (platform + moped) method - small-angle oscillations recorded and converted to inertia values from oscillation period and geometry.
  • Yaw moment: measured by the bifilar-pendulum principle.
  • Multiple runs recommended (e.g., averaging repeated 50-cycle timings) and strict alignment/angle limits (oscillation < ~5°).
• Reporting
  • Test conditions, geometry, masses and averaged periods recorded in the specified format (Annex A).

Applications and users

• Vehicle dynamics engineers using inertia data for modelling and simulation (control systems, handling studies).
• Motorcycle/moped manufacturers validating mass distribution and design changes.
• Independent test laboratories performing standardized inertia measurements for certification or R&D.
• Academic and regulatory researchers studying moped kinetics and rider effects.

Related standards

• ISO 8705 - Mopeds: measurement method for location of centre of gravity (used as a prerequisite).
• 49 CFR Part 572 Subpart B - test dummy specification referenced for rider simulation.
• ISO 3779 referenced for vehicle identification documentation.

Keywords: ISO 9043:2008, mopeds, moments of inertia, measurement method, physical pendulum, bifilar pendulum, centre of gravity, moped/rider combination, vehicle stability.

INTERNATIONAL ISO
STANDARD 9043
Second edition
2008-02-15
Mopeds — Measurement method for
moments of inertia
Cyclomoteurs — Méthode de mesure des moments d'inertie

Reference number
©
ISO 2008
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.

©  ISO 2008
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.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail [e-mail]
Web www.iso.org
Published in Switzerland
ii © ISO 2008 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 Measurement conditions . 2
5 Measuring instruments . 2
6 Measuring procedure . 3
6.1 Measurement of location of centre of gravity.3
6.2 Roll moment of inertia about x-axis (physical pendulum principle) . 3
6.3 Pitch moment of inertia about y-axis (physical pendulum principle) . 7
6.4 Yaw moment of inertia about z-axis (bifilar pendulum principle). 11
7 Test results. 16
Annex A (normative) Format for measurement results. 17

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 9043 was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee SC 23, Mopeds.
This second edition cancels and replaces the first edition (ISO 9043:1991), which has been technically revised.
iv © ISO 2008 – All rights reserved

Introduction
The stability of a moped is a very important element of its active safety. The moped/rider combination and the
environment in which this combination is used form a unique closed-loop system. However, the evaluation of
moped/rider combination stability is extremely complex because of interaction of the intrinsic moped stability,
the influence of the position of the rider and his response to continuously changing conditions.
In the evaluation of moped stability, the determination of the kinetic characteristics of the moped/rider
combination is considered an important part of the design parameters of the vehicle itself.
The test procedure described in this International Standard deals with one aspect of the kinetic characteristics:
the determination of the moments of inertia of the moped and of the moped/rider combination.

INTERNATIONAL STANDARD ISO 9043:2008(E)

Mopeds — Measurement method for moments of inertia
1 Scope
This International Standard specifies a measuring method for determining the moments of inertia of the
moped and of the moped/rider combination. It applies to two-wheeled mopeds.
Other measuring methods can be used if it is demonstrated that the results are equivalent.
Measurement results obtained exclusively by the method described in this International Standard (see
Annex A) cannot be used for an evaluation of vehicle stability because they deal with only one aspect of this
very complex phenomenon.
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 3779, Road vehicles — Vehicle identification number (VIN) — Content and structure
ISO 8705, Mopeds — Measurement method for location of centre of gravity
49 CFR Part 572 Subpart B [Code of Federal Regulations, issued by the National Highway Traffic
Administration (NHTSA)]
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
moped-fixed axis system (x, y, z)
right-hand orthogonal axis system fixed in the moped, such that when the moped is moving in a straight line
on a level road, the x-axis is substantially horizontal, points forwards and is in the longitudinal plane of
symmetry of the moped, the y-axis points to the rider’s left side and the z-axis points upwards
NOTE 1 This coordinate system performs translation motion and rotational motion together with the moped.
NOTE 2 Assuming that the moped is fixed to a platform, the coordinate system is also applied to the platform.
3.2
earth-fixed axis system (X, Y, Z)
right-hand orthogonal axis system fixed on the Earth, such that the X-axis and the Y-axis are in a horizontal
plane and the Z-axis points upwards
4 Measurement conditions
4.1 Measurement conditions for a moped shall be as follows:
a) the moped shall be quite clean and free from mud and deformation, and shall operate normally;
b) the fuel shall be filled up to the top level specified in the operation manual;
c) lubricating oil and cooling water, for water-cooled engines, shall be filled up to the level specified in the
operation manual;
d) tyre pressure shall be as specified in the operation manual;
e) tools shall be provided at the regular storage positions;
f) front and rear suspension systems shall be fixed at a static position;
g) the front wheel shall be positioned along the x-axis.
If the conditions are to be modified depending on the object of measurement, the modified conditions shall be
recorded in the measurement results (see Annex A).
4.2 Measurement conditions when a rider is on the moped shall be as follows:
a) measurement conditions of the moped shall be as specified in 4.1;
b) a test dummy as specified in 49 CFR Part 572 Subpart B (or equivalent), with a mass of 73,4 kg, or an
equivalent human being, shall be used as the rider;
c) the rider shall be positioned as follows:
1) positioned on the vertical centre surface of the moped;
2) sitting on the seat, holding the handle bar by both hands, with both feet placed on the foot rests;
3) with an angle of posture formed by the line connecting the point S (indicating the centre of rotation of
the torso and the arms of the rider) and point H (indicating the centre of rotation of the torso and
femoral regions of the rider) and the x-axis;
4) at a seating position that is the distance between the front axle and the point H along the x-axis.
However, if the conditions are to be modified depending on the object of measurement, the modified
conditions shall be recorded in the measurement results (see Annex A).
5 Measuring instruments
Measuring instruments to measure the moments of inertia shall be as follows or shall have equivalent
functions and accuracy:
a) a precision square level that can measure up to 0,1 mm/1 m (≈20”);
b) a steel tape measure with a tolerance of ± [0,3 + 0,1(L − 1)] mm at the length of L m;
c) weighing stands with enough accuracy to weigh the object up to 0,1 kg;
d) a stop watch that can measure up to 0,01 s, used for measuring the oscillation time;
2 © ISO 2008 – All rights reserved

e) a platform with the highest possible rigidity, and of light weight;
f) a knife edge, where the roundness at the edge shall be below 1 mm in radius, and an edge angle below
90 degrees is recommended;
NOTE The roundness at the edge is the form of the edge finished sharply when rounded with the load.
g) weights, to incline the platform.
6 Measuring procedure
6.1 Measurement of location of centre of gravity
Calculate the mass and location of centre of gravity of the platform, moped, and the platform with the moped
placed on it, in accordance with ISO 8705.
6.2 Roll moment of inertia about x-axis (physical pendulum principle)
6.2.1 Roll moment of inertia about AB-axis for empty platform
Inertia moment about the AB-axis for the empty platform shall be measured in the procedure described below
(see Figure 1).
a) Place the knife edges A and B on the stay so that they can freely oscillate around the AB-axis.
b) Oscillate the platform gently around the AB-axis. It is desirable to keep total oscillating angle below 5°.
c) Make sure that the platform oscillates in a stable way and measure the time required for the platform to
oscillate 50 times by a stop watch. Repeat this process 3 times and obtain the average value of
3 average cycle times. The result shall be the period.
d) Calculate the inertia moment of the platform about the AB-axis, I , expressed in kgm , using
xp
Equation (1):
⎛⎞T
xp
I=+cymg (1)
⎜⎟
xp p p p
⎜⎟
2π
⎝⎠
where
T is the period for the platform to oscillate around the AB-axis, in s;
xp
c is the distance along the z-axis from the knife edge to the centre of gravity of the platform, in m;
p
y is the distance along the y-axis from the knife edge to the centre of gravity of the platform, in m;
p
m is the mass of the platform, in kg;
p
g is acceleration due to gravity (9,81 m/s ).

a)  Side view
b)  Rear view
Key
c distance along the z-axis from the knife edge to the centre of gravity of the platform
p
m mass of platform
p
y distance along the y-axis from the knife edge to the centre of gravity of the platform
p
Figure 1 — Measurement procedure for roll moment of inertia of empty platform
(procedure with physical pendulum principle)
4 © ISO 2008 – All rights reserved

6.2.2 Roll moment of inertia of moped about x-axis
Roll moment of inertia of the moped about the x-axis shall be measured in the procedure described below
(see Figure 2).
NOTE This measurement applies to both the empty moped and the moped with a rider.
a) Place the moped on the platform and fix it so that it cannot move. The lateral inclination angle of the
moped to the platform shall be 0° ± 0,5°.
b) Place the knife edges A and B on the stay so that they can freely oscillate around the AB-axis.
c) Oscillate the moped/platform combination gently around the AB-axis. It is desirable to keep total
oscillating angle below 5°.
d) Make sure that the platform oscillates in a stable way and measure the time required for the platform to
oscillate 50 times by a stop watch. Repeat this process 3 times and obtain the average value of
3 average cycle times. The result shall be the period.
e) Calculate the inertia moment of the moped about the x-axis, I , expressed in kgm , using Equation (2):
xm
T
⎛⎞
xT 22 2 2
Ic=+ymg−I−mc+y (2)
()
xm⎜⎟ T T T xp m m m
2π
⎝⎠
where
T is the period for the platform with the moped on it to oscillate around the AB-axis, in s;
xT
c is the distance along the z-axis from the knife edge to the centre of gravity of the moped/platform
T
combination, in m;
y is the distance along the y-axis from the knife edge to the centre of gravity of the moped/platform
T
combination, in m;
m is the mass of moped/platform combination, in kg;
T
I is the inertia moment of the platform about the AB-axis, in kgm [see Equation (1)];
xp
g is acceleration due to gravity (9,81 m/s );
m is the mass of moped, in kg;
m
c is the distance along the z-axis from the knife edge to the centre of gravity of the moped, in m;
m
y is the distance along the y-axis from the knife edge to the centre of gravity of the moped, in m.
m
a)  Side view
b)  Rear view
Key
c distance along the z-axis from the knife edge to the centre of gravity of the moped
m
c distance along the z-axis from the knife edge to the centre of gravity of the platform
p
c distance along the z-axis from the knife edge to the centre of gravity of the moped/platform combination
T
m mass of moped
m
m mass of platform
p
m mass of moped/platform combination
T
y distance along the y-axis from the knife edge to the centre of gravity of the moped
m
y distance along the y-axis from the knife edge to the centre of gravity of the platform
p
y distance along the y-axis from the knife edge to the centre of gravity of the moped/platform combination
T
Figure 2 — Measurement procedure for roll moment of inertia of the moped
(procedure with physical pendulum principle using a platform)

6 © ISO 2008 – All rights reserved

6.3 Pitch moment of inertia about y-axis (physical pendulum principle)
6.3.1 Pitch moment of inertia about CD-axis for empty platform
Inertia moment about the CD-axis for the empty platform shall be measured in the procedure described below
(see Figure 3).
a) Place the knife edges C and D on the stay so that they can freely oscillate around the CD-axis.
b) Oscillate the platform gently around the CD-axis. It is desirable to keep total oscillating angle below 5°.
c) Make sure that the platform oscillates in a stable way and measure the time required for the platform to
oscillate 50 times by a stop watch. Repeat this process 3 times and obtain the average value of
3 average cycle times. The result shal
...