ISO 8608:2016

INTERNATIONAL ISO
STANDARD 8608
Second edition
2016-11-01
Mechanical vibration — Road surface
profiles — Reporting of measured data
Vibrations mécaniques — Profils de routes — Méthode de
présentation des résultats de mesures
Reference number
©
ISO 2016
© ISO 2016, Published in Switzerland
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ii © ISO 2016 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 Uniform method of reporting. 3
5.1 One-track data . 3
5.1.1 Description of the road profile. 3
5.1.2 Presentation of the smoothed power spectral density . 4
5.2 Multiple-track data . 7
5.3 Report . 7
5.3.1 General. 7
5.3.2 One-track data curve sheet . 7
5.3.3 Multiple-track data curve sheet . 8
5.3.4 Parameters of analysis . 8
5.3.5 Test conditions. 9
Annex A (informative) Example of a report .11
Annex B (informative) Road profile characterization and PSD fitting .17
Annex C (informative) General guidance for use of the statistical road profile description.20
Annex D (informative) Considerations for PSD processing and precision .30
Bibliography .36
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
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committee has been established has the right to be represented on that committee. International
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ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
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constitute an endorsement.
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as well as information about ISO’s adherence to the World Trade Organization (WTO) principles in the
Technical Barriers to Trade (TBT) see the following URL: www.iso.org/iso/foreword.html.
The committee responsible for this document is ISO/TC 108, Mechanical vibration, shock and condition
monitoring, Subcommittee SC 2, Measurement and evaluation of mechanical vibration and shock as applied
to machines, vehicles and structures.
This second edition cancels and replaces the first edition (ISO 8608:1995), of which it constitutes a
minor revision. The following changes have been made:
— normative references have been updated;
— subclause numbering has been adjusted;
— figures have been made language independent;
— bibliography has been updated;
— editorially revised.
iv © ISO 2016 – All rights reserved

Introduction
The purpose of this document is to facilitate the compilation and comparison of measured vertical road
profile data from various sources. It therefore specifies a uniform method of reporting data from one-
track and multiple-track measurements.
It specifies how measurements are to be reported, but not how the measurements are to be made. The
measuring equipment can influence the results of the measurement; therefore certain characteristics
of the measuring system have also to be reported.
Annex A is an example of a report which meets the minimum requirements of this document.
Annex B gives means of approximately characterizing specific road profiles in order to facilitate the
division of road profiles into general classifications. A general classification is also given. A curve fitting
method is presented for characterizing spectral data.
Annex C provides general guidance for the use of road profile statistical data for simulation studies and
for related studies such as evaluation of comfort, suspensions and road profiles.
Annex D discusses the processing of the power spectral density (PSD) with the fast Fourier transform
(FFT) technique. A discussion on the statistical precision is also given.
INTERNATIONAL STANDARD ISO 8608:2016(E)
Mechanical vibration — Road surface profiles — Reporting
of measured data
1 Scope
This document specifies a uniform method of reporting measured vertical road profile data for either
one-track or multiple-track measurements.
It applies to the reporting of measured vertical profile data taken on roads, streets and highways, and
on off-road terrain. It does not apply to rail-track data. Measurement and processing equipment and
methods are not included.
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.
IEC 61260-1, Electroacoustics — Octave-band and fractional-octave-band filters — Part 1: Specifications
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 2041 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
3.1
spatial frequency
reciprocal of the wavelength
Note 1 to entry: The spatial frequency is expressed in cycles per metre (cycles/m).
3.2
power spectral density
PSD
limiting mean-square value of a signal per unit frequency bandwidth
Note 1 to entry: For a one-sided spectrum, the area located between the graphic plot and the horizontal axis in a
linear plot should be equal to the variance σ of the original signal for the evaluated frequency range. This leads
to a doubling of the spectral amplitude when the calculation process is only estimating the spectrum for positive
frequencies.
3.3
displacement PSD
power spectral density of the vertical road profile displacement
3.4
velocity PSD
power spectral density of the rate of change of the vertical road profile displacement per unit distance
travelled (slope of the vertical road profile)
3.5
acceleration PSD
power spectral density of the rate of change of the slope of the vertical road profile per unit distance
travelled
3.6
decolouring
procedure to eliminate the influence of the transfer function of the measuring system on the power
spectral density
Note 1 to entry: The raw power spectral density should be decoloured before any further processing by dividing
it by the square of the modulus of the measuring equipment transfer function.
3.7
smoothing
averaging process in which a data block is shifted and averaged
Note 1 to entry: In this document, “unsmoothed PSD” means the power spectral density as calculated from the
measured data, i.e. with the bandwidths used in or following from the calculations and which are different from
those indicated in Table 2. The term “smoothed PSD” is the power spectral density which is obtained after using
the averaging process described in 5.1.2.
4 Symbols
The symbols used in this document are given in Table 1.
Table 1 — Symbols
Symbol Description Unit
B Frequency resolution cycles/m
e
f Time frequency Hz
G (.) Displacement PSD m
d
G (.) Velocity PSD m
v
–1
G (.) Acceleration PSD m
a
G (.) PSD of track 1 —
G (.) PSD of track 2 —
G (.) Cross spectrum between tracks 1 and 2 —
l Wheelbase m
n Spatial frequency cycles/m
t Time s
v Vehicle speed m/s
γ Coherence function —
σ Variance
ω Angular frequency (= 2πf ) rad/s
Ω Angular spatial frequency (= 2πn) rad/m
NOTE   The indication (.) means that the parameter of the function can be spatial
frequency (n) or angular spatial frequency (Ω).
2 © ISO 2016 – All rights reserved

5 Uniform method of reporting
5.1 One-track data
5.1.1 Description of the road profile
5.1.1.1 General
The road profile shall be described by one or both of the following methods, with preference for the
first, the displacement PSD.
The reporting of the non-smoothed data is always required.
5.1.1.2 First method — Displacement PSD: G (.)
d
The road profile shall be described by the power spectral density (PSD) of its vertical displacement.
The report shall include the displacement PSD versus (angular) spatial frequency, both on logarithmic
axes. The dimensions are metres cubed (m ) versus reciprocal metres (cycles/m and rad/m).
Two scales shall be given on the ordinate, one for G (n) and one for G (Ω). Both n and Ω scales shall be
d d
indicated in the abscissa. The grid, however, shall only be drawn for G (n) and n (see Figure A.2, for
d
example).
5.1.1.3 Second method — Acceleration PSD: G (.)
a
The acceleration power spectral density (PSD) is an allowed alternative method of reporting data.
In this case, the road profile shall be described as the PSD of its acceleration in terms of the rate of
change of the slope of the road surface per unit distance travelled. The dimension of the acceleration
–1
PSD is reciprocal metres (m ).
The scales shall be logarithmic on both axes. Two scales shall be given on the ordinate, one for G (n) and
a
one for G (Ω). On the abscissa, both n and Ω shall be indicated. The grid, however, shall only be drawn
a
for G (n) and n.
a
5.1.1.4 Relationship between the two reporting methods
The relationship between the two reporting methods (see 5.1.1.2 and 5.1.1.3) is given by Formulae (1)
and (2):
G (n) = (2πn) · G (n) (1)
a d
G (Ω) = Ω · G (Ω) (2)
a d
5.1.1.5 Spatial frequency range
The reported PSD shall be restricted between the limits allowed by the measuring equipment. For the
report, the user may select any spatial frequency range appropriate to his/her particular road surface,
problem and product.
The measured surface depends on the measuring equipment, which has a certain smoothing effect.
This equipment is to be reported (see Note 4 and 5.3.5.2.1).
NOTE 1 Figure C.1 gives the relationship between the vehicle speed, the spatial frequency and the time
frequency. Knowledge of the frequency and speed characteristics for a given class of vehicles makes it possible to
choose the useful limits for that class of vehicle (e.g. on-road or off-road vehicles).
NOTE 2 For the lower limit, the spatial frequency need not in general be measured lower than 0,01 cycles/m
for on-road vehicles and 0,05 cycles/m for off-road vehicles.
NOTE 3 The enveloping effect of the tyre acts as a low-pass filter for the road vibration input to the vehicle.
This effect depends on the size and construction of the tyre. For general on-road measurements, this results in
a recommended upper limit of 10 cycles/m. Of course for suspension vibration purposes, the interesting upper
limit depends on the maximum allowed speed on the particular road. For noise purposes, the interesting upper
limit may be much higher, and may go as high as 1 000 cycles/m.
NOTE 4 Due to the tyre width there is also an enveloping effect in the lateral direction. This means that for
vibration purposes, the mean of the footprint is usually measured. The width depends on the problem (e.g.
vibration, noise) and the product (e.g. motorcycle tyres, truck tyres). For general on-road measurements not
intended for a specific product, a track of about 100 mm wide is often used for vibration purposes. For noise
purposes, a point measurement is often used.
NOTE 5 For off-road measurements, care needs to be taken when interpreting the high frequencies. For soft
(e.g. sandy) surfaces, short undulations could be flattened by the wheel load and filtered out. For hard (e.g. stone)
surfaces, however, only the enveloping effect of the tyre acts as a filter. In this situation, the surface needs to be
described accurately in the data sheet (see 5.3.5.3.2).
NOTE 6 Annex B gives recommended methods for the characterization of the road profile and for the fitting of
the measured data.
5.1.2 Presentation of the smoothed power spectral density
When the power spectral densities are calculated with a constant bandwidth method, their
representation in a log-log diagram give an appearance or visual impression at high frequencies which
over-emphasizes the fluctuations of the PSD generated by the real power distribution and by the
statistical noise.
For this reason, the PSD shall also be represented in a smoothed form, i.e. by the mean PSD in the
following frequency bands:
— octave bands from the lowest calculated frequency (except zero) up to a centre frequency of
0,031 2 cycles/m (0,196 3 rad/m);
— one-third-octave bands from the last octave band up to a centre frequency of 0,25 cycles/m
(1,570 8 rad/m);
— for the rest of the frequency range, one-twelfth-octave bands up to the highest calculated frequency.
The centre frequencies to be used for the calculation of the smoothed PSD are given in Table 2.
Table 2 — Centre frequencies and cut-off frequencies for PSD smoothing,
expressed in spatial frequency n
Lower cut-off Upper cut-off
Centre frequency
Exponent frequency frequency
EXP
n = 2
c
EXP n n
l h
cycles/m
cycles/m cycles/m
Octave bands
–9 0,001 4 0,002 0 0,002 8
–8 0,002 8 0,003 9 0,005 5
–7 0,005 5 0,007 8 0,011 0
–6 0,011 0 0,015 6 0,022 1
–5 0,022 1 0,031 2 0,044 2
4 © ISO 2016 – All rights reserved

Table 2 (continued)
Lower cut-off Upper cut-off
Centre frequency
Exponent frequency frequency
EXP
n = 2
c
EXP n n
l h
cycles/m
cycles/m cycles/m
One-third-octave bands
–4,333 0,044 2 0,049 6 0,055 7
–4 0,055 7 0,062 5 0,070 2
–3,667 0,070 2 0,078 7 0,088 4
–3,333 0,088 4 0,099 2 0,111 4
–3 0,111 4 0,125 0 0,140 3
–2,667 0,140 3 0,157 5 0,176 8
–2,333 0,176 8 0,198 4 0,222 7
–2 0,222 7 0,250 0 0,280 6
One-twelfth-octave bands
–1,833 0,272 6 0,280 6 0,288 8
–1,750 0,288 8 0,297 3 0,306 0
–1,667 0,306 0 0,315 0 0,324 2
–1,583 0,324 2 0,333 7 0,343 5
–1,500 0,343 5 0,353 6 0,363 9
–1,417 0,363 9 0,374 6 0,385 6
–1,333 0,385 6 0,396 9 0,408 5
–1,250 0,408 5 0,420 4 0,432 8
–1,167 0,432 8 0,445 4 0,458 5
–1,083 0,458 5 0,471 9 0,485 8
–1 0,485 8 0,5 0,514 7
–0,917 0,514 7 0,529 7 0,545 3
–0,833 0,545 3 0,561 2 0,577 7
–0,750 0,577 7 0,594 6 0,612 0
–0,667 0,612 0 0,630 0 0,648 4
–0,583 0,648 4 0,667 4 0,687 0
–0,500 0,687 0 0,707 1 0,727 8
–0,417 0,727 8 0,749 2 0,771 1
–0,333 0,771 1 0,793 7 0,817 0
–0,250 0,817 0 0,840 9 0,865 5
–0,167 0,865 5 0,890 9 0,917 0
–0,083 0,917 0 0,943 9 0,971 5
0 0,971 5 1 1,029 3
0,083 1,029 3 1,059 5 1,090 5
0,167 1,090 5 1,122 5 1,155 4
0,250 1,155 4 1,189 2 1,224 1
0,333 1,224 1 1,259 9 1,296 8
0,417 1,296 8 1,334 8 1,374 0
0,500 1,374 0 1,414 2 1,455 7
0,583 1,455 7 1,498 3 1,542 2
0,667 1,542 2 1,587 4 1,633 9
Table 2 (continued)
Lower cut-off Upper cut-off
Centre frequency
Exponent frequency frequency
EXP
n = 2
c
EXP n n
l h
cycles/m
cycles/m cycles/m
0,750 1,633 9 1,681 8 1,731 1
0,833 1,731 1 1,781 8 1,834 0
0,917 1,834 0 1,887 7 1,943 1
1 1,943 1 2 2,058 6
1,083 2,058 6 2,118 9 2,181 0
1,167 2,181 0 2,244 9 2,310 7
1,250 2,310 7 2,378 4 2,448 1
1,333 2,448 1 2,519 8 2,593 7
1,417 2,593 7 2,669 7 2,747 9
1,500 2,747 9 2,828 4 2,911 3
1,583 2,911 3 2,996 6 3,084 4
1,667 3,084 4 3,174 8 3,267 8
1,750 3,267 8 3,363 6 3,462 1
1,833 3,462 1 3,563 6 3,668 0
1,917 3,668 0 3,775 5 3,886 1
2 3,886 1 4 4,117 2
2,083 4,117 2 4,237 9 4,362 0
2,167 4,362 0 4,489 8 4,621 4
2,250 4,621 4 4,756 8 4,896 2
2,333 4,896 2 5,039 7 5,187 4
2,417 5,187 4 5,339 4 5,495 8
2,500 5,495 8 5,656 9 5,822 6
2,583 5,822 6 5,993 2 6,168 8
2,667 6,168 8 6,349 6 6,535 7
2,750 6,535 7 6,727 2 6,924 3
2,833 6,924 3 7,127 2 7,336 0
2,917 7,336 0 7,551 0 7,772 3
3 7,772 3 8 8,234 4
NOTE A small overlap exists between the lowest one-twelfth-octave band and
the highest one-third-octave band. This overlap maintains the values 0,5; 1; 2; 4 as
centre frequencies in the one-twelfth-octave bands. This makes it convenient to
calculate the road characterization (see B.4) immediately from the one-twelfth-
octave band smoothing.
6 © ISO 2016 – All rights reserved

The mean PSD in a defined band should be calculated as given by Formula (3):
n −1
H
   
nB+05,(⋅−ni)(Gn + Gj ⋅+Bn iin),−−05 ⋅BG n
() () () () ()
   
Le lL eh He H
∑
   
jn=+1
L
Gi() = (3)
s
ni()−ni()
hl
where
G (i ) is the smoothed PSD in smoothing band i;
s
 
ni()


h


n =+INT 05, (n : see Table 2);
 h

H


 B 
 
e
 
ni()


l


n =+INT 05,
 (n : see Table 2).
l

L 

B 

 
e
The other symbols are as defined in Table 1. INT is the integer function.
The first and the third terms of the right hand side of Formula (3), respectively, calculate the parts of
the original n and n in the calculated smoothing band i.
L H
If this scheme cannot be followed, due to the calculations, the differences shall be noted in the report.
The same rules shall be followed when the smoothing is to be done in angular spatial frequency.
The same rules shall be followed for analogue computation.
A small and easy supplementary calculation following the processing of the smoothed PSD leads to the
characterization of the road profile as described in Annex B.
5.2 Multiple-track data
The multiple-track road profile data shall be described as the PSD curves of each track as described in
5.1, and their relationship curves expressed as their coherence function [see Formula (4)].
G (.)
γ = (4)
GG(.)(⋅ .)
When more than two tracks are measured, the most travelled track near the edge of the road shall be
taken as the reference track for the calculation of coherence functions.
The curve shall be smoothed as described in 5.1.2.
5.3 Report
5.3.1 General
The report shall contain one or more curve sheets and general information.
5.3.2 One-track data curve sheet
The curve sheet for one-track data shall contain the non-smoothed PSD and the smoothed PSD. When
the information is given on one sheet, the separate curves should be carefully differentiated.
The PSD curve sheet shall also include the information given in 5.3.4.1.3, 5.3.4.1.4, 5.3.4.1.5, 5.3.5.3.1
and 5.3.5.3.2.
It is also recommended to indicate on the data sheet the road profile characterization described in
Annex B, i.e. the general and octave-band characterization of the road and the fitted PSD (see Figures A.3
and A.5 for examples).
5.3.3 Multiple-track data curve sheet
For multiple-track data, the sheets of each PSD shall be reported as described in 5.3.2, together with
a similar curve sheet for their coherence function. This sheet shall contain the smoothed coherence
curve. The track width shall be indicated on this sheet.
When the information is given on one sheet, the separate curves should be carefully differentiated.
5.3.4 Parameters of analysis
5.3.4.1 For all forms of spatial analysis, the following information shall be reported.
5.3.4.1.1 The analysis method used, analogue or digital.
5.3.4.1.2 Pre-processing filters shall be reported in terms of cut-off spatial frequency, slope (dB/octave)
and type of filter (e.g. Butterworth). In the case of the digital analysis, this includes the anti-aliasing filter.
5.3.4.1.3 The resolution bandwidth: in the case of a relative constant bandwidth analysis, it is sufficient
to state the proportion octave bandwidth only.
5.3.4.1.4 The real distance travelled of the data, in metres, analysed and reported.
In order to quantify wavelengths of 100 m with a statistical precision of 60 % at a spatial frequency
resolution of 0,01 cycles/m, the distance travelled shall be at least 1 000 m.
In some cases, it may be impossible or perhaps of no interest to reach this limit, e.g. for short roads or for
the study of special forms of surfaces. In this case, a remark in the report is required. For a discussion of
statistical precision, see Annex D.
5.3.4.1.5 The statistical precision of spectral estimates of the data: in the case of a relative constant
bandwidth analysis, the statistical precision of the narrowest bandwidth shall be reported. The statistical
precision shall be stated as ± % value, calculated for a 95 % confidence level (i.e. the statistical precision
shall be stated as 1,96 times the normalized standard error) on the basis of random error.
5.3.4.2 For analogue spectral analyses, the following information shall be reported, in addition to that
specified in 5.3.4.1.
5.3.4.2.1 The class of bandwidth filters in accordance with IEC 61260-1.
5.3.4.2.2 The slopes (dB/octave) and type of constant bandwidth filter.
5.3.4.3 For digital spectral analyses, the following information shall be reported, in addition to that
specified in 5.3.4.1.
5.3.4.3.1 The specific method used (such as fast Fourier transform, mean lagged product, continuous
digital filter).
5.3.4.3.2 The sampling spatial frequency.
5.3.4.3.3 The sampling window function and correction factor used.
8 © ISO 2016 – All rights reserved

5.3.4.3.4 The reported resolution bandwidth, if it is different from the analysis bandwidth (e.g. when
frequency smoothing is used).
5.3.5 Test conditions
5.3.5.1 The date of the measurement shall be reported.
5.3.5.2 The instrumentation used shall be reported as follows.
5.3.5.2.1 Short description of the measuring system.
a) Mechanical design.
b) Scanning device
— in the case of a contacting device (e.g. a wheel): description of the design (e.g. a soft wheel),
mass, tyre pressure, tyre dimensions, effective diameter, nominal test load and dimensions of
the contact area under nominal test load;
— in the case of a non-contacting device (e.g. a radar system): resolution, dimensions of the
effective measured area, etc.
c) The capability of the equipment to take into account slope bias and transverse slope effects over
long distances and long wavelengths.
5.3.5.2.2 A flowchart showing transducers, telemetry, recorder, filters, etc.
5.3.5.2.3 The instrumentation and calibration chain of the measuring system should be carefully
reported. Details of the design, the guaranteed transfer function and the accuracy should be given, either
in the report or in a source reference.
5.3.5.2.4 The cut-off frequencies of any filter used in conjunction with the recording of the data.
5.3.5.3 The road or terrain description shall be reported as follows.
5.3.5.3.1 Definition of the road: country, road number, location, village, direction and, if possible,
a small map. Also, traffic density [annual average daily traffic (AADT), when possible], typical vehicle
speed and other relevant descriptive information shall be reported.
5.3.5.3.2 The road profile shall be reported with respect to at least the type of surface (concrete
pavement, compacted soil, cobblestone, etc.) and the surface condition (new pavement, rutted road,
poorly maintained, etc.), the grade (longitudinal slope), the cross-fall (lateral slope) and the curve radius
(if any). In the case of off-road measurements, the cone penetration resistance of the soil should be
reported together with a reference or a description of the measurement method used (see ISO 22476-1,
ISO 22476-3 and Reference [18]).
5.3.5.3.3 Definition of the measured track: distance from the measured track to the near side of the
road. A sketch of the road, with indication of the tracks reserved for bicycles, parking and traffic is
recommended. All unusual facts should be indicated.
5.3.5.3.4 A photograph of the road shall be included. It shall be taken from a height of 1,4 m
(approximately the height of the eyes of the driver of a passenger car). The photograph shall also show a
two-dimensional scale indication and the position of the measured tracks.
5.3.5.3.5 If two- or multiple-track data are given, they shall be described as in 5.3.5.3.3. The distance
between the tracks shall also be given.
10 © ISO 2016 – All rights reserved

Annex A
(informative)
Example of a report
A.1 General
This annex contains fictitious data arranged to form an example for two-track reporting which meets
the minimum requirements of this document. However, the measuring system description and the
photograph are omitted.
The parts of Figure A.3 and Figure A.5 placed in a double frame are the recommended characterizations
of the road profile described in Annex B. They are not required, but recommended.
The format of the data sheets is not standardized.
NOTE The numbers in parentheses refer to the subclauses in this document.
A.2 Parameters of analysis
Analysis (5.3.4.1.1, 5.3.4.3.1): FFT
anti-aliasing filter (5.3.4.1.2): 48 dB/octave
Butterworth: 0,5 cycles/m low-pass
Sampling spatial frequency (5.3.4.3.2): 1,4 cycles/m
Sampling window function (5.3.4.3.3): Hanning
Correction factor (PSD) (5.3.4.3.3): 1,63
A.3 Test conditions
1)
Measuring system (5.3.5.2.1, 5.3.5.2.3, 5.3.5.2.4): .
Flow chart (5.3.5.2.2), see Figure A.1.
Figure A.1 — Flow chart of the measuring system
1) Detailed description or reference given.
A.4 Road description
Road definition (5.3.5.3.1), see Figure A.2:
traffic: AADT, 4 200 vehicles/day
typical vehicle speed: 90 km/h
Road profile (5.3.5.3.2):
concrete pavement, 10 years old
grade: 0 %
slope: 0,06 %
no curve
2)
Photograph (5.3.5.3.4): .
A.5 Road characterization
See Figures A.2 to A.5.
General and octave characterizations for Figures A.3 and A.5 are given in Table A.1.
Table A.1 — General and octave characterizations
Figure A.3 Figure A.5
Centre frequency n r.m.s. displacement G (n ) r.m.s. displacement G (n )
c d c d c
−6 3 −6 3
cycles/m m 10 m m 10 m
0,007 8 0,020 5 76 157,20 0,021 3 81 768,91
0,015 6 0,023 2 48 894,71 0,020 2 36 987,61
0,031 2 0,016 7 12 599,47 0,012 6 7 164,66
0,062 5 0,011 3 2 895,00 0,013 0 3 827,58
0,125 0,007 7 673,55 0,008 5 819,90
0,25 0,005 5 172,26 0,004 3 106,68
0,5 0,003 4 32,12 0,003 1 26,45
1 0,001 8 4,42 0,001 7 4,21
2 0,001 4 1,46 0,001 2 1,08
0,011 cycles/m < n < 2,83 cycles/m; linear fitting
General
r.m.s. displacement = 0,038 4 m; r.m.s. displacement = 0,035 9 m;
characterization
r.m.s. velocity = 0,033 7 m/s; w = 2,16; r.m.s. velocity = 0,030 1 m/s; w = 2,22;
−6 3 −6 3
G (0,1 cycles/m) = 892 × 10 m G (0,1 cycles/m) = 830 × 10 m
d d
2) Omitted in this example.
12 © ISO 2016 – All rights reserved

Key
λ wavelength, m n spatial frequency, cycles/m
G (n), G (Ω) displacement power spectral density, m Ω angular spatial frequency, rad/m
d d
NOTE Country: Belgium; Road: N 1000; Place: Xstad; Direction: north to south; Surface: concrete pavement;
Distance of track to right road side: 1 m; Distance travelled: 3 571 m; B = 0,002 8 cycles/m; ε = 0,31; Statistical
e r
precision: ±61 %.
Figure A.2 — Non-smoothed PSD of track 1
Key
λ wavelength, m n spatial frequency, cycles/m
G (n), G (Ω) displacement power spectral density, m Ω angular spatial frequency, rad/m
d d
NOTE 1 Country: Belgium; Road: N 1000; Place: Xstad; Direction: north to south; Surface: concrete pavement;
Distance of track to right road side: 1 m; Distance travelled: 3 571 m; B = 0,005 5 cycles/m; ε = 0,23; Statistical
e r
precision: ±44 %.
NOTE 2 For the octave characterization, see Table A.1; see also Annex B.
Figure A.3 — Smoothed PSD of track 1
14 © ISO 2016 – All rights reserved

Key
λ wavelength, m n spatial frequency, cycles/m
G (n), G (Ω) displacement power spectral density, m Ω angular spatial frequency, rad/m
d d
NOTE Country: Belgium; Road: N 1000; Place: Xstad; Direction: north to south; Surface: concrete pavement;
Distance of track to right road side: 2,4 m; Distance travelled: 3 571 m; B = 0,002 8 cycles/m; ε = 0,31; Statistical
e r
precision: ±61 %.
Figure A.4 — Non-smoothed PSD of track 2
Key
λ wavelength, m n spatial frequency, cycles/m
G (n), G (Ω) displacement power spectral density, m Ω angular spatial frequency, rad/m
d d
NOTE 1 Country: Belgium; Road: N 1000; Place: Xstad; Direction: north to south; Surface: concrete pavement;
Distance of track to right road side: 2,4 m; Distance travelled: 3 571 m; B = 0,005 5 cycles/m; ε = 0,23; Statistical
e r
precision: ±44 %.
NOTE 2 For the octave characterization, see Table A.1; see also Annex B.
Figure A.5 — Smoothed PSD of track 2
16 © ISO 2016 – All rights reserved

Annex B
(informative)
Road profile characterization and PSD fitting
B.1 General
This annex gives means of approximately characterizing specific road profiles in order to facilitate the
division of road profiles into general classifications. A general classification is also given. A curve-fitting
method is presented for characterizing spectral data.
B.2 Symbols
The symbols used in this annex are given in Table B.1.
Table B.1 — Symbols
Symbol Description Unit
n Spatial frequency cycles/m
n Reference spatial frequency (= 0,1 cycles/m) cycles/m
G (.) Displacement PSD m
d
–1
G (.) Acceleration PSD m
a
w Exponent of fitted PSD calculated on G (.) —
d
w’ Exponent of fitted PSD calculated on G (.) —
a
Ω Angular spatial frequency rad/m
Ω Reference angular spatial frequency (= 1 rad/m) rad/m
NOTE The indication (.) means that the parameter of the function can be spatial
frequency (n) or angular spatial frequency (Ω).
B.3 General characterization of the road profile
The root-mean-square (r.m.s.) value between n = 0,011 cycles/m (Ω = 0,063 rad/m) and n = 2,83 cycles/m
(Ω = 17,77 rad/m), calculated from the displacement PSD, shall be reported. These limits are band
limits for the octave bands to be calculated in 5.1.2 and B.4. These limits were chosen in relation to the
frequency data existing in the literature.
However, for off-road data, special studies and limited distances travelled, this spatial frequency range
may be reduced. In that case the spatial frequency range shall be reported.
B.4 Characterization in octave bands
In order to obtain surveyable and classifiable data, the spectrum should be divided into octave bands
and the r.m.s. values, calculated from the displacement PSD, should be noted for each band. The centre
frequencies are given in Table B.2 for both the spatial frequency n and the angular spatial frequency Ω.
The characterizations described in B.3 and B.4 can be calculated with a small and easy supplementary
calculation following the processing of the smoothed PSD.
B.5 Fitted PSD
The smoothed form of the PSD may be fitted by a straight line on the smoothed data (5.1.2) by the least-
mean-square method in the spatial frequency range 0,011 cycles/m to 2,83 cycles/m. This fitting may
be represented on the general presentation plot. The formula of the fitting shall be reported.
The general form of the fitted PSD is given by Formula (B.1):
–w
G (n) = G (n ) · (n/n ) (B.1)
d d 0 0
or by Formula (B.2):
–w
G (Ω) = G (Ω ) · (Ω/Ω ) (B.2)
d d 0 0
where
n (= 0,1 cycles/m) is the reference spatial frequency;
Ω (= 1 rad/m) is the reference angular spatial frequency;
w is the exponent of the fitted PSD.
When the fitting is calculated on the acceleration PSD the exponent is w′ = w – 4.
NOTE In this annex, only a one-straight line fitting is presented. In the literature, a two- or more-straight line
fitting is often used, but then the standardization of a method which guarantees a unique solution is practically
impossible.
18 © ISO 2016 – All rights reserved

Table B.2 — Centre frequencies and cut-off frequencies for PSD characterization in octave bands
Exponent
Lower cut-off Upper cut-off Centre wavelength
a
Centre frequency
frequency frequency m
EXP
Spatial frequency n, cycles/m
–9 0,001 4 0,002 0 0,002 8 512
–8 0,002 8 0,003 9 0,005 5 256
–7 0,005 5 0,007 8 0,011 0 128
–6 0,011 0 0,015 6 0,022 1 64
–5 0,022 1 0,031 2 0,044 2 32
–4 0,044 2 0,062 5 0,088 4 16
–3 0,088 4 0,125 0,176 8 8
–2 0,176 8 0,25 0,353 6 4
–1 0,353 6 0,5 0,707 1 2
0 0,707 1 1 1,414 2 1
1 1,414 2 2 2,828 4 0,5
2 2,828 4 4 5,656 9 0,25
3 5,656 9 8 11,313 7 0,125
Angular spatial frequency Ω, rad/m
–6,35 0,008 7 0,012 3 0,017 4 512
–5,35 0,017 4 0,024 5 0,034 7 256
–4,35 0,034 7 0,049 1 0,069 4 128
–3,35 0,069 4 0,098 2 0,138 8 64
–2,35 0,138 8 0,196 3 0,277 7 32
–1,35 0,277 7 0,392 7 0,555 4 16
–0,35 0,555 4 0,785 4 1,110 7 8
0,65 1,110 7 1,570 8 2,221 4 4
1,65 2,221 4 3,141 6 4,442 9 2
2,65 4,442 9 6,283 2 8,885 8 1
3,65 8,885 8 12,566 4 17,771 6 0,5
4,65 17,771 6 25,132 8 35,543 1 0,25
5,65 35,543 1 50,265 6 71,086 3 0,125
a EXP
Centre frequency = 2 .
Annex C
(informative)
General guidance for use of the statistical road profile description
C.1 General
This annex provides general guidance for the use of road profile statistical data for simulation studies
and for related studies such as evaluation of comfort, suspensions and road profiles. It is assumed that
the exponent of the fitted PSD is w = 2 so that the velocity PSD is constant.
C.2 Symbols
The symbols used in this annex are given in Table C.1.
Table C.1 — Symbols
Symbol Description Unit
f Time frequency Hz
G (.) Displacement PSD m
d
G (.) Velocity PSD m
v
–1
G (.) Acceleration PSD m
a
l Wheelbase m
n Spatial frequency cycles/m
n Centre spatial frequency of a frequency band cycles/m
c
n Reference spatial frequency (= 0,1 cycles/m) cycles/m
R Tyre radius m
T Time constant of a filter s
Δt Time delay for four-track (two-axle) simulation s
v Vehicle speed m/s
w Exponent of the fitted PSD calculated on G (.) —
d
ω Angular frequency (= 2πf ) rad/s
Ω Angular spatial frequency (= 2πn) rad/m
Ω Centre angular spatial frequency of a frequency band rad/m
c
Ω Reference angular spatial frequency (= 1 rad/m) rad/m
NOTE The indication (.) means that the parameter of the function can be spatial frequency
(n) or angular spatial frequency (Ω).
C.3 Relationship between time frequency and spatial frequency
Figure C.1 gives the relationship between the vehicle speed, the spatial frequency and the time
frequency. Knowledge of the resonance frequencies and the speed range for a given class of vehicle
makes it possible to choose the useful limits for that class of vehicle.
20 © ISO 2016 – All rights reserved

The general expression for this relationship is given by Formula (C.1):
fn=⋅v (C.1)
or by Formula (C.2):
ω =⋅Ω v (C.2)
Key
λ wavelength, m n spatial frequency, cycles/m
t time frequency, Hz Ω angular spatial frequency, rad/m
Figure C.1 — Relationship between time frequency and spatial frequency
as a function of vehicle speed
C.4 Velocity PSD
For simulation studies, it is often convenient to use the velocity PSD, in terms of change of the vertical
ordinate of the road surface per unit distance travelled. The relationship between the displacement
PSD G (n) and the velocity PSD G (n) is given by Formulae (C.3) and (C.4):
d v
G (n) = G (n) · (2πn) (C.3)
v d
G (Ω) = G (Ω) · Ω (C.4)
v d
When in Formula (C.5):
–w
G (n) = G (n ) · (n/n ) (C.5)
d d 0 0
the exponent of the fitted PSD is w = 2 (see Annex B), then the velocity PSD is constant, as given by
Formulae (C.6) and (C.7):
G (n) = G (n ) = constant (C.6)
v v 0
G (Ω) = G (Ω ) = constant (C.7)
v v 0
C.5 Classification of roads
An estimate of the degree of roughness of the road can be made by the G (n ) value of the fitted PSD
d 0
(see B.5). Table C.2 gives the power spectral densities for different classes of roads. In Figure C.2, the
class limits are graphed on the displacement PSD. This classification is made by assuming a constant-
velocity PSD, which means w = 2 (see C.4).
However, due to the fact that the PSD is not always a straight line, more information is given by the
power spectral density or the r.m.s. displacement in the different octave bands. This makes it possible
to classify the road for every octave band in an appropriate class. It can give some information for the
repair need and method. It is also possible to classify the road for an appropriate band of speeds. For
example, for highways, when assuming that the velocities are between 70 km/h and 120 km/h, the band
between 0,022 1 cycles/m (0,138 8 rad/m) and 1,414 2 cycles/m (8,885 8 rad/m) is the most significant.
Table C.3 gives the mean values and limits of G (n ) and G (Ω ) for the different classes of road in the
d c d c
different octave bands.
Table C.4 gives the mean values and limits of r.m.s. displacement for the different classes of road in the
different octave bands.
The relationships given in Formulae (C.8), (C.9) and (C.10) are used:
G (n ) = 2πG (Ω ) · [Ω /(2πn )] = 16 G (Ω) (C.8)
d 0 d 0 0 0 d 0
G (n) = G (n ) · (2πn ) (C.9)
v d 0 0
G (Ω) = G (Ω ) · W (C.10)
v d 0
NOTE The word “limit” as used in this annex refers to the mathematical meaning of the word in connection
with the word “mean”. In other words, a range of values has a mean value and limits which denote the extremes
of the range of values. The word “limit”, as used in this annex, is not to be construed to mean the limit of
acceptability of a road surface.
22 © ISO 2016 – All rights reserved

Key
λ wavelength, m n spatial frequency, cycles/m
G (n), G (Ω) displacement power spectral density, m Ω angular spatial frequency, rad/m
d d
Figure C.2 — Classification of roads, classes A to H
C.6 General guidance for road simulation
C.6.1 General
The statistical road profile description can be used for computer and laboratory road simulation.
However, it may only be used for the determination of output PSDs. Because no information is given
about phase shift, there is no guarantee as to the magnitude distribution of the road profile.
C.6.2 One-track (one-axle) simulation
For simulation purposes, it is convenient to describe the road profile as a constant-velocity PSD (w = 2,
see C.4).
The advantage of this description is a very easy simulation of the displacement by integrating white noise.
The use of any other characteristic can require much effort and, due
...