ISO 8855:2011
(Main)Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary
Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary
ISO 8855:2011 defines the principal terms used for road vehicle dynamics. The terms apply to passenger cars, buses and commercial vehicles with one or more steered axles, and to multi-unit vehicle combinations.
Véhicules routiers — Dynamique des véhicules et tenue de route — Vocabulaire
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 8855
Second edition
2011-12-15
Road vehicles — Vehicle dynamics and
road-holding ability — Vocabulary
Véhicules routiers — Dynamique des véhicules et tenue de route —
Vocabulaire
Reference number
ISO 8855:2011(E)
©
ISO 2011
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ISO 8855:2011(E)
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© ISO 2011
The reproduction of the terms and definitions contained in this International Standard is permitted in teaching manuals, instruction
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Published in Switzerland
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ISO 8855:2011(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Axis system.1
3 Vehicle unit.5
4 Vehicle geometry and masses.6
5 Vehicle motion variables .8
5.1 Linear motion variables .8
5.2 Angular motion variables .10
5.3 Terms relating to vehicle trajectory measures.14
6 Forces and moments .15
6.1 Forces.15
6.2 Moments.16
7 Suspension and steering geometry .16
7.1 Steer and camber angles .16
7.2 Steering-axis geometry.20
8 Kinematics and compliances.23
8.1 Kinematics.23
8.2 Compliances.25
9 Ride and roll stiffness.25
10 Tyres.26
10.1 Tyre geometry.26
10.2 Tyre forces and moments.27
10.3 Terms relating to tyre measures.28
11 Input types and control modes.30
11.1 Input types.30
11.2 Control modes .30
12 Responses.31
12.1 General response types.31
12.2 Equilibrium and stability.31
12.3 Lateral response measures.32
12.4 Understeer and oversteer measures .33
Annex A (informative) Comments on terms and definitions .37
Bibliography.39
Alphabetical index.40
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ISO 8855:2011(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 8855 was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee SC 9, Vehicle
dynamics and road-holding ability.
This second edition cancels and replaces the first edition (ISO 8855:1991), which has been technically
revised. It also incorporates the Addendum ISO 8855:1991/Add.1:1992.
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ISO 8855:2011(E)
Introduction
This International Standard defines terms appertaining to road vehicle dynamics, principally for use by design,
simulation and development engineers in the automotive industries. This second edition has been prepared in
response to a requirement to update the first, and to harmonize its contents with that of the comparable
standard published by SAE International (SAE J670:JAN2008). This revision extends the scope to include
provision for separate tyre and wheel axis systems, inclined and non-uniform road surfaces, tyre forces and
moments, multiple unit commercial vehicles, and two-axle vehicles possessed of four-wheel steer geometry.
The vocabulary contained in this International Standard has been developed from the previous edition, and
SAE J670, in order to facilitate accurate and unambiguous communication of the terms and definitions
employed in the test, analysis and general description of the lateral, longitudinal, vertical and rotational
dynamics of road vehicles.
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INTERNATIONAL STANDARD ISO 8855:2011(E)
Road vehicles — Vehicle dynamics and road-holding ability —
Vocabulary
1 Scope
This International Standard defines the principal terms used for road vehicle dynamics. The terms apply to
passenger cars, buses and commercial vehicles with one or more steered axles, and to multi-unit vehicle
combinations.
2 Axis system
2.1
reference frame
geometric environment in which all points remain fixed with respect to each other at all times
2.2
inertial reference frame
Newtonian reference frame
reference frame (2.1) that is assumed to have zero linear and angular acceleration and zero angular velocity
NOTE In Newtonian physics, the Earth is assumed to be an inertial reference frame.
2.3
axis system
set of three orthogonal directions associated with X, Y and Z axes
GGG
NOTE A right-handed axis system is assumed throughout this International Standard, where: Z=×XY .
2.4
coordinate system
numbering convention used to assign a unique ordered trio (x, y, z) of values to each point in a reference
frame (2.1), and which consists of an axis system (2.3) plus an origin point
2.5
ground plane
horizontal plane in the inertial reference frame (2.2), normal to the gravitational vector
2.6
road surface
surface supporting the tyre and providing friction necessary to generate shear forces in the road plane (2.7)
NOTE The surface may be flat, curved, undulated or of other shape.
2.7
road plane
plane representing the road surface (2.6) within the tyre contact patch
NOTE 1 For an uneven road, a different road plane may exist at each tyre contact patch.
NOTE 2 For a planar road surface, the road plane is coincident with the road surface. For road surfaces with surface
contours having a wavelength similar to or less than the size of the tyre contact patch, as in the case of many ride events,
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ISO 8855:2011(E)
it is intended that an equivalent road plane be determined. Determination of the equivalent road plane is dependent on the
requirements of the analysis being performed. The equivalent road plane may not be coincident with the actual road
surface at the contact centre (4.1.4).
2.7.1
road plane elevation angle
λ
angle from the normal projection of the X axis on to the ground plane (2.5) to the X axis
T T
2.7.2
road plane camber angle
η
angle from the normal projection of the Y axis on to the ground plane (2.5) to the Y axis
T T
2.8
earth-fixed axis system
(X , Y , Z )
E E E
axis system (2.3) fixed in the inertial reference frame (2.2), in which the X and Y axes are parallel to the
E E
ground plane (2.5), and the Z axis points upward and is aligned with the gravitational vector
E
NOTE The orientation of the X and Y axes is arbitrary and is intended to be based on the needs of the analysis or test.
E E
2.9
earth-fixed coordinate system
(x , y , z )
E E E
coordinate system (2.4) based on the earth-fixed axis system (2.8) with an origin that is fixed in the
ground plane (2.5)
NOTE The location of the origin is generally an arbitrary point defined by the user.
2.10
vehicle axis system
(X , Y , Z )
V V V
axis system (2.3) fixed in the reference frame (2.1) of the vehicle sprung mass (4.12), so that the X axis is
V
substantially horizontal and forwards (with the vehicle at rest), and is parallel to the vehicle's longitudinal plane
of symmetry, and the Y axis is perpendicular to the vehicle's longitudinal plane of symmetry and points to the
V
left with the Z axis pointing upward
V
See Figure 1.
NOTE 1 For multi-unit combinations a separate vehicle axis system may be defined for each vehicle unit (3.1)
(see Figure 2).
NOTE 2 The symbolic notation (X , Y , Z ), (X , Y , Z ), …, (X , Y , Z ) may be assigned to the vehicle
V,1 V,1 V,1 V,2 V,2 V,2 V,n V,n V,n
axis systems of a multi-unit combination with n vehicle units (3.1).
2.11
vehicle coordinate system
(x , y , z )
V V V
coordinate system (2.4) based on the vehicle axis system (2.10) with the origin located at the vehicle
reference point (2.12)
2.12
vehicle reference point
point fixed in the vehicle sprung mass (4.12)
NOTE The vehicle reference point may be defined in a variety of locations, based on the needs of the analysis or test.
Commonly used locations include the total vehicle centre of gravity, the sprung mass centre of gravity, the mid-wheelbase
(4.2) point at the height of the centre of gravity, and the centre of the front axle. For multi-unit combinations, a vehicle
reference point may be defined for each vehicle unit (3.1).
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ISO 8855:2011(E)
2.13
intermediate axis system
(X, Y, Z)
axis system (2.3) whose X and Y axes are parallel to the ground plane (2.5), with the X axis aligned with the
vertical projection of the X axis on to the ground plane (2.5)
V
See Figure 1.
NOTE 1 For multi-unit combinations, a separate intermediate axis system may be defined for each vehicle unit (3.1).
NOTE 2 The intermediate axis system is used to facilitate the definition of angular orientation terms and the
components of force, moment, and motion vectors. An intermediate coordinate system is not defined herein.
Key
1 vehicle reference point
2 ground plane
Figure 1 — Vehicle and intermediate axis systems
Figure 2 — Multi-unit axis systems
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ISO 8855:2011(E)
2.14
tyre axis system
(X , Y , Z )
T T T
axis system (2.3) whose X and Y axes are parallel to the local road plane (2.7), with the Z axis normal to
T T T
the local road plane, where the orientation of the X axis is defined by the intersection of the wheel plane
T
(4.1) and the road plane, and the positive Z axis points upward
T
NOTE A local tyre axis system may be defined at each wheel (see Figure 3).
2.15
tyre coordinate system
(x , y , z )
T T T
coordinate system (2.4) based on the tyre axis system (2.14) with the origin fixed at the contact centre
(4.1.4)
2.16
wheel axis system
(X , Y , Z )
W W W
axis system (2.3) whose X and Z axes are parallel to the wheel plane (4.1), whose Y axis is parallel to
W W W
the wheel-spin axis (4.1.1), and whose X axis is parallel to the local road plane (2.7), and where the
W
positive Z axis points upward
W
NOTE A local wheel axis system may be defined for each wheel (see Figure 3).
Key
1 wheel plane
2 road plane
3 wheel-spin axis
Figure 3 — Tyre and wheel axis system
2.17
wheel coordinate system
(x , y , z )
W W W
coordinate system (2.4) based on the wheel axis system (2.16) with the origin fixed at the wheel centre
(4.1.2)
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ISO 8855:2011(E)
2.18
cab axis system
(X , Y , Z )
C C C
axis system (2.3) fixed in the reference frame (2.1) of the cab sprung mass, so that the X axis is
C
substantially horizontal and forwards (with the vehicle at rest), and is parallel to the vehicle’s longitudinal plane
of symmetry, and where the Y axis is perpendicular to the cab’s longitudinal plane of symmetry and points to
C
the left with the Z axis pointing upward
C
NOTE A cab axis system applies only to vehicles with a suspended cab only.
2.19
cab coordinate system
(x , y , z )
C C C
coordinate system (2.4) based on the cab axis system (2.18) with the origin fixed at an arbitrary point
defined by the user
3 Vehicle unit
3.1
vehicle unit
rigid (i.e. non-articulating) vehicle element operating alone or in combination with one or more other rigid
elements joined at yaw-articulation joints
NOTE Tractor, semi trailer (3.2.2) and dolly (3.2.4) are examples of vehicle units. A drawbar trailer (3.2) may consist
of more than one vehicle unit.
3.2
trailer
vehicle unit (3.1) or combination of multiple vehicle units that is towed by another vehicle unit and can be
disconnected from its towing vehicle unit
NOTE A trailer may have a single axle or multiple axles positioned along its length.
3.2.1
full trailer
trailer (3.2) that has both front and rear running gear and, hence, provides fully its own vertical support
3.2.2
semi trailer
trailer (3.2) that has only rear running gear and hence depends on its towing vehicle unit (3.1) for a
substantial part of its vertical support
NOTE A semi trailer is typically coupled to the towing vehicle unit using a fifth-wheel coupling (3.2.6).
3.2.3
centre-axle trailer
trailer (3.2) with only rear running gear located only slightly aft of the nominal position of the centre of gravity
of the unit
NOTE A centre-axle trailer is typically coupled to the towing unit with a hitch coupling (3.2.7).
3.2.4
dolly
portion of a full trailer (3.2.1) that includes the steerable front running gear and tow bar
3.2.5
converter dolly
dolly (3.2.4) unit that couples to a semi trailer (3.2.2) with a fifth-wheel coupling (3.2.6) and thereby
“converts” the semi trailer to a full trailer (3.2.1)
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ISO 8855:2011(E)
3.2.6
fifth-wheel coupling
device used to connect a semi trailer (3.2.2) to its towing vehicle unit (3.1) that is designed to bear the very
substantial vertical load imposed by the front of the semi trailer
NOTE A fifth-wheel coupling provides rotational degrees of freedom in the Y and Z directions, but transmits moments
V V
about the X axis (all axes are in the towing vehicle unit).
V
3.2.7
hitch coupling
device used to connect a trailer (3.2) or converter dolly (3.2.5) tow bar to its towing vehicle unit (3.1), which
approximates a spherical joint by providing three rotational degrees of freedom within the normal operating
range
NOTE Typical examples of hitch couplings include ball hitches and pintle hitches.
4 Vehicle geometry and masses
4.1
wheel plane
plane normal to the wheel-spin axis (4.1.1), which is located halfway between the rim flanges
4.1.1
wheel-spin axis
axis of wheel rotation
NOTE This axis is coincident with the Y axis.
W
4.1.2
wheel centre
point at which the wheel-spin axis (4.1.1) intersects the wheel plane (4.1)
NOTE This point is the origin of the wheel coordinate system (2.17).
4.1.3
contact line
intersection of the wheel plane (4.1) and the road plane (2.7)
4.1.4
contact centre
intersection of the contact line (4.1.3) and the normal projection of the wheel-spin axis (4.1.1) on to the road
plane (2.7)
NOTE This point is the origin of the tyre coordinate system (2.15). The contact centre may not be the geometric centre
of the tyre contact patch (4.1.5) due to distortion of the tyre produced by external forces.
4.1.5
contact patch
footprint
portion of the tyre touching the road surface (2.6)
4.2
wheelbase
l
distance between the contact centres (4.1.4) on the same side of the vehicle, measured parallel to the X
axis, with the vehicle at rest on a horizontal surface, with zero steer angle (7.1.1)
NOTE 1 A vehicle may have a different wheelbase on the left and right sides by design. It is common practice to
average the left and right wheelbases; however, the difference may need to be taken into account in performing some
analyses. The wheelbase typically changes as the suspension trim height changes.
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ISO 8855:2011(E)
NOTE 2 This applies to two-axle vehicles only. ISO 21308-2:2006, 6.1, defines the “configuration wheelbase”, for
multi-axle vehicles, as the distance between the centre of the first front axle to the centre of the first driven rear axle. This
term is a dimensional description and is not used in dynamic analysis.
4.3
equivalent wheelbase
l
eq
wheelbase (4.2) of a conventional two-axle vehicle (i.e. a vehicle with one steering front axle and one non-
steering rear axle) which, given similar front and rear cornering compliance properties, would exhibit the same
steady state (12.2.1) turning behaviour as is exhibited by the multi-axle vehicle
Key
1 turn centre
Figure 4 — Equivalent wheelbase
4.4
track
b
distance between the contact centres (4.1.4), on a single wheel axle, measured parallel to the Y axis, with
the vehicle at rest on a horizontal surface
NOTE For dual wheel axles, it is the distance between the points centrally located between the contact centres of the
inner and outer dual wheels.
4.5
articulation point
instant centre of rotation of two vehicle units (3.1) established by the mechanical coupling device joining
those two units, typically on the plane of symmetry of both units
NOTE 1 An articulation point may establish one, two, or three degrees of rotational freedom between the two coupled
units.
NOTE 2 For semi trailers (3.2.2), the longitudinal (X) coordinate of the articulation point is equal to the fifth-wheel
position (4.9). For full trailers (3.2.1), the longitudinal (X) coordinate of the articulation point is equal to the hitch
position (4.10). For vehicle combinations with more than one trailer (3.2), several articulation points may exist.
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ISO 8855:2011(E)
4.6
axle distance
average longitudinal distance between the contact centres (4.1.4), on two consecutive axles, measured
parallel to the X axis, with the vehicle at rest on a horizontal surface, at zero steer angle (7.1.1)
4.7
axle position
average longitudinal distance between the vehicle reference point (2.12) and the contact centres (4.1.4) of
the axle, measured parallel to the X axis, with the vehicle combination at rest on a horizontal surface at zero
steer angle (7.1.1)
4.8
trailer-axle position
average longitudinal distance between the contact centres (4.1.4) of the trailer (3.2) axle and the vertical
projection of the articulation point (4.5) (of the first trailer) on to the ground plane (2.5), with the vehicle
combination at rest on a horizontal surface in a straight-ahead condition
NOTE Trailers may consist of more than one axle and/or articulation points.
4.9
fifth-wheel position
kingpin position
average longitudinal distance between the contact centres (4.1.4) of the first driven rear axle of the towing
vehicle unit (3.1) and the projection of the articulation point (4.5) on to the ground plane (2.5), with the
vehicle combination at rest on a horizontal surface in a straight-ahead condition
NOTE Applicable to semi trailers (3.2.2) only.
4.10
hitch position
average longitudinal distance between the contact centres (4.1.4) of the first driven rear axle of the towing
vehicle unit (3.1) and the projection of the articulation point (4.5) on to the ground plane (2.5), with the
vehicle combination at rest on a horizontal surface in a straight-ahead condition
NOTE Applicable to full trailers (3.2.1) only.
4.11
unsprung mass
mass that is not carried by the suspension, but is supported directly by the tyres
4.12
sprung mass
mass that is supported by the suspension, i.e. the total vehicle mass less the unsprung mass (4.11)
NOTE It is common practice to allocate a portion of the mass of the suspension linkage, driveshafts and springs in the
sprung mass and the remainder in the unsprung mass.
5 Vehicle motion variables
5.1 Linear motion variables
For the definitions in this subclause, velocity and acceleration are relative to the earth-fixed axis system
(2.8) (X , Y , Z ). They are resolved into components in the intermediate axis system (2.13) (X, Y, Z).
E E E
NOTE It is also possible to resolve velocity and acceleration vectors into components in other axis systems (2.3). For
example, velocity and acceleration vectors may be resolved in the vehicle axis system (2.10) (X , Y , Z ) to produce v ,
V V V Xv
v , v and a , a , a .
Yv Zv Xv Yv Zv
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ISO 8855:2011(E)
5.1.1
vehicle velocity
G
v
vector quantity expressing the velocity of the vehicle reference point (2.12)
5.1.2
longitudinal velocity
G
v
X
component of the vehicle velocity (5.1.1) in the direction of the X axis
5.1.3
lateral velocity
G
v
Y
component of the vehicle velocity (5.1.1) in the direction of the Y axis
5.1.4
vertical velocity
G
v
Z
component of the vehicle velocity (5.1.1) in the direction of the Z axis
5.1.5
horizontal velocity
G
v
h
resultant of the longitudinal velocity (5.1.2) and the lateral velocity (5.1.3)
5.1.6
tyre trajectory velocity
G
T
v
vector quantity expressing the velocity of the contact centre (4.1.4)
5.1.7
tyre longitudinal velocity
G
v
XT
component of the tyre trajectory velocity (5.1.6) in the X direction
T
5.1.8
tyre lateral velocity
G
v
YT
component of the tyre trajectory velocity (5.1.6) in the Y direction
T
5.1.9
tyre vertical velocity
G
v
ZT
component of the tyre trajectory velocity (5.1.6) in the Z direction
T
5.1.10
vehicle acceleration
G
a
vector quantity expressing the acceleration of the vehicle reference point (2.12)
5.1.11
longitudinal acceleration
G
a
X
component of the vehicle acceleration (5.1.10) in the direction of the X axis
5.1.12
lateral acceleration
G
a
Y
component of the vehicle acceleration (5.1.10) in the direction of the Y axis
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ISO 8855:2011(E)
5.1.13
vertical acceleration
G
a
Z
component of the vehicle acceleration (5.1.10) in the direction of the Z axis
5.1.14
tangential acceleration
G
a
t
component of the vehicle acceleration (5.1.10) in the direction of the horizontal velocity (5.1.5)
5.1.15
centripetal acceleration
G
a
c
component of the vehicle acceleration (5.1.10) in the direction of the horizontal normal to the horizontal
velocity (5.1.5)
5.1.16
horizontal acceleration
G
a
h
resultant of the longitudinal acceleration (5.1.11) and the lateral acceleration (5.1.12), or the resultant of
the tangential acceleration (5.1.14) and the centripal acceleration (5.1.15)
5.2 Angular motion variables
For the definitions in this subclause, the sign of angles resulting from angular rotations is determined in
accordance with the right-hand rule and angular velocities and accelerations are relative to the earth-fixed
axis system (2.8) (X , Y , Z ); they are resolved into components in the intermediate axis system (2.13) (X,
E E E
Y, Z).
NOTE It is also possible to resolve angular velocity and acceleration vectors into components in other axis systems
(2.3). For example, angular velocity and acceleration vectors may be resolved in the vehicle axis system (2.10) (X , Y ,
V V
Z ) to produce ω , ω , ω and
ωω,,ω .
V Xv Yv Zv XYVV ZV
5.2.1
yaw angle
ψ
angle from the X axis to the X axis, about the Z axis
E E
5.2.2
pitch angle
θ
angle from the X axis to the X axis, about the Y axis
V
NOTE The pitch angle is not measured relative to the road surface (2.6), thus a vehicle at rest on an inclined road
surface has a non-zero pitch angle.
5.2.3
roll angle
ϕ
angle from the Y axis to the Y axis, about the X axis
V V
NOTE These three angles; ψ, θ, ϕ are called the Vehicle Euler Angles. They define the orientation of the vehicle axis
system (2.10) (X , Y , Z ) with respect to the earth-fixed axis system (2.8) (X , Y , Z ), as a sequence of consecutive
V V V E E E
angular rotations as defined in Table 1.
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ISO 8855:2011(E)
Table 1 — Euler rotations
Angle produced
Rotation order Rotation nature
by rotation
X axis to the X axis
E
First rotation Yaw, ψ
about the Z axis
E
X axis to the X axis
V
Second rotation Pitch, θ
about the Y axis
Y axis to the Y axis
V
Third rotation Roll, ϕ
about the X axis
V
5.2.4
vehicle roll angle
ϕ
V
angle from the Y axis to the Y axis, about the X axis
V
NOTE This angle is different from ro
...
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