Moped and moped-rider kinematics -- Vocabulary

1.1 This International Standard defines terms, symbols and conventions related to moped and moped-rider motions and kinematics and to the modelling thereof. 1.2 It does not deal with methods of measurement, nor with the units used in reporting the results, nor with accuracy. 1.3 The definitions in this International Standard apply to two-wheeled mopeds as defined in ISO 3833. 1.4 This International Standard does not cover road mopeds which are controlled by a pedestrian or which are used for the carriage of goods to the exclusion of persons.

Cinématique relative au cyclomoteur et à son conducteur -- Vocabulaire

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Status
Published
Publication Date
16-Dec-1998
Current Stage
9020 - International Standard under periodical review
Start Date
15-Oct-2020
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INTERNATIONAL ISO
STANDARD 14722
First edition
1998-12-15
Moped and moped-rider kinematics —
Vocabulary
Cinématique relative au cyclomoteur et à son conducteur — Vocabulaire
A Reference number
ISO 14722:1998(E)
---------------------- Page: 1 ----------------------
ISO 14722:1998(E)
Contents Page

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

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

3 Steering system .......................................................................................................................................................1

3.1 Axis and angles of the steering assembly .........................................................................................................1

3.2 Dynamic quantities of the steering assembly....................................................................................................2

3.3 Steering characteristics of the steering assembly............................................................................................3

4 Suspension system .................................................................................................................................................3

4.1 Suspension geometry ..........................................................................................................................................3

4.2 Suspension dynamic rates ..................................................................................................................................4

5 Tyres and wheels.....................................................................................................................................................5

5.1 Tyre axis system and variables...........................................................................................................................5

5.2 Forces applied to tyres and their coefficients ...................................................................................................6

5.3 Moments applied to tyres ....................................................................................................................................8

5.4 Phenomena related with tyres.............................................................................................................................8

6 Basic principles of axis systems and kinematics ................................................................................................8

6.1 Axis systems.........................................................................................................................................................8

6.2 Horizontal axis systems.......................................................................................................................................9

6.3 Component and assembly axis systems............................................................................................................9

6.4 Ground contact axes ............................................................................................................................................9

6.5 Moped masses and weight distribution ...........................................................................................................11

© ISO 1998

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 the publisher.

International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet iso@iso.ch
Printed in Switzerland
---------------------- Page: 2 ----------------------
ISO ISO 14722:1998(E)

6.6 Moments of inertia.............................................................................................................................................. 11

6.7 Motion variables ................................................................................................................................................. 11

6.8 Forces .................................................................................................................................................................. 15

6.9 Moments .............................................................................................................................................................. 15

7 Directional dynamics............................................................................................................................................. 16

7.1 Controls ............................................................................................................................................................... 16

7.2 Control modes .................................................................................................................................................... 16

7.3 Moped response ................................................................................................................................................. 17

7.4 Steer properties .................................................................................................................................................. 18

7.5 Stability................................................................................................................................................................ 19

8 Moped motion characteristics.............................................................................................................................. 19

9 Aerodynamic characteristics of the moped-rider combination ........................................................................ 21

9.1 Winds ................................................................................................................................................................... 21

9.2 Aerodynamic variables ...................................................................................................................................... 21

9.3 Aerodynamic forces, moments and coefficients............................................................................................. 22

10 Riding postures and behaviours........................................................................................................................ 23

11 Tests ..................................................................................................................................................................... 24

11.1 Constant environment influence..................................................................................................................... 24

11.2 Changeable environment influence................................................................................................................ 25

11.3 Other tests......................................................................................................................................................... 26

Bibliography.............................................................................................................................................................. 31

iii
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ISO 14722:1998(E) ISO
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 3.

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.

International Standard ISO 14722 was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee

SC 23, Mopeds.
---------------------- Page: 4 ----------------------
INTERNATIONAL STANDARD ISO ISO 14722:1998(E)
Moped and moped-rider kinematics — Vocabulary
1 Scope

1.1 This International Standard defines terms, symbols and conventions related to moped and moped-rider

motions and kinematics and to the modelling thereof.

1.2 It does not deal with methods of measurement, nor with the units used in reporting the results, nor with

accuracy.

1.3 The definitions in this International Standard apply to two-wheeled mopeds as defined in ISO 3833.

1.4 This International Standard does not cover road mopeds which are controlled by a pedestrian or which are

used for the carriage of goods to the exclusion of persons.
2 Normative references

The following normative documents contain provisions which, through reference in this text, constitute provisions of

this International Standard. For dated references, subsequent amendments to, or revisions of, any of these

publications do not apply. However, parties to agreements based on this International Standard are encouraged to

investigate the possibility of applying the most recent editions of the normative documents indicated below. For

undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC

maintain registers of currently valid International Standards.
ISO 3833:1977, Road vehicles — Types — Terms and definitions.

ISO 6725:1981, Road vehicles — Dimensions of two-wheeled mopeds and motorcycles — Terms and definitions.

3 Steering system
3.1 Axis and angles of the steering assembly
3.1.1
steer axis

rotational axis of the steering assembly for steering control which coincides with the axis of the steering stem and

with the axis of the steering head pipe
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ISO
ISO 14722:1998(E)
3.1.2
steer angle

angle of motion of the steering assembly about the steer axis (3.1.1) which is zero when the front wheel plane is

parallel to the moped longitudinal plane
3.1.3
wheel steer angle

angle formed by the intersection with the road surface plane of the moped longitudinal plane and the front wheel

plane
3.2 Dynamic quantities of the steering assembly
3.2.1
steering velocity
angular velocity of the sprung part of the steering assembly about the z -axis
3.2.2
steering velocity of the handlebars
angular velocity of the handlebars about the z -axis
3.2.3
steer torque
torque about the (3.1.1)
steer axis
3.2.4
steer force

value obtained from dividing the steer torque (3.2.3) and the effective rotational radius of the steering handle

NOTE The effective rotational radius of the steering handle is the distance between the steer axis (3.1.1) and the centre

point of the steering handlegrip projected on the plane perpendicular to the steer axis.

3.2.5
steady state steer torque

torque applied to the steering handle in order to maintain the motion of the moped-rider combination in a given state

NOTE When the moped-rider combination is turning, this torque is classified as positive steer torque (3.2.5.1), neutral

steer torque (3.2.5.2) or negative steer torque (3.2.5.3).
3.2.5.1
positive steer torque

steady state steer torque (3.2.5) applied in the direction equal to that in which the moped-rider combination is

turning
3.2.5.2
neutral steer torque

amount of steady state steer torque (3.2.5) equal to zero, required when the moped-rider combination is turning

3.2.5.3
negative steer torque

steady state steer torque (3.2.5) applied in the direction opposite to that in which the moped-rider combination is

turning
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ISO
ISO 14722:1998(E)
3.2.6
steady state steer force

value obtained from dividing the steady state steer torque (3.2.5) and the effective rotational radius of the steering

handle
3.2.7
stiffness of the steering assembly

resistance against the deformation caused by the loads applied to the steering assembly

NOTE There are torsional and bending stiffnesses.
3.2.8
friction torque of the steering assembly

torque about the steer axis (3.1.1) required to initiate the motion of the steering assembly which does not include

the friction between the tyre and the road surface
3.2.9
damping torque of the steering assembly

damping torque about the steer axis (3.1.1) at a certain steering velocity (3.2.1) which does not include the

damping between the tyre and the road surface
3.2.10
moment of inertia of the steering assembly

moment of inertia of the steering assembly about the steering axis (3.1.1) under defined load conditions

3.3 Steering characteristics of the steering assembly
3.3.1
steering under stationary conditions
steering operation of the moped-rider combination under stationary conditions
3.3.2
counter steering

positive action on the steering handle in order to compensate (cancel out) the change in the state of the moped

3.3.3
disturbed steer

very short and quick rotation of the steering handle caused by an outside disturbance

3.3.4
loss of control in steering
uncontrollable rotation of the steering handle caused by a disturbance
4 Suspension system
4.1 Suspension geometry
4.1.1
wheel plane
centre plane of the wheel which is perpendicular to the wheel spin axis
4.1.2
wheel centre
intersection of the wheel spin axis and the wheel plane (4.1.1)
4.1.3
front and rear wheel alignment

position of the front and the rear wheel planes relative to some reference frame planes

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ISO
ISO 14722:1998(E)
4.1.4
steering system alignment
relation between the wheel(s) and the body or the road surface

NOTE This term is often applied to the fork off-set (4.1.8), castor (4.1.7), castor angle (4.1.6).

4.1.5
alignment variation

displacements and deformations of the suspension system caused by forces applied to the wheels

4.1.6
castor angle
See ISO 6725:1981, 6.12.
4.1.7
castor
See ISO 6725:1981, 6.11.
4.1.8
fork off-set
distance between the steering shaft centreline and the front wheel spin axis
4.1.9
vertical wheel travel

vertical distance between the wheel spin axis position when the suspension is fully stretched and when it is fully

compressed according to the manufacturer's indication
4.1.10
spring and/or damper stroke

displacement between the spring and/or damper unit positions when fully stretched and when fully compressed

according to the manufacturer's indication
4.2 Suspension dynamic rates
4.2.1
suspension rate

increase of ground contacting load necessary to approximate the wheel spin axis and the sprung mass projected on

the vertical line passing through the wheel centre by the unit distance under the designated load

4.2.2
ride rate

increase of ground contacting load necessary to approximate the road plane and the sprung mass projected on the

vertical line passing through the wheel centre by the unit distance under the designated load

4.2.3
link ratio of spring and/or damper

ratio of the vertical wheel travel (4.1.9) and the spring and/or damper stroke (4.1.10)

NOTE 1 The link ratio can be more or less than 1, depending on the location and the way of geometrical linking of the spring

and/or damper in relation to the position of the wheel axis.
NOTE 2 The link ratio can be a function of the wheel travel.
4.2.4
damping characteristics

relation between the damping force occurring at the damper unit and the damper piston speed

NOTE The sign is positive when the damper is compressed; it is negative when the damper is stretched.

---------------------- Page: 8 ----------------------
ISO
ISO 14722:1998(E)
5 Tyres and wheels
See Figure 1.
5.1 Tyre axis system and variables
5.1.1
conventional centre of tyre contact

intersection of the wheel plane and the vertical projection of the spin axis of the wheel onto the road plane

5.1.2
geometrical centre of tyre contact
geometrical centre of the contact area between the tyre and the road plane
5.1.3
effective centre of tyre contact
centre of pressures in the contact area of the tyre and the road plane

NOTE 1 When the wheel is cambered, the effective centre of tyre contact can be displaced in the direction of the camber.

NOTE 2 The effective centre of tyre contact may not be the geometrical centre of tyre contact (5.1.2) area due to

distortion of the tyre produced by applied forces.
5.1.4
camber angle
angle between the vertical and the wheel plane
5.1.5
tyre slip angle

angle between the x -axis and the direction of wheel travel in the conventional centre of tyre contact (5.1.1)

See Figure 2.
5.1.6
slip ratio
Ædrivingæ
uucos α −
tx tc
S =
5.1.7
slip ratio
Æbrakingæ
uucos α −
tx tc
S =
u cos α
where
u is the forward velocity of the conventional centre of the wheel;

u is the peripheral velocity of the conventional centre of tyre contact (5.1.1) in reference to the centre of

the wheel;
a is the tyre slip angle (5.1.5).
---------------------- Page: 9 ----------------------
ISO
ISO 14722:1998(E)
5.2 Forces applied to tyres and their coefficients
5.2.1
tyre vertical load
z -component of the force applied from the road plane to the tyre
5.2.2
tyre lateral force
y -component of the force applied from the road plane to the tyre
5.2.3
tyre longitudinal force
x -component of the force applied from the road plane to the tyre
5.2.4
tyre vertical stiffness

variation in the vertical load required to shift the distance between the conventional centre of tyre contact (5.1.1)

and the wheel centre (4.1.2) in the vertical direction by the length, when the camber angle (5.1.4) is zero

5.2.5
tyre lateral stiffness

variation in the tyre lateral force (5.2.2) required to vary the wheel centre (4.1.2) in the y -direction by the length

relative to the supporting surface, when the camber angle (5.1.4) is zero and a specified tyre vertical load (5.2.1)

is applied
5.2.6
driving force

positive tyre longitudinal force (5.2.3) caused by application of driving torque in the x -direction

5.2.7
braking force

negative tyre longitudinal force (5.2.3) caused by application of braking torque in the y -direction

5.2.8
conicity force

tyre lateral force (5.2.2) which changes sign [with respect the horizontal tyre axis system (6.2.2)] with a change

in direction of rotation when the tyre slip angle (5.1.5) and the camber angle (5.1.4) are zero

5.2.9
plysteer force

tyre lateral force (5.2.2) which does not change sign [with respect to the horizontal tyre axis system (6.2.2)] with

a change in direction of rotation when the tyre slip angle (5.1.5) and the camber angle (5.1.4) are zero

5.2.10
camber force
camber thrust

tyre lateral force (5.2.2) applied to the tyre having some camber angle (5.1.4) when the tyre slip angle (5.1.5) is

zero and the plysteer force (5.2.9) and conicity force (5.2.8) have been subtracted

5.2.11
cornering force

horizontal component, in the direction perpendicular to the direction of wheel travel, of the force applied from the

road plane to the wheel having some tyre slip angle (5.1.5) when the camber angle (5.1.4) is zero

See Figure 2.
---------------------- Page: 10 ----------------------
ISO
ISO 14722:1998(E)
5.2.12
tyre side force

tyre lateral force (5.2.2) when the camber angle (5.1.4) is zero and the plysteer force (5.2.9) and conicity force

(5.2.8) have been subtracted
See Figure 2.
5.2.13
tractive force

component of the tyre force vector in the direction of wheel travel of the effective centre of tyre contact (5.1.3), is

equal to the tyre lateral force (5.2.2) times the sine of the tyre slip angle (5.1.5) plus the tyre longitudinal force

(5.2.3) times the cosine of the tyre slip angle (5.1.5)
5.2.14
drag force
negative tractive force (5.2.13)
See Figure 2.
5.2.15
rolling resistance

force opposite to the direction of wheel heading mainly resulting from deformation of a rolling tyre

5.2.16
rolling resistance coefficient
ratio between the rolling resistance and the tyre vertical load (5.2.1)
5.2.17
camber stiffness

rate of change of tyre lateral force (5.2.2) with respect to the change in camber angle (5.1.4), usually evaluated at

zero camber angle and at zero tyre slip angle (5.1.5)
5.2.18
camber stiffness coefficient

ratio of camber stiffness (5.2.17) of a free straight-rolling tyre to the tyre vertical load (5.2.1)

5.2.19
cornering stiffness

rate of change of tyre lateral force (5.2.2) with respect to the change in tyre slip angle (5.1.5), usually evaluated

at zero tyre slip angle and at zero camber angle (5.1.4)
5.2.20
cornering stiffness coefficient

ratio of cornering stiffness (5.2.19) of a free straight-rolling tyre to the tyre vertical load (5.2.1)

5.2.21
pneumatic trail

horizontal distance between the point of action of the tyre side force (5.2.12) and the conventional centre of tyre

contact (5.1.1)

NOTE This is a way of defining the aligning torque relative to the tyre side force (5.2.12).

5.2.22
tyre lag

delay that occurs in the change of the tyre lateral force (5.2.2) resulting from a change in tyre slip angle (5.1.5) or

camber angle (5.1.4)
---------------------- Page: 11 ----------------------
ISO
ISO 14722:1998(E)
5.2.23
relaxation length
distance covered during the (5.2.22)
tyre lag

NOTE Normally, the relaxation length is defined as the distance rolled by the tyre until a value of 63,2 % of the normal

value of tyre lateral force (5.2.2) is obtained when the tyre slip angle (5.1.5) and/or the camber angle (5.1.4) change(s) in

steps from zero.
5.3 Moments applied to tyres
5.3.1
overturning moment
component about x -axis of moments applied from the road plane to the tyres
5.3.2
rolling resistance moment

component of the tyre moment vector about the y -axis resulting from the rolling resistance (5.2.15)

5.3.3
camber torque

component about the z -axis of moments applied from the road plane to the wheel having some camber angle

(5.1.4) when the tyre slip angle (5.1.5) is zero
5.3.4
aligning torque
component of the tyre moment vector tending to rotate the tyre about the z -axis
5.4 Phenomena related with tyres
5.4.1
standing wave

phenomenon that occurs when the tyre peripheral speed exceeds a given peripheral velocity while it is rotating at a

high speed

NOTE Deformations caused by the tyre contact tend to remain without recovery even after the deformed portions of the

tyre have left the road surface, which results in steady standing waves on the tyre surface.

6 Basic principles of axis systems and kinematics
6.1 Axis systems
See Figure 3.
6.1.1
earth-fixed axis system
(X, Y, Z)

right-hand orthogonal axis system fixed on the earth, in which the X- and Y-axis are in a horizontal plane and the Z-

axis is directed upwards

NOTE The trajectory of the moped is described with respect to this earth fixed axis system.

6.1.2
moped axis system
(x', y', z')

right-hand orthogonal axis system which has its origin at the centre of gravity of 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

parallel to the moped longitudinal plane, the y'-axis points to the rider's left and the z'-axis points upwards

NOTE The moped-rider combination axis system (x' , y' , z' ) replaces the moped axis system in every corresponding

res res res

definition when considering the moped-rider combination instead of the moped only.

---------------------- Page: 12 ----------------------
ISO
ISO 14722:1998(E)
6.2 Horizontal axis systems
6.2.1
horizontal moped axis system
(x, y, z)

right-hand orthogonal axis system which has its origin at the centre of gravity of the moped and moves together with

the moped body such that the x-y plane is always parallel to the X-Y plane of the earth-fixed axis system (6.1.1);

the x-axis is the projection of the x'-axis of the moped axis system (6.1.2) on the x-y plane and points forwards and

the z-axis is parallel to the Z-axis of the earth-fixed axis system and points upwards

6.2.2
horizontal tyre axis system
(x , y , z )
t t t

right-hand orthogonal axis system which has its origin at the conventional centre of tyre contact (5.1.1); the x -

axis is the intersection of the wheel plane (4.1.1) and the road plane with a positive direction forward, the z -axis is

perpendicular to the road plane with a positive direction upward and the y -axis is in the road plane

NOTE In order to differentiate between front and rear horizontal tyre axis systems, the indices “f” and “r” are used.

6.3 Component and assembly axis systems

The following component and assembly axis systems are right-hand orthogonal axis systems which have an origin

at the centre of gravity of the component or the assembly.
6.3.1
steering assembly axis system
(x' , y' , z' )
fu fu fu

axis system of the steering assembly in which the z' -axis is parallel to the steering head pipe axis and points

upwards and the x' -axis points forwards and is parallel to the wheel plane (4.1.1)

6.3.2
frame fixed axis system
(x , y , z )
ru ru ru
horizontal axis system of the frame without the steering assembly
6.3.3
steering assembly sprung part fixed axis system
(x' , y' , z' )
f f f

assembly axis system which applies to the sprung part of the steering assembly and is parallel to the steering

assembly axis system (6.3.1) and has axes pointing in the same directions
6.3.4
frame sprung part fixed axis system
(x , y , z )
r r r

horizontal assembly axis system which applies to the sprung part of the frame without the steering assembly

6.3.5
moped longitudinal plane

plane that passes through the steering head pipe axis and that is parallel to the rear wheel plane

6.4 Ground contact axes
6.4.1
conventional ground contact axis
(x )

axis through both conventional centres of tyre contact (5.1.1) of the front and rear tyres; the direction of this axis

is positive in the forward direction of the moped
---------------------- Page: 13 ----------------------
ISO
ISO 14722:1998(E)
6.4.2
geometrical ground contact axis
(x )

axis through both geometrical centres of tyre contact (5.1.2) of the front and rear tyres; the direction of the axes

is positive in the forward direction of the moped
6.4.3
effective ground contact axis
(x )

axis through both effective centres of tyre contact (5.1.3) of the front and rear tyres; the direction of the axis is

positive in the forward direction of the moped
6.4.4
angular orientation of the moped

orientation of the moped axis system (6.1.2) with respect to the earth-fixed axis system (6.1.1) which is given by

the following sequence of three angular rotations starting from a condition in which the two sets of axes are initially

aligned:
 yaw rotation, Y, about the aligned z'- and Z-axis;
 pitch rotation, q, about the moped y'-axis;
 roll rotation, F, about the moped x'-axis.

NOTE 1 Roll rotations can also be considered about axes x , x and x . The respective angles will then be F , F and

go gg ge go gg
F .

NOTE 2 Angular rotations are positive if clockwise when looking in the positive direction of the axis about which the rotation

occurs.
6.4.5
rolling
banking

angular rotation of the moped or of the moped-rider combination about the x'-axis or x' -axis respectively

res

NOTE Rolling can also be considered about the axes x , x and x , as defined in 6.4.5.1, 6.4.5.2 and 6.4.5.3.

go gg ge
6.4.5.1
conventional rolling
rolling (6.4.5) about the x -axis
6.4.5.2
geometrical rolling
rolling (6.4.5) about the x -axis
6.4.5.3
effective rolling
rolling (6.4.5) about the x -axis
6.4.6
pitching

angular rotation of the moped or of the moped-rider combination about the y'-axis or y' -axis respectively

res
6.4.7
yawing

angular rotation of the moped or of the moped-rider combination about the z'-axis or z' -axis respectively

res
---------------------- Page: 14 ----------------------
ISO
ISO 14722:1998(E)
6.5 Moped masses and weight distribution
6.5.1
moped mass
mass of the moped under a given loading condition
NOTE Some particular conditions of moped mass are defined in ISO 6726.
6.5.2
sprung mass
mass corresponding to the load supported by the suspension

NOTE In cases where some of the masses of the propeller shaft, roller chain, suspension system, steering system, braking

system, etc., constitute the sprung mass, such masses should be added to the corresponding masses according to the

structure of the moped.
6.5.3
unsprung mass
mass which corresponds to the difference between moped mass and sprung mass
6.5.4
weight distribution ratio

percentage of weight distributed to each axle under well-defined loading conditions

6.6 Moments of inertia
6.6.1
moment of inertia

sum of the products of the elements of mass and the squares of their distances from an axis

NOTE This axis may be the axis that passes through the centre of gravity of the moped, the assembly or the component.

EXAMPLE Moments of inertia about the axes of the moped axis system (6.1.2) are indicated by I , I or I .

x'x' y'y' z'z'
6.6.2
product of inertia
sum of the products of the elements of mass and their distances from two axes

NOTE The two axes should be clearly stipulated and indices used to indicate which axes are relevant.

EXAMPLE Product of inertia about x'-axis and z'-axis is indicated by I .
z'x'
6.7 Motion variables
6.7.1
pitch angle
angle formed between the x -axis and the X-Y pla
...

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