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VTI PM 2015-09-18 Diarienummer: 2015/0161-8.2 Nordic certification system for road marking materials Results of initial performance measurements at the Swedish test site 2015 Carina Fors Trond Cato Johansen

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Page 1: Nordic certification system for road marking materials · A Nordic certification system for road marking materials was introduced in 2015. In the first stage, the certification system

VTI PM

2015-09-18

Diarienummer: 2015/0161-8.2

Nordic certification system for road

marking materials

Results of initial performance measurements at the

Swedish test site 2015

Carina Fors

Trond Cato Johansen

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VTI PM

Preface

A Nordic certification system for road marking materials was introduced in 2015. In the first stage, the

certification system applies to the countries of Norway and Sweden. In these countries, a documented

product approval will be required in order to use a road marking material on roads managed by the

national road authorities. Product approval will be based on monitored and documented performance

measurements of material samples applied on test fields on public roads.

The present report documents the results of the initial measurements taken shortly after application at

the Swedish test site in Sunne 2015. The results show whether the materials qualify for continued

participation in the road trials.

Performance measurements were carried out by operators from Ramböll and VTI. The mathematical

procedures to convert PFT data to SRT units were carried out by Olle Eriksson, researcher/statistician

at VTI.

The road trials are administered by Trond Cato Johansen at Ramböll and Carina Fors at VTI. Contact

persons at the national road authorities are Bjørn Skaar, The Norwegian Public Roads Administration

and Lars Petersson, The Swedish Transport Administration.

Linköping, September 2015

Carina Fors

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Table of content

Abstract ...................................................................................................................................................7

1. Introduction ....................................................................................................................................9

2. Measurements ...............................................................................................................................10

2.1. General .......................................................................................................................................10

2.2. Methods and measuring instrument ...........................................................................................10

2.2.1. Thickness measurements .......................................................................................................10

2.2.2. Retroreflection RL and luminance coefficient Qd ..................................................................10

2.2.3. Chromaticity coordinates .......................................................................................................11

2.2.4. Friction ...................................................................................................................................12

2.3. Weather conditions ....................................................................................................................12

3. Performance requirements ..........................................................................................................14

4. Results ...........................................................................................................................................15

4.1. White materials ..........................................................................................................................16

4.2. Yellow materials ........................................................................................................................19

References .............................................................................................................................................21

Appendix 1 – Friction measurements .................................................................................................22

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Abstract

Nordic certification system for road marking materials – Results of initial performance

measurements at the Swedish test site 2015

by Carina Fors (VTI) and Trond Cato Johansen (Ramböll)

This report documents the results of the initial performance measurements at the Swedish test site

2015. In total, 81 materials were applied at the test field. 78 participated as certification materials

while 3 were test materials.

Performance measurements of coefficient of retroreflected luminance RL, luminance coefficient under

diffuse illumination Qd, chromaticity in daylight, chromaticity of retroreflected light (yellow materials

only) and friction were carried out approximately two weeks after applications. The aim of these

measurements was to determine whether the materials qualify for continued participation in the road

trials.

Out of the 78 certification materials, 70 were approved for continued participation. Two materials

were disqualified because the requirements on chromaticity coordinates were not fulfilled. Six

materials were disqualified because the requirements on friction were not fulfilled. For seven

materials, one or more lines were disqualified at application because the requirements on thickness

and/or geometry were not fulfilled.

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1. Introduction

A Nordic certification system for road marking materials was introduced in 2015. In the first stage, the

certification system applies to the countries of Norway and Sweden. In these countries, a documented

product approval will be required in order to use a road marking material on roads managed by the

national road authorities. Product approval will be based on monitored and documented performance

measurements of material samples applied on test fields on public roads.

The first round of material tests started in May 2015, when 81 materials were applied at the Swedish

test site in Sunne. The present report documents the results of the application and of the initial

performance measurements that were carried out shortly after application.

At the application, the materials were examined with respect to material thickness and geometrical

requirements. The performance measurements included coefficient of retroreflected luminance RL,

luminance coefficient under diffuse illumination Qd, chromaticity in daylight, chromaticity of

retroreflected light (yellow materials only) and friction.

The aim of the initial examination and measurements was to determine whether the materials qualify

for continued participation in the road trials. Follow-up measurements will be carried out only on

materials that are approved at the initial measurements.

No material certification will be given based on the initial measurements (i.e. the results presented in

this report). Certification will be given based on the results at the follow-up measurements in 2016 and

2017.

The report includes results of materials registered as certification materials. Results of materials

registered as test materials will be available only to the participant.

The certification system is further described in the document Nordic certification system for road

marking materials – Version 1:2015 (Fors, Johansen and Lundkvist, 2015) which is freely available at

www.vti.se/en/publications The document is referred to as NCSRM-1:2015 in the present report.

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2. Measurements

2.1. General

The performance measurements of retroreflection RL, luminance coefficient Qd and chromaticity

coordinates were carried out 5–20 days after application. Friction measurements were carried out 13–

23 days after application.

Measurements of retroreflection, luminance coefficient and chromaticity coordinates were carried out

by operators from Ramböll, supervised by an observer from VTI. Measurements of friction were

carried out by operators from VTI.

All measurement equipment were calibrated according to recommended procedures.

2.2. Methods and measuring instrument

2.2.1. Thickness measurements

The thickness of the applied materials was measured immediately after application. When applying the

lines, material was applied also on two steel plates that were placed in the end of two of the seven

lines. One of the plates were applied with drop on material, and the other without any drop on. The

plates were weighed before and after application. The thickness was measured from these plates, and

also controlled by the weight of the material on the plate.

Deviation from the document NCSRM-1:2015:

In the original instruction for the road trial, it is stated that thickness would be measured including

drop-on glass beads (except for paint). At the start of the application process, it became clear for us

that this was too complicated. The big variation in types and amount of drop on aggregates made it

impossible to have consistent method for thickness calculation or measurement on materials with

applied drop on aggregates. We decided to measure thickness on plates without drop on beads and -

aggregates. The instruction will be revised on this point in the next version. The thickness was also

randomly checked on the applied lines directly, when possible (depending on surface roughness).

2.2.2. Retroreflection RL and luminance coefficient Qd

The coefficient of retroreflected luminance, RL, and the luminance coefficient under diffuse

illumination, Qd, were measured using an LTL-XL (Delta, Denmark). Measurements were taken at

three points diagonally within the measurement area defined by EN 1824, Figure 1. The result of an

individual line was calculated as the average of the three measurements.

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Figure 1. The measurement points (red crosses) for RL and Qd were placed diagonally within the

measurement area (grey) defined by EN 1824.

The markings were not cleaned before the measurements, but in case a substantial part of the

measurement area was abnormally dirty (e.g. oil stain), the instrument was moved in the longitudinal

direction to the closest area not affected by abnormal dirt.

2.2.3. Chromaticity coordinates

Chromaticity coordinates were measured in one point on each line, located at the centre of the line,

Figure 2. A Konica Minolta Spectrophotometer CM-2500c was used to measure the colour coordinates

of white materials and the daytime colour coordinates of yellow materials. Night-time colour

coordinates of yellow materials were measured using an LTL-2000Y (Delta, Denmark).

Figure 2. The measurement points (blue crosses) for chromaticity coordinates were placed in the

centre of the lines.

For materials that had a very non-homogenous surface (due to unevenly distributed drop-on), an area

that appeared to represent the average surface of the material was selected as measurement point. In

some cases several measurement points were selected, to ensure correct chromaticity coordinates.

These points had to be located within the grey area in Figure 2.

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The markings were not cleaned before the measurements, but in case a substantial part of the

measurement area was abnormally dirty (e.g. oil stain), the instrument was moved to the closest area

not affected by abnormal dirt.

2.2.4. Friction

Friction measurements were carried out using a Portable Friction Tester version 4 (PFT), along the

centre of each line, Figure 3. This equipment takes a sample approximately every 1.9 cm and thus,

about 70 samples are taken on each line. The result of an individual line is calculated as the average of

all samples from that line.

All data was visually inspected before averaging the samples. Major spikes/outliers in the data were

removed, after having verified the cause of the spikes/outliers from photographs of the materials.

Identified causes were pebbles or other small objects on the surface, and traces from wheels or

pebbles.

The PFT instrument is further described in (Wälivaara 2007).

Figure 3. The measurement areas (green lines) for friction.

Deviation from the document NCSRM-1:2015:

In the original instruction for the road trial, it is stated that in case the PFT measurement indicates that

the friction of a material is lower than the requirements, a new measurement will be carried out using

the standard instrument Skid Resistance Tester (SRT). However, due to the fact that many materials

had a non-homogenous surface with respect to friction, which was confirmed by PFT as well as by

SRT measurements, it was clear that SRT measurements would not give reliable and fair results, since

the measurement area is very small.

The performance of the materials with respect to friction was thus evaluated based on the PFT

measurements, using a statistical procedure to convert the PFT measurements into estimated SRT units

and, by adding an error margin, making sure that disqualified materials have, with 95 % probability,

an average SRT value that is lower than 50. This procedure is further described in Appendix 1.

2.3. Weather conditions

All performance measurements were carried out in dry weather. There had been no rainfall for at least

24 h when the measurements were taken.

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During the measurements of retroreflection RL, luminance coefficient Qd and chromaticity

coordinates, the air temperature was 13–27 ˚C, the temperature of the road marking surface was 14–32

˚C and the relative humidity was 25–65 %. The temperature of the road marking surface was well

above the dew point at all measurements (according to the dew point table in EN 1824).

During the measurements of friction, the air temperature was 16–26 ˚C and the temperature on the

road marking surface was 19–30 ˚C.

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3. Performance requirements

The performance requirements of the four parameters are given in Table 1.

Table 1. Performance requirements.

Performance parameter White

markings Yellow

markings

Coefficient of retroreflected luminance, RL dry [mcd/m2/lx] 150 100

Luminance coefficient under diffuse illumination, Qd [mcd/m2/lx] 130 100

Friction, [SRT units] 50 50

Chromaticity coordinates, x, y * **

*) According to EN 1436

**) Includes both daytime and night-time colour. Daytime colour: according to class Y1 in EN 1436. Night-time colour:

according to ASTM D6628.

The measurement results from the seven lines were averaged, and compared to the performance

requirements in Table 1. The results of individual lines were not evaluated. In order for a material to

be approved for continued participation, all four performance parameters must fulfil the requirements.

Regarding the requirements on thickness and geometry, individual lines were disqualified if they

didn’t fulfil the requirements.

The reason for evaluating RL, Qd, friction and chromaticy coordinates based on the average of the

seven lines, but evaluating thickness and geometry for individual lines is that the four former represent

the properties of the material and the most representative data on these properties is the average of all

measurements taken. But for thickness and geometry, all individual lines must fulfil the requirement,

since at the follow-up measurement the performance is evaluated for different P classes, where one or

a few lines may represent a certain P class. The performance of a single line will then have a large

impact on the result, and in case it was too thick at application, this will give unfair results. This

however implies that, for material where one or more lines were disqualified because they didn’t fulfil

the requirements on thickness and geometry, there is a risk that these materials cannot be evaluated

and certified for certain P classes1.

1 Measurements of wheel passages will be carried out in September-October 2015.

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4. Results

The tables in Section 4.1 and 4.2 show the results of the initial measurements of retroreflection RL,

luminance coefficient Qd, friction, chromaticity coordinates, and thickness for all materials registered

and applied as certification materials, at the Swedish test site in Sunne 2015.

In total, 78 materials, of which 49 were white and 29 were yellow, participated as certification

materials. Out of these 78 materials, 70 were approved for continued participation. Two materials were

disqualified because the requirements on chromaticity coordinates were not fulfilled. Six materials

were disqualified because the requirements on friction were not fulfilled. For seven materials, one or

more lines were disqualified at application because the requirements on thickness and/or geometry

were not fulfilled.

Explanation of the columns in the result tables

RL Mean value of retroreflection RL [mcd/m2/lx]

Qd Mean value of luminance coefficient Qd [mcd/m2/lx]

Friction Mean value of friction including error margins [SRT units] (converted from PFT measurements, according to the procedures described in Appendix 1)

Colour Approved (A) or Not Approved (NA) chromaticy coordinates

NTY Approved (A) or Not Approved (NA) NTY chromaticy coordinates

Thickness Material thickness [mm]

Disq. lines Lines that were disqualified at application (too thick, wrong size or missing)

Approved Approved (A) or Not Approved (NA) for continued participation. A* = one or more lines are disqualified.

Values that do not fulfil the performance requirements are indicated in orange.

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4.1. White materials

Supplier Material name RL Qd Friction Colour Thickness Disq. lines Approved

Cleanosol AB AQ 6010 331 261 76,9 A 0,35 A

Cleanosol AB CL AQ 6007 288 180 81,9 A 0,35 A

Cleanosol AB/AS CL 35E1 R3 282 191 60,0 A 3,3 A

Cleanosol AB/AS CL 35E2 R3 237 184 61,0 A 2,9 A

Cleanosol AB/AS CL 71E1 R3 262 197 57,8 A 3,3 A

Cleanosol AB/AS, LKF AS 31 E35 NO 253 196 63,0 A 3,1 A

Cleanosol AB/AS, LKF AS 50 EP40 Agglo 298 196 62,0 A 3,5 A

Cleanosol AB/AS, LKF AS 31 E35 231 183 58,9 A 3,2 A

Cleanosol AB/AS, LKF AS 45 S30 N 274 210 58,1 A 1,8 A

Ennis Flint (Prismo road mark. Ltd) Crystalex W2015.5 296 189 50,9 A 3,0 A

Ennis Flint (Prismo road mark. Ltd) Crystalex W2015.6 337 195 53,1 A 2,9 A

Ennis Flint (Prismo road mark. Ltd) W2015.2 366 222 49,8 A 2,0 NA

Ennis Flint (Prismo road mark. Ltd) Sprayplastic W2015.1 300 218 53,0 A 1,5 A

Hermseal AS MeltMark ESP 316 227 55,3 A 3,4 A

Hitex HiBrite WR EXTR 322 179 52,9 A 2,8 A

Hot Mix Oy Hot Mix 3000 M (white) 346 219 48,4 A 3,1 NA

Hot Mix Oy Hot Mix 1A white 353 216 51,3 A 3,0 A

Kelly Bros (Erinline) Ltd Extr./Screed Briteline 150 (SW1) 199 223 57,9 A 3,5 A

Kelly Bros (Erinline) Ltd Extr./Screed Briteline 150 (SW) 292 217 60,1 A 3,2 A

Kelly Bros (Erinline) Ltd Spray Briteline 150 (SW) 290 213 62,0 A 2,0 A

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Supplier Material name RL Qd Friction Colour Thickness Disq. lines Approved

LKF Materials A/S Viatherm SK20 194 201 68,0 A 3,1 A

LKF Materials A/S Viatherm Viking 311 222 53,8 A 3,3 A

LKF Materials A/S Viatherm SK60 249 198 61,2 A 3,4 A

LKF Materials A/S Viatherm SK25 266 214 61,6 A 2,0 A

LKF Materials A/S Premark SK151 284 236 58,5 A 2,8 A

LKF Materials A/S Premark SK152 284 238 59,9 A 3,0 A

LKF Materials A/S Premark SK153 225 238 64,3 A 2,9 A

Plastiroute GmbH AquaRoute BST-NO 180 179 76,9 A 0,4 A

Plastiroute GmbH AquaRoute HD BST 214 195 71,7 A 0,35 A

Promax Industries ApS Promax white prime 300 222 61,5 A 2,3 A

Swarco Limburger Lackf. Gmbh Limboroute W13 278 200 66,4 A 0,4 A

Swarco Limburger Lackf. Gmbh Limboroute W15 277 197 67,1 A 0,4 A

Swarco Limburger Lackf. Gmbh Limboroute W16 278 193 67,5 A 0,35 A

Swarco Vestglas Gmbh Swarcotherm SRP 15 white 343 173 64,8 A 1,2 A

Swarco Vestglas Gmbh Swarcotherm ERP 15 white 394 183 61,7 A 2,0 A

Svevia X204 249 193 69,6 A 2,0 1, 6, 7 A*

Svevia X205 214 220 63,0 A 2,0 7 A*

Svevia X206 269 208 70,8 A 1,3 1, 2, 3, 4, 5 A*

Svevia X201 171 247 62,6 A 2,2 7 A*

Svevia X202 253 209 62,8 A 2,2 A

Teknos Oy TEKNOROAD 3059 (white) 336 179 74,9 A 0,35 A

Tielinja Oy Hotmark VH35N 289 206 58,0 A 2,5 5, 6, 7 A*

Tielinja Oy Hotmark VH spray 35N 191 213 67,1 A 0,8 A

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Supplier Material name RL Qd Friction Colour Thickness Disq. lines Approved

Trafikmarkering TTP 30 384 206 50,8 A 3,0 A

Veluvine Thermolit Nausta 327 217 59,5 A 3,0 A

Veluvine Thermolit Gaula 241 227 66,8 A 2,8 A

Vernicol Hidrocryl WBM F500 288 191 76,8 A 0,4 A

Visafo VIT VISA 15 273 189 72,9 A 0,35 A

Visafo VIT VISA 12 199 177 83,0 A 0,3 A

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4.2. Yellow materials

Supplier Material name RL Qd Friction Colour NTY Thickness Disq. lines Approved

Cleanosol AB/AS CL 29E2 R2 Yellow 215 140 55,4 A A 3,3 A

Cleanosol AB/AS CL 27EP2 R2 Yellow 190 137 56 A A 3,0 A

Cleanosol AB/AS CL 71E1 R2 Yellow 204 135 56,1 A A 3,0 A

Cleanosol AB/AS CL 71S1 R2 Yellow 188 144 58,9 A A 2,0 A

Cleanosol AB/AS CL 29S2 R2 Yellow 150 132 62,6 A A 2,0 A

Cleanosol AB/AS, LKF AS NTY 29E Yellow 216 142 55,2 A A 2,7 A

Cleanosol AB/AS, LKF AS NTY 27 Agglo Yellow 203 140 54,9 A A 3,5 A

Cleanosol AB/AS, LKF AS NTY 29S Yellow 191 156 50,8 A A 1,9 A

Ennis Flint (Prismo road mark. Ltd) Crystalex Y2015.8 191 132 48,6 A A 2,5 NA

Ennis Flint (Prismo road mark. Ltd) Crystalex Y2015.7 228 137 46,3 A A 2,9 NA

Ennis Flint (Prismo road mark. Ltd) Sprayplastic Y2015.3 202 147 50,2 A A 1,5 A

Ennis Flint (Prismo road mark. Ltd) Sprayplastic Y2015.4 146 152 54,2 A A 1,5 A

Hitex HiBrite Yellow EXTR 1 222 145 55,1 A A 3,1 A

Hitex HiBrite Yellow EXTR 2 296 133 46,9 A A 2,7 NA

Hot Mix Oy Hot Mix 3000 M (yellow) 160 152 51,8 A A 2,7 A

Hot Mix Oy Hot Mix 1A yellow 136 167 53,8 A A 2,9 A

Kelly Bros (Erinline) Ltd Extr./Screed Briteline 100 (SW) 296 133 50,6 A A 2,8 A

Kelly Bros (Erinline) Ltd Spray Briteline 100 (SW) 288 150 54,4 A A 2,0 A

LKF Materials A/S Viatherm SK55 yellow 192 151 56,2 A A 2,0 A

LKF Materials A/S Viatherm SK50 yellow 236 140 58,8 A A 3,0 A

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Supplier Material name RL Qd Friction Colour NTY Thickness Disq. lines Approved

Plastiroute GmbH AquaRoute HD BST Yellow 103 130 71,7 A A 0,4 A

Promax Industries ApS Promax yellow prime 298 137 49,5 A A 2,0 NA

Swarco Vestglas Gmbh Swarcotherm ERP 15 218 133 68,9 NA A 2,0 NA

Swarco Vestglas Gmbh Swarcotherm SRP 15 234 131 60,6 NA A 1,3 NA

Svevia Y313 101 188 64,2 A A 1,9 1, 2, 3, 4 A*

Svevia Y314 144 159 61,1 A A 1,8 1, 2 A*

Svevia Y311 155 152 59,1 A A 2,4 A

Teknos Oy TEKNOROAD 3059 (yellow) 148 102 78,1 A A 0,35 A

Tielinja Oy Hotmark KH40N 182 139 63,2 A A 3,4 A

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References

Fors, C., Johansen, T-C. and Lundkvist, S-O. (2015). Nordic certification system for road marking

materials – Version 1:2015. VTI notat 16-2007. Swedish National Road and Transport Research

Institute, Linköping, Sweden.

Wälivaara, B. (2007). Validering av VTI-PFT version 4. Mätningar på plana och profilerade

vägmarkeringar. VTI notat 16-2007. Swedish National Road and Transport Research Institute,

Linköping, Sweden.

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Appendix 1 – Friction measurements

The measurement procedure for friction is described as follows in NCSRM-1:2015:

Chapter 5.3

Friction will be measured in the centre of each line (one measurement per line). Measurements will be

carried out using a Portable Friction Tester version 4 (PFT), which allows for relatively fast and

simple measurements. In case the PFT indicates that the friction of a material is lower than the

requirements, a new measurement will be carried out using the standard instrument Skid Resistance

Tester (SRT). The evaluation of the material will then be based on the value obtained from the SRT.

Chapter 7.3

Friction will primarily be measured by a PFT. Conversion between SRT units and PFT units are done

according to (Wälivaara 2007):

��� = 78.6 ∗ �� + 9.2 ± 9.0 An SRT value of 50 corresponds to a PFT value of 0.52.

The PFT measurements indicated that 19 out of the 78 certification materials had an average PFT

value lower than 0.52. SRT measurements that were carried out on a portion of these materials showed

that the variations in friction across the surface of the material were rather large for several of the

materials. This observation indicated that SRT measurements in one or a few points (EN 1824

suggests that at least two points shall be selected) would not give reliable and fair results.

Analysis of friction variation

An analysis of the PFT data, where about 70 samples are taken from each line, showed that the

standard deviation in friction per line, varied between 0.02 and 0.12. A histogram of the standard

deviation for all lines is shown in Figure 4.

Figure 4: Histogram of the standard deviation of the PFT measurements, for all lines.

An example of PFT data from a material with standard deviation 0.05 is shown in Figure 5.

0 0.02 0.04 0.06 0.08 0.1 0.120

50

100

150

Standard deviation (PFT units)

Number of lines

Histogram of standard deviation, all lines

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Figure 5: Example of PFT data (blue line) from one line, where the standard deviation is 0.05. The

red line indicates the requirement of 0.52.

These figures quantify and confirm the observations made during the measurements regarding

variations in friction across the surface of the materials. Based on this, it is obvious that for materials

that has a PFT value close to 0.52 and an inhomogeneous surface with respect to friction, a relatively

large number of SRT measurements would be needed in order to obtain a reliable result.

It was estimated that assessing the friction of the 19 materials that had a PFT value < 0.52 with the

SRT would require hundreds (or even more) of measurements in total, which is not practicable.

The relationship between SRT and PFT given by the report by Wälivaara (2007) however provides a

possibility to transform the PFT measurements to SRT units, using a mathematical procedure to take

into account the uncertainties in the relationship, to identify materials that, with a very high

probability, have an SRT value that is lower than the requirement of 50 SRT units. Using this

procedure implies that all materials can be evaluated in an identical way (which is not the case if only

material have PFT values lower than 0.52 are assessed with the SRT). The procedure and the

calculations are described below.

Transformation of PFT measurements into estimated SRT units

When transforming friction according to PFT into estimated friction according to SRT, a

transformation formula and an error margin is needed. The transformation is based on an assumption

of a straight line relation. A positive error margin should then be added, such that there is only a 5%

risk of rejecting a material that exactly reaches the SRT friction requirement. All components are

available in (Wälivaara 2007) but needs preparation in varying degree before it can be used here.

In (Wälivaara 2007), the straight line transformation is estimated with a simple linear regression.

There are also results that show how measures vary around the line, uncertainty in the estimated line

and variation between PFTs. Our procedure is based on that and on data collected for this study. The

error margin consists of similar components, namely how the mean of 7 observations (i.e. from the 7

markings) vary around the line, uncertainty in the estimated line, variation in the difference between

two PFTs and variation between SRTs. All components are estimated in the following order:

1) The straight line is estimated in (Wälivaara 2007), section 6.1.1, SRT = 9.2 + 78.6*PFT

0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Samples

PFT units

Example of PFT data where std=0.05

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2) The estimated uncertainty in the regression line can be extracted from the confidence bands in

(Wälivaara 2007) Figure 4. We have assumed that they are on the average ± 2 SRT units from the line.

3) An estimate of how the mean of 7 observations vary around the line can be extracted from the

prediction bands in (Wälivaara 2007) Figure 4 after adjusting for variation as described in 2) above. It

can be found in (Wälivaara 2007) section 6.1.1. that the prediction bands are on the average ± 9 SRT

units from the line.

4) The standard deviation in the distribution of PFTs is assumed to be 0.01, based on (Wälivaara 2007)

Figure 5a. It is transformed to SRT units by multiplying with the slope 78.6.

5) The standard deviation in the distribution of SRTs is assumed to the same as for PFTs (transformed

to SRT units).

We cannot decide a degree of freedom for this combination of variation sources. It was assumed that

that the components are estimated in a way such that it is not needed to find an exact degree of

freedom. An estimated SRT for a mean (of 7) PFT then becomes

������ = 9.2 + 78.6�������� + ��9� − 2���� + 2��� + 3 ∙ 0.01�� � where the expression inside the square root represents the sum of variation components 2-5 described

above, and where z = 1.6449, m = number of observations (markings), t = 1.9879 and b1= 78.6.

In short, this implies that an error margin of approximately 3.9 is added to the transformed SRT value.