The effect of water and snow on the road surface on rolling resistance

Annelie Carlson Tiago Vieira

VTI rapport 971A Published 2021 vti.se/publications

VTI rapport 971 A

The effect of water and snow on the road surface on rolling resistance

Annelie Carlson

Tiago Vieira

Author: Annelie Carlson, VTI, http://orcid.org/0000-0002-8957-8727 Tiago Vieira, VTI, https://orcid.org/0000-0001-8057-6031 Reg.No.: 2016/0589-9.1 Publication: VTI rapport 971A Published by VTI, 2021 Publikationsuppgifter – Publication Information

Titel/Title Effekten på rullmotstånd av vatten och snö på vägytan/The effect of water and snow on the road surface on rolling resistance

Författare/Author Annelie Carlson, Linköpings Universitet, http://orcid.org/0000-0002-8957-8727 Tiago Vieira, VTI, https://orcid.org/0000-0001-8057-6031

Utgivare/Publisher VTI, Statens väg- och transportforskningsinstitut/ Swedish National Road and Transport Research Institute (VTI) www.vti.se/

Serie och nr/Publication No. VTI rapport 971A

Utgivningsår/Published 2021

VTI:s diarienr/Reg. No., VTI 2016/0589-9.1

ISSN 0347–6030

Projektnamn/Project State-of-the-art om påverkan av vatten och snö på rullmotstånd/State-of-the-art om påverkan av vatten och snö på rullmotstånd

Uppdragsgivare/Commissioned by Trafikverket/Swedish Transport Administration

Språk/Language Engelska/English

Antal sidor inkl. bilagor/No. of pages incl. appendices 43

VTI rapport 971A 3 Sammanfattning

Effekten på rullmotstånd av vatten och snö på vägytan av Annelie Carlson (VTI) och Tiago Vieira (VTI)

Rullmotstånd uppkommer vid interaktionen mellan vägyta och däck och utgör en del av det färdmotstånd som ett fordon behöver överkomma för att röra sig framåt. De av vägytans egenskaper som anses ha störst betydelse för rullmotstånd är makrotextur och ojämnhet längs med vägen. Men även vatten och snö på vägytan bidrar till att påverka rullmotståndet. Nederbörd som ligger kvar på vägen innebär att hjulen behöver drivas genom och flytta undan vatten eller snö, och det leder till ett ökat motstånd. Dessutom kyler vatten mer effektivt jämfört med luft, vilket har en påverkan på däckens beteende då deras viskoelastiska egenskaper är temperaturberoende. Att de kyls av på grund av nederbörd på vägytan gör att däcken arbetar vid en lägre temperatur, vilket i sig ökar motståndet. Hastighet, temperatur och vattendjup är de förklarande variabler som ofta hittas i litteraturen för att beskriva effekten på rullmotstånd på grund av vatten på vägytan. Man har visat att rullmotståndet ökar med ökad hastighet, ökat vattendjup och minskad däcktemperatur. Resultaten pekar på att effekten kan vara betydande och bör inte ignoreras. Senare mätningar visar en ökning med 30 till 40 procent av rullmotståndskoefficienten beroende på hastighet och tjocklek på vattenfilmen. Litteraturen i området är dock relativt begränsad och orsaken till detta är förmodligen kopplat till de svårigheter som finns att mäta och modellera rullmotståndseffekten i vatten. Dessa svårigheter beror bland annat på att mäta vattenfilmens djup och däckens temperatur samt att temperaturen på däcken behöver vara stabil vid mätningar. Att studera snöns påverkan på rullmotstånd innebär också en del svårigheter i och med att det finns många olika typer av snö med mycket varierande egenskaper och beteende vid deformation. De data som finns tillgängliga är dessutom begränsade och de samband som tagits fram är inte tillräckligt utvecklade så att de kan användas för att kunna beskriva snöns beteende med avseende på deformation och belastning. Komplexiteten avseende snöns påverkan på rullmotstånd innebär att det behövs en kombination av teoretiska beräkningar och fältstudier för att bestämma värden på de komponenter som ingår i rullmotståndet. En del studier har dock genomförts som syftar till att förklara påverkan av snö, både teoretiska samt mätningar i fält. De förklarande variabler som ofta använts är snödjup, snöns densitet och däckens kontaktyta med vägyta. I stort visar resultaten att snö har en stor effekt på motståndet och att det därför bör tas hänsyn till, speciellt i områden där snö ligger kvar på marken en längre tid. En aspekt som bör beaktas är den osäkerhet som är kopplad till de fältstudier som redovisats där de flesta har genomförts under 70- och 80-talet. Sedan dess har såväl mätmetoder som mätutrustning utvecklats och blivit bättre. För de tester som gjorts för snöns påverkan har dessutom flertalet studier genomförts med fordon, som till exempel terrängfordon och flygplan, vilka inte är representativa för de som trafikerar normala vägar. Även däckens egenskaper har förbättrats vilket i sig har haft en effekt på rullmotståndet. För att få mätdata för rullmotstånd i snö och vatten som är anpassad för däck och fordon som används på vanliga vägar idag borde därför nya mätningar genomföras. Dessa mätningar ska använda de senast utvecklade mätmetoderna och mätutrustningar, vilket inkluderar bättre kontroll och mer exakta mättekniker för att utvärdera effekten av olika faktorer på rullmotstånd. Det skulle minska osäkerheten i mätresultat och ge aktuell information som kan användas för att uppdatera samband mellan bränsleförbrukning och vatten och snö på vägytan. Informationen kan sedan användas för att optimera beläggningar med avseende på rullmotstånd där textur, ojämnhet och avvattningsförmåga ingår samt till att förbättra rekommendationer till vinterväghållning.

Nyckelord Rullmotstånd, vägyta. snö, vatten, bränsleförbrukning

4 VTI rapport 971A Abstract

The effect of water and snow on the road surface on rolling resistance by Annelie Carlson (VTI) and Tiago Vieira (VTI)

Rolling resistance is due to the interaction between road surface and tires and forms part of the driving resistance that a vehicle needs to overcome to move forward. Those of the road surface properties that are seen as most important for rolling resistance are macro texture and unevenness along the road. But water and snow on the road surface also contribute to the rolling resistance. Precipitation that remains on the road means that the wheels need to be driven through and displace water or snow, and this leads to increased resistance. In addition, water cools more efficiently than air, which has an effect on the behavior of the tires as their viscoelastic properties are temperature dependent. The tires work at a lower temperature in the presence of precipitation, which in itself increases the resistance. Speed, temperature and water depth are the explanatory variables often found in the literature to describe the effect on rolling resistance due to water on the road surface. It has been shown that rolling resistance increases with increasing speed, increasing water depth and decreasing tire temperature. The results indicate that the effect can be significant, with measurements showing an increase of 30 to 40 percent of the rolling resistance coefficient depending on the speed and thickness of the water film. However, the literature in the area is relatively limited, and the reason for this is probably linked to the difficulties that exist in measuring and modeling the rolling resistance effect in water. These difficulties are due to, among other things, measuring the depth of the water film and the temperature of the tires and that the temperature of the tires needs to be stable during measurements. Studying the impact of snow on rolling resistance also involves some difficulties in that there are many different types of snow with varying properties and behavior during deformation. Data available is also limited and the relationships are not sufficiently developed so that they can be fully used to describe the behavior of the snow with respect to deformation and load. The complexity of the impact of snow on rolling resistance means that a combination of theoretical calculations and field studies is needed to determine the values of the components included. However, some studies have been carried out that aim to explain the impact of snow, both theoretical and via field measurements. The explanatory variables often used are snow depth, snow density and tire contact surface with road surface. In general, the results show that snow has a large effect on the resistance and that it should therefore be considered, especially in areas where snow remains on the ground for a long time. One aspect that should also be considered is the uncertainty associated with the field studies that have been reported, most of which were carried out during the 1970s and 1980s. Since then, both measuring methods and measuring equipment have been developed and improved. In addition, for tests of the impact of snow, most studies have been carried out with vehicles that are not representative of those who operate on normal roads. The properties of the tires have also been improved, which in itself has had an effect on rolling resistance. In order to obtain measurement data for rolling resistance in snow and water that is adapted for tires and vehicles used on ordinary roads today, new measurements should therefore be carried out. These measurements will use the most recently developed measurement methods and measuring equipment, which includes better control and more accurate measurement techniques to evaluate the effect of various factors on rolling resistance. It would reduce the uncertainty in measurement results and provide up-to-date information that can be used to update the relationship between fuel consumption and water and snow on the road surface. The information can then be used to optimize road surface with respect to rolling resistance where texture, unevenness and drainage ability are included and to improve recommendations for winter road maintenance.

Key words Rolling resistance, road surface, snow, water, fuel consumption

VTI rapport 971A 5 Preface The report is an overview of knowledge about how the presence of water and snow on the road surface affects the rolling resistance of road vehicles. The work has been financed by the Swedish Transport Administration via BVFF on behalf of Åsa Lindgren, and it is one of four sub-projects included in VTI's framework project Rolling resistance in a societal perspective – MIRIAM III. Linköping, April 2018

Annelie Carlson Project manager

6 VTI rapport 971A Quality review An internal peer review was performed on 14 February 2018 by research engineer Thomas Lundberg and acting manager Leif Sjögren. Annelie Carlson and Tiago Vieira have made alterations to the final manuscript of the report. The research director, Mikael Johannesson, examined and approved the report for publication on 3 April 2018. In 2021 the report was translated to English. The conclusions and recommendations expressed are the authors’ and do not necessarily reflect VTI’s opinion as government agency.

Kvalitetsgranskning Intern peer review har genomförts 14 februari 2018 av forskningsingenjör Thomas Lundberg och tf. forskningschef Leif Sjögren. Annelie Carlson och Tiago Vieira har genomfört justeringar av slutligt rapportmanus. Forskningschef Mikael Johannesson har därefter granskat och godkänt publikationen för publicering 3 april 2018. Rapporten översattes till engelska 2021. De slutsatser och rekommendationer som uttrycks är författarnas egna och speglar inte nödvändigtvis myndigheten VTI:s uppfattning.

VTI rapport 971A 7 Innehållsförteckning

Publikationsuppgifter – Publication Information ...... 3 Abstract ...... 5 1. Introduction ...... 9 1.1. Background ...... 9 1.2. Purpose ...... 10 1.3. Method ...... 10 1.4. Disposition ...... 11 2. Impact on rolling resistance due to water on the road surface ...... 12 2.1. Theory ...... 12 2.2. Light vehicles ...... 13 2.3. Heavy duty vehicles ...... 17 2.4. Temperature effect on rolling resistance ...... 18 2.5. Electric vehicles ...... 20 2.6. Aircraft ...... 21 2.7. Strategies for road maintenance, transport costs and energy use ...... 22 3. Impact on rolling resistance due to snow on the road surface ...... 23 3.1. Theory ...... 24 3.2. Measurements ...... 28 3.3. Model calculations with respect to traffic and snow ...... 32 3.3.1. Models for tires and for simulators ...... 32 3.3.2. Fuel consumption of vehicles ...... 33 3.3.3. Strategies for winter road maintenance ...... 35 4. Discussion ...... 37 References ...... 40

8 VTI rapport 971A 1. Introduction

1.1. Background Rolling resistance is part of the driving resistance that a vehicle needs to overcome in order to move forward. The other parts are air resistance, gravity due to the horizontal inclination of the road, internal friction, inertia during acceleration and deceleration and lateral forces that occur at curves (Michelin 2003, Sandberg 2011). The higher the travel resistance a vehicle needs to overcome, the more energy, and thus fuel, is needed. The contribution the different parts of travel resistance stand for varies with respect to speed and vehicle type (Beuving et al. 2004, National research council 2006, Sandberg 2011). For example, the relative importance of air resistance increases with speed and becomes the factor that has the greatest significance at higher speeds. For rolling resistance, it is relatively more important for heavy vehicles compared with passenger cars (Sandberg 2011). The rolling resistance arises during the interaction between road surface and tires and depends on what properties they have. The contribution of the tires to the rolling resistance depends on their structure, how they are deformed on contact with the road surface when the tire rolls and on hysteresis in the tire rubber (Sandberg 2011). Temperature, the air pressure in the tire and how the tires are aligned are also important factors (National research council 2006). The texture and unevenness of the road surface affect the deformation of the tires and thus the rolling resistance (National research council 2006). The texture is usually described with three different dimensions that represent the roughness of the road surface (micro-), the shape and size of the stones in the pavement (macro-) and whether there are potholes and joints (mega-). There is unevenness both across the road and along the road. Unevenness across the road is rutting, which occurs due to wear and deformation, while unevenness along the road describes a balanced image of, for example, bumps. The properties of the road surface that are considered to be of the greatest importance for rolling resistance are macro texture and unevenness along the road. The measures that describe these properties are MPD (mean profile depth) and IRI (International Roughness Index). When vehicles travel on a road with a high texture and/or a high unevenness, the tires will be more deformed. In addition, larger losses will occur in the suspension system relative to a smooth surface, with more energy losses (Sandberg 2011). Previous studies have shown that the impact of rolling resistance on fuel consumption can account for a relatively large share of total fuel consumption. Depending on the driving conditions that apply, the rolling resistance can be between 5 and 30 percent of the fuel consumption for a typical passenger car and between 15 and 40 percent for heavy vehicles (Barrand & Bokar 2009). Fontaras and Samaras (2010) have calculated that fuel consumption could be reduced by 2.5 per cent for passenger cars and by 3.6 per cent for heavy vehicles if rolling resistance is reduced by 10 to 20 per cent. Hammarström et al. (2012) have calculated for Swedish roads that a passenger car at 90 km/h would use approximately 4.6 and 15.1 percent more fuel, respectively, if IRI and MPD increased by one unit. They also showed that for heavy duty traffic, the increase in fuel consumption would be relatively greater under the same conditions. According to the studies described above, there is thus a potential for energy savings if the rolling resistance can be reduced. Research is currently underway aimed at achieving this without adversely affecting road safety. An example is the international collaboration MIRIAM (Models for rolling resistance In Road Infrastructure Management systems). The collaboration focuses on rolling resistance and aims to reduce carbon dioxide emissions from traffic and road infrastructure and to achieve better energy efficiency1. Most of the research is based on conditions where the road surface is dry and with ambient temperatures that are representative of spring to autumn. However, it has been shown that fuel

1 miriam-co2.net

VTI rapport 971A 9 economy in vehicles is affected by temperature, slippery roads and snow on the roads. According to studies in Canada and the USA, driving on winter roads with packed snow and which are icy requires up to 33 percent more fuel. For short journeys, up to 50 percent more fuel may be required in winter compared with the same distance in summer (Ye et al. 2013). Water on the road surface also affects fuel economy as it increases the resistance that the tire encounters, and that effect can be significant (Ejsmont et al. 2015). In Sweden, the roads are wet a large part of the year due to rain or melting snow and ice. In some parts of the country, there is also snow on the roads during part of the year. To be able to evaluate the importance of rolling resistance and its size and development over time, road managers need to have reliable information about the relationship between the condition of the road surface and rolling resistance.

1.2. Purpose The purpose of the report is to compile the state of knowledge on how rolling resistance is affected by water and snow on the road surface. This information can, in a next step, be used to update the relationship between fuel consumption and wet and snow on the road surface. This information can be used to update the calculation module for fuel consumption with regard to snow road conditions in the Winter Model2 (Möller 2014) and for both wet and snowy roads in the VETO model3 (Hammarström, Karlsson 1987). The information can then be used to optimize road surfaces with respect to rolling resistance where texture, unevenness and drainage ability are included and to improve recommendations for winter road maintenance. When optimizing pavements and maintenance it is important to consider that other properties that the road has, such as friction and the risk of aquaplaning, should not be impaired. However, these are aspects that are not included in this report.

1.3. Method A literature search for scientific literature and other relevant publications has been done with the help of VTI's libraries in the databases to which they have access. Furthermore, the authors have done supplementary searches on the internet to find additional material. The keywords used in Swedish, English and German were as follows:

• rullmotstånd/rolling resistance/ rollwiderstand, radwiderstand

• snö/snow/snee

• vatten/water/wasser

• fukt/moist, moisture/nässer

• temperatur/temperature/temperatur

A total of 51 scientific articles and reports were selected as the basis for the knowledge overview. These were published between 1970 and 2018.

2 With the Winter Model, one can calculate and evaluate the socio-economic effects of various strategies and measures within winter road maintenance. 3 VETO is a simulation model for calculating fuel consumption for individual vehicles where vehicles, the road and the road surface can be described in detail.

10 VTI rapport 971A 1.4. Disposition Chapter 1 covers the background with a brief description of rolling resistance as well as method, purpose and delimitations. Chapter 2 summarizes studies on the effect on rolling resistance of the presence of water on the road surface, which is followed by the snow's effect on rolling resistance in Chapter 3. At the end of the compilation, conclusions are made and suggestions for further work are given.

VTI rapport 971A 11 2. Impact on rolling resistance due to water on the road surface

2.1. Theory Water on the road surface has noticeable effects on the functional aspects of the road surface, which includes rolling resistance. When a tire rolls over a wet road, it must displace water before making direct contact with the texture of the road surface. Rolling resistance on wet roads is affected by the volume of water, which is determined by the water depth, the width of the tire and the speed of the tire (Mitschke & Wallentowitz 2004). In addition, the movement of water is not the only important phenomenon for rolling resistance on wet roads. Water affects, for example, the contact temperature of the tires, which in turn affects the rolling resistance. Figure 1 illustrates a tire on a dry road surface. The tire rolls at an angular velocity ω and the corresponding linear velocity v. The normal force, FN, presses the tire against the road surface and initiates a contact pressure over that contact length Lc. FT is the total braking force equal to the rolling resistance plus the air resistance, = + . The contact pressure fc is greater in the front part than the rear part, which leads to a torque in the tire. The reason is that the contact pressure distribution is 𝑇𝑇 𝑅𝑅 𝐿𝐿 affected by viscoelastic properties𝐹𝐹 in the𝐹𝐹 tire.𝐹𝐹 The figure describes the effect of rolling resistance as a force, Fc, with the horizontal distance Δc till FN.

Figure 1. The interaction of the tire with a dry road surface.

When the tire rolls on a wet road surface at the same speed, the rolling resistance force is affected by the water film, which is shown in Figure 2. There, the rolling resistance effect is described as a braking force against the movement of the tire. To make it clearer, the rolling resistance is divided into different sub-components. An alternative, more comprehensive description of rolling resistance could be made by means of a division into energy components. The water depth also affects the tire's deformation, which leads to a changed contact surface between the tire and the road surface. The contact area in Figure 2 is smaller compared to Figure 1.

12 VTI rapport 971A

Figure 2. The interaction of the tire with a wet road surface.

The power balance will then be affected by an extra force due to water, Fv. Total forces will be: = + + [1]

Thus,𝐹𝐹𝑇𝑇 𝐹𝐹it𝑅𝑅 is possible𝐹𝐹𝐿𝐿 𝐹𝐹𝑉𝑉 to calculate the effects of the water by comparing rolling resistance measurements made on dry road surfaces with those made on wet road surfaces. To be able to compare rolling resistance with and without water on the same road surface and thereby calculate how the size of the water film affects rolling resistance, all other variables that can affect the result must be kept constant. This means that they must be controlled and registered, concerning for example, temperatures, speed, water depth and metrological conditions such as air density. It is also important to mention that a high water level and/or high speed lead(s) to aquaplaning (Mitschke, Wallentowitz 2004), which is an undesirable effect when measuring rolling resistance. A comprehensive model that contains a good description of rolling resistance and how it is affected by several different variables can be found, for example, in Hammström et al. (2009).

2.2. Light vehicles Since rolling resistance in water is affected by water volume at the contact surface between road and tire, the width of the tire's contact surface and speed play an important role. Gengenbach (1967) has measured rolling resistance in water by comparing results from dry and wet surfaces. The result is shown in part in Figure 3 and applies to a tire with a landing width b=14 cm, water depth between 0.2 and 2 mm and speeds between 5.6 and 19.4 m/s (20 and 70 km/h). The measurements were made in a stationary state.

VTI rapport 971A 13 Rolling resistance in water (Gengenbach, 1967)

d = 0.2 mm 1,0E+02 d = 0.5 mm d = 1.0 mm d = 1.5 mm d = 2.0 mm 1,0E+01 Fv [N]

1,0E+00

1,0E-01 1 2 3 4 5 6 7 8 9 10 20 velocity [m/s] Figure 3. Rolling resistance Fv component, for different water depths and speeds (logarithmic scale, adapted from Gengenbach, 1967).

The results show that the rolling resistance in water increases exponentially with speed. When aquaplaning occurred, the rolling resistance became independent of the speed during steady state. According to Gengenbach (1967), the rolling resistance will increase in the short term in case of a rapid increase in water depth. It is possible to adapt an exponential model that calculates rolling resistance in water for a given value of water depth and speed, MG1:

, 1: = [2] 9 807 𝑣𝑣 𝐸𝐸 𝑀𝑀𝑀𝑀: 𝐹𝐹𝑉𝑉 𝑏𝑏 ∗ Rolling100 � 𝑁𝑁resistance� in water [N], b𝐹𝐹:𝑉𝑉 Width of the tire’s contact surface [cm], v: Speed [km/h], N: Constant for each water depth (Table 1), E: Constant for each water depth (Table 1).

Table 1. Values of N and E depending on water depth (Gengenbach 1967). Water depth N E [cm] 0.2 35 2.2 0.5 15 1.6 1.0 9.375 1.6 1.5 6.25 1.6 2.0 4.375 1.6

In a study at VTI, Olsson (1984) measured rolling resistance in water at greater water depths (2 and 9 mm). The measurements were made with a Saab Turbo APC model year 1983, which was borrowed from Saab-Scania in Trollhättan. The car was equipped with a wheel force meter on the left front

14 VTI rapport 971A wheel. The front wheel where the meter was located was equipped with a Pirelli P6 tire with the dimension 195/60 R15. The measuring surface was an asphalt section outside VTI in Linköping. The distance was divided into 25 sections, and the water depth was measured 5 times on each section. Measured speed was between 20 and 70 km/h. Rolling resistance measurements were made on both dry and wet road conditions. Besides the road conditions, the measurements would be as similar as possible to give a fair comparison and to make it possible to calculate rolling resistance in water. The results are shown in Figure 4.

Rolling resistance in water (Olsson, 1984)

d = 2.0 mm 1,0E+02 d = 5.0 mm d = 7.0 mm d = 9.0 mm 1,0E+01 Fv [N]

1,0E+00

1,0E-01 1 2 3 4 5 6 7 8 9 10 20 velocity [m/s]

Figure 4. Measurement data: Rolling resistance due to water (logarithmic scale, calculated according to Appendix 2, pages 1 and 2, Olsson 1984).

Olsson (1984) compared the results against the Gengenbachs model and then proposed two new models. The first new model, MO1, would better adapt to rolling resistance measurements with large water depths: 1: = 102,30 , . [3] 1 43 0 33 𝑀𝑀𝑀𝑀The model𝐹𝐹𝑣𝑣 only applies𝑏𝑏𝑣𝑣 to water𝑑𝑑 depths greater than 2 mm, which is not so common on roadways. For water depths of 2 mm, MO1's rolling resistance calculations correspond to MG1, according to Olsson (1984). For water depths < 2 mm, the model gives an overestimation against MG1. The model adapts to measured values, that is, within different measuring speeds and measuring water depths. When the water depth becomes less than the minimum value of measurement data, there will be a difference between MO1 and MG1. This means that adaptation to water depth < 2 mm is very poor in Model 1. It was, therefore, desirable to find another model that adapts better to water depths less than 2 mm. Measurement values for 2 mm and MG1 for 2 mm should be equal. Instead of using MG1 data together with measurement data to calculate a new model, the author used his measurement values for rolling resistance in a different way. There were some measurement values for rolling resistance that lacked associated values for the water depth. MG1 values were then used to identify the water depth for these measurements. The measurement values for the rolling resistance were plotted together with MG1 values to identify the water depth. By comparing the values, it was estimated that the water depth was about 0.7 mm. The most suitable model for the water depth of 0.7 mm was:

VTI rapport 971A 15 MO2: = 11945,50 , , . 1 81−68 01𝑑𝑑 1 23 Model𝐹𝐹𝑣𝑣 2 uses water depths𝑏𝑏𝑣𝑣 that are more𝑑𝑑 common than Model 1, namely water depths less than 2 mm. However, Model 2 is not based entirely on measurement data but uses data from Model MG1 as described above. In addition, MO2 is used in the VETO model under the calculation module for rolling resistance on wet roads. A comparison between the three models is shown in Figure 5.

Rolling resistance, water depth d = 0.7 mm 1,0E+02 MG1 MO1 MO2 1,0E+01 Fv [N]

1,0E+00

1,0E-01 1 2 3 4 5 6 7 8 9 10 20 velocity [m/s]

Figure 5. Comparison between the models: MG1, MO1 and MO2.

Some sources of error for MO1 and MO2, according to Olsson (1984), are:

1. the water level was difficult to keep constant

2. the speed varied between trials

3. a lot of noise in measurement data made the readings uncertain in some cases.

The European project MIRIAM conducted a study of rolling resistance on wet roads (Ejsmont et al. 2015). The survey used a measuring trolley from the Gdansk University of Technology (TUG), as shown in Figure 6. The measuring trolley is equipped with infrared temperature sensors that measure temperatures on the sidewall of the tire, the surrounding air and the road surface.

16 VTI rapport 971A

Figure 6. TUG's rolling resistance measuring trailer (Photo: Tiago Vieira).

The measurements were made in 2013 at an abandoned airfield in Denmark. The road was equipped with water depth sensors that made it easier to check water depth during tests. The road had an ABT11 pavement (dense asphalt concrete with a maximum stone size of 11 mm) with an average MPD value of 0.44 mm. Measurements were made at speeds of 30, 50 and 80 km/h and water depths between 0 and 0.8 mm. In addition to the tests in Denmark, measurements were also made in Sweden on an ABS8 (asphalt concrete with a maximum rock size of 8 mm) near Rökinge. The Swedish test section had an average MPD of 1.5 mm, and measurements were made at a speed of 50 km/h. The results show that the rolling resistance increases with a deeper water film. A positive correlation between rolling resistance coefficient (Cr) and water depth was observed for a speed of 30 km/h. For 0.8 mm water film, the value Cr was approximately 30 percent higher compared to dry road surface. For the other speeds, that is, 50 and 80 km/h, Cr increased even more. A 40% increase in Cr was observed for water depths of 0.3 mm. No aquaplaning occurred at 80 km/h, according to the authors. Also, the results show that temperature plays an important role in rolling resistance on wet roads. The sidewall temperature of the tire can decrease by between 6 and 8 degrees due to the presence of water on the road surface. A model that calculates the effect of tire temperature on rolling resistance is: = [1 + ( )] [4]

𝐶𝐶Where:𝑟𝑟𝑡𝑡1 𝐶𝐶𝑟𝑟𝑡𝑡0 𝐾𝐾𝑡𝑡 𝑡𝑡0 − 𝑡𝑡1

: Rolling resistance coefficient for temperature t1

𝐶𝐶𝑟𝑟𝑡𝑡1: Rolling resistance coefficient for temperature t0 𝐶𝐶𝑟𝑟𝑡𝑡: 0 Temperature influence coefficient, calculated for each tire. 𝐾𝐾𝑡𝑡 The results are in line with previously known results, that is, that rolling resistance on wet roads is affected by speed and water depth. In addition, the results show a way to calculate the effect of temperature on rolling resistance.

2.3. Heavy duty vehicles The rolling resistance of trucks is also affected by water on the road. Bode and Bode (2013) used a truck trailer set up to calculate rolling resistance on wet roads. A force meter between the coupling of the measuring car and the truck made it possible to measure rolling resistance effects. An image of the trailer for rolling resistance measurement used in this study can be found in the ROSANNE project report D3.1 “State of the art on rolling resistance measurement devices”.

VTI rapport 971A 17 Rolling resistance measurements were made at low speed, 15 km/h, and a water depth of 0.8 mm. For an asphalt pavement, they discovered that the rolling resistance increased by about 8 percent and the tire temperature decreased by 5° C. For a concrete pavement, they detected an increase in rolling resistance by about 6.5 percent and a decrease in tire temperature by 5° C. According to the authors, the increase in rolling resistance was due to a combination of temperature reduction and the amount of water that the tire must displace from the contact surface. The water leads to an increase in the effects of hysteresis on the tire, which is also affected by the temperature. Unfortunately, the temperature of the tires was not measured in the tire belts (or the steel belt of the tire), but only from the outside with an infrared meter in the tire's shoulder.

2.4. Temperature effect on rolling resistance Since both speed and temperature play an important role in rolling resistance on wet roads, it is also interesting to describe more about their impact on rolling resistance on dry roads. Tires are made up of different materials, one of which is rubber, which is a viscoelastic material. Because of this, road/tire behavior is temperature dependent. The tire's materials are optimized for a certain operating temperature, and the energy distribution usually decreases when the operating temperature increases for the most common operating conditions (Gent & Walter 2005). Sandberg (2001) mentions two different models that describe the impact of rolling resistance on speed during steady state. The first, MWO, was calculated from truck radial tires and applies up to 100 km/h (Wong 1993). : = 0,006 + 0,23 10 [5] 6 2 𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶𝑟𝑟 ∗ 𝑣𝑣 The other, from Michelin, MMI, uses the results of measurements according to ISO 9948 (kg/ton) below the speed of vISO=80 km/h and calculates the coefficient for another speed, v, between 0 and 90 km/h. The model also has two constants, a and b. : = + ( ) + ( ) [6] 2 2 Figure𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶 7𝑟𝑟 shows𝐶𝐶𝑟𝑟𝐼𝐼𝐼𝐼𝐼𝐼 a comparison𝑎𝑎 𝑣𝑣 − 𝑣𝑣 between𝐼𝐼𝐼𝐼𝐼𝐼 𝑏𝑏 the𝑣𝑣 − two𝑣𝑣𝐼𝐼𝐼𝐼𝐼𝐼 models.

9,0

8,5

8,0

7,5

Cr [kg/ton]Cr 7,0

6,5

6,0 0 20 40 60 80 100 velocity [km/h]

MWO MMI

Figure 7. Comparison of Wong's and Michelin's model for the rolling resistance coefficient for dry surfaces (adapted from Sandberg, 2001). Sandberg (2001) has measured rolling resistance for a Scania R124 truck by measuring torque on the truck's drive shaft at speeds of 40, 60, 80, 85 and 90 km/h. The results showed that the temperature is of great importance for the rolling resistance of trucks, even on dry road surfaces. When a tire heats up, the air pressure inside the tires increases and the rolling resistance decreases. Sandberg (2001) proposed a dynamic model that can calculate the rolling resistance of a non-stationary temperature

18 VTI rapport 971A condition. The model is relevant for rolling resistance in water as it can happen that a vehicle driving on a dry road suddenly comes to a wet stretch. In that case, it gives a rapid surface temperature change. It can take about an hour under constant speed to reach a new stationary (constant) temperature state because the inner temperature of the tire does not have time to change so fast. In addition, it is also relevant to consider non-stationary conditions when making measurements because it takes a while before the tire reaches steady state temperature. Sandberg's proposed model (MSA) is shown below:

= ( , ) [7]

𝐹𝐹𝑅𝑅 ( ,𝐶𝐶𝑅𝑅) =𝑇𝑇 𝑣𝑣 𝑁𝑁( ) + ( ) [8] 2 2 𝐶𝐶𝑅𝑅 𝑇𝑇=𝑣𝑣 (𝐶𝐶𝑅𝑅) 0 𝑇𝑇 𝐶𝐶𝑅𝑅1 𝑣𝑣 − 𝑣𝑣𝑆𝑆𝑆𝑆 [9] −1 𝑣𝑣𝑆𝑆𝑆𝑆= 𝑔𝑔𝑆𝑆𝑆𝑆( 𝑇𝑇 ) [10] 𝑑𝑑𝑑𝑑 1 𝑑𝑑𝑑𝑑 =− τ 𝑇𝑇( −) 𝑇𝑇𝑆𝑆𝑆𝑆 [11]

𝑇𝑇𝑆𝑆𝑆𝑆 𝑔𝑔𝑆𝑆𝑆𝑆 𝑣𝑣

FR: Rolling resistance

CR: The rolling resistance coefficient at temperature T and speed v N: Normal force

CR0: Rolling resistance coefficient at steady state (constant)

CR1: Coefficient vSC: Speed under steady state (constant) : A function that describes the tire temperature for the speed v, under steady state (constant) condition 𝑔𝑔𝑆𝑆𝑆𝑆 : A time constant

τ An example is shown in Figure 8.

Figure 8. The MSA model for a truck traveling at 80 km/h in steady state (1), reducing its speed from 80 km/h to 50 km/h (2) and continuing at 50 km/h until it reaches stationary state again (3) (Sandberg, 2001).

VTI rapport 971A 19 Sandberg (2001) showed that temperature plays an important role in the rolling resistance of trucks because it takes a long time to reach a stationary temperature state for truck tires, where the time constant (τ) is about 30 minutes. Srirangam et al. (2015a) developed a model with the finite element method for analyzing tire thermomechanical behavior. The model involves two steps. The first step is a static 3D tire model that rolls over a smooth road surface. During this step, deformations, tire footprint and the rolling radius of the tire are calculated. The second stage receives data about stresses, strains and displacements from the first stage and with this information the contact with an asphalt surface is simulated. During the second step, the behavior of the tire is simulated according to Prony's coefficients. Energy analysis is performed and the tire temperatures are calculated during this step. With the temperature information, the first step of the model is updated and the simulation is repeated until temperature convergence is reached. The process is shown in Figure 9.

Figure 9. Tires – thermomechanical interaction model from Srirangam et al. (2015a) The model was later compared with measurement data (Srirangam et al. 2015b), and the rolling resistance was analyzed at different speeds and on different road surfaces. Rolling resistance measurements were made with a Renault Clio 3 equipped with, among other things, temperature and speed sensors. The test sections are available at IFSTTAR, in France, and are ABT10, TSK4 (thin- layer coating combination with maximum stone size 4 mm) UTS (ultra-thin road surface), SA 0/4. The test speed was between 40 and 140 km/h, slip ratio was 0 percent, tire pressure 150 kPa and tire load 4.0 kN. The results showed that simulated rolling resistance coefficients correspond to the coefficients of the tests. In short, both simulation and test results showed that rolling resistance increases with speed and decreases with tire load and air pressure in the tire.

2.5. Electric vehicles Since energy use is an important aspect in electric vehicles due to how it affects the driving range, it is also important to analyze how rolling resistance is affected for electric vehicles. Unfortunately, no investigations of rolling resistance for electric vehicles on wet roads were found. But Wang et al. (2015) analyzed energy use for electric vehicles. The model for rolling resistance is shown below and includes the effects of temperature and speed. ( , ) = ( ) + [12]

𝐶𝐶𝑟𝑟 𝑇𝑇=𝑎𝑎𝑎𝑎𝑎𝑎 1.9𝑣𝑣 10 𝐶𝐶𝑟𝑟0 𝑇𝑇𝑎𝑎𝑎𝑎𝑎𝑎 2.1𝐶𝐶𝑟𝑟101𝑣𝑣 + 0.013 [13] −6 2 −4 𝐶𝐶𝑟𝑟0 ∗ 𝑇𝑇𝑎𝑎𝑎𝑎𝑎𝑎 − ∗ 𝑇𝑇𝑎𝑎𝑎𝑎𝑎𝑎

20 VTI rapport 971A Cr is the rolling resistance coefficient at the temperature Tamb and the velocity v. Cr1 is the velocity effect, and Cr0 is the temperature effect. The model was built based on several coast-down measurements with a test car. The test temperatures were 2.5 °C during the winter and 29 °C during the summer. The purpose was to develop a model that can be used to predict the energy use of an electric vehicle with a maximum error of 5 percent. According to the authors' conclusions, the coefficient of rolling resistance varied too much, which means that a more comprehensive study of the variation of the rolling resistance under different road conditions is needed to cope with this margin of error.

2.6. Aircraft Rolling resistance also affects the aircraft's behavior and is an important parameter when the aircraft's tires roll over a wet surface. Specification CS-25 describes EASA (European Aviation Safety Agency) aircraft interaction with wet road surfaces (EASA 2017). In the event of surface pollution on the road or runway (for example, water), there will be an energy use component according to the equations below:

= + [14]

𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑎𝑎𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑1 𝑑𝑑 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝐷𝐷 𝐷𝐷 = 2 𝐷𝐷 [15] 2 𝐷𝐷𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑎𝑎𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐶𝐶𝐷𝐷 � 𝜌𝜌𝑉𝑉 𝑆𝑆 = 2 1 [16] 2 𝛿𝛿+𝑑𝑑 𝛿𝛿+𝑑𝑑 2 𝑏𝑏 = 𝑊𝑊 � � 𝑊𝑊 � − � 𝑊𝑊 � � [17]

𝑆𝑆 𝑏𝑏 ∗ 𝑑𝑑 : The density of the surface contaminant,

𝜌𝜌 : Usually 0.75 for a single tire and speed below the aquaplaning speed, Vp, d𝐶𝐶:𝐷𝐷 Depth of surface contamination, S: The frontal area of the tire in contact with the surface contamination, V: Ground speed, W: Maximum tire width (from manufacturer's deflection curve), : Tire deflection (from the manufacturer's load-deflection curve)

𝛿𝛿 The equations describe the tire's behavior during aquaplaning speeds. Giesberts (2001) tested the interaction of aircraft wheels with water and how rolling resistance was affected with two different aircraft: NLR Citation II (12 mm water depth) and Dassault Falcon 2000 (20 mm water depth). The test section is located at Cranfield University, UK, which contains a 600 m long wet section between two dry sections. The impact of the water was calculated by comparing acceleration before, during and after the aircraft traveled on the wet route. The author also suggested that water depth affects the rolling resistance effect according to a linear relationship. This makes it possible to calculate the resistance effect of NLR Citation II at 10 mm water depth and Dassault Falcon 2000 at 20 mm water depth. Aquaplaning was controlled by tire rotation. During aquaplaning, tire rotation would decrease due to aquaplaning torque, which reduces the angular velocity. The tire pressure for Citation was between 130 psi and 150 psi during the test. The effect of the water was calculated by comparing the results of the wet surface with the results of the dry surface. The results show that the impact of water on the rolling resistance of an entire aircraft is between 15 and 40 percent greater than what was calculated with the equations. In addition, aquaplaning takes

VTI rapport 971A 21 place at lower speeds than calculated with the equations, up to 20 percent lower speed. With consideration to this, the author recommended an update of the AMJ 25X1591 method (now equivalent to EASA CS-25).

2.7. Strategies for road maintenance, transport costs and energy use The importance of rolling resistance on wet roads was already shown in the 1980s with VTI's VETO model, which was originally developed to calculate transport costs. One way to calculate and control how rolling resistance affects fuel consumption is to use the so-called return factor, R (Gent, Walter 2005). It expresses how much fuel consumption decreases with reduced rolling resistance. The return factor is calculated according to the equation below.

= ∆𝐹𝐹𝐹𝐹 [18] 𝐹𝐹𝐹𝐹 ∆𝐹𝐹𝑅𝑅 𝑅𝑅 − 𝐹𝐹𝑅𝑅 where FE is fuel economy and FR is rolling resistance. The value of the return factor is between 0.08 and 0.20 for light vehicles and approximately 0.33 for a fully loaded truck. Unfortunately, no current calculations of the return factor for wet roads were found. On the other hand, it is obvious that wet roads play an important role in transport costs and energy use because (i) rolling resistance is usually measured under dry conditions, (ii) fuel economy due to rolling resistance plays an important role even on dry roads, and (iii) rolling resistance increases heavily under wet conditions. The potential for savings for heavy vehicles is particularly relevant because, according to the literature, they have high return factors. Carlson et al. (2016) investigated how to choose a strategy for road maintenance that reduces the total energy use for traffic and maintenance that also takes into account cost-effectiveness and uncertainty. The VETO model is used to take into account the effects of water and snow on the road surface. The results showed that, by choosing certain maintenance strategies, one can reduce rolling resistance by about 1 percent. The report shows that rolling resistance increases when water is on the road surface, which is in line with other results in this report.

22 VTI rapport 971A 3. Impact on rolling resistance due to snow on the road surface The impact of snow on rolling resistance is complex and depends on several factors such as the thickness of the snow layer, the density and type of snow, and the speed of the vehicle (Shoop et al. 2006, Hjort 2012). The properties of the snow also change over time due to, for example, wind, temperature and rain (van Es 1999), and this change can occur quickly. It is, therefore, also complicated to carry out comparable measurements. In order to be able to say how a vehicle will be affected by snow-covered surfaces, it is important to know the mechanistic properties of the snow and to identify the parameters that are important in this context (Pytka 2009). Snow consists of ice, water and air and is made up of snow crystals that are formed as they freeze. The properties of the snow depend on the size, shape and temperature of the snow crystals and how they are packed (Lidström 1979). Large snowflakes, which have an intricate shape, give rise to airy volume with low density, while small snow crystals, which have a simpler shape, pack more easily and lead to higher density. The properties of the snow also depend on the circumstances in which it was formed, such as air temperature (Pytka 2010). The type of snow crystal that is formed can be seen in a so- called Nakaya diagram (Libbrecht 2012). This shows that the temperature mainly affects the shape of the snow crystals, whether they become columns or plates, while the saturation of moisture affects how complex the structure becomes. Generally, a denser snow is formed at higher temperatures. Important properties of snow, according to Pytka (2010), are:

• size and shape of the snow crystals

• density

• temperature of the snow

• water content of the snow.

In van Es (1999), a proposal is given for the classification of snow types and their density, stated with an interval, as seen in Table 2. Density has proven to be the most useful parameter to describe snow and its structural properties (van Es 1999). There is also an international classification for seasonal snow, which, in addition to the properties mentioned in Pytka (2010), also addresses the hardness, impurities and thickness of the snow layer (Fierz et al. 2009). The classification also provides definitions of how snow can be described.

Table 2. Proposals for the classification of snow types and their density (van Es 1999).

Snow type Density (kg/m3)

New snow 50–200

Powder snow 200–450

Wet snow 300–700

Compact snow 450–700

Snow that is subjected to pressure will have a changed density and the bonds between the snow crystals will also change. The fact that snow crystals have a stronger bond between each other during compaction means that such snow will be stronger relative to a natural snow with the same density (Kihlberg 1979, Giesberts 2001). However, snow can only be compacted up to a certain limit before it turns to ice. This occurs when the pores in the snow become sealed, closed air bubbles are formed and

VTI rapport 971A 23 the material becomes impermeable to air (Kihlberg 1979). CRREL4 has theoretically calculated what the final density will be with respect to the maximum pressure against the ground (Richmond 1990), as shown in Table 3.

Table 3. Final theoretical density of snow in CRREL's model for mobility in shallow snow (Richmond 1990).

Maximum ground pressure (kPa) Theoretical final density (kg/m3)

<210 500

211–350 550

351–700 600

>700 650

3.1. Theory How a vehicle behaves in snow usually depends on the bearing capacity, which determines how much a vehicle will sink. The bearing capacity, in turn, depends on how much the snow can be compressed and how strong the bond between the snow crystals is in relation to the load of the vehicle. Since the strength of the snow is difficult to measure, other variables are used that are easier to obtain a value for, such as snow depth and snow density (Shoop 2001). When a wheel drives through snow, it will exert an increased pressure that compresses the snow, and tracks are formed (Richmond 1995). In this track, both the thickness, density and strength of the snow crystal bonds change relatively untouched snow. The energy required to perform this compaction, corresponding to the dotted area in Figure 10, can be used to describe the additional rolling resistance that occurs. In the figure, h0 represents the thickness of the pristine snow and ρ0 its density. hf and ρf are the resulting thickness and density after driving through. In general, the bearing capacity of natural snow is usually quite low, especially for snow with a density lower than 400 kg/m3 (van Es 1999). As a result, the compaction of snow, that is, rutting, becomes significant. The fact that the thickness, density and internal strength of the snow change, in turn, affects the rolling resistance of the following pairs of wheels and of subsequent vehicles. How the vehicles are driven, whether all the wheel pairs on a vehicle follow in the same wheel track and whether a driver chooses to drive in existing wheel tracks or not will thus have an effect on how large the rolling resistance will be for a vehicle.

Figure 10. Snow compaction of wheels (from Lidström 1979).

4 Cold Regions Research & Engineering Laboratory at U.S. Army Corps of Engineers.

24 VTI rapport 971A In Harrison (1981), previous work was compiled on how to analyze the vehicles' travel resistance in snow. All in all, most of the studies described in the report are based on the compaction of snow in order to estimate the increased driving resistance that it entails. Based on the previous studies, some functions are given to describe the resistance for, among other things, shallow snow, snowdrifts and ice/hard-packed snow. For shallow snow, the suggested function is: = 2 [19]

𝑅𝑅where𝑐𝑐 b𝑏𝑏𝑏𝑏 is ℎthe width of the track, h is the snow depth and ω is the work needed to compact the snow. Wet snow has a behavior that is more like a liquid than snow and will be displaced rather than compressed when a wheel passes. Therefore, Harrison (1981) suggests that models based on hydrostatic properties be used for such a type of snow. Based on an ad hoc model, the function given is:

= 2 [20] 𝛾𝛾ℎ where𝑅𝑅𝑐𝑐 γ2 and h are the density and thickness of the snow layer, respectively. For wet snow, the density is stated at 750 kg/m3. Hard-packed snow is assumed to have a negligible effect on driving resistance. Harrison (1981) notes, however, that the biggest weakness in the studies is the lack of field tests and that the functions listed in the report need to be validated. One method that has been used to determine the magnitude of the energy needed to compress snow is to apply a vertical force to the snow cover, measure how deep the weight drops, and, based on that, estimate how large the horizontal resistance is. However, early experiments have shown that this method tends to underestimate driving resistance (Blaisdell 1981) because a wheel affects the snow in two ways. Blaisdell (1981) presents a developed method that should better take into account that compaction occurs both due to weight and due to a forward movement. The wheel is divided into an infinite number of flat sections, each of which forms a pressure against the snow during driving, represented by FT1, FT2 and FT3 in Figure 11. The size of the resistance is a function of how the plates sink down along the curved surface of the wheel. Each part of the tire's surface is exposed to different forces because they are in different positions in terms of how far they have come in the track and compressed the snow. To calculate the total resistance caused by the snow, all force vectors are summed along the distance that constitutes the formation of the track.

Figure 11. Force vectors resisting forward wheel motion in snow (Blaisdell 1981). According to the report, it was found that it is possible to describe the force vs sinkage with the formula: = 1 + 2 + 3 + 4 + 5 [21] 4 3 2 𝐹𝐹 𝑎𝑎 𝑠𝑠 𝑎𝑎 𝑠𝑠 𝑎𝑎 𝑠𝑠 𝑎𝑎 𝑠𝑠 𝑎𝑎 VTI rapport 971A 25 F is the force at each plate, a1 to a5 are constants and s is the length of how much the wheel sinks into the snow. Furthermore, the force required for compaction is described as a vector ( ) for each point along a trochoid5, which describe the sinkage path [22]. F is the vertical force and t is the direction of the � device key vector. 𝐹𝐹 = × [22]

𝐹𝐹In� order𝐹𝐹 to𝑡𝑡 describe the force required for a wheel to be able to displace snow, Blaisdell (1981) suggested two expressions, one for s and one for t, which can be used in [21] and [22]. CRREL has since further developed the function for calculating the resistance that snow contributes (Blaisdell et al. 1990, Richmond et al. 1990). It describes the driving resistance using tire pressure, tire width, snow depth and snow density before and after compaction. With the assumptions that the amount of snow moved laterally is insignificant, that is, that compaction takes place only in the track, and that the total mass of snow is unchanged, the travel resistance can be expressed as follows:

= × 1 × ln 1 om < ( > 0) [23]

𝑅𝑅𝑠𝑠 = 𝑝𝑝 0𝑝𝑝 ℎ 𝜌𝜌𝑜𝑜 �� ⁄�𝜌𝜌𝑓𝑓 − 𝜌𝜌𝑜𝑜�� �𝜌𝜌𝑓𝑓⁄𝜌𝜌𝑜𝑜� − � ⁄𝜌𝜌𝑓𝑓�� om 𝜌𝜌𝑜𝑜 = 𝜌𝜌𝑓𝑓 (𝑧𝑧 = 0) [24]

𝑅𝑅Rs𝑠𝑠: Driving resistance in snow, 𝜌𝜌𝑜𝑜 𝜌𝜌𝑓𝑓 𝑧𝑧 pbh: Tire pressure × Maximum tire/track width × Snow depth,

ρo: Snow density before,

ρf: Snow density after, z: Track depth.

Since the following wheels will run on already compressed snow and also, to some extent, untouched snow, a modified function was developed that takes this into account. See [25] - [27]. 1 1 = ln + 𝜌𝜌𝑖𝑖 𝑅𝑅𝑠𝑠𝑖𝑖 𝛼𝛼 �𝑝𝑝𝑖𝑖𝑏𝑏𝑖𝑖ℎ𝑜𝑜𝜌𝜌𝑜𝑜 � − �� (1 ) 𝜌𝜌𝑖𝑖−𝜌𝜌𝑜𝑜 𝜌𝜌𝑜𝑜 𝜌𝜌𝑖𝑖ln om > [25] 1 𝜌𝜌𝑖𝑖 1 𝑖𝑖 𝑖𝑖−1 𝑖𝑖−1 𝑖𝑖 𝑖𝑖−1 𝑖𝑖−1 𝑖𝑖 𝑖𝑖 𝑖𝑖−1 = − 𝛼𝛼 �𝑝𝑝𝑏𝑏 ℎ 𝜌𝜌 ln �𝜌𝜌 −𝜌𝜌 𝜌𝜌 − 𝜌𝜌 �� om 𝜌𝜌 = 𝜌𝜌 > [26] 1 𝜌𝜌𝑖𝑖 1 𝑖𝑖 𝑅𝑅𝑠𝑠 = 𝛼𝛼0 �𝑝𝑝𝑖𝑖𝑏𝑏𝑖𝑖ℎ𝑜𝑜𝜌𝜌𝑜𝑜 �𝜌𝜌𝑖𝑖−𝜌𝜌𝑜𝑜 𝜌𝜌𝑜𝑜 − 𝜌𝜌𝑖𝑖�� om 𝜌𝜌𝑖𝑖 = 𝜌𝜌𝑖𝑖− 1 𝜌𝜌𝑜𝑜 [27]

𝑅𝑅𝑠𝑠𝑖𝑖 𝜌𝜌𝑖𝑖 𝜌𝜌𝑜𝑜 Where i represents which wheel it is and i-1 is the state that is before wheel i passes; for example, ρi-1 and hi-1 are the snow density and snow depth respectively that wheel i passes over. When comparing calculated and measured values, it turned out that coherence between them was poor, and it was concluded that the description of how resistance is affected by snow needs to be improved (Blaisdell et al. 1990). One problem that was identified was the calculation of resistance for subsequent wheels since they run completely or partially in already made tracks. Tests performed show that the resistance of subsequent wheels can be about 20 percent of the front, leading wheel (Richmond et al. 1990). The study suggests that more tests and analyses are needed to clarify the resistance of subsequent wheels.

5. A roulette formed by a circle rolling along a line.

26 VTI rapport 971A Lidström (1979) describes an overall and general function for rolling resistance (FR) for an aircraft wheel on a snow-covered surface: = + + [28]

𝐹𝐹where𝑟𝑟 𝐹𝐹 F𝑜𝑜o is𝐹𝐹 the𝑐𝑐 internal𝐹𝐹𝑑𝑑 friction that is independent of snow. Fc is rolling resistance due to compaction that contains information about the width of the contact surface between tire and snow, density and depth for untouched snow, compressive strength and density for ice [29]. Formerly, the contribution to rolling resistance is due to that the wheel's forward movement exposes snow crystals to a dynamic energy, which means that they are compressed. Fd is a function of the width and length of the contact surface between tires and snow, density and depth for untouched snow, density and compressive strength for ice, speed and radius and load on tires [30].

× = × ( 1) + × ( 1) × × [29] × 3⁄2 𝑏𝑏𝑘𝑘 𝜎𝜎𝑖𝑖 √𝜋𝜋 𝑏𝑏 3 𝑐𝑐 𝑖𝑖 𝑜𝑜 𝑜𝑜 𝐹𝐹 = 𝜌𝜌 √1𝑏𝑏 � 2 −×√𝑏𝑏+ 𝑎𝑎 ×− 3 × 𝑎𝑎ln− �× 𝜌𝜌 × ℎ × 2 , [30] 𝑏𝑏𝑘𝑘 𝜌𝜌𝑜𝑜 𝜌𝜌𝑜𝑜 𝚤𝚤 𝜌𝜌𝑜𝑜 2 2 𝐹𝐹𝑑𝑑 𝑅𝑅 � − 𝑎𝑎 𝜌𝜌𝑖𝑖 �𝑎𝑎 𝜌𝜌𝑖𝑖 − 8𝑅𝑅ℎ𝑜𝑜� 𝑎𝑎 𝜌𝜌𝑖𝑖 � 𝑣𝑣 𝜌𝜌𝑜𝑜 ℎ𝑜𝑜 = 1 + 1 with × [31] 1 𝐹𝐹𝑧𝑧 A: 𝑎𝑎 The �area𝑏𝑏 � on− the𝐴𝐴 𝜎𝜎flat𝑖𝑖� part of the contact surface between tire and snow, bk: The width of the contact surface between tires and snow,

Fz: Static load on the tire, ho: Snow depth, untouched snow, ℓ: The length of the flat part of the contact surface between tire and snow,

ρo: Density, untouched snow,

ρi: Density, ice,

σi: Compressive strength, ice, R: The radius of the tire, v: Speed, b, a: Constants.

Lidström's (1979) general function for rolling resistance was later used by van Es (1999) and Giesberts (2001), then described as: = + + [32] where𝐷𝐷𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑟𝑟Dr is 𝐷𝐷rolling𝑟𝑟 𝐷𝐷 𝑐𝑐resistance𝐷𝐷𝑑𝑑 on snow free ground, Dc is rolling resistance due to compaction of snow and Dd represents rolling resistance due to snow being displaced. In this case, Dc and Dd apply to an aircraft wheel, which means that they need to be produced for each wheel and then summed to get the total rolling resistance of a vehicle. In van Es (1999), the general function is developed according to:

× × = [33] × 2 𝑏𝑏𝑏𝑏𝑖𝑖 𝜌𝜌0 ℎ0 𝑢𝑢0 −𝑢𝑢 𝐷𝐷𝑐𝑐 𝜌𝜌𝑖𝑖 √𝜆𝜆 ∫𝑢𝑢𝑓𝑓 𝑒𝑒 𝑑𝑑𝑑𝑑 with = 1 and = 1 𝜌𝜌𝑖𝑖 𝜌𝜌𝑖𝑖 𝑢𝑢0 √𝜆𝜆 �𝜌𝜌0 − � 𝑢𝑢𝑓𝑓 √𝜆𝜆 �𝜌𝜌𝑓𝑓 − �

VTI rapport 971A 27 = 1 cos 2 ln + cos + 𝑓𝑓 𝑓𝑓 𝑏𝑏 2 2 2 ℎ ℎ0 2 2ℎ 2 2 𝐷𝐷𝑑𝑑 2 ℎ0𝜌𝜌0𝑉𝑉𝑔𝑔 �� − 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼1 − 𝑅𝑅 ℎ𝑓𝑓 𝛼𝛼1 − 𝑅𝑅 � �ℎ𝑓𝑓�� �ℎ0 − ℎ𝑓𝑓� �𝑅𝑅 𝛼𝛼1 𝑅𝑅 � − [34] 1 2 2 2 b: 2𝑅𝑅 The�ℎ0 width− ℎ𝑓𝑓 � of the tire's contact surface with the snow,

σi: Unlimited compressive strength of snow, h0: Snow depth, untouched snow, hf: Snow depth, after compaction,

ρi: Density of ice,

ρf: Density of snow after compaction,

ρo: Density of untouched snow, λ: Index of snow grain structure, r: Proportion of voids in the snow,

Vg: Speed on the ground, α: Angle of wheel movement of snow, R: The radius of the tire.

Some differences compared to Lidström (1979) are that van Es (1999) has included more variables that describe the properties of the snow, such as the index of grain size and the proportion of voids. The report also describes that the resistance due to compaction, Dc, increases linearly with the snow density up to 350 kg/m3 and then flattens out and reaches a maximum at about 420 kg/m3. The reason is that the bearing capacity is higher for densities greater than 420 kg/m3, which reduces the deformation of the snow. Dd is, in turn, a complex function of the tire's radius, the initial and final snow depth and the length of the tire's contact surface. The density at which the maximum resistance occurs will therefore vary between different combinations of vehicles and tires. For aircraft, van Es (1999) was able to show that this occurs when the density of snow is approximately 200 kg/m3. Via an example, he was also able to show that speed is of great importance for rolling resistance when the snow density is low, around 150 to 300 kg/m3.

3.2. Measurements Some experiments regarding the measurement of rolling resistance/driving resistance and snow have been carried out, especially between the late 1970s and the mid-1990s. As the measurement methods have been continuously improved, this means that there is a lack of updated data. Another aspect to take into account is that most of the studies and experiments carried out are not about wheels for ordinary road vehicles but about aircraft wheels (for example. Kihlgren 1977, Lidström 1979, Giesberts 2001, van Es 1999) or off-road vehicles that have wheels or tires (e.g., Blaisdell 1981, Shoop 1992, Richmond 1995, Bodin 2001, Pytka 2009). But the studies are still interesting because they can show the relative importance of snow on rolling resistance. Some of the measurement results produced are described below. Kihlgren (1977) reports measurements of rolling resistance in dry fresh snow for an aircraft wheel and a tire that is intended for tests between road surface and tires (ASTM). For the assignment, a measuring trailer that measured friction was modified to be able to measure rolling resistance. When dry snow fell, they took the measuring trailer to an airfield and carried out measurements by driving in untouched snow layers and on a surface that had been cleared of snow. For the aircraft wheel, measurements were performed with two different air pressures in the tires, 410 and 550 kPa, at a speed

28 VTI rapport 971A of 50 km/h. For ASTM, measurements were made at three different speeds, 20, 65 and 80 km/h and with an air pressure in the tire of 165 kPa. A total of 180 measurements were performed, 104 for aircraft wheels and 76 for ASTM. The depth, density and temperature of the snow were also registered at each time. Figure 12 and Figure 13 show the measured measurement values for rolling resistance related to snow depth. A conclusion drawn in the study is that the rolling resistance generally seems to increase linearly with the snow depth and that a lower air pressure in the tires gives higher rolling resistance. Furthermore, it also appeared that the rolling resistance increases linearly at a higher speed. As shown in the figures, however, there are large variations in the values of the rolling resistance on snow free ground. One explanation given is that there is probably a lack of accuracy in the measurement method used. The same shortcoming should, therefore, also exist for other measurement data. The measured values collected by Kihlberg (1977) were then used in Lidström (1979) to produce values of parameters for the function that describe the influence of the physical factors on the wheel's rolling resistance in snow. The method used was regression analysis with the least-squares method. With this, Lidström (1979) made estimates of the rolling resistance coefficient for aircraft wheels with respect to speed and snow depth, as seen in Figure 14. The data on which the calculations are based is a static load = 100,000 N, snow density = 100 kg/m3, radius and width on wheels = 0.55 m and 0.3 m respectively.

1 800

1 600

1 400

1 200

1 000

800

600 Rolling Rolling resistance [N] 400

200

0 0 10 20 30 40 50 60 70 80 90 100 Snow depth [mm]

410 kPa 550 kPa Trend line (410 kPa) Trend line (550 kPa)

Figure 12. Rolling resistance – Results of measurements with aircraft tires (Kihlgren 1977).

VTI rapport 971A 29 600

500

400

300

200 Rolling Rolling resistance [N]

100

0 0 10 20 30 40 50 60 70 80 90 100 Snow depth [mm]

50km/h 65 km/h 80 km/h Trend line 80 km/h Trend line 65 km/h Trend line 50 km/h

Figure 13. Rolling resistance – Results of measurements with ASTM tires (Kihlgren 1977).

Figure 14. Estimated rolling resistance coefficient for aircraft wheels, depending on snow depth, h0. From Lidström (1979).

CRREL conducted experiments to investigate the driving resistance that snow contributes to. An experimental off-road vehicle, CIV (CRREL Instrumented research Vehicle) was used for the experiments, which was driven or towed at 5 km/h. Results of measurements performed on three measurement occasions, 1988, 1989 and 1993, are reported in Figure 15 (Richmond 1996). To

30 VTI rapport 971A calibrate the measuring vehicle, at least four tests were performed on a hard surface. The measured values presented in the figure below are the measured resistances minus the resistance measured for a hard surface. Since the normal load for vehicles is half the axle load, the values are also divided in two, which means that they represent half of the resistance that can be attributed to snow (Richmond 1995).

1600

1400

1200

1000

800

600 Rolling Rolling resistance [N] 400

200

0 0 50 100 150 200 250 300 Snow depth [mm]

CIV 1993 data CIV 1988 and 1989 data

Figure 15. Rolling resistance – Results of measurements made by CRREL (Richmond 1996).

Giesbert (2001) has used measurement data produced in the EU project CONTAMRUNWAY to compare two methods of calculating expected rolling resistance in snow for aircraft and how well they correspond to the actual measurements. The two methods that were compared are both described in van Es (1999). One, JAA AMJ 25XJ1591, was at the time the method used to determine the performance of aircraft in water and snow on runways. The second method is developed by van Es (1999). The experiments used three different aircraft types, a Citation II, a SAAB 2000 and a Dassault Falcon 2000. These were run in natural fresh snow at Skavsta Airport in Nyköping, Malmen Airport in Linköping and Ivalo Airport in northern Finland. The resistances measured are reported in Table 4 and are given as a range with the lowest and highest measured value. The results show that there is a speed-dependent part as the rolling resistance increases with increasing speed and that snow depth and density have an effect on the resistance as a function of the ground speed. It was also seen that the rolling resistance at low speeds is significant. The method developed in van Es (1999) proved to be more in line with measurement data than the method according to JAA AMJ 25X1591 did. The latter method generally underestimated the resistance, especially at low speeds.

VTI rapport 971A 31 Table 4. Measured values of rolling resistance for aircraft (Giesbert 2001).

Aircraft Conditions Resistance *

Citation II Snow depth: 40 mm new snow About 1 200 to 2 000 N Density: 140 kg/m3

SAAB 2000 Snow depth: 87,5 mm new snow About 2 000 to 10 300 N Density: 109 kg/m3

Falcon 2000 Snow depth: 100 mm new snow About 7 600 to 15 000 N Density: 110 kg/m3

* The values are read from figures in Giesbert (2001) and are given as approximate in the table above.

A new study in Japan that examined rolling resistance on snowy roads has shown that longitudinal unevenness (IRI) is affected by snow on the road surface (Mariyama & Kimura 2018). This provides an additional dimension to consider in order to find how the snow affects rolling resistance and fuel efficiency. In addition to the tires needing extra energy to displace snow, an increased unevenness on the road will also give an increased rolling resistance. The results have been produced through coast down experiments with an instrumented truck, which drove on dry roads and in different types and amounts of snow and ice. The experiments showed that fuel efficiency can decrease by up to 70 percent due to snow and ice, with an average value of 21 percent. This means that the increase in fuel due to the presence of snow on the road surface is not negligible. The experiments also showed that the rolling resistance decreases with increasing density on the snow, which may seem contradictory relative to previous studies. But the results can also be seen as complementary; see further in Chapter 4. Discussion.

3.3. Model calculations with respect to traffic and snow

3.3.1. Models for tires and for simulators A three-dimensional model for tires in terrain in cold regions, based on finite elements (FEM), has been developed at CRREL (Shoop 2001, Shoop 2006). It is intended to simulate a tire on CIV (CRREL Instrumented research Vehicle) that travels through fresh snow with a density of 200 kg/m3 and in a snow depth between 5 and 50 cm. Models describing fresh snow and thawing soil were created, and these were validated against measurements in both the laboratory and in the field. Comparisons show that the developed tire model's rolling resistance corresponds well with both measured values and with values calculated with NATO Reference Mobility Model II (NRMM) (Shoop 2006). Both the FEM model's and the NRMM's calculated values are slightly above those measured, where the FEM model also generates higher values for rolling resistance than the NRMM. CRREL has further developed a simulator for vehicles that drive in terrain and under different conditions, such as mud, snow, ice and asphalt (Parker et al. 2009). The simulator has previously included relationships describing rolling resistance: one for a hard surface (Rh) that takes into account the tire pressure, and one for a soft surface (Rs) where the initial snow depth, tire width and length of tire contact with the snow are explanatory variables. The tire component in the simulator has since been replaced by a new code, VTI (Vehicle Terrain Interaction), which should be able to reproduce realistic values while driving. One difference is also that the new code simulates an entire vehicle while the older one simulates a quarter of a vehicle. A comparison between the two different codes shows that the rolling resistance increases with increased initial snow depth and that the calculated values agree well with each other. These calculation methods have then been verified against measured values and against NRMM. That comparison also shows coherence, which Parker et al.

32 VTI rapport 971A (2009) take as evidence that the algorithms that form the basis for the development of the connections are correct.

3.3.2. Fuel consumption of vehicles VETO began to be developed in the 1980s with the primary purpose of calculating vehicle costs as a function of the road standard (Hammarström & Karlsson 1987). The tool has since continued to be developed, and in recent decades it has mainly been used to calculate energy and fuel consumption for road vehicles with regard to the design of the road and the properties of the road surface. VETO can, among other things, take into account the road conditions and whether it is dry or if there is wet or snow on the road surface. In the original version of the model, it is assumed that the snow is loose. The rolling resistance in loose snow is calculated in VETO according to the model developed in Lidström (1979), which describes the resistance that results from the compaction and displacement of loose snow. The function used in VETO consists of the following parts:

• the width of the contact surface of the wheels with the road surface

• proportion of the wheels' contact surface that is exposed to loose snow

• compressive strength of ice

• density of ice

• density of snow

• snow depth.

In VETO, it is assumed as standard that the front wheels are completely exposed to loose snow (Hammarström & Karlsson 1987). The same applies to subsequent pairs of wheels that do not go in exactly the same wheel tracks as the front ones. For the rear wheel pairs that follow the same track, it is assumed that they are exposed to packed snow/ice. The report presents some calculations with the VETO program regarding the impact of snow on fuel consumption for a car and a truck with a trailer. The results show that for a passenger car driving at 90 km/h, fuel consumption can increase by 9 and 21 percent at a snow depth of 10 and 30 mm, respectively. For a truck with a trailer that drives at 70 km/h, the corresponding increase in fuel consumption is 7 and 20 percent, respectively (Hammarström & Karlsson 1987). The calculation tool has also been used to produce the effect on fuel consumption for the three vehicle categories, passenger car, truck and truck with trailer, with respect to wet and snowy road surfaces (Carlson et al. 2016). In the study, calculations were made for different vehicle types, road types, road unevenness (IRI), texture (MPD), snow types and snow depth. Fuel consumption when there was snow on the road surface was related to a dry road surface. A comparison was also made between the alternatives that the front wheel axle was exposed to the defined snow depth to 100 percent and 25 percent, respectively. In general, fuel consumption increases with increasing snow depth and with the proportion of the front axle that is exposed to untouched snow. But there is also a speed effect, which means that the speed of the vehicles decreases as the resistance increases due to the properties of the road surface. The reduced fuel consumption that accompanies lower speeds may, in some cases, outweigh the increased fuel demand due to increased driving resistance. The result for a passenger car on a country road with a speed limit of 90 km/h is shown in Figure 16. The relative fuel consumption will be higher according to an essentially linear relationship.

VTI rapport 971A 33 5,0 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0 10 20 30 40 50 Relative fuel use. Dry roadsurface = 1.0 Snow depth (mm)

New snow Powder snow Wet snow Compacted snow

Figure 16. Fuel consumption in the event of snow on the road surface relative to a dry road surface. Passenger car, 90 km/h, IRI = 2. Data from Carlson et al. (2016).

Blokhin et al. (2016) have developed two functions to be able to describe how fuel consumption is affected by the vehicles passing in snow. Rc describes the deformation of the snow, [35], and Rdoz describes the effect of moving the snow [36]. These two functions correspond to Lidström (1979) and van Es (1999) Fc, Dc and Fd, Dd, respectively.

= 2 ln [35] 2 𝛾𝛾ℎ𝑚𝑚𝑚𝑚𝑚𝑚 𝑞𝑞𝑚𝑚𝑚𝑚𝑚𝑚 𝑅𝑅𝑐𝑐 𝑏𝑏𝑏𝑏ℎ𝑚𝑚𝑚𝑚𝑚𝑚 �− �𝛾𝛾ℎ𝑚𝑚𝑚𝑚𝑚𝑚+𝑞𝑞𝑚𝑚𝑚𝑚𝑚𝑚� − 𝛾𝛾ℎ𝑚𝑚𝑚𝑚𝑚𝑚+𝑞𝑞𝑚𝑚𝑚𝑚𝑚𝑚� = 2 ln 1 + 1 + [36] 2 ∆ℎ 𝑞𝑞𝑚𝑚𝑚𝑚𝑚𝑚 ∆ℎ 𝑅𝑅𝑑𝑑𝑑𝑑𝑑𝑑 𝑏𝑏𝑏𝑏ℎ𝑚𝑚𝑚𝑚𝑚𝑚 � � ℎ𝑚𝑚𝑚𝑚𝑚𝑚 � 𝛾𝛾ℎ𝑚𝑚𝑚𝑚𝑚𝑚�� − ℎ𝑚𝑚𝑚𝑚𝑚𝑚� b: Wheel width. γ: Coefficient of stiffness. ∆h: The depth of the snow that is displaced from the contact surface and to the side. hmax: Deformation of snow corresponding to maximum compaction. qmax: Maximum ground pressure under tires.

These functions have been used to calculate the effect on fuel consumption at different snow depths and densities. By using [35] and [36] in a fuel consumption function, according to the authors, it is seen that fuel consumption increases when the density becomes greater at the same snow depth. The same applies when the snow depth increases at the same density on the snow. The relationship is non- linear and can be described with a quadratic equation where snow depth and snow density are included as variables. According to the figures presented in the article, it is seen that fuel consumption reaches a breaking point where it goes from following a relatively flat increase to increasing exponentially. Where that breaking point is located depends on density and snow depth. The greater the snow depth and the higher the density, the faster it is reached. The theoretical calculations were compared with field trials of an instrumented off-road vehicle (Blokhin et al. 2016). The results show that the agreement was relatively good, with a difference of

34 VTI rapport 971A less than 15 percent. The comparison was carried out within the limits for density and snow depth, where the increase in fuel consumption, according to the calculations, was relatively flat. In the RekkeVidde project, coast down were carried out with an electric car on a snow-covered road surface to investigate the impact of the road surface on rolling resistance (Haakana et al. 2013). The coast downs were made on a dry road surface at temperatures +23 +C, ± 0˚C and -20˚C, and at -20˚C when there was snow on the road surface. At least three attempts were made per alternative. The properties of the snow stated in the report were whether it was old or new but there is no additional information about, for example, density or depth. To get the size of the effect on energy demand, the amount of electricity the battery needed to be charged with was measured after each test. These values then used in a calculation model at the Technical Research Center of Finland (VTT) to find out how the energy needs of different driving cycles are affected by the presence of snow, see Table 5. According to the study, snow leads to at most about 20 percent higher energy needs in city driving, which consists of a higher proportion of “stop and go”. For the driving cycles NEDC (New European Driving Cycle) and Road in Finland, which to a greater extent consist of higher and smoother speeds, the presence of snow meant between 2 and 7 percent higher energy needs compared to bare ground. Table 5. Measured amount of electricity charged to the battery after coast down. Outdoor temperature -20˚C (Haakana et al. 2013).

Driving cycle Dry road surface Old snow New snow kWh/km kWh/km kWh/km

NEDC 0.192 0.196 0.201

City driving, City of Helsinki 0.173 0.211 0.208

Road in Finland 0.251 0.267 0.267

3.3.3. Strategies for winter road maintenance VETO has also been used to calculate fuel consumption to be implemented in the Winter Model. The Winter Model is a model for maintenance strategies for roads in winter and which, in addition to fuel consumption, also includes effect models for, for example, accidents, accessibility, the environment and costs for maintenance measures (Möller 2014, Arvidsson 2017). The Winter Model has since formed the basis for calculations of energy-efficient winter maintenance. In Nordin & Arvidsson (2014), the energy requirement for implementing measures for de-icing and clearing roads from snow, respectively, was compared with the reduced energy use that traffic would have as a result of reduced driving resistance. Two different densities of snow were included in the study, 100 and 400 kg/m3, and three snow depths, 0, 2 and 5 cm. The results show that there is a speed dependency for when snow removal becomes effective. At 90 km/h, there needs to be at least 1 cm of snow, and at 120 km/h, 2.5 cm of snow is needed on the road before snow removal can be effective. According to Nordin and Arvidsson (2014), by changing guidelines for when snow removal should be carried out, from 1 cm to 2 cm of snow, it would be possible to save 10.7 percent of fuel consumption on a road with a speed of 90 km/h. Arvidsson (2017) reports more results from calculations with the Winter Model. The example mentioned is a road with an AADT of 2,000 and a snow depth of 2 cm. A comparison is made between the alternative of salting and plowing where you have 4 hours to complete the work, with the alternative of only plowing and where you have 5 hours to perform the work. The Winter Model shows that fuel consumption will be lower for the alternative that means vehicles are driving in snow for a longer period of time, that is, when the contractors have 5 hours to carry out the maintenance. The reason is the assumption that drivers choose to reduce their speed when driving in snow. In other words, the lower fuel consumption as a result of a lower speed will offset the increased fuel consumption that arises due to the vehicles encountering a higher rolling resistance due to snow.

VTI rapport 971A 35 Min et al. (2016) have also studied winter road maintenance and its effect on fuel consumption. Min (2016) used models to calculate how speed was affected by precipitation, as well as to produce an index that describes the nature of the road surface (RSI), where a higher value represents a better road surface. This information was then used in a simulation program called MOVES to calculate emissions and fuel consumption. As expected, the results showed that the lower the RSI, the higher the fuel consumption. By taking measures for winter maintenance, the authors showed that it was possible to reduce emissions by 2 percent if the road surface was improved by 10 percent. The earlier the measures could be implemented in a snowstorm, the greater the benefit. Ye et al. (2013) quantified some benefits, such as road safety, travel time and fuel savings, in performing winter road maintenance. One starting point was that good winter road maintenance has a positive effect on fuel economy by reducing delays and improving road surface conditions. An estimate that Ye et al. (2013) does for Minnesota's road network, with approximately 123 million km driven per day, is that just over $48 million could be saved due to reduced fuel use during a winter season through improved winter road maintenance. A disadvantage of the calculations is that to describe the effect of driving in winter conditions a general extra fuel consumption is included for roads with no winter maintenance. This means that one does not take into account how vehicles are really affected by different winter conditions.

36 VTI rapport 971A 4. Discussion Precipitation increases the rolling resistance of a vehicle because the wheels need to be driven through water or snow on the road surface. In addition, water cools more efficiently compared to air, which means that the tires, and also lubricants, work at a lower and less-efficient temperature. This means that water affects rolling resistance both as a displacement means and as a coolant between the road surface and the tire. As a displacement means, rolling resistance is affected by water volume for the contact surface between road/tire, due to which tire width, water depth and speed play important roles. According to measurement results, the rolling resistance increases exponentially with the water depth and speed. Different authors have developed different exponential models, but all describe a sharp increase in rolling resistance with speed. The effect is thus greatest for motorways where you usually drive at speeds higher than 100 km/h. In addition, rolling resistance measurements have been performed especially for trucks on wet roads, both on asphalt and concrete surfaces. The measurements were made with a truck-trailer measurement set up, and the results showed, in the same way as for light vehicles, an increased rolling resistance. The increase in rolling resistance was greater for the asphalt surface than for the concrete surface. The authors also noted that the increase in rolling resistance was affected not only by displacing water but also by changes in temperature and by the tire pressure. Since the temperature affects the rolling resistance, it is important to have control over and measure it during rolling resistance measurements. Temperature and energy distribution are affected in different ways in different tire parts. The tire belt accounts for a large part of a tire's energy distribution, approximately 34 percent of the total energy distribution (Gent, Walters 2005). It is, therefore, important to check the temperature of the relevant parts of the tire. The stability of the temperature should also be monitored, as it takes more than an hour to stabilize the temperature while driving at a constant speed. Although it is not so common to drive at a constant speed for such a long time, it is important to monitor temperature transition effects while measuring rolling resistance. Energy use in the operation of electric vehicles has become a current research object, and, of course, rolling resistance plays an important role when it comes to building a more energy-efficient and climate-adapted transport system. Unfortunately, no specific measurements or models were found for electric vehicles on wet roads, but the report includes a description of rolling resistance in electric vehicles that includes speed and temperature. However, according to these results, the rolling resistance coefficient varied too much, which means that a more comprehensive study of rolling resistance under different road conditions is needed. In addition, it is shown that it is a strategically interesting topic to investigate rolling resistance for electric vehicles on wet roads because it affects the use of the electric vehicle. In addition, aircraft are also affected by rolling resistance on wet surfaces. Although there are models for calculating the effect of water on the road surface, the measurement results showed that the impact of the water is between 15 and 40 percent higher than for theoretical calculations. In addition, aquaplaning takes place at lower speeds than theoretical calculations, up to 20 percent lower. The author of this study recommended an update of the calculation method. Finally, regarding wet roads, several of the previous studies point to a need for renewed measurements of rolling resistance on wet road surfaces. Some possibilities to produce updated measurements and more realistic models are to carefully control the measurement speed, water depth, tire temperature, tire pressure, and road surface properties. One should also check non-stationary effects while measuring and check that aquaplaning does not happen. One way to check whether aquaplaning is taking place or not is to measure the rotation of the wheel. The difficulty with studying the impact of snow on rolling resistance lies in the fact that there are many different types of snow, with several different characteristics and behaviors during deformation. The properties that snow can have are very variable and depend, among other things, on the current

VTI rapport 971A 37 outdoor temperature, the temperature during the snowfall, how long the snow has been lying, the humidity of the air, the density of the snow, the size and shape of the snow crystals and more. Shapiro (1997) believes that research on snow mechanics is relatively deficient as there is not much research in the field. The data available are also relatively limited, and the relationships that have been developed are not sufficiently developed so that they can be used to describe the behavior of the snow with respect to conditions for deformation and load. There are some studies that have tested some empirical and analytical possibilities, but where it is best to reach about 25 percent precision on average between measurements and calculations (Shapiro 1997). It has been seen that measurements can differ markedly in results, although they are made in snow that has similar physical properties (Shapiro 1997). One reason for this may be differences in the internal strength of the snow that depend on historical conditions with regard to, for example, compacting. The complexity of the impact of snow on rolling resistance means that a combination of theoretical calculations and field tests is needed to determine the values the components that should be included in the resistance function (Blokhin et al. 2016). However, some studies have been carried out regarding the effect on driving resistance that the presence of snow leads to. It is both theoretical studies that intend to explain the impact of snow using functions that describe the relationships involved. In these functions, it is often snow depth, snow density and the contact surface of the tires with the road surface that are the constituent explanatory variables. These have then been compared with measurements of driving resistance and rolling resistance to see how well they match. In general, the results show that snow has a great effect on resistance and that it is not negligible, especially in areas where snow remains on the ground for a long time. The size of the driving resistance depends, among other things, on the density and thickness of the snow. Several of the previous studies have shown that rolling resistance increases with increased snow thickness and higher density (see, for example, Kihlgren 1977, Richmond 1996, Blokhin et al. 2016). Mariyama & Kimura (2018) partly showed opposing results in that their measurements resulted in the travel resistance decreasing with higher density. These differences can probably be explained by the fact that the measurements presented in Mariyama & Kimura (2018) were made with snow densities between 300 and 850 kg/m3, while the other studies were based on snow densities below 250 kg/m3. There is probably a breaking point where the inner strength of the snow means that the tires do not sink so deep into the snow, and the amount of snow that needs to be pushed away or compressed is thus smaller. This is also in line with what van Es (1999) has concluded, that even if a snow with a higher density requires a larger force to be displaced, the extra force required to do this is counteracted by the need to displace or compact a smaller volume since the tires do not sink as deep. A disadvantage in this context is that the measurements carried out have been made with and for vehicles, which are not representative of the vehicles that operate on normal roads, that is, ordinary cars and lorries. The measurements that have been carried out have instead been for off-road vehicles or aircraft. In addition, most measurements were carried out during the 70s and 80s. Since then, both measuring methods and measuring equipment have been developed and improved. The properties of the tires have also been improved. Some experiments carried out in recent years have been carried out without important factors such as the density and temperature of the snow having been registered or reported, which is why it is not possible to get a good description of how snow affects rolling resistance. To obtain measurement data for rolling resistance in snow and water that is adapted for tires and vehicles used on ordinary roads, new measurements should be carried out with the measurement methods and measuring equipment that are relevant today. A recent study that can be used as a starting point and supplementary measurements is Maruyama and Kiruma (2018) and their coast down trials with an instrumented truck. A lesson from the Japanese study is that in this context it is also important to measure IRI as it has been shown that snow on the road leads to higher IRI, which in turn affects rolling resistance. The results from such new measurements can provide current information that can be used to update the relationship between wet on the road and winter road conditions and rolling

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VTI rapport 971A 43 ABOUT VTI

he Swedish National Road and Transport Research Institute (VTI), is an independent and internationally prominent research institute in the Ttransport sector. Our principal task is to conduct research and develop- ment related to infrastructure, traffic and transport. We are dedicated to the con- tinuous development of knowledge pertaining to the transport sector, and in this way contribute actively to the attainment of the goals of Swedish transport policy.

Our operations cover all modes of transport, and the subjects of pavement technology, infrastructure maintenance, vehicle technology, traffic safety, traffic analysis, users of the transport system, the environment, the planning and deci- sion making processes, transport economics and transport systems. Knowledge that the institute develops provides a basis for decisions made by stakeholders in the transport sector. In many cases our findings lead to direct applications in both national and international transport policies.

VTI conducts commissioned research in an interdisciplinary organisation. Employ- ees also conduct investigations, provide counseling and perform various services in measurement and testing. The institute has a wide range of advanced research equipment and world-class driving simulators. There are also laboratories for road material testing and crash safety testing.

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