ISO 10392:2011

INTERNATIONAL ISO
STANDARD 10392
Second edition
2011-03-15
Road vehicles — Determination of centre
of gravity
Véhicules routiers — Détermination du centre de gravité

Reference number
©
ISO 2011
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©  ISO 2011
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ii © ISO 2011 – All rights reserved

Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Test conditions and preliminary measurements .1
4.1 Operating and other liquids .1
4.2 Preliminary measurements .1
5 Determination of coordinates in horizontal plane .2
5.1 Location of CG longitudinally .2
5.2 Location of CG laterally .2
6 Determination of CG height: Axle lift method .2
6.1 Loading conditions, suspensions and mechanical parts .2
6.2 Measuring procedure.3
6.3 Accuracy of determined parameters.4
6.4 Determination of axle load and lifting angle.4
6.5 Location of CG above ground.4
6.6 Data presentation .5
7 Determination of CG height: Stable pendulum method .5
7.1 General .5
7.2 Loading conditions, vehicle restraints, and mechanical parts.6
7.3 Measuring procedure.6
7.4 Accuracy of determined parameters.7
7.5 Determination of platform properties.7
7.6 Determination of applied torque .7
7.7 Consideration of platform deflection .8
7.8 Location of CG above ground.8
7.9 Data presentation .8
Annex A (informative) Example of test report — Axle lift method.9
Annex B (informative) Example of test report — Stable pendulum method.11
Bibliography.13

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 10392 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 10392:1992). Clause 7 has been added.
iv © ISO 2011 – All rights reserved

Introduction
Two methods for determining the height of the centre of gravity above the ground are presented. The first
method, the axle lift method, was the only method contained in ISO 10392:1992. The second method, a stable
pendulum method, was added to this second edition of ISO 10392. The model, assumptions, and
measurements used for the stable pendulum method have many analogies to the unstable pendulum method
(often referred to as the tilt table method). Clause 7 includes a brief discussion of the unstable pendulum
method for determining vehicle centre of gravity (CG) height. Other procedures such as vertical balance
methods and vehicle hang methods are also used.

INTERNATIONAL STANDARD ISO 10392:2011(E)

Road vehicles — Determination of centre of gravity
1 Scope
This International Standard specifies methods for determining the location of the centre of gravity (CG) of a
road vehicle, as defined in ISO 3833. A method for determining the coordinates of the CG in the horizontal
plane is provided. Two methods for determining the height of the CG above the ground are specified.
The axle lift and the stable pendulum methods are the most common methods for determining vehicle CG
height. The axle lift method requires less dedicated equipment and is typically an easier and less expensive
method than the stable pendulum method. The axle lift method can generally provide CG height accuracy in
the range of a few percent, while the stable pendulum method can provide accuracy in the range of 0,5 %.
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 612, Road vehicles — Dimensions of motor vehicles and towed vehicles — Terms and definitions
ISO 3833, Road vehicles — Types — Terms and definitions
ISO 8855, Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 612, ISO 3833 and ISO 8855 apply.
4 Test conditions and preliminary measurements
4.1 Operating and other liquids
The fuel tank shall be completely full. Fuel motion within an unfilled fuel tank can have an adverse effect on
the test results. If the displacement of other liquids (operating and other) due to the inclination of the vehicle
during testing is considered significant, this shall be taken into account.
4.2 Preliminary measurements
With the vehicle horizontal, and in accordance with the dimensions given in ISO 612 and ISO 8855, measure
and record:
l , the wheelbase, left, in millimetres;
left
l , the wheelbase, right, in millimetres;
right
b , the track, front, in millimetres;
f
b , the track, rear, in millimetres;
r
m , the wheel load, front left, in kilograms;
m , the wheel load, front right, in kilograms;
m , the wheel load, rear left, in kilograms;
m , the wheel load, rear right, in kilograms.
5 Determination of coordinates in horizontal plane
5.1 Location of CG longitudinally
The horizontal distance between centre of front axle and CG, x , in millimetres, is determined by the
CG
equation:
m
r
x =× l (1)
CG
m
v
where
m = m + m (as defined in 4.2) (2)
r 3 4
is rear axle load, in kilograms;
m = m + m + m + m (as defined in 4.2) (3)
v 1 2 3 4
is total mass of vehicle, in kilograms;
l = 0,5 (l + l ) (as defined in 4.2) (4)
left right
is wheelbase of the vehicle, in millimetres.
5.2 Location of CG laterally
The horizontal distance between the longitudinal median plane of the vehicle and the CG (positive to the left),
y , in millimetres, is determined by the equation:
CG
bm()−+m b(m−m)
f1 2 r 3 4
y = (5)
CG
2m
v
where all symbols are as defined in 4.2.
6 Determination of CG height: Axle lift method
6.1 Loading conditions, suspensions and mechanical parts
Any load shall be held in place to avoid displacement due to the inclination of the vehicle.
After loading the vehicle to the desired loading conditions, the wheel suspension can be blocked if necessary,
to avoid changes in deflection due to the inclination of the vehicle. This may also apply to other vehicle
components that could affect the test result due to flexible mounting.
2 © ISO 2011 – All rights reserved

When lifting the vehicle, the gear-box shall be in neutral. The parking-brake shall be released; rolling of the
wheels of one axle only shall be avoided by wedges or other means. The front wheels shall remain pointing
straight ahead as far as possible.
6.2 Measuring procedure
6.2.1 With the vehicle horizontal, measure and record the static radii:
r , the static loaded radius, front left, in millimetres;
stat,1
r , the static loaded radius, front right, in millimetres;
stat,2
r , the static loaded radius, rear left, in millimetres;
stat,3
r , the static loaded radius, rear right, in millimetres.
stat,4
The static loaded radius may be determined as shown in Figure 1. The formula is sufficiently accurate for the
test procedure described in this International Standard.

′
rd= −d / 2
stat
ww
Key
d wheel diameter
w
d ′ loaded wheel diameter
w
r static loaded radius
stat
Figure 1 — Determination of static loaded radius, r
stat
6.2.2 Lift one axle in steps (three or more steps are recommended). Record the axle load of the other axle
and the lifting angle for each position. The maximum lifting angle and the accuracy of the scale used to
measure axle load affect the accuracy of the computation of the CG height.
6.2.3 To take the hysteresis into account, lower the lifted axle by steps back to the level position and record
axle loads and lifting angle as described in 6.2.2.
6.2.4 Plot the axle loads against the tangent of the corresponding lifting angles and determine the mean
value of axle load for a corresponding lifting angle. The plot can also be useful for checking the linearity of the
measurements. An alternative to generating the plot is to compute the individual CG heights using the
individual load and angle measurements, using the equations provided in 6.5, and then averaging these
values to get a final answer.
6.2.5 It is recommended that all the measurements be repeated lifting the other axle.
6.2.6 It may also be desirable to determine the lifting angle from the wheelbase and the elevation of the
wheels above the ground for each inclination position. In this case the change in tyre deformation caused by
lifting one end of the vehicle shall be taken into consideration.
6.3 Accuracy of determined parameters
The following accuracies are required:
⎯ absolute axle load value: ±0,2 %;
⎯ change in axle loads
due to lifting: ±2,5 %;
NOTE Applies to scales which do not measure absolute loads, but changes in loads.
⎯ dimensions: < 2,000 mm: ±1 mm;
> 2,000 mm: ±0,05 %;
⎯ angles: ±0,5 %.
6.4 Determination of axle load and lifting angle
The following values are obtained from the plotted data by linear curve fitting:
⎯ m′ and m′ which are axle loads at front and rear respectively of the axle remaining on the ground while
f r
the vehicle is inclined;
⎯ θ which is the corresponding lifting angle.
6.5 Location of CG above ground
The height of the CG above ground, z , in millimetres, is determined by the equations:
CG
′
lm()−m
ff
zr=+ (6)
CG stat,f
m × tanθ
v
or
lm()′−m
rr
zr=+ (7)
CG stat,r
m × tanθ
v
where
m = m + m (as defined in 4.2) (8)
f 1 2
is front axle load, in kilograms;
m = m + m (as defined in 4.2) (9)
r 3 4
is rear axle load, in kilograms;
r = 0,5(r + r) (10)
stat,f stat,1 stat,2
is static loaded radius, front, in millimetres;
r = 0,5(r + r) (11)
stat,r stat,2 stat,3
is static loaded radius, rear, in millimetres;
l and m are as defined in 5.1.
v
NOTE m and m may be measured directly if only the height of the CG is required, in which case m , m , m and m
f r 1 2 3 4
are not needed.
4 © ISO 2011 – All rights reserved

6.6 Data presentation
Measured data and test results shall be presented in a test report as shown in Annex A.
7 Determination of CG height: Stable pendulum method
7.1 General
This section contains a detailed description of the stable pendulum method for determining vehicle CG height.
Figure 2 is a diagram of the stable pendulum method for determining vehicle CG height. For the stable
pendulum method, the CG of the combined vehicle and vehicle support platform system are below the pivot
axis. This diagram shows the stable pendulum method in a pitch configuration, with a lateral pivot axis parallel
to the road plane. The stable pendulum method can also be configured in a roll configuration, with a
longitudinal pivot axis parallel to the road plane. The equations provided in this clause are derived from a
static torque balance about the pivot axis. In this case, a static disturbance torque is applied to the system by
hanging known masses at a known distance from the pivot axis.
A similar model and formulation of equilibrium equations can be used for the unstable pendulum method,
except that the pivot axis is below the CG of the combined vehicle and vehic
...