Road surface effects on rolling resistance coastdown measurements with uncertainty analysis in focus. Deliverable D5(a)

Transcription

1 Road surface effects on rolling resistance coastdown measurements with uncertainty analysis in focus. Deliverable D5(a) Ulf Hammarström Rune Karlsson Harry Sörensen Velocity [km/h] Position [m] With the support of: 1

2 Preface VTI has on commission of the EU participated in the project Integration of the Measurement of Energy Conservation in Road Pavement Design, Maintenance and Utilisation (ECRPD) : Coordinator of the ECRPD project has been Ray Vincent at Waterford County Council, Ireland. This study of rolling resistance constitutes one part of WP5 in the ECRPD project. The following persons at VTI have contributed in this study: Ulf Hammarström has been project leader for the VTI part of ECRPD. Bengt-Åke Hultqvist, Mikael Bladlund and Håkan Wilhelmsson carried out coastdown measurements with the heavy truck (RDT). Bo Karlsson, simulations with the VETO program Rune Karlsson has been the main responsible for data processing, implementations, analyses and documentation. Thomas Lundberg and Peter Andrén have carried out the road measurements including coastdown measurements with the RST. Harry Sörensen has been responsible for the coastdown measurement equipment and has carried out most of the coastdown measurements. Mohammad-Reza Yahya, statistical analyses. 2

3 List of content Summary Introduction Objective Characterization of driving and rolling resistance What do we mean with driving resistance and rolling resistance? Feasible methods for determining rolling resistance Modelling the resistance components Summary of a literature survey Problem description PART 1: Coastdown measurements of rolling resistance Description of the coastdown method Introduction The physical model Test vehicles Measurement equipment on the test vehicles Road measures Selection procedure of suitable road segments Measurement procedure Meteorological conditions Numerical considerations in data processing: correlations, filtering, undulations in acceleration Quality control of data Summary of actual models and data processing methods used in the computations 38 7 Results Main results for the car (Volvo) Results for the light duty vehicle (RST) Results for the heavy truck (RDT) Uncertainty analysis for the car Introduction Checking the quality of the measurements Perturbation analysis on fictitious data Perturbation analysis on real data Comparisons with alternative regression models Summary of uncertainty analysis Comparisons with other work Discussion and conclusion Coast down versus other methods The coastdown methodology elaborated in this project Results PART 2: Comparison between coastdown measurements and vehicle simulations Validation and comparison with vehicle simulations Introduction Validation of VETO roughness subroutine Validation of VETO side force subroutine

4 11.4 Discussion and conclusion PART 3: A general driving resistance model General driving resistance model Introduction A general model for road surface effects on driving resistance Vehicle speed Discussion and conclusion References Appendix A Description of test vehicles Appendix B Description of the selected road strips Appendix C Description of the coastdowns Appendix D Instructions for coastdown measurements Appendix E Road surface quantities measured by the RST vehicle Appendix F Tyre temperature and pressure Appendix G A filtering method for the acceleration

5 Summary The main objective of the ECPRD-project is to develop models and methods to minimize the sum of energy use for road construction, for road maintenance and for the traffic. In order to estimate energy use for road traffic the influence of road surface conditions on driving resistance and energy use is of main importance. This part of driving resistance effects have been categorized as rolling resistance. The literature presents effects of road surface condition on rolling resistance in a wide range of values. The background to this wide range could be: different methods: fuel consumption; coast down; laboratory methods etc. a measuring problem in general isolating small additional forces use of different measures for characterizing a specific road condition a lack of control of other variables than for the road surface high correlations in the group of road surface variables high correlations between road surface and other variables depending on study design When adding a new study of road surface rolling resistance effects to the long list of other studies it should be of big importance to prove that the accuracy is high. It is difficult to judge the level of accuracy in different studies. A possible criterion in such comparisons could be: which variables are under control. Another criterion could be if these variables are included or not into the analysis. If they have not been included, effects will still be there but may appear disguised in other variables like road roughness and macrotexture. In this study the coastdown method is used to estimate driving resistance. The reason for selecting this method is: the acceleration level gives a true measure of the driving resistance under real conditions the costs for equipment is comparatively low to avoid uncertainties caused by the engine and used fuel if compared to fuel consumption measurements there is a good potential for recording of all explanatory variables of importance. Used explanatory variables in analyses: speed and acceleration gradient curvature crossfall roughness macrotexture ruts ambient temperature wind speed air pressure. In total, 34 road strips have been used for the measurements. These strips have been selected in order to cover the main variation in roughness and macrotexture for Swedish roads with the extra requirement that there should be a low correlation. 5

6 Road surface conditions have been recorded with a Road Surface Tester (RST). The RST system reports roughness and macrotexture by several different measures. In total three test vehicles have been used: a car; a van (RST) and a truck (RDT). The operating weights have approximately been 1700, 3300 and kg. The literature points out that even small effects on rolling resistance should be possible to detect. This raises a high demand in registration of conditions with high accuracy or controlled conditions. One very important condition used should be: the same tyre pressure before measurements on each test strip. Estimated effects per unit change of IRI and MPD for the car are depending on speed level: at 15 m/sec: - IRI: increase in rolling resistance by 2.3% - MPD: increase in rolling resistance by 5.5 % at 25 m/sec: - IRI: increase in rolling resistance by 6.2 % - MPD: increase in rolling resistance by 9.3 % In the function used for regression an ambient temperature correction term is included. The presented effects then represent 25 C. The IRI and MPD results for the other two test vehicles are not proved speed dependent. For the RST the road surface effects are not proved different from zero. The RDT results in some cases having a wrong sign are judged being not reliable. Compared to the literature, IRI effects are in the middle of the survey interval and MPD effects are in the upper part of the survey interval. The analyses include tests with different road surface measures for roughness and macrotexture. Even if differences are small, IRI and MPD gives the best fit of measured coastdown data to the model function compared to other alternative measures. The dynamic behaviour of a road vehicle on an uneven road is possible to simulate. The additional driving resistance from road roughness is then estimated based on damping losses in tyres and shock absorbers. The coastdown measurements were used to validate such a simulation routine: the simulated additional resistances were far below those estimated by measurements the correlation between simulated and measured values was very good. Simulations should at least be possible to use after calibration. In ECRPD there is need for a general model representative for all type of vehicles and all models of tyre per vehicle type. Such a general model has been expressed based on the coastdown results and on literature. The results of this ECRPD study should represent an important contribution to road surface rolling resistance effects both for methodology and for presented effects. Still there are several shortcomings: the quality in describing road conditions the importance of different aggregation levels the lack of data for other vehicle types than cars 6

7 the lack of data for different tyre models the lack of data for different load conditions the lack of data for different load levels the discrepancy between simulations and measurements etc. It should be of big importance for the future to reduce the mentioned shortcomings. 7

8 1 Introduction In order to find the optimal socio economic time schedule for replacing the road surface it is necessary to describe the deterioration speed of the road surface, the cost for repavements and the cost for the road traffic The main objective of the ECPRD-project is to develop models and methods to minimize the sum of energy use for road construction, for road maintenance and for the traffic. In order to estimate energy use for road traffic the influence of road surface conditions on driving resistance and energy use is of main importance. The ECRPD-project constitutes a continuation of the IERD-project, see (IERD, 2006). In IERD a software system called JOULESAVE was developed. JOULESAVE includes estimation of energy use for road construction and for the road traffic. Energy use for the traffic is estimated with the VETO program (Hammarström and Karlsson, 1987), one part of JOULESAVE. Another important part of road planning is the maintenance part. This part will be added to JOULESAVE by means of the ECRPD project. Road maintenance influences the road surface conditions. In order to estimate the influence of road maintenance on traffic energy use one needs a representative description of the influence of road surface conditions on driving resistance which finally influence the fuel consumption of road traffic. A dry road surface could influence driving resistance and fuel consumption by means of different measures. An influence on driving resistance is expected by: roughness macrotexture cross fall. For ruts it is not obvious if there is an expected effect and what sign would be expected. All these road surface measures are affected by the strength in the road construction and of used material in the wearing course. According to the literature an increase in road roughness and in macrotexture results in increasing fuel consumption. Unfortunately the interval, which these effects are determined to lie within for a specific variation of road surface measures, is proportionally large, see for example the literature study by (Sandberg, 1997): when road roughness increases from IRI=1 to 10 fuel consumption increases between 2 to 16 % when the road surface macrotexture (MPD) increases from 0.3 mm to 3 mm fuel consumption increases between 2 and 21 %. These results derive from both fuel consumption measurements and from rolling resistance measurements expressed as fuel consumption. One explanation to this wide range of results could be that the road surface effects are small or of the same size as the expected influence from a set of other variables not easy to control. The translation of rolling resistance effects to fuel consumption effects also contribute to increasing the total deviation in results since such a translation depends strongly of several quantities like speed- air resistance, type of engine, vehicle mass etc.. The air resistance increases with the squared speed when the rolling resistance is more or less constant. 8

9 Effect of roughness on driving resistance can be estimated in two ways: by means of measurements by means of vehicle dynamic simulation to some extent. Simulation alone can not give a complete description of driving resistance as a function of the road surface. It has to be supplemented by measurements, at least in order to estimate necessary parameter values describing the vehicle and the road surface. The simulation of course gives advantages for more general applications. One alternative to simulating road surface effects are coastdown measurements. By means of coastdowns it is possible to describe driving resistance, from which fuel consumption for different vehicles can be calculated. A critical part of coastdown measurements is good accuracy of the retardation level, the indirect measure on driving resistance, and all external variables contributing to an observed driving pattern. These external variables consist mainly of weather and road data. VETO describes the influence of road roughness on driving resistance, based on dampening work in tyres and shock absorbers. A successful mechanistic simulation of macrotexture effects on rolling resistance has to our knowledge never been done. The macrotexture effect has to be described based on a statistical analysis. One important question is if the roughness effects calculated by VETO are representative. This is probably not the case since these simulated effects are close to the lower limit value found in the literature. If new studies of road surface effects will be performed an important issue should be how to judge new results compared to old results. The conclusion should be that the accuracy part of new studies needs to be in focus. The ECRPD project covers several of the issues discussed above. Results concerning the connection between traffic load and road surface conditions (such as macrotexture and road roughness) are presented in a separate report. In the present report we are focussing on how road surface conditions affect the driving resistance. The report has been divided into three parts. In Part 1, a study of the rolling resistance dependence of various road surface quantities is presented based on comprehensive coastdown measurements. A very careful perturbation analysis is performed in order to investigate the stability of the method for various sizes on the measurements and to explore the potential influence of various disturbances and errors on the results. In Part 2, a comparison between results from measurements in Part 1 and from simulations using VETO is performed. In Part 1 the driving resistance model has been estimated for a few vehicles only. In Part 3, an attempt is done to formulate a more general driving resistance model valid for arbitrary vehicles. The general model is to a large extent based upon the model in Part 1 but some additional components are added. We start, however, with an introductory chapter where basic problems are discussed. 9

10 2 Objective The overall purpose of this work has been to formulate a general model for the impact of road surface properties on the driving resistance of a general road vehicle. This general model is to be implemented in the VETO program. In order to formulate such a model results from literature have been combined with own measurements. The measurements involve not only quantitative results but also a development of methodology, with special focus on uncertainty issues. The objectives include both testing and quantifying, based on measurements, of the effects of road surface variables: roughness; macrotexture; ruts and cross fall. By adjusting such functions after mechanistic principles one could expect a better fit to measured data and an increased possibility for meaningful validation. Due to financial restrictions, measurements will include only three test vehicles. Effects on driving resistance from the road surface on these three vehicles will be estimated. The VETO program includes a subroutine for a mechanistic simulation of the influence from road roughness on a road vehicle. The simulation model constitutes a simplified description of the real process. A mechanistic approach for simulation should also be possible to use for description of the cross fall effect. Both these effects will be validated based on results from measurements. The influence of macrotexture can not be simulated based on mechanistic principles to our knowledge. One needs statistical functions. The function, if statistical testing has proved an effect, for macrotexture will be integrated into VETO in order to calculate fuel consumption. If the validation of VETO results in unacceptable estimations of roughness effects the statistically estimated functions will be implemented into VETO. Resulting road surface effects follows from both effects on rolling resistance and on speed level. A complete model for energy evaluation of road surface conditions then demands both rolling resistance and speed effects. Speed effects will influence both rolling resistance and other types of resistance. 3 Characterization of driving and rolling resistance 3.1 What do we mean with driving resistance and rolling resistance? The total resistance that the engine has to overcome can be categorized in the following components: air resistance rolling resistance inertial resistance gradient resistance side force resistance transmission losses losses from the use of auxiliaries engine friction. 10

11 A confusing matter when discussing driving resistance and rolling resistance is the varying definitions in use. They are usually related to the measurement method that is applied. If, for instance, fuel consumption is measured, then driving resistance will probably include all the resistances in the list above. If, on the other hand, coastdown measurements are applied, then engine friction, auxiliaries and part of the transmission losses will not be included in total driving resistance. If comparisons between different measurement methods are to be done then results must be properly translated. There are similar problems for the rolling resistance. Depending on used method for estimation, the rolling resistance will include a different set of resistance components. Rolling resistance in the literature could include a large number of different components: influence from the tyre construction when driving on a smooth surface influence from different tyre dimensions influence from the macrotexture on the tyre influence from road roughness on the tyre, on the suspension system and on total air resistance influence from wheel bearings influence from parts of the transmission influence from wheel brakes if not controled influence from air resistance on the wheel influence from road deflection influence from micro-slip influence from the side force influence from a bogie in horizontal curves influence from selected tyre pressure influence from ambient air temperature or air pressure on tyre pressure influence from driving conditions on tyre pressure. The total driving resistance for a road vehicle is a function of many variable groups: vehicle parameters road surface properties road alignment weather conditions speed pattern also including: - the gear position - the use of wheel brakes - the use of auxiliaries. When making outdoor measurements of driving resistance with focus on rolling resistance the following conditions should be of special interest: ambient temperature wind speed and direction aerodynamic effects from surrounding road traffic air pressure road gradient road horizontal curvature and cross fall road surface conditions 11

12 vehicle mass and other vehicle parameters. The ambient air temperature and pressure will influence both air and rolling resistance. Air temperature also influences transmission losses. In the ECRPD study focus is on additional resistances from road surface conditions for fully warmed up vehicles. The wind speed and direction has more than minor importance on driving resistance. These variables then have to be measured for data adjustment, if possible, or for selection of measured data with the wind speed below a low limit value. To measure a representative wind speed and direction is not an easy task since there will be variations along the road strip as well as between the road area and a position where wind speed is suitable to measure. Surrounding traffic will also cause aerodynamic effects on the test vehicle. In principle there should be no opposing traffic or vehicles behind or in front of the test vehicle (Hammarström, 2000a) The air pressure influence both air resistance and rolling resistance. Since the air pressure can vary during a day the tyre pressure need to be controlled several times during a measuring day. Rolling resistance measurements in general are done on horizontal road segments. One then should notice that the additional resistance from a gradient equal to 1% is approximately equal to the rolling resistance of a car. The road condition effects on rolling resistance of interest are from some percents and upwards i.e. corresponding to a gradient smaller than 1/1000. Both horizontal curvature and crossfall generates side forces, which affects the driving resistance. The vehicle mass will change with the amount of fuel in the tank. If the vehicle mass decreases by one percent the rolling resistance will also decrease by approximately one percent 3.2 Feasible methods for determining rolling resistance In the literature, a number of different methods have been applied to estimate how driving resistance is influenced by the road surface. These can be summarized in the following main categories: coastdown measurements including different methods in order to measure acceleration force or torque measurements in the wheel suspension or in special designed trailers torque measurement in the transmission fuel consumption measurements test bench measurements of shock absorbers test bench measurements of vertical pulsating force on tyre laboratory measurements inside or outside a drum with a smooth or a rough surface mechanistic simulation of roughness and side forces based on properties for the tyre and the suspension. In this case one needs measured data including for example: spring and damping parameters for the tyres and for the vehicle suspension. Of course, validation measurements are also needed. detailed numeric simulation of tyre dynamics by solving partial differential equations. There are also other types of laboratory measurements, but not that often used for road surface effects. 12

13 There is an ISO standard for rolling resistance measurements at laboratory conditions, see section 4. This standardized method includes adjustment functions for temperature and the radius of the roller for laboratory measurements. 3.3 Modelling the resistance components In this section we introduce some notation that will be used in this report and some useful expressions for the resistance components. Air resistance: At zero wind speed we have F air 2 = k v (3.1) where 1 k = ρ A yz C L 2 (3.2) p ρ = 1000 T (3.3) ( ) v is the velocity [m/s] ρ is the density of air [kg/m 3 ] is the projected frontal area of the vehicle [m A yz C L is the air dynamic coefficient [dimensionless] p is the air pressure [mbar] T is the air temperature [ C] Inertial force: F = dv rot (3.4) where ( m + m ) dt dv is the acceleration level [m/s 2 ] dt m is the total mass of the vehicle [kg] 2 m = n K J r (3.5) rot m rot n wh wh J / wh is the inertial mass of rotating parts (wheels and transmission system) [kg] is the total number of wheels on the vehicle r wh is the wheel radius [m] J is the inertial moment per wheel [kgm 2 ] K J is a correction factor of J to include moving parts in the transmission system. (Usually set to 1.1) Gradient resistance: F g = m 9.81 sin β (3.6) where ( ) β is the longitudinal slope [rad] 13 2 ]

14 Side force resistance: 2 Fy Fside = (3.7) C A where 2 F y = m cos γ v / R 9.81 sin γ cos β (3.8) F y C A ( ( ) ( ) ( )) is the side force acting on the vehicle is the tyre stiffness [N/rad] γ is the crossfall angle [rad] β is the longitudinal slope [rad] R is the radius of curvature [m] See (Mitschke, 1982) about side force resistance. Rolling resistance: The following simple model will be used in this report. F roll = m η0 + η1 ( 25 T ) + µ 0 MPD + µ 1 v MPD + λ0 IRI + λ1 v IRI (3.9) where MPD is the macrotexture measure [mm] IRI is the road roughness measure [mm/m] m is the vehicle mass [kg] v is the velocity [m/s] T is the air temperature [ C] η, µ, µ, λ λ are constant coefficients , ( ) 1 The constant term, η 0, should be independent of road surface conditions. It should contain, besides losses in the tyre also the transmission losses. The rolling resistance is dependent on temperature, both in the air, in the tyres and in the transmission system. All measurements in this study are performed at equilibrium temperature, i.e. after the vehicle has been driven for some time. Hence, the air temperature should be sufficient as explanatory variable. It is reasonable to assume that the effect of the temperature is unrelated to the road surface conditions (at least if the temperature is not warm enough to soften the surface). Therefore, the temperature correction term in eq. (3.9) should be considered as a correction term for η 0. The reason for adding 25 is that 25 C is often used as a reference temperature, see (ISO, 2005). In analogy with friction, it is customary to characterize rolling resistance in terms of a dimensionless quantity, the rolling resistance coefficient: Froll = Fz CR (3.10) where F z is the normal vertical force acting on the vehicle [N] is the rolling resistance coefficient [dimensionless] C R 14

15 The rolling resistance coefficient can refer to the entire vehicle as well as a single wheel. Note that these two interpretations will, in general, give different values for the coefficient (even if the four wheels are located in perfect symmetry) since transmission losses are usually not taken into account when discussing a single wheel. The additional rolling resistance due to road roughness and macrotexture will be denoted by dc R. This is in general a function of macrotexture, roughness and velocity. In terms of the notation used in eq. (3.9) it may be expressed as: 1 dc R ( MPD, IRI, v) = ( µ 0 MPD + µ 1 v MPD + λ0 IRI + λ1 v IRI ) 9.81 Transmission losses include two types of losses: gear wheel rotating losses and mechanical losses. In coastdown measurements the rotating losses part will be included in the rolling resistance. These losses appear in the gear box and in the final gear box. Transmission losses will be included in the constant term in eq (3.9). 4 Summary of a literature survey A literature survey has been performed as part of the ECRPD project. The search parameters: published data bases: TRAX; ITRD; TRIS; SAE; SCOPUS key words: Roughness; Evenness; surface; Macrotexture; Macro texture; MPD ; Mean profile depth; Sand patch; coast down; highway; road; pavement; PMS; world bank Problems when evaluating the literature: some important explanatory variables might not be considered different measures for the same explanatory variable results originate from different years with different types of tyres and other vehicle parameters different types of measurement have been used: coastdown, fuel consumption, trailer, laboratory etc. in some reports results have been adjusted to reference conditions and other not some reports are based on constant conditions like keeping tyre pressure constant and other not. If, for example, roughness is excluded in road measurements but not macrotexture there is a risk that both roughness and macrotexture effects are explained by the only used variable, macrotexture. In most studies of road surface effects some important variables are missing. Measurements for laboratory conditions give the possibility to completely isolate the effect of, for example, macrotexture. An overview of the literature until approximately 1995 is presented in (Sandberg, 1997). In this report all rolling resistance data as a function of macrotexture, megatexture and roughness has been expressed as percentage changes in fuel consumption. If road surface effects have been expressed as changes in rolling resistance, the corresponding fuel consumption effect has 15

16 been estimated. Sandberg has converted rolling resistance effects to fuel consumption effects by multiplying by A summary of the results for cars: when roughness increases with a factor 10 from IRI approximately 1 the fuel consumption increases with 2 to 16 % when the megatexture increases with a factor 10 compared to the most even surfaces fuel consumption increases by 8 to 14 % when the macrotexture, expressed as MPD, increases from 0.3 to 3 approximately fuel consumption increases by 2 to 21 %. In order to get the rolling resistance intervals one should divide the limit values above by The survey also includes some results for trucks: one report with macro texture results. The effects for a truck is lower than the effects for a car two reports with roughness results. Both report bigger effects for a truck than for a car. Since this is a survey giving a rough overview most background data is missing. One drawback with studies based on fuel consumption measurements is that the results expressed as percentage changes will be depending on air resistance. For a test vehicle with high air resistance per kg vehicle one can expect lower percent changes compared to a vehicle with low air resistance per kg vehicle. For the Volvo used in the ECRPD study one should multiply the rolling resistance effect by In (Popov et al, 2002) the influence of dynamic load on truck tyre rolling resistance was examined for laboratory conditions. A unique facility for measuring the rolling resistance of truck tyres under dynamic vertical loading has been developed. The conclusion was: there is no discernible effect of dynamic load on mean rolling resistance. 1 In (Fraggstedt, 2006) a waveguide finite elements model based on design data was used to describe the dynamic properties of passenger car tyre. 2 The road roughness is seen to have a significant effect on the dissipated power. The HDM-4 model, see (Bennett and Greenwood, 2003) should include most of the knowledge in road surface effects up to year In this report a complete model for rolling resistance effects from roughness and macrotexture is included. where Fr = CR2 x (b11 x Nw + CR1 x (b12 x M + b13 x V 2 )) Fr denotes the rolling resistance CR2 = a0 + a1 x Tdsp + a2 x IRI CR2: factor for macrotexture and roughness. 1 Tyre dimension: 385/65R Tyre dimension: 205/55ZR16 16

17 Table 4.1 HDM-4 parameter values for macrotexture and roughness for surface class bituminous. Surface type: asphaltic mix or surface treatment WGT_OPER WGT_OPER>2500kg <=2500kg a0 a1 a2 a0 a1 a b11= 37 x Dw b12= 0.064/Dw for new technology tyres b13=0.012 x Nw/Dw 2 CR1: =1.0 for radial tyres =0.9 for low profile tyres. Tdsp: macrotexture expressed in the Sandpatch measure Nw: number of wheels M: vehicle mass (kg) V: vehicle speed (m/s) Dw: wheel diameter (m) The HDM-4 rolling resistance function can be commented as follows: the road surface effects are multiplicative with the basic resistance the basic resistance is a function of the wheel diameter one term in the basic resistance is a function of number of wheels one term in the basic resistance is a function of vehicle mass one term in the basic resistance is a function of speed but not of mass. In Table 4.2 and 4.3 the relative change in rolling resistance with road surface measures is described. Table 4.2 Relative change in rolling resistance as a function of MPD and IRI based on HDM-4. Light vehicles (operating weight 2500 kg) Macrotexture Roughness (IRI) MPD Tdsp

18 Table 4.3 Relative change in rolling resistance as a function of MPD and IRI based on HDM-4. Heavy vehicles (operating weight>2500 kg) Macrotexture Roughness (IRI) MPD Tdsp The first version of HDM-4 was available in One can notice that in the last version, the one here presented, the IRI effect has been reduced by a factor 5 but with unchanged macrotexture parameter. This change gives indirectly a measure on the degree of uncertainty about the roughness effect. For heavy traffic, in the last version, both roughness and macrotexture effects have been reduced to the same extent. VTI has on commission of the Swedish Road Administration performed a study of road surface effects on rolling resistance and fuel consumption (Hammarström, 2001). The study is not published. Comments: in total 18 road strips length of road strips are approximately 400 m test vehicle: Volvo 940 year model 1992 road condition variables: the same as in the ECRPD study speed levels for fuel consumption measurements: 50, 60, 70 for speed limit 70 km/h and 50, 70, 90 for speed limit 90 km/h initial speeds for coastdown were the same as for fuel consumption five measurements per road strip and speed level both for fuel consumption and coastdown. Correlation analyses were performed between all road variables both on 20 and 400 m level. The correlation between IRI and MPD was 0.68 and 0.92 for 20 and 400 m respectively. Since measurements per road strip was only done at one occasion the correlations between road conditions and weather variables could not be neglected. The results of the coastdown measurements were judged to be not representative. The analyses of fuel consumption measurements were split into two alternatives: one with observations per 7.56 m and one with one observation per road strip (400 m). The second alternative, with the highest correlation between IRI and MPD, gave no MPD effect but only for IRI. For the first alternative an increase of IRI from 1 to 4 mm/m and MPD from 0.4 to 1.2 gave an increase in fuel consumption with approximately 4 %. In the documentation an individual converting factor from rolling resistance change to fuel consumption change is presented, The rolling resistance effect then would be 22 %. At standardized rolling resistance measurements measured values are adjusted for ambient temperature deviating from 25 C (ISO, 2005): Cr25 = Cramb * (1 + K * (tamb 25)) tamb: ambient test temperature K: 18

19 =0.008 för PC och MC =0.01 for truck and bus tyres (with load index <= 121) =0.006 for truck and bus tyres (with load index >=122) Measurements of rolling resistance have recently been made on different road surfaces with a trailer (Sandberg, 2007). Measurements were made for three speed levels: 50, 70 and 90 km/h. The measurements also included use of five different tyres. The test routes had MPD values in the interval: The rolling resistance coefficient, as defined by eq. (3.10), is presented as an average for the used tyres and speed levels: C R = MPD (4.1) In (Gent and Walter, 2005) the importance of tyre pressure for rolling resistance is described: for cars a change of the pressure from a nominal level with 14 % will give a change in rolling resistance by 6 % for trucks a change of the pressure by 14 % will give a change in rolling resistance by 4 to 6 %. The influence from road surface conditions on average speed is described in (Ihs and Velin, 2002). Car, daytime: Vpb= *RUT 1.33 * IRI 4.98 * NARROW 0.71 * NORMAL * HG * HG * MV Heavy truck, daytime: Vlb = * RUT 1.17 * IRI 3.48 * NARROW 0.62 * NORMAL * HG * HG *MV Truck with trailer, daytime: Vlbs= * rut 2.31 * IRI 0.71 * NARROW * NORMAL * HG * HG * MV Vpb: average speed for light vehicles (km/h) Vlb: average speed for heavy vehicles (km/h) Vlbs: average speed for heavy vehicle with trailer (km/h) RUT: rut depth (mm) NARROW: 1 if road width<8 m, else 0 NORMAL: 1 if 8-11 m, else 0 HG90: 1 if speed limit=90, else 0 HG110: 1 if speed limit=110, else 0 19

20 The speed level is also depending on road surface conditions caused by weather conditions. In (Wallman et al, 2006) the influence from different such road conditions on speed is documented. Conditions included: moist wet packed snow or ice thin ice loose snow ruts in ice with or without loose snow To summarize, the literature includes not much new useful information about road surface effects after the literature survey from (Sandberg, 1997). One could expect the HDM-4 model to represent the state of the art. The way of updating the rolling resistance parameter values for macrotexture and roughness in the last HDM-4 version indicates a lack of reliable knowledge. 5 Problem description The potential problems in general when measuring and estimating effects of the road surface on driving resistance based on road measurements include: which explanatory variables to include and how to record them with good accuracy there exist different measures for the same type of road surface condition correlations between road surface variables correlations between road surface variables and other independent variables depending on test design correlations between explanatory variables is expected to depend on the interval length of road descriptions small expected rolling resistance effects cannot be excluded each road surface and driving speed will result in a tyre temperature and a corresponding tyre pressure variation by time of ambient temperature and air pressure influencing tyre pressure there is a variation in road surface conditions across the road, introducing an uncertainty concerning which conditions the test vehicle has been exposed for changes in the test vehicle during a day and between days. The explanatory variables to include should primarily be: those with more than minor effects on total driving resistance those of special interest in the ECRPD project. In principle all variables described in section 3.3 should be of importance. The need in ECRPD is at least variables describing the road surface conditions: roughness, macrotexture, rut depth and crossfall. Other variables of interest are those that give a possibility to present results for a reference situation. One purpose of such variables is to make measured data under different conditions comparable. Ambient temperature could be such a variable. If variables of importance for driving resistance are not included in used functions these effects will still be there but without control. 20

21 For some variables, especially roughness and macrotexture, there exist many different standardized measures. An example of such measures is macrotexture. The most frequent used measures for this variable should be MPD and Sandpatch. Criterias for selection of one measure per variable could be: a measure in frequent use a measure with maximum degree of explanation of important effects like driving resistance. In an earlier VTI study of road surface effects (Hammarström, 2001) road data was available for 20 m sections. The study included both coastdown and fuel consumption measurements. Fuel consumption was analyzed for two aggregation levels: 7.56 and 400 m. The latter alternative was equal to the length of the entire road strip. The resulting road surface effects were to a large extent depending on which alternative was used. The study pointed out several problems, see chapter 5. In (Hammarström, 2001) high correlations between road surface variables and weather variables caused problems in the analysis. Also, the choice of road block lengths had a strong influence on the results for unknown reasons. Based on the literature the interval for expected road surface effects is wide, from low to high effects. In order to be able to estimate small effects from measurements the accuracy needs to be high. Even small effects for the traffic should be of interest compared to energy used for construction and pavements. From the literature survey (Sandberg, 1997): lower effect limit for IRI, 0.8 % rolling resistance per IRI unit lower effect limit for MPD, 2.5 % rolling resistance per MPD unit. The method used for estimations of IRI and MPD effects should be able to detect effects of this size or smaller. Increasing tyre pressure reduces rolling resistance. The tyre pressure is influenced by: the air pressure: increasing air pressure will decrease the tyre pressure the air temperature: increasing air temperature will increase the tyre pressure the tyre work: increasing work will increase the tyre temperature and the pressure. These changes will be expected if there are no adjustments of the tyre pressure. For each new driving condition it will take some time to reach equilibrium. The resulting rolling resistance effect of road conditions can then be expected to depend on the road length with constant conditions. If tyre pressure is not adjusted between different road strips then measurements on one strip can influence measurements on the next strip. Tyre temperature is not only of importance for tyre pressure but also directly for driving resistance. Even if one uses standardized measures for road surface conditions with high degree of explanation for driving resistance, problems can follow from the variation in conditions across the road. Standardized road measures for road surface conditions represent special positions across the road: IRI is measured in the ruts 21

22 MPD is measured in the ruts and in two positions between the ruts The impact of road surface conditions on the motion of the vehicle will depend on the side position of the vehicle and the width between the wheels on the left and right side of the vehicle. For heavy vehicles with four wheels on the rear axle there will be a difference between road condition exposure for the wheels on the front and rear axle. If rolling resistance effects are estimated based on measurements in an ideal situation the side location for each wheel and the road conditions in these positions should be known along the test route. In practice this will be difficult to fulfil. The test vehicle represents a part of the measuring system. The driving resistance for constant conditions may not vary by time. Using coastdown measurements, compared to fuel consumption measurements, should reduce the risk for a change in the measuring system by time since the influence of the engine is excluded. Before start of measurement the test vehicle needs to be fully warmed up. It is not only the tyres but the transmission etc. to warm up. The change by time, during a day, in driving resistance or in engine efficiency is demonstrated in (Hammarström, 2002). In this study fuel consumption and exhaust emissions were measured for laboratory conditions. In several cases there were systematic changes by time during a day. Estimated road surface effects should be representative for normal use of road vehicles. The instruction to the car owner for tyre pressure adjustment is for cold tyres. One could expect that there is a time period of at least some weeks between tyre pressure adjustments during normal use. If measurements were based on this instruction, adjustments for cold tyres only, the tyre temperature and pressure would be different on all road strips. Another type of problem is how to develop a general model based on the literature and own measurements. General problems include: how to reach a general model for all vehicle types and tyre models? the rolling resistance is different between free rolling and drive wheels the rolling resistance coefficient is changing by tyre load The ECRPD project needs a general driving resistance model for all types of road vehicles and all tyre models used per vehicle type. Per type of tyre there also is an expected variation from the tyre age and tyre pressure. In the literature results about road surface effects are available mainly for cars. In the normal case each study includes one tyre model. The rolling resistance is different between driving and free rolling wheels, see (Gent and Walter, 2005). The resistance is higher for driving wheels than for free rolling wheels. If representative such information was available, it should be used. Road surface effects estimated from fuel consumption measurements includes a mix of free rolling and driving wheels while coastdown measurements only include free rolling wheels. If rolling resistance is measured in a laboratory, in general the measured wheel is situated inside a drum or on a roller. The measured values, if used for simulation, need to be adjusted to represent a flat surface. 22

23 PART 1: Coastdown measurements of rolling resistance 6 Description of the coastdown method 6.1 Introduction Suppose a specific road strip with well-defined start and end points is given. A coastdown measurement on this road strip is performed by letting the vehicle roll freely (clutch down, gear in neutral position) between the start and end points. The velocity is measured 3 continuously along the road strip, see Figure 6.1. The acceleration is either measured directly or derived from the velocities. 80 Road number=9 Västerlösa1 0.8 Road number=9 Västerlösa1 Coast down nr = Velocity [km/h] Acceleration [m/s 2 ] Position [m] Position [m] Figure 6.1 Velocity curves for several coastdowns with varying initial velocities along one particular road strip (Västerlösa1). The curves are almost parallel which indicates that the measurement conditions have been identical. To the right, the acceleration curve for one specific coastdown. Typically, strong fluctuations occur, caused by small measurement errors. The various forces (resistances) acting on the vehicle, see section 3.3, will make the velocity slow down. The rolling resistance is one of these forces. The larger the rolling resistance the larger the retardation becomes. By performing several coastdown measurements, under various conditions, it is possible, by using regression analysis, to distinguish and separate the contributions of the different resistances acting on the vehicle. Moreover, if the measurements are performed on different roads with varying road surface properties, which are measured independently, it is even possible to model the additional rolling resistance as a function of road surface variables. The wide-spread range of results in literature, and, also, the high sensitivity of the method for some types of disturbances, indicates that there is a need to analyze the accuracy in results. This is one important purpose of our study. In the next section we derive the model on which our study is based. Then follows a description of the test vehicles and their measurement equipment. In the next sections road measures are described and the procedure for selection of road strips. In section 6.7 a summary of the measurement instructions are presented. This is followed by a section on meteorological conditions. Some numerical considerations concerning data processing are 3 A possible alternative could be to measure the velocity only at the start and end points. This would imply a somewhat different analysis method than has been used in this project. 23

24 discussed in section 6.9.Next the important topic on quality control of data is discussed. Finally, the data processing is summarized. 6.2 The physical model The approach used in this report to determine the rolling resistance of a vehicle is based on a physical model of the movement of the vehicle taking into account various forces acting on the vehicle. The sound theoretical basis is the assumption that all forces acting on the vehicle are additive. With the notation used in section 3.3 we have: F = F + F + F + F (6.1) roll air g side Substituting expressions (3.1) (3.9) into (6.1) yields: dv ( m + mrot ) = m η0 + η1 ( 25 T ) + µ 0 MPD + µ 1 v MPD + λ0 IRI + λ1 v IRI dt 2 CL Ayz F 2 y ρ( p, T ) v m 9.81 sin( β ) 2 C ( ) We here use the notation, ρ ( p, T ), to emphasize that the air density is a function of air temperature and pressure, see eq (3.3). A (6.2) It is our purpose to compute the unknown coefficients of the rolling resistance terms, η i, µ i, λi. Unfortunately, the precision in the coefficients CL and C A is in general not sufficient for our purposes and should therefore also be regarded as unknown quantities which must be determined. Rearranging (6.2) yields: dv dt where + κ 9.81 sin ( β ) = κ ( η + η ( 25 T ) + µ MPD + µ v MPD + λ IRI + λ v IRI ) C L A 2 m κ = m + (6.3) yz m rot 0 1 ( p, T ) ρ m + m 0 v 2 1 C A 0 F 2 y m + m rot Finally, we obtain by substituting for constants, c i : dv dt where + κ 9.81 sin c 4 MPD + c ( β ) = c + c ( 25 T ) + c IRI + c IRI ( v 20) ( v 20) MPD + c Fy m + m rot 3 + c 7 ( p, T ) 2 ρ m + m rot + v (6.4) c 0 = κ η 0 (6.5a) c = κ (6.5b) 1 η 1 24

25 ( λ + ) c (6.5c) 2 = κ 0 20 λ1 c = κ (6.5d) 3 λ 1 4 = κ 0 20 µ 1 ( µ + ) c (6.5e) c = κ (6.5f) c c 5 µ 1 1 = (6.5g) 6 C A 7 C L A yz = (6.5h) 2 Equation (6.4) constitutes the basic model used in this report. All quantities are known or estimated for each observation, except the unknown coefficients (=parameters), c i, which are determined by regression. Each observation used in the analysis consists of data collected during a segment of the coast down, typically of length 25 m. A very large number of such observations inserted into eq. (6.4) results in a strongly overdetermined equation system. Since the vehicle mass can vary slightly from one coastdown to another, the quantity κ, and hence also the coefficients c i, are not strictly constants. This is a reason for trying to keep the vehicle mass as constant as possible so that the variation in κ should be very small. The (relative) variation in the expression 1 ( m + m rot ) is considerably larger and therefore we have chosen not to include these in the coefficients in the last to terms. Equation (6.4) does not take meteorological wind into account. If the wind direction is parallel to the vehicle movement, then the air resistance in eq (3.1) can be written: 2 2 = k v w = k v 2 k v w + k w (6.6) F air ( ) 2 where w denotes the wind speed in the forward direction. A corresponding expression can be derived for skewed angle wind. These expressions can be used to adjust eq. (6.4) with respect to non-zero wind speed. 6.3 Test vehicles Three test vehicles, representing different size classes, have been used for measurements in this report: a car (Volvo 940) of operating weight approximatly1700 kg. a light duty lorry ( RST ) of operating weight approximately 3300 kg. a heavy lorry ( RDT ) of operating weight approximately kg. The Volvo is depicted in Figure 6.3 while the last two test vehicles are depicted in Figure 6.2. The reason for using vehicles of different weights is that the proportions between various forces acting on the vehicle may differ considerably for different weight classes. The performance of a general method for rolling resistance measurements may therefore differ when applied to vehicles of various size classes. Another important reason is to investigate if the macrotexture and roughness effects are different for different type of vehicles. From systematic differences in tyre and suspension construction follows expected differences for the road surface effects. 25

26 Still, the main part of the measurements has been done using the Volvo. We wanted to develop and study a reliable method for rolling resistance measurements. Due to financial limitations the amount of measurements with the other two test vehicles is small compared to the Volvo. A detailed description of the test vehicles can be found in Appendix A. Figure 6.2 Two of the test vehicles used for coastdown measurements. To the left, the light duty vehicle, RST, and, to the right, the heavy lorry, RDT. The RST has also been used for the road measurements. 6.4 Measurement equipment on the test vehicles The equipment mounted in the test vehicles consists of four parts: A. The wheel pulse instrument. A digital system that measures time intervals between equidistant points. From these data speed and acceleration of the vehicle is computed. This is the main system. B. A photo sensor to determine the position of the vehicle. C. An analogue system for measuring accelerations and yaw velocity. It consists of accelerometers and a gyro. It measures and logs with a rate of 250 Hz during each test run. The purpose of these measurements has been to compare with data from the wheel pulse instrument and to investigate the movement of the vehicle in greater detail. In this report data from accelerometers and gyro has not been used. D. A system for logging GPS-data. This system is used for avoiding mistakes when and where a test has been done. It continuously logs the NMEA-strings that give date, time position and speed The wheel pulse instrument The car has a pulse encoder mounted on its right rear wheel for measuring of speed and distance, see Figure 6.3. The system is described in more detail in Figure 6.4. The encoder delivers 1250 pulses per turn of the wheel. Thus, each pulse corresponds to a distance of a few millimetres. The frequency of the original pulse signal is divided by With a tyre circumference of for example approximately 190 cm (the Volvo) this gives a pulse change each 78 th 26

27 cm (approx). This distance interval is very accurate and the time for each interval is measured with a clock that has 1µs resolution. The pulse signal is connected to a data acquisition card (NI DAQCard-700) in a laptop and the distance and speed values are calculated and saved for each test run. Each counter counts the 1 MHz clock only when the gate is high level. When a counter becomes inactive (gate low), the computer reads its value and resets it to zero. The two gates are active in an alternating way making it possible for the computer to read values from each counter without disturbing the measurements. Hence, we obtain a continuous sequence of measurement data. From the time measurements and known distances the vehicle speed is computed. However, the length of each distance interval (appr. 78 cm) is not known with sufficient accuracy. Therefore, a calibration is done based on length estimations of road strips of known lengths. Figure 6.3 Test vehicle with wheel pulse instrument. NI DAQCard-700 Photosensor Dig in 1 MHz clock Pulse encoder 1250 pulses per turn 1024 divider inverter gate gate count Counter 1 count Counter 2 Laptop Figure 6.4 Wheel pulse instrument. 27

28 6.4.2 The photosensor It is very important that the position of the test vehicle along the road is known for every time point. This is achieved by placing self-adhesive reflective tapes on the road at start and endpoints of the road strips, see Figure 6.5. (Additionally, tapes were placed also in some intermediate points.) A photosensor mounted on, for instance, the rear bumper of the car was used for detection of the tapestripes. The time points for the signals from the photosensor are included in the coastdown measurement data, see Figure 6.4. Figure 6.5 Self-adhesive tapes are placed at start- and endpoints of each road strip. 6.5 Road measures We are primarily interested in how road surface properties affect the rolling resistance of a vehicle. In the current project, road surface properties have been measured by the RST vehicle described in the previous section. A large number of properties have been measured. An exhaustive list of all variables and their definitions can be found in Appendix E. The road surface measures can be summarized as follows (all these quantities have been measured for each one meter interval): road roughness (IRI) texture (MPD) longitudinal gradient (%) 28

29 cross fall (%) curvature rut depth (mm) RMS values for various wavelengths. An international accepted measure to describe roughness is the International Roughness Index (IRI). This index is based on a mechanistic model of a quarter car. A measured roughness profile is used for simulation in a speed of 80 km/h. The measure is calculated as the sum of damper expansions and compressions for a distance divided with the length of the distance. In Table 11.1, calculated IRI values are presented for different wave lengths and amplitudes. A measured IRI value for a section of length ds represents roughness conditions before and on ds. Besides, a longitudinal roughness profile with 0.1 meter resolution has also been recorded for each road section as a basis for vehicle simulations with VETO. The RST vehicle measures many of the quantities along several parallel paths. E.g. the MPD is measured along the left and right wheel tracks as well as along two other intermediate paths. Since the rolling resistance should depend on the road surface properties along the wheel paths, we have in general used an average between the left and right wheel paths. A principle problem in this context is that the wheel width for the RST vehicle may differ from the one for the test vehicle, see Appendix A. Also, although the driver of the test vehicle were given specific instructions, it may be difficult to perform the measurements along exactly the same wheel path as the RST vehicle. Since the MPD value may vary significantly across a road section this is a potential error source. This problem is investigated in more detail in section Concerning the choice of texture and road roughness measures a large number of possible conceivable alternative measures other than MPD and IRI exists. Some experiments using various RMS values have been carried out. 6.6 Selection procedure of suitable road segments Much effort has been put into the process of selecting appropriate road segments for the coastdown measurements. Several considerations were taken into account: the longitudinal slope the curvature in order to avoid high correlations between the MPD and IRI values a wide spread in these values is desired. The variation in roughness and macrotexture should cover most of the variation on Swedish surfaced roads in order to reduce the costs for the measurements the distance from VTI should not be too large the segments should be long enough for performing the coastdowns different speed limits should be represented in order to allow a broad range of velocities. The general approach when looking for proper road segments in order to study road surface effects on rolling resistance is to look for horizontal and straight segments. Since these 29

30 variables were included in the analysis there was no need to impose absolute limits on them. In Appendix B min, max and mean values per measure and road strip are presented. An upper limit for mean gradient is approximately 1 % and a lower limit for the horizontal radius is approximately 1000 m. Using these criteria a search in a road database was performed. A limited number of candidates were then found. The final road strips were selected by hand, with particular considerations that a wide spread of IRI and MPD values were obtained, see section for more details on this. Since this is a research project involving method development, the dimension of the experimental design has been exaggerated to facilitate stability studies. Thus, more road segments than was originally expected to be needed have been selected. A description of the final road segments is found in Appendix B. Experiences from previous attempts to apply coastdown measurements for determining rolling resistance have shown the importance to avoid correlations between the model parameters. Therefore, a careful correlation analysis between various road quantities, mainly IRI and MPD, for the selected roads was performed. Some results from this correlation analysis can be found in Appendix B. The procedure described here was applied in the measurements with the Volvo. For various reasons it was not possible follow this procedure strictly for RST and RDT. 6.7 Measurement procedure The following rules were applied for measurements with the Volvo 940. For the other test vehicles measurements were performed less strictly. Main principles for the experimental design have been: to have full control over all variables of importance to avoid systematic changes of important variables, such as meteorological conditions, between different measurements. An exception is of course variations in road surface quantities. to avoid the influence of systematic changes of the test vehicle by changing the individual order of road strips at repeated measurements to assure that vehicle parameters, such as tyre pressure, should be constant before a series of measurements. A series of measurement consists of a series of coastdowns with varying initial velocities for one specific road segment. This means, for instance, that the tyre pressure is checked and calibrated before each measurement series. This is, however, not done before each individual coastdown. to assure that the vehicle mass for each coastdown is possible to estimate. to avoid systematic changes of the test vehicle from day to day. Before the measurements were performed, detailed instructions were formulated (see Appendix D). The instructions can be summarized as follows: formulated meteorological requirements must be satisfied. the road surface must be dry. full information about the vehicle weight before each individual measurement must be available, including changes in amount of fuel in the tank. 30

31 an equilibrium temperature must have been attained for the vehicle. This means that the car must have been driven at least during 30 minutes before the first measurement series is started. Correspondingly, 90 minutes for the more heavy vehicles. the tyre pressure is correct before each measurement series. All measurement series have been started using the same tyre pressure, see Appendix F. the coastdowns should be performed along the correct track on the road. all windows must be closed. during each coastdown the gear lever must be in neutral position and the clutch pressed down. if the measurement can be suspected to be disturbed by the surrounding traffic during some part of the coastdown then the event button must be pressed, signalising that data should be excluded. each day, when measurements are performed, should be started with a reference measurement on a special road segment. The purpose is to check that measurement conditions (and equipment) are the same every day. For all road sections coastdowns were performed in both directions. Thus, altogether 28 road strips (= road section and direction) were given (for the Volvo measurements). The total accumulated length of these strips is 17.4 km. For each road strip two series of measurements were performed. Each series of measurements comprises seven coastdowns. In order to ensure good stability in the results (see section ) the initial velocity has been varied according to the following schedule: If speed limit is 70 km/h then the initial speed is 70; 65; 60; 70; 60; 65 and 70 km/h If speed limit is 90 km/h then the initial speed is 90; 80; 70; 90; 70; 80 and 90 km/h. The idea behind these series is to avoid an effect from a systematic increase or decrease in starting speeds. There also can be a systematic change by time as reported in (Hammarström, 2002). In reality, it is difficult to precisely control the initial speed for the coastdown and, consequently, it deviates from these attempted ones. This is not important; the crucial point here is to obtain a broad spectrum of velocities yielding more stable results. The length of every coastdown is without exception the same as the length of the road segment. If a coastdown is interrupted prematurely then the event button is pressed and data discarded. For each road segment two measurement series has been performed. In order to minimize weather effects the two series where measured at two different days. Also the order in which the road segments were measured was changed in a semi-random way. In order to register meteorological conditions different sources have been used, see section 6.8. The tyre pressure should be the same before starting measurements on each road strip. This pressure should represent the pressure in warmed up tyres. The manufacturers of road vehicles give recommendation for pressure in cold tyres. For the Volvo a special measuring series was performed, see Appendix F. At first the tyre pressure recommended of the manufacturer for cold tyres was adjusted. Then the vehicle was driven in constant speed km/h until a stable temperature and pressure was reached. The tyre temperature and pressure was 31

32 measured each fifth minute during warming up and cold down and each tenth minute during stable conditions. Results: the tyre temperature increased approximately 15 C the tyre pressure increased approximately 0.2 bar stable conditions were reached after approximately 20 minutes stable conditions after a trip were reached after approximately 60 minutes. Based on these results the tyre pressure before each road strip was adjusted to a value 0.2 bar above the recommended value from the manufacturer. For the RDT test vehicle tyre temperature and pressure was registered during coastdowns, see Appendix F. In Appendix D the measurement instructions are presented in full detail. 6.8 Meteorological conditions Meteorological conditions influence driving resistance. We may deal with this problem in two ways: adjustment for meteorological conditions to one reference condition all measurements are performed during the same conditions. In practice there is no possibility to make all measurements for the same conditions. In this study a mix of both alternatives is used. For every coast down measurement, air temperature, air pressure 4 and wind speed was recorded or estimated. One demand (for the Volvo 940 coastdowns) has been to make measurements at each test site at least two times (two different days) in order to avoid high level correlations between weather condition variables and road surface variables. In order to register meteorological conditions from different sources have been collected. a national station (Malmen) fixed measuring stations (VVIS)for the Road Administration (Klockrike) ambient temperature registered from the test vehicle wind speed estimation from the test vehicle. For the Volvo measurements, air temperature and wind speed (and direction) were measured at the arrival at each road section. A balloon was mounted beside the road and from the movements of the balloon any changes in wind speed or direction could be observed by the driver of the test vehicle. Whenever such a change occurred a new wind speed measurement was performed. In this way, reasonably accurate wind observations were obtained for each coastdown. Air pressure data was obtained from the Malmen weather station. For the RST measurements all meteorological data (wind, air temperature and pressure) were obtained from Malmen weather station. The wind speed was measured on a level 10m above 4 Air pressure data were always obtained from a fix meteorological station. These data were then adjusted to each road strip by taking into account the altitude difference between the station and the road strip (8 meter height difference corresponds to 1 mbar). 32

33 the surface. Wind speed for the RDT was measured both on 10 m, one case of five, and on 2 m. A translation of 10 m to 2 m above surface was not done. In Appendix C, average meteorological data per road strip for the coastdown measurements is presented. Table C2 displays correlations between meteorological variables and road data. For the Volvo measurements there is a significant correlation between air temperature and MPD and also between air temperature and wind speed (see Table C5). These correlations might have some effects on the result, see section Numerical considerations in data processing: correlations, filtering, undulations in acceleration Although the computational procedure described in section 6.2 may seem very simple, a number of subtle but important issues should be considered in order to avoid unnecessary errors in the result. We will here discuss three such issues: correlations between variables, fluctuations in computed acceleration, undulations in acceleration due to vehicle nicking and the aggregation procedure Correlation between variables It is well known that the precision in estimated parameters from linear regression can be destroyed when the variables are highly correlated ( almost linear dependent ). In the model (7), two types of correlations may arise: those between MPD and IRI and those 2 between the term v and. Let us discuss these separately. v Correlation between v and v. Consider for simplicity eq (6.7). 2 a = c + c v + c 0 1 2v (6.7) We wish to compute the parameters c i by multiple regression. A necessary requirement for 2 obtaining unique values for the parameters, is that the functions 1, v and v must be linearly independent 5. Mathematically, this is also a sufficient condition. However, in numerical computations we can get trouble (large errors in parameters) also when these functions are almost linearly dependent, i.e., when the correlation between the functions are high. In other words the more similar these functions are, the higher uncertainty in the values for the corresponding parameters is obtained from the regression. The problem here is the potentially high correlation that may arise between the quadratic term and the linear terms when the speed interval is very narrow. The quadratic bending is then so weak that it almost looks like a linear function. This may lead to an ill-conditioned least squares problem and large uncertainties in the solution (i.e. regression parameters). There are (at least) two possible remedies for this problem. The first one is to collect data from a wide variety of speeds. In other words, in order to better be able to distinguish the 5 The functions are here considered as elements in a vector space (linear function space). 33

34 quadratic effects from the linear, i.e. air resistance from the rolling resistance, we should collect data from as broad a speed interval as possible. The other possible approach would be to linearize the quadratic term (air resistance) in eq (6.7). This may be done by the trick used in eq. (6.8). The constant v a could appropriately be chosen as the mean value in the velocity interval of available data. F 2 2 ( v va ) + 2 k va v k va d1 v d0 2 air k v = k + = (6.8) The quadratic term, ( v ) 2 k, corresponds to the deviation in Figure 6.6 and is small as long v a as the velocity is close to v a and can then be neglected. Only linear terms (in velocity) then remain. The advantage of this method is that it results in stable regression parameters. A severe disadvantage is that the terms ( and d ) will only be possible to distinguish from the d 0 1 c0 1 linear rolling resistance coefficients ( and c ) if a reliable ad hoc value for the air coefficient, k, is available. Then the equations d1 = 2 k v a and d0 = k va could be used. Otherwise, the air and rolling resistances will be indistinguishable and it is only possible to compute the total travel resistance. This may be considered a manifestation of a lack of information in collected data. 2 air resistance Figure 6.6 Linearization of air resistance term v 1 v a v 2 velocity Correlation between MPD and IRI. A similar low precision in the regression parameters may arise if the texture and roughness measures of the investigated road segments are correlated. In the extreme case when MPD and IRI would be linearly dependent, no possibility exists in a regression analysis to estimate the corresponding parameters. Our strategy to prevent this phenomenon to occur has been to carefully select the road segments so that the correlation between MPD and IRI is low. The procedure has been to select road segments so that a rectangular area in the MPD/IRI-plane is well spanned, see Figure

35 3 IRI and MPD for each road strip 3 IRI and MPD for each 25 meter segment MPD 1.5 MPD IRI IRI Figure 6.7 The distribution of MPD and IRI values for the Volvo test roads. To the left, one sample per road strip. To the right, one sample per 25 meter segment Fluctuations in acceleration When logging a coastdown experiment using a wheel pulse instrument velocity and acceleration are computed by numerically differentiating 6 data. For each differentiation small errors tend to be dramatically amplified. In particular, the computed accelerations usually exhibit large fluctuations not having any correspondence in the real behaviour of the vehicle. When using the wheel pulse instrument the velocity is sampled for each 0.78m-interval. The error in velocity is essentially caused by the discretization of measured distance (the error caused by the time measurements is negligible). A wheel rotation is partitioned into 2500 parts and the error in velocity can be shown to be (for the car): v 2π r 0.1% (6.9) v vi+ 1 vi 1 Correspondingly, for the acceleration (computed by a i = ) : t t v v a = = v t 0.78 v For the velocity v = 25 m / s we get a 0.77m / s 2 (6.10) 2 i+ 1 i 1. This upper bound agrees well with the the normal measured level of the oscillations, see for instance Figure 6.1. The normal oscillations in speed are so small that they can be neglected here. On the other hand, the oscillations in acceleration are very large, see Figure 6.1. Their effect on the regression parameters is investigated in section It is possible to effectively filter the high frequency oscillations using repeated averaging. In Appendix G a description and discussion of this method is given. 6 These kind of fluctuations do not occur when accelerations are measured directly, using for instance accelerometers. 35

36 6.9.5 Undulations in acceleration due to the nicking of the vehicle A remarkable phenomenon in acceleration values has been observed when measurements are based on wheel pulse instruments. It manifests itself in undulations of rather long wavelengths (in the order of 20m for a lorry), see Figure 6.8. These undulations were discovered only after filtering the high frequency oscillations in the acceleration with the method described in Appendix G. Without the filtering the undulations are difficult to distinguish from the background short wave fluctuations (noise). The undulations are stable in the sense that they reappear with high precision each time a coastdown is repeated along a specific road strip. If the initial velocity is reduced the amplitudes of the undulations are also reduced. The undulations are particularly strong when measurements are performed with a heavy lorry. Acceleration curves for coast downs with initial speed 90 km/h Acceleration curves for coast downs with initial speed 60 km/h Acceleration [m/s2] Cd_2 Cd_3 Cd_4 Cd_5 Cd_7 Cd_8 Cd_9 Cd_10 Acceleration [m/s2] Cd_12 Cd_13 Cd_ Distance [m] Distance [m] Figure 6.8 Undulations in measured acceleration caused by nicking of the vehicle. In the left diagram the initial velocity is 90km/h, in the right diagram it is 60 km/h. Measurements were done with a heavy lorry (RDT). An explanation for this phenomenon is that the chassis of the vehicle undulates (rotates) around the centre of gravity (nick) for the sprung mass. Since shock absorbers and the wheel suspension system must also rotate around the same axis, the wheel pulse instrument also undulates in the same manner and consequently also its position relative to the road surface. The measurements are very sensitive to such oscillations; it can be shown that variations in nick angle as small as 0.2 degrees may give rise to the undulations in Figure 6.8. A direct verification of the correctness of this explanation can be done by measuring the nick angle using a gyro. The undulations might be possible to reduce by compensating for the nick angle acceleration. Some attempts to do this were, however, not very successful. An alternative approach to avoid the impacts of these undulations would be to aggregate measurements over a longer period. The extent to which these undulations may affect the final result is investigated in section It should be pointed out here that these undulations do not occur when accelerometers are used instead of a wheel pulse instrument. 36

37 6.9.6 Using aggregated quantities Given that data has been collected with high sampling frequency, we can choose to use all individual samples for the regression model (6.4), or we can choose to first aggregate data for longer segments. In the extreme it is possible to use only initial and final velocities for the coastdowns. The measurements could be designed to collect only initial and final quantities. (In fact, this is implicitly done when directly measuring fuel consumption.) One detail regarding the aggregation is easily neglected. Applying the averaging operator, A, to eq (6.4), and using that it is linear and that T, p, m and m rot are constant for each costdown, yields: dv A dt + c κ 9.81 A 4 A ( sin( β )) = c + c ( 25 T ) + c A( IRI ) + c A( IRI ( v 20) ) ( MPD) + c A( MPD ( v 20) ) ( ) () c ( y ) ρ( p, T ) 2 + c A( v ) A F m + m rot 7 m + m Note that A v 2 A v. However, we have for simplicity regarded IRI and (v-20) as independent and used the approximation: A IRI v 20 A IRI A v 20. ( ( )) ( ) ( ) It might be tempting to believe that it would be advantageous to compute quantities aggregated over a longer time period. The effect of resistance forces can be more clearly seen after some time when the forces have acted on the vehicle. Moreover, various random errors tend to cancel out when averaged over a longer time. On the other hand it may be argued that we are indeed searching for relations between various quantities (such as road conditions and rolling resistance) and taking averages tends to smoothen such relations. A consequence of this is that the correlation between various quantities tends to increase, resulting in problems discussed in section Moreover, the number of observations decreases when aggregation lengths increase. Also, for disaggregated data various filtering techniques can be used for reducing the effect of random errors. Thus, it is far from obvious whether short or long aggregation periods yield the best results. In section the impact on results of different aggregation periods is studied. rot Quality control of data After measurements some checks were made that no evident errors exist in data: For the coastdowns the following checks are made: a visual inspection of the velocity curves for all coastdowns along a specific road segment. These curves reveal very clearly if, for instance, the coastdown has been interrupted prematurely, i.e., if the vehicle has begun to accelerate before the end of the road strip. Also, if the wind speed differs for two separate coastdowns this can often be seen by the differing slopes of the curves. every coastdown (along a specific road strip) gives an estimate of the length of the road strip. All these lengths should be approximately equal. a comparison between computed acceleration and the gradient of the road reduces the risk for confusion of road strips or directions. The measurement of a particular road strip is checked by: 37

38 the gradient (slope) in direction 1 should mirror the gradient (slope) in direction 2. computing (by integrating the gradient) the height difference between start and end points. This height difference in direction 1 plus the height difference in direction 2 should be close to zero. the curvature in one direction should be equal to the curvature in the other direction if the curvature for one direction is a left hand curve the other direction should be a right hand curve Summary of actual models and data processing methods used in the computations In the details of modelling and data processing, as we have seen, a large number of possible alternatives exist. In this section we summarize the models and methods used for data collection and computations that has been used in this project Data collection The logging of the coastdowns is done using the wheel pulse instrument described in section and, independently, the gyro and accelerometers. The data from the gyro and accelerometers have not been used in this report. For the RST vehicle a different kind of wheel pulse instrument was used than the one described in this report Regression models The regression models used in this report are all based on eq (6.4). Since different amounts of data have been collected for the different test vehicles we use different models for different vehicles. For the Volvo the basic model is (with some notations used in the next sections): dv agrav = c0 + c1 *( 25 TEMP) + c2 * IRI + c3 * IRI *( v 20) + dt c4 * MPD + c5 * MPD* ( v 20) + c6 * SIDEQUAD+ 2 c * DNSL* v + c * DNSL* v * w*cos( ALFA) (6.11) 7 8 Where 2 Fy SIDEQUAD = m + mrot ρ( p, T ) DNSL = ( m + mrot ) mˆ mˆ is the nominal weight of the vehicle (see section 6.3) w is the wind speed [m/s] ALFA is the angle between the wind direction and the driving direction [rad] a = 9.81 κ sin β grav ( ) 38

39 c 7 CL Ayz = 2 mˆ Note that the parameters c 0 to c 5 contains the mass correction term, κ. This means that the original rolling resistance parameters η i, µ i, λi in (6.2) should be obtained by dividing by κ. This has not been done in chapters 7 and 8. Thus, the original terms are approximately 2.2 % larger than presented here. Note also that the parameter c 7 in (6.11) is not consistent with eq (6.5). The last term in eq. (6.11) has been introduced to adjust for the wind. It is based on eq. (6.6) but has been modified to handle skew wind angles. This term is not entirely satisfactory. More 2 sophisticated formulas should maybe have been used. Also, the term containing w has been neglected. Although the magnitude of this term is in general very small, this might possibly affect the constant term, c 0. In section 8.5 some alternative models are investigated for the Volvo. For the RST and RDT a simpler regression model is used: dv agrav = c0 + c1 * IRI + c2 * MPD + c3 * SIDEQUAD + c7 * DNSL * v dt 2 (6.12) Data processing Data were collected from four different types of sources: road data, meteorological data, coastdown data, and data from the gyro and accelerometers. From coastdown data velocity was computed by measuring the time for a segment of specific length (approx. 78 cm) to pass. From this acceleration was computed using a standard central difference quotient (step length equal to 1 unit). Acceleration was then filtered using the method described in Appendix G, with degree N=30 as default. Road data was measured with 1meter intervals. The road curvature was filtered using the method described in Appendix G with degree N=1000. Also the nick angle acceleration was filtered using the same method with degree N=50. The longitudinal gradient was filtered by applying a moving average. The longitudinal gradient of the vehicle is determined by the position of the wheel axles. Therefore, the degree of the moving average was chosen to be consistent with the distance of the wheel axles. Thus, for the Volvo 940 the filter degree=3 (since wheel axle distance is 2.77 m), for the RST the filter degree=3 (wheel axle distance is 3.18 m) and for the RDT the filter degree=5 (wheel axle distance is 5 m). In order to synchronize data a particular signal was used that was generated at the beginning and end (and at some intermediate points as well) of each road segment. The position of the sensor can be regarded as the reference point for the vehicle. This varied from one vehicle to another: for the Volvo it was situated on the rear bumper, for the RST near the front wheel and for the RDT two meter behind the front wheels. No compensation for the displacement of the sensor relative the centre of gravity of the vehicle was done. 39

40 Finally, road and coastdown data was aggregated (in general by taking means over distances) and merged into longer segments. Data from aggregated segments from all coastdowns and all road segments was then collected and the regression carried through. The computations have been implemented in a MATLAB program in which various parameters can be conveniently chosen for experiments. E.g. filtering degrees, aggregation sizes, step lengths in numerical differentiation and regression models. Also one can conveniently select various subsets of data as well as impose various disturbances. 40

41 7 Results 7.1 Main results for the car (Volvo) In this section we present the main results for the Volvo 940. It is based on a total of 424 coastdowns performed along all 2 x 14 road strips. The model used is given by eq. (6.11) and the results represent the best estimate of rolling resistance that we could deduce from our measurements. An extensive perturbation analysis is presented in chapter 8 indicating the sensitivity of our results and the size of the errors Regression parameters The regression parameters for the model are presented in Table 7.1. Table 7.1 Regression parameters and confidence intervals for the basic model for the Volvo. 95% confidence interval Term Coeff Lower Upper const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) A crude check can be done for the accuracy in the parameter for air resistance, DNSL*V*V, Theoretically, the value of this parameter should be equal to 1 cair = A CL / mˆ (7.1) 2 where CL denotes the aerodynamic drag coefficient, A the vertical cross section area and mˆ the (nominal) mass of the vehicle. For the Volvo the area A= 2.15 m 2 and m ˆ =1700 kg. The drag coefficient is, according to the manufacturer, C L = 0.37, which yields: cair = The computed estimate, c air = , is slightly lower. The drag coefficient might, however, have changed somewhat due to, for instance, the measuring equipment mounted on the vehicle. The values for the other parameters are difficult to check but they all have correct signs, including the 95% confidence intervals 7. It is interesting to note that the parameter for the wind correction term, , differs from the air resistance term, Theoretically, these should be identical. The discrepancy between these values is probably a consequence of the improper handling of skewed wind angles, see section The confidence intervals here are generated from the regression procedure and are measures of the error in the coefficients based on the spread of the single observations. They do, of course, not take into account any systematic errors in data. 41

42 7.1.2 How large are the various components of the total driving resistance force? The answer to this question depends on the velocity as well as on a number of other quantities. Representative values in this and the next two subsections are (if not otherwise stated) IRI=2, MPD=1, and cross fall = -2.5 %. In Figure 7.1 the sizes of each resistance component as a function of the vehicle speed are shown. (Wind speed is assumed to be zero). The total rolling resistance consists of the sum of all the components except the air resistance (DNSL*V*V). We see that the constant component of the rolling resistance dominates, and that the MPD dependent part is also significant, while the IRI dependent part, as well as the effects of side forces, is rather small. 0 Stacked plot of resistance components Acceleration m/s Const IRI MPD SideQuad AirResistance Velocity [km/h] Figure 7.1 The contributions of various resistance components to the retardation of the Volvo. The diagram has been computed for IRI=2, MPD=1, air temperature = 25 C and cross fall = -2.5 % How does the rolling resistance vary with macrotexture and road roughness? In Table 7.2 the contribution to rolling resistance of road macrotexture and roughness is presented. We remind the reader that rolling resistance always contains transmission losses in our results. The unit here is [N/kg]. For MPD=1, IRI=2 and velocity 20 m/s, the contribution is m/s 2, which is little more than half of the constant rolling resistance (0.088 m/s 2 in Table 7.1). 42

43 Table 7.2 Effects of road macrotexture and roughness on rolling resistance. For various values on MPD, IRI and velocity, the table presents the increase in rolling resistance [N/kg] as compared to a smooth road surface. MPD v [m/s] IRI The relative increase of the total rolling for varying levels of macrotexture is presented in Table 7.3. At 50 km/h the increase in rolling resistance is 17 % per MPD unit, while at 90 km/h the increase is 30%. Table 7.3 Effects of road macrotexture on total rolling resistance. For various MPD values and velocities [km/h], the table displays the quotient between total rolling resistance at the particular MPD value and at MPD=0. The total rolling resistance contains all terms in the model except wind speed. Results have been computed for IRI=2, air temperature = 25 C and cross fall = -2.5 %. Speed\MPD The relative increase of the total rolling for varying levels of road roughness is presented in Table 7.4. At 50 km/h the increase in rolling resistance is 1.8 % per IRI unit, while at 90 km/h the increase is 6%. 43

44 Table 7.4 Effects of road roughness on total rolling resistance. For various IRI values and velocities [km/h], the table displays the quotient between total rolling resistance at the particular IRI value and at IRI=0. The total rolling resistance contains all terms in the model except wind speed. Results have been computed for MPD=1, air temperature = 25 C and cross fall = -2.5 %. Speed\IRI How does the total driving resistance vary with macrotexture and road roughness? If total driving resistance is considered, i.e., the air resistance is included, the dependence of macrotexture is as in Table 7.5. If MPD is increased from 0 to 1 unit at 50 km/h, the total driving resistance is increased by 10.5% Table 7.5 Quotients for total driving resistances at various MPD values relative to MPD=0, for various velocities [km/h]. Results have been computed for IRI=2, air temperature = 25 C and cross fall = -2.5 %. Speed\MPD The corresponding result for IRI is displayed in Table 7.6. If IRI is increased from 0 to 1 unit at 50 km/h, the total driving resistance is increased by 1.2%. 44

45 Table 7.6 Quotients for total driving resistances at various IRI values relative to IRI=0, for various velocities [km/h]. Results have been computed for MPD=1, air temperature = 25 C and cross fall = -2.5 %. Speed\IRI Results for the light duty vehicle (RST) The results for the RST vehicle is based on 12 coastdowns performed along 2 x 6 road strips. The model used is given by eq. (6.12). The regression parameters for the model are presented in Table 7.7. Table 7.7 Regression parameters for the RST vehicle. 95% confidence interval Term Coeff Lower Upper const IRI MPD SideQuad DNSL*V*V We immediately observe that the sign for the parameter for the side force, SideQuad, is positive, which is not realistic. We know that the side force should exercise a retarding and not an accelerated force. The parameters for IRI and MPD have a correct sign and are almost significantly (95%) different from 0. The parameter for the air resistance can be estimated in the same way as in the previous section by applying eq. (7.1). Using C L = 0.5, A = 4.79 m 2 and mˆ = 3300 kg, yields c = This is smaller than the measured air quantity in Table 7.7, c = However, the value for C is very uncertain. air The constant for the constant term, , has a magnitude somewhat higher than the corresponding value for the Volvo. A comparison is however difficult here since transmission losses are included in this term, and, also, since the models differ. (Note that the temperature correction term, 25-TEMP, in the Volvo model, should, at least partly, be contained in the constant term of the RST model.) How large is the rolling resistance as compared to the total driving resistance? In Figure 7.2 some results are presented. Note that the simple model used here does not provide us with any information about the velocity dependency of the rolling resistance. L 45

46 0 Stacked plot of resistance components Acceleration m/s const IRI MPD SideQuad DNSL*V*V Velocity [km/h] Figure 7.2 The contributions of various resistance components to the retardation of the RST vehicle. The diagram has been computed for IRI=2, MPD=1 and cross fall = -2.5 %. In spite of the very small number of measurements performed with the RST vehicle reasonable (but not reliable) results are obtained, with the striking exception of the effect of the side force, SideQuad. The results indicate that our method works excellent in principle, but that a larger set of coastdowns are necessary to obtain reliable values for the parameters. 7.3 Results for the heavy truck (RDT) The results for the RDT vehicle is based on 34 coastdowns performed along 2 x 2 road strips plus one road strip. The model used is given by eq. (6.12). The regression parameters for the model are displayed in Table 7.8. Table 7.8 Regression parameters for the RDT vehicle. 95% confidence interval Term Coeff Lower Upper const IRI MPD SideQuad DNSL*V*V Although the confidence intervals for the constant term and the air resistance term are rather narrow, the parameter for the MPD term bears the wrong sign (for the whole confidence interval). This fact jeopardizes the whole result. 46

47 The parameter for the air resistance can be estimated as in the previous sections by applying eq. (7.1). Using = 0.5, A = 7.62 m 2 and mˆ = kg, yields c = This is C L much larger than the measured quantity in Table 7.8, c air = The parameter for the constant term, , is much larger than the corresponding values for the Volvo and for the RST. This may either be due to a larger resistance from the transmission system or that the current results are erroneous. The number of coastdowns for the heavy truck was larger than for the RST vehicle. In spite of this fact the result seems less accurate for the heavier vehicle. The reason for this has not been determined but a number of possible explanations exist: the coastdowns for the RDT vehicle were performed for a smaller number of road strips (less than half as many as for the RST) with less variation in MPD and IRI. for the RDT the undulations in acceleration described in section are much larger than for the other vehicles, possibly disturbing the results. the RDT measurements were partly performed along other road strips for which the gradient was measured with less accuracy than for other road strips. the retardation level for a heavier vehicle is smaller than for a lighter one. Thus, any errors in mass independent quantities (such as the gradient) will have larger influence on a heavier vehicle. the road strips included two with cement concrete surface. The rolling resistance on a cement concrete road surface, all other conditions equal, is expected to be lower compared to an asphalt concrete surface. This difference in conditions is not included in the analysis. air 47

48 8 Uncertainty analysis for the car 8.1 Introduction In the literature, a very wide range of rolling resistance estimates from measurements can be found, see chapter 4 or (Sandberg, 1997). One may suspect that many of these results may have been corrupted by errors of various kinds. A large number of possible error sources (both in the measurements as well as in data processing) can significantly affect the results. Even small errors or disturbances can destroy the result, since the expected result interval includes small effects. In spite of the great need for error estimations in this field, most reports dedicate none or little considerations to uncertainty. To make results credible these issues should be taken seriously. The task of uncertainty estimation is one of great complexity. Error sources of very different types may occur: Errors caused by insufficient or inappropriate selection of study objects: insufficient number of road segments high correlations between explanatory variables (e.g., MPD and IRI). insufficient spread of measured velocities insufficient number of coastdowns Measurement errors: physical disturbances of other types than modelled (e.g., wind caused by other vehicles, various temperature effects) varying conditions between different measurement occasions (e.g., temperature, air pressure, vehicle weight, tyre conditions) errors caused by incorrect road data (e.g., the test vehicle does not drive in exactly the same wheel path as the road measurement vehicle) errors caused by the measurement equipments, systematic or random (e.g., discretization of measured distance, error in clock time, vehicle undulations, other casual disturbances). Errors introduced or enlarged during data processing: modelling errors (e.g. approximating reality with a linear regression model or neglecting various forces, such as longitudinal gradient force or the side force) aggregation errors when grouping data together or computing averages (e.g., forming averages over road segments) computation of acceleration by numerical differentiation There exist a number of different possible approaches to estimate the errors, e.g.: 1. perturbation analysis 2. repeated measurements 3. residuals from regression analysis An advantage of perturbation analysis is that it can provide a measure of the influence of every individual error source. In this way it can be estimated to what degree every error source is a threat to the final result. It is very suitable for estimating the effect of systematic 48

49 errors. One possible disadvantage of perturbation analysis may be that in order to estimate the error in the result one needs additionally an estimation of the size of the actual error source. Error estimations using repeated measurements (and computing the standard deviation) is suitable for estimating the total random error irrespectively of its origins. Studying residuals and R 2 values may give a hint of the modelling errors. Unfortunately, the R 2 values are often determined by other imperfections of data rather than the modelling error, and hence, may differ very little between different models. It is therefore often useless to determine which model is the best one. The choice of model should preferably be based on physical grounds (simulations). In the next sections we describe how perturbation analyses may be applied to the coastdown data. The procedure is slightly differing depending on whether the analysis is based on purely fictitious (simulated) data or on measurement data. In section 8.3 a brief summary of some results from a perturbation analysis on fictitious data) is given. In section 8.4 a comprehensive perturbation analysis on real data is presented. 8.2 Checking the quality of the measurements The results of two methods for checking the quality of data is presented. The first method is a check of the coastdowns while the other checks the road measurements Coastdown lengths The data from the wheel pulse instrument can, after calibration, be used for length measurements. For each coastdown an estimate of the length of the road strip can be obtained. The variation in these estimates, as well as the deviations from the nominal lengths of the road strips, can give some hint of the quality of data. It can reveal for which measurements a serious error might have occurred. In Figure 8.1 the deviation between the (calibrated) coastdown length estimates and the nominal length of the road strips is displayed for each coastdown. In most cases, the length estimates for each particular road are well gathered. A few isolated samples, signifying a possibly erroneous measurement should maybe have been discarded. (Already, a number of coastdowns with larger deviations have been discarded.) For the first two road strips (Flygrakan1 and 2) the spread is rather large. This might be a consequence of the fact that measurements there were done on several occasions. For all road strips measurements have been done for at least two series. The deviation varies somewhat from one road strip to another, indicating that the nominal length of the road strips were measured with less accuracy than estimates from the wheel pulse instrument. 49

50 Absolute error [m] Relative error 4 x Road number Road number Figure 8.1 Absolute and relative errors for length measurements by the coastdown equipment. The error is the deviation from the nominal length of the road strip. Each cross represents a single coastdown Antisymmetry of gradient and curvature in opposite road directions Longitudinal gradient and curvature data were collected for each meter. Integrating (summing) the gradient over the whole road strip in both directions should yield a height difference very close to zero. The deviation from zero in the height differences estimated in this way is a measure of the inaccuracy of gradient data. In Table 8.1 the estimated height difference for each road section are presented. It is reasonable to believe that the true height differences should be less than 1 or 2 dm. For some road sections, in particular Maspelösa B and Brokind, the height differences are very large indicating that the gradients have been computed with less accuracy. Table 8.1 Some measures of the error in longitudinal gradient curvature for the road sections. Number Name Height diff [m] Correlation for Gradients Mean of Absolute Gradients [%] Correlation for Curvatures Mean of Absolute Curvatures 1 Flygrakan StoraAska Vikingstad Fornåsa Västerlösa Vattenskidklubben MaspelösaA MaspelösaB MaspelösaC Brokind Hundklubben Hycklinge Kisa Rimforsa Another measure is the correlation between the gradient in forward and backward directions. This correlation should be close to one. In reality correlations of 0.9 seems possible to achieve. From Table 8.1 it is seen that for some road sections the correlation is very low (in particular Fornåsa, Maspelösa B and Brokind) giving further doubts regarding the quality of the gradient measurements. Note however, that this correlation depends also on the absolute variation of the road, see the Mean of Absolute Gradients in Table 8.1. Both Fornåsa and Maspelösa B have small mean absolute gradients, which may be a cause for the low correlations. Brokind, however, have high mean absolute gradients. Hence, one may raise 50

51 serious doubts regarding the quality of the gradient measurements for Brokind. In spite of this, coast down measurements from Brokind has not been discarded in the analysis. 8.3 Perturbation analysis on fictitious data Before the actual coastdown measurements were designed, an a priori perturbation analysis was performed, which was based entirely on fictitious data. The purpose was to identify which potential error sources would be most threatening to the results, and, hence, to support the planning of the measurements. This was done by simulating the whole measurement procedure and data processing. A physical model similar to eq (6.7) was used but including an adjustment term for the gradient. The road surface properties, roughness and macrotexture were not included. The costdowns were simulated by solving an ordinary differential equation yielding the position (or velocity) of the vehicle as a function of time. By introducing various kinds of foreseeable, possible errors in the simulations their effect on the final result could be studied. Some conclusions from this investigation were: the error caused by the differentiation of position and velocity seems to have little affect on the result (the regression parameters). the error reduces with the time duration of the coastdown until it reaches a limit at approximately 50 seconds. If the coastdown continues longer than no increase in precision is obtained. Although not further investigated it is reasonable to believe that this (optimal) time limit depends on initial speed and other variables. the precision does increase with the number of runs but not very rapidly. The distribution of data (with respect to velocity) is more important than the number of data points. (For instance, one coastdown during 75 seconds resulted in fewer measurement points but much smaller error than 5 coastdowns during 20 seconds.) A conclusion from this is that a wide velocity spectrum is preferable in the coastdown measurements, at least for the particular model used here. the faster the fluctuations in acceleration (for instance due to fluctuating wind speed) the smaller the final errors. This is natural since the positive and negative contributions are more probable to cancel out for faster fluctuations. 8.4 Perturbation analysis on real data We investigate how the regression parameters are affected by the error sources stated in section 8.1. Other quantities could have been studied instead, such as the total rolling resistance for some values on the parameters. The advantage of using regression parameters is that they contain all information about the model. The regression parameters are often more sensitive than, for instance, the total rolling resistance. A perturbation may cause parts of the total resistance to move from one component to another, but the total may be rather constant (at least for medium values of the variables). We are primarily interested in the parameters containing IRI and MPD terms and the constant term. The road strips have been chosen so that a large variation of IRI and MPD values are obtained and, hence, good precision in the parameters. The reason for introducing other terms (such as SideQuad and 25-TEMP) into the model has primarily been to eliminate the disturbances of those other effects, not to determine their parameters in great detail. (We did 51

52 not, for instance, select road strips with large curvatures or crossfalls.) Therefore, we are quite content when the IRI and MPD parameters are stable, although other parameters may be unstable How does the amount of measurement data influence results? The amount of data to collect is important for the cost of the measurements. We here investigate how the size of the experiment affects the results and what size is required to yield acceptable results. The general procedure here is to select a subset of the available objects and compute results for each of these subsets without changing anything else Results for the two measurement series The coastdown measurements were performed in two series of approximately equal size. The order of the road strips were permutated in the second series in order to minimize systematic meteorological influences on the whole set of measurements. In Table 8.2 the results for the two series are compared. Table 8.2 Regression parameters when measurements of different series are used. Term Series 1 Series 2 Series 1+2 const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Number of 25 meter segments: The parameter for the temperature correction term, 25-TEMP, dramatically differs for the two series. As a consequence, the constant term is also affected rather much. (Note that the mean temperature for all coastdowns was 8.8 C. If we, for the temperature correction, had used 8.8-TEMP instead of 25-TEMP, and hereby, implicitly, included the difference into the const parameter, the variation in the latter would become small.) The parameters for the MPD terms differ very little, while the difference in the IRI parameters is somewhat larger Varying the number of road segments The following subsets of roads are investigated: A. All roads (2 x 14 strips) B. All roads but only forward directions (14 strips) C. All roads but only backward directions (14 strips) 52

53 D. A subset of 2 x 10 strips E. A subset of 2 x 7 strips F. A subset of 2 x 4 strips G. A subset of 2 x 2 strips The subsets of roads have been selected in a favourable way so that a large spread in the IRI and MPD values is obtained. Hereby, high correlations between the IRI and MPD values have been avoided. The result is shown in Table 8.3. Table 8.3 Regression parameters when measurements from various subsets of roads are used. Term Subset A Subset B Subset C Subset D Subset E Subset F Subset G const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Number of 25 meter segments: It is reasonable to assume that Subset A yields the best estimate of the regression parameters. It is remarkable that a small subset as Subset G yields rather good precision for some of the parameters, while there still seem to be instabilities in some of the much larger subsets. The parameter for the term IRI*(v-20) deviates strongly for Subset B. The large difference in some parameters for forward and backward directions (SubsetB and C) is difficult to explain Varying the number of coastdowns Here we use all roads but not all coastdowns. In general, approximately 14 coastdowns per road segment and direction were performed. Restrict these to 12, 8, 6, 4, 2 and 1 coastdowns per road and direction. The result is shown in Table 8.4. Table 8.4 Regression parameters for various number of coastdowns per road strip and direction. Max number of coast downs per road strip Term Infinity const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Number of 25 meter segments: A weakness with the procedure used here is that the last coastdowns were removed, instead of randomly skipping them. A systematic error may therefore have been introduced. 53

54 A conclusion from this is that, provided the coastdowns are performed with acceptable accuracy, the number of coastdowns per road strip can be rather small. 54

55 Restricting the spread in velocities As discussed in section the band width of velocities during coastdowns may be expected to influence the precision in results. Let us investigate this effect by removing all 25- meter segments having average speeds lower than a lower limit or larger than an upper limit. The result is displayed in Table 8.5. Table 8.5 Results for observations restricted to various intervals in velocity. Upper velocity limit [km/h] infinity infinity infinity infinity Lower velocity limit [km/h] const TEMP IRI IRI * (V 20) MPD MPD * (V 20) E SideQuad E E E E E 05 DNSL*V*V DNSL*V*W*cos(alfa) Number of 25 meter segments: The parameters IRI*(V-20) and MPD*(V-20) seem rather unstable when the velocity interval is narrowed. Whether this effect is due to an increased linear dependence or simply that the number of observations decreases is unclear Varying the correlations between MPD and IRI In order to study the effect that correlations between MPD and IRI may have on the result we select three different subsets of all the road strips. Each subset contains 10 road strips and they have very different degree of correlations between MPD and IRI. Subset CorrA: Rimforsa, Fornåsa, Vikingstad, Hundklubben, Västerlösa Subset CorrB: Kisa, Vikingstad, Hundklubben, MaspelösaC, Västerlösa Subset CorrC: StAska, Hundklubben, Kisa, MaspelösaC, Hycklinge Table 8.6 Results for subsets having different correlations between MPD and IRI Term Base case Subset CorrA Subset CorrB Subset CorrC const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad 2.9E DNSL*V*V DNSL*V*W*cos(alfa) Correlation between IRI and MPD Number of 25 meter segments:

56 Somewhat counter intuitively, the subset CorrA seems to produce regression parameters deviating the least from the base case. A conclusion from this may be that a high correlation may not necessarily be a threat to the precision. Instead other error sources may have been more important in this case What precision could be expected from the RST measurements? The coastdown measurement for the RST vehicle were performed for a much smaller set of roads (six road sections in both directions) than for the Volvo, and only one coastdown per road strip (=road section and direction). Judging from the Volvo results, what precision could be expected in the results from the RST measurements if we assume that they were performed with the same care as for the Volvo? In Table 8.7 regression parameters are displayed for two models, (6.11) and (6.12), the complete model and the restricted model, and for two datasets. In both datasets we use coastdown data from the Volvo, but in the RST subset case we restrict the coastdowns to that of an equivalent amount for the RST measurements presented in section 7.2. Thus, only 2x6 road strips were considered and only one coastdown from each road strip 8. We can see that model (6.11) is too complex for the RST subset, since some of the parameters have wrong sign. This is the reason why we chose model (6.12) for the RST (and RDT) measurements. One can also see that even for the simpler model the disagreement between the results for the two subsets is not very good. Thus, we cannot expect very god precision in the results for the RST vehicle, although at least the sign should be correct for all parameters. Table 8.7 Results for different models and datasets. Complete model Restricted model Term Full dataset RST subset Full dataset RST subset const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Number of 25 meter segment A similar analysis for the RDT measurements has not been done, since these were, to a large extent, performed on other road strips than those for in the Volvo measurements How may errors in road data affect results? The longitudinal slope (gradient) Theoretically, the longitudinal gradient is compensated for by adjusting the measured acceleration by subtracting the resultant gravitational component. In reality, various errors may affect results. We here study these effects using different approaches. 8 The RST coastdowns were performed on a subset of the roads where the Volvo coastdowns were done, but with one exception. This road (Horn) has been replaced by a similar road (MaspelösaA) in the current analysis. 56

57 How does neglecting the gradient affect results? It may be tempting to believe that the gradient could be neglected if the road strips are sufficiently horizontal, or, if the coastdown experiments are performed in both directions so that the (anti-)symmetry of the gradient will cancel the slope effects in the two directions. The result in Table 8.8 shows that such simplifications may destroy results completely. Many parameters have wrong sign and even the air resistance parameter, which usually tends to be very stable, is incorrect. This occurs in spite of the fact that most of the road strips are rather horizontal (see Appendix B). Table 8.8 The consequences of neglecting the gradient in the analysis Term Base case Neglecting gradients const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Constant perturbation of gradient We assume here a constant uniform error in the measured gradient for all roads 9. From Table 8.9 we see that only the constant term (const) is affected. The error in the constant term is in the order of 1% for each 0.01 % error in the gradient. A one meter error per 1000 meter may result in a 10 percent error in the constant. Table 8.9 Results for constant perturbations of the road gradient Constant gradient perturbation Term 0% 0.01% 0.02% 0.05% 0.10% const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Note that averaging the gradients over opposite road directions, which is done in the base case, does not make sense here, since the perturbations in two opposite road directions then would cancel each other. Therefore, no averaging is done here over the two road directions. Hence the differing results between the base case in Table 8.8 and in Table

58 Random perturbation of gradient We assume here a positive random error in the measured gradient has been artificially added. The error is constant for each individual road but may vary from one road to another from 0% up to a maximum, Grad max. Different directions may have different perturbations. As in the previous section no averaging of gradients is done over opposite road directions. In Table 8.11 results for different values of Grad max is shown. Table 8.10 Results for random perturbations of the road gradient Gradient perturbation Term 0% 0.01% 0.02% 0.05% 0.10% const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad 3.7E E E E E 05 DNSL*V*V DNSL*V*W*cos(alfa) Estimating the effect of the gradient by regression An alternative approach to firmly compensate for the gravitational component is to let the gravitational effects on the vehicle be included in the regression model. Thus, the gravitational component is added as an extra term in the model, and the unknown parameter is determined in the regression. This parameter should ideally be equal to 1. The deviation from 1 might then be interpreted as a measure of the quality of gradient data. From Table 8.11 we see that the optimal gradient should be 94% of the gradient obtained from measurements. The difference has some effects on the other parameters, primarily the velocity dependent IRI and MPD terms, but also the constant term. It is an open question which alternative yields the most representative value for the IRI and MPD parameters. Table 8.11 Estimating the gradient term using regression. Term Without gradient term With gradient term const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad Gradient DNSL*V*V DNSL*V*W*cos(alfa)

59 The curvature The curvature affects result through the side forces acting on the vehicle. We assume here a positive random error in the measured curvature has been artificially added. The error is constant for each individual road but may vary from one road to another from 0 up to a maximum, Curve max. From Table 8.12 we may conclude that perturbations in curvatures less than 5 seem rather harmless. Table 8.12 Results for random perturbations of the road curvature Curvature perturbations Term const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad 3.7E E E E 05 6E 06 DNSL*V*V DNSL*V*W*cos(alfa) The crossfall The crossfall affects result through the side forces acting on the vehicle. We assume here a random error in the measured crossfall has been artificially added. The error is constant for each individual road but may vary from one road to another from 0% up to a maximum, Cross max. Table 8.13 Results for random perturbations of the road crossfall Crossfall perturbations Term 2% 1% 0 1% 2% 3% const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad 2.2E E E E E 05 5E 06 DNSL*V*V DNSL*V*W*cos(alfa) Ruts In the basic regression model, ruts are not included and therefore no perturbation analysis is possible. However, in section 8.5, an alternative model, including the ruts, is investigated, giving some hints on the influence of the ruts. 59

60 The road surface conditions The road surface conditions may vary quite a lot over a cross-section of the road. This is the reason why we aim at performing the road measurements in the same wheel paths as the coastdown measurements. However, in spite of strict instructions to the drivers a deviation can be expected, not the least because the wheel path distance differ between the road measurement vehicle and the Volvo. This means that the Volvo will be exposed for other MPD and IRI values than the measured quantities. The road measurement vehicle produces four different values for MPD along different tracks (see Appendix E) and two different values for IRI. By varying the MPD and IRI data sources an idea of the size of the influence of this error type on the result can be achieved. However, the variation here is probably overestimating the true error. The following sets of data will be examined: Base Case: IRI=0.5*(IRI_0+IRI_1) and MPD=0.5*( MPD_1+ MPD_2) A. IRI=0.5*(IRI_0+IRI_1) and MPD=0.25*(MPD_0+ MPD_1+ MPD_2+ MPD_3) B. IRI=IRI_0 and MPD=0.25*(MPD_0+ MPD_1+ MPD_2+ MPD_3) C. IRI=IRI_1 and MPD=0.25*(MPD_0+ MPD_1+ MPD_2+ MPD_3) D. IRI=0.5*(IRI_0+IRI_1) and MPD=MPD_0 E. IRI=0.5*(IRI_0+IRI_1) and MPD=MPD_1 F. IRI=0.5*(IRI_0+IRI_1) and MPD=MPD_2 G. IRI=0.5*(IRI_0+IRI_1) and MPD=MPD_3 Table 8.14 Results for various combinations of IRI and MPD measures. Term Base case A B C D E F G const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) The temperature correction term seems rather sensitive to the differing MPD and IRI values. An explanation for this might be the rather high correlation between the air temperature and MPD, see Appendix D. Also, the IRI term is significantly affected by MPD_0 and MPD_ How may meteorological conditions affect results? The model we are using cannot possibly take into account all accidental physical disturbances that may occur. We here study to what extent may such disturbances affect results. We generally perturb these quantities with a (random) constant for each costdown. No perturbations varying along a coastdown is applied. In reality we do not know exactly the size and shape of the disturbances but we may have some reasonable feeling of possible order of magnitudes. 60

61 Meteorological wind speed We analyze the influence of wind speed in a number of different ways Constant perturbation of wind speed measurements In this section we apply a multiplicative constant perturbation to the measured wind speeds. The purpose of multiplication is to avoid complications with changes of wind direction that may occur if perturbations are applied additively. From Table 8.15 it is seen that only the wind correction term is affected by erroneous wind speed data of this structure. Table 8.15 Results from multiplying all wind speed measurements by a constant factor. Constant factor by which all wind speed measurements are multiplied Term Base case const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Random perturbation of wind speed Here we multiply the measured quantity by a factor, a random number between 0 and maximum, different for each coastdown. The same conclusion as in the previous section. Table 8.16 Results from multiplying all wind speed measurements by a random factor. Upper limit of random factor by which all wind speed measurements are multiplied Term Base case const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa)

62 Restricting observations to wind speeds less than a limit What is the effect of restricting observations, by only allowing wind speeds less than a specific limit? From Table 8.17 we see that IRI parameters are fairly unaffected. The speed dependent MPD and the temperature correction term drifts. This can possibly be explained by the high correlation between wind speed and air temperature and also MPD and air temperature (see Appendix D). One interesting observation is that almost 1/3 of the observations were done for wind speeds not exceeding 0.5 m/s. This indicates that the measurements were done under excellent meteorological conditions. Table 8.17 Results when observations are restricted to below a maximum permitted wind speed. Maximum wind speed permitted [m/s] Term Infinity const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad 2.9E E E E E E E 05 DNSL*V*V DNSL*V*W*cos(alfa) # of observations Air temperature We assume here a random error in the measured air temperature has been artificially added. The error is constant for each individual road but may vary from one road to another from 0% up to a maximum, Temp max. Table 8.18 Results for additive perturbation of air temperature Limit of size of air temperature perturbation [ C] Term Base case const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Not surprisingly, the temperature correction term, 25-TEMP, seems strongly affected by this perturbation. Since the constant term is closely coupled to the temperature correction term it is also affected. All the other terms seem rather unaffected. 62

63 Air pressure We here apply a random additative perturbation of the air pressure measurement for each coastdown. From Table 8.19 it may be concluded that errors in the air pressure may affect results very little. Table 8.19 Results for additive perturbation of air pressure Limit of size of air pressure perturbation [mbar] Term Base case const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) How may errors caused by the measurement equipment affect results? We here consider known properties of the measurement equipment. Other casual disturbances have been removed by carefully observing vehicle trajectories. Basically, we are measuring only two quantities: time and distance. Since the clock is very precise the major 10 error source is the error in distance How may errors in StepSize affect the result? As described in section the coastdown measurement equipment discretise the measurements into segments of approximately 0.7m length. The exact length of these segments, which is here called the StepSize, depends on the wheel radius, hence also the tyre pressure, and cannot be measured precisely. It is instead indirectly calibrated by comparing the measured distance of each coastdown (which depends linearly on the StepSize) with the nominal length of the road strip. In Table 8.20 the impact of (constant) perturbations of the StepSize parameter is shown. 10 Actually, any error in time can be translated into an error in distance. 63

64 Table 8.20 Results of perturbations in StepSize parameter. Perturbations in StepSize [%] Term Base case const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) # of observations The IRI quantities seem sensitive to perturbations larger than 0.5%. 64

65 How may the undulations in acceleration affect results? The vehicle movements themselves can affect the equipment thereby causing a rather large error in measured acceleration (see section 6.9.5). How much can this phenomenon affect results? The amplitude of the sinusoidal waves is usually (for the Volvo) in the interval m/s 2, depending on the roughness of the road, but may occasionally increase significantly at particular spots. The maximum amplitude for all measured coastdowns is approximately 0.7 m/s 2. The wave length varies (sometimes irregularly) but is often between 15 and 20 meters. In order to simulate the effects of such undulations, sinusoidal perturbations of various amplitude and wavelength have been added to the (filtered) acceleration. The result is shown in Table Table 8.21 Results of applying artificial undulations to the measured acceleration. Different amplitudes. Wavelength is kept constant to 15 meters. Amplitude of sinusoidal acceleration perturbations [m/s^2] Term const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Table 8.22 Results of applying artificial undulations to the measured acceleration. Different wavelengths. Amplitude is kept constant to 0.2 m/s 2. Wavelength of sinusoidal acceleration perturbations [m] Term Base case const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) A conclusion from this is that the undulations do not seem to be a threat to the precision of the results for the Volvo. For the RDT vehicle, for which the undulations are larger and the retardations are smaller, the importance of the undulations may be different How may results be affected by differing data processing? Varying aggregation periods 65

66 In the previous section all data were aggregated to 20 meter segments before the models were estimated. How does the aggregation size affect the results? In Table 8.23 we show how estimated parameters vary with the aggregation size. Data from measurement series 1+2 is used. The same assumptions as for Table 7.1 are used here. Table 8.23 Parameter estimates for varying aggregation sizes Agg const 25 TEMP IRI IRI MPD MPD SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Some parameters, in particular IRI, seem to vary quite much with the aggregation size. This is a matter of major concern since the result (theoretically) should be independent of the aggregation size. The cause of this phenomenon has not been clarified How does filtering data affect results? Filtering the acceleration removes high frequency components arising during the differentiation of the velocities. These high frequency fluctuations often have large amplitudes and look very threatening to the results. Filtering these undulations yields a smooth curve which, intuitively, should improve the precision in the regression parameters. From Table 8.24 we see that the filtering does not affect results very much. Thus it may be inferred that these fluctuations are rather harmless. The regression procedure acts by itself as a low pass filter on the acceleration. Table 8.24 Affects of different filter degrees of the acceleration Filter degree Term No filter const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) Comparisons with alternative regression models In all computations in this chapter sofar model (6.11) has been used (exception in section ). In the current section we compare various alternative regression models. All models have been applied to the same data set. 66

67 In Table 8.25 parameter estimates are presented for various models. The models are implicitly defined in the table by the terms included. For all models the terms are included linearly. For all models the sign of each parameter is correct. The side force resistance (SideQuad) is very stable, i.e., does not vary with the model. Also the air resistance term (DNSL*V*V) is stable, except maybe for models number 35 and 36. For model number 36 a velocity term is included that may possibly interfere with the v 2 in the air resistance. In model nr 35 and 36, where the velocity dependent road surface terms, IRI*(v-20) and MPD*(v-20), have been excluded both the IRI and the MPD have dropped as well as the constant term. This should be kept in mind when comparing results from the Volvo 940 and the RST and RDT vehicles. Table 8.25 Parameter estimates for different models. All the models are linear and implicitly defined by the included terms in the left column. Modell numbers Term const TEMP IRI IRI * (V 20) MPD MPD * (V 20) V Trace SideQuad DNSL*V*V DNSL*V*W*cos(alfa) R Although the R 2 values do not differ much between the models we may note that model nr 30 has the highest value of the ones investigated. It is far from obvious which road surface measures are the most appropriate to use in the model. There are plenty of possible candidates for this, see Appendix E. In Table 8.26 we investigate various combinations of roughness (=unevenness) and texture measures. (The IRI in the left column represent the roughness measure, similarly for MPD.) There are two effects. Firstly, if IRI is replaced by RMS1 then certainly the corresponding parameter will change for scaling reasons. Secondly, a spill over from roughness to other parameters may occur if RMS1 explains rolling resistance differently than IRI. It seems that the air resistance parameter (DNSL*V*V) and the constant term does not vary much for different road surface measures. The temperature correction and the side force parameters are more affected. Table 8.26 Results for various measures of road roughness and macrotexture. Uneveness measure IRI IRI RMS1 RMS2 RMS3 RMS4 RMS5 RMS2 RMS3 RMS4 Texture measure MPD FRMS MPD MPD MPD MPD MPD FRMS FRMS FRMS const TEMP IRI IRI * (V 20) MPD MPD * (V 20) SideQuad DNSL*V*V DNSL*V*W*cos(alfa) R

68 8.6 Summary of uncertainty analysis In this chapter the potential impact of various sources of disturbances and errors on the results have been studied. With results we here refer to the regression parameters. These are in general more sensitive to disturbances than the entire rolling resistance (at least for moderate values of the variables). Some definitive conclusions may be drawn. From Table 8.24 it can be concluded that the high frequency fluctuations in acceleration do not affect results much. Also, from Table 8.21 and Table 8.22 it follows that the undulations in measured acceleration caused by the nicking of the vehicle is not a serious threat to the result (at least not for the Volvo). From Table 8.3 and Table 8.4 follows that a rather small set of measurements can be enough for attaining reasonable accuracy in the results. Quality of data is much more important than quantity! (Theoretically, 8 observations are enough to determine 8 parameters if data are exact.) The impact of small errors in longitudinal gradient can be very large. Table 8.8 clearly demonstrates that neglecting the gradient, with argument that performing coastdowns in opposite direction will cancel the errors, can yield useless results. From Table 8.1 follows that for some of the road strips used in this study the gradient has been measured with dubious quality. These errors may have given rise to some of the results difficult to explain in section 8.4. Although an interpretation of the results in Table 8.11 is difficult, one possibility might be that the error in the gradient values might result in overestimations of the IRI and MPD effects. The wind correction term has not been constructed optimally in the models. In spite of this, Table 8.17 shows that the impact of the meteorological wind on the result seems to be small except for the temperature correction term. Still, it seems wise to perform the measurements under low wind speed conditions. 68

69 9 Comparisons with other work In the literature survey (Sandberg, 1997) the increase in rolling resistance when IRI and MPD increases is presented as intervals. Results for cars: IRI from 1 to 10: increase in rolling resistance between 8 and 64 % MPD from 0.3 to 3: increase in rolling resistance between 8 and 84 % In the survey there also is some information about HDV. At least IRI effects are higher for HDVs compared to cars. Increases in car rolling resistance based on ECRPD results for the same changes as in (Sandberg, 1997) in IRI and MPD: at 15 m/sec: - IRI: increase in rolling resistance by 19% - MPD: increase in rolling resistance by 46 % at 25 m/sec: - IRI: increase in rolling resistance by 48 % - MPD: increase in rolling resistance by 72 % The ECRPD results are in the intervals of the survey. IRI effects are in the middle of the survey interval and MPD effects are in the higher part of the survey interval. Increases in HDV (RST) rolling resistance based on ECRPD for the same changes in IRI and MPD as in the survey: IRI: increase in rolling resistance by 47 % MPD: increase in rolling resistance by 60 %. The HDM-4 relative effects of IRI and MPD are independent of speed. The effects of IRI and MPD can be expressed in the same way as in the presented literature survey above: IRI (an increase from 1 to 10): - car: increase in rolling resistance by 21 % - >2500 kg: increase in rolling resistance by 30 % MPD (an increase from 0.3 to 3): - car: increase in rolling resistance by 6 % - >2500 kg: increase in rolling resistance by 8 % For MPD the HDM-4 effect (car) then is below the lower limit of the survey interval and the IRI effect is in the lower part of the interval. Compared to ECRPD the HDM-4 relative effects are much below the ECRPD effects. Another comparison of interest is the effect relation between vehicles with operating weight <2500 kg and > 2500 kg respectively in HDM-4. IRI: higher effects for >2500 kg MPD: approximately the same effect for both vehicle categories For a car an increase of MPD from 0.3 to 3 will, based on (Sandberg, 2007), give a rolling resistance increase by 71 %. 11 The corresponding ECRPD effect varies with speed: 46 % at 15 m/sec 60 % at 20 m/sec 11 Five different tyres measured in three speed levels: 50, 70 and 90 km/h. 69

70 72 % at 25 m/sec. At a speed of 25 m/sec the additional MPD effect (dcr(mpd)) is approximately the same for the two studies. For lower speeds ECRPD values are smaller. The comparison of the absolute additional effect dcr(mpd) could be the most representative alternative to chose, compared to a relative effect for the total rolling resistance, since the ECRPD constant includes other effects than just the tyre. The way of estimating relative effects for ECRPD rolling resistance will give an underestimation since the constant includes both rolling resistance and transmission resistance. In (Hammarström, 2001) road surface effects have been estimated based on fuel consumption measurements with the same car as in ECRPD. An increase in IRI from 1 to 4 and in MPD from 0.4 to 1.2 gave an increase in fuel consumption by 4 %. For the car used (Volvo 940) this corresponds to an increase in rolling resistance by 22 %. The corresponding quotient for ECRPD is 28 % at 70 km/h. The quotient in ECRPD increases when speed increases. Based on (Hammarström and Karlsson, 1987) the transmission resistance has been estimated: for the car: (N/kg) for the RDT: (N/kg) For the automatic transmission in the RST there is no information available. In order to estimate rolling resistance on a flat surface for ECRPD transmission losses shall be subtracted from the constant. After a subtraction the remaining constant should correspond to rolling resistance per kg. The remaining value of the constant after subtracting the transmission resistance per kg should be below the expected value. Increasing tyre vertical force can, based on literature, be expected to reduce the rolling resistance coefficient Cr 0. For the Volvo test vehicle the average maximum wheel load, force between tyre and road surface, has been 4170 N. The maximum tyre load at maximum gross vehicle weight is 4560 N. In order to make more detailed and representative comparisons between studies one should know the tyre load in these studies. There is no information available about tyre load and road surface rolling resistance effects. The conclusion of the comparison is that obtained results are in good correspondence with other results, with exception of the HDM-4. 70

71 10 Discussion and conclusion 10.1 Coast down versus other methods Although a comparison between different methods is not within the frames of the current project we give a brief summary of the advantages and disadvantages with different methods. There exist (essentially) four different approaches for determining the road surface influence on rolling resistance and fuel consumption: direct measurement of rolling resistance forces acting on a wheel (either in laboratory or in field measurement). coastdown measurements fuel consumption measurements or transmission torque measurements computer simulations Each of these approaches has advantages and disadvantages. As compared to direct measurements of forces on a wheel, the coastdown method measures the resulting behaviour of the entire vehicle, and thus, includes all possible forces acting on the vehicle. Fuel consumption measurements also include all forces. However, in contrast to fuel consumption measurements, any disturbances caused by the engine (which have nothing to do with the road surface conditions) are excluded from the coastdown method. One drawback with coastdown is that all wheels are freely rolling which is not the most frequent situation in real traffic. The rolling resistance for a freely rolling wheel is lower compared to a drive wheel with a torque necessary to overcome the rolling and air resistance. One advantage with coastdown measurements, as the present study convincingly shows, is that it is possible to distinguish, with high accuracy, the different contributions to the total driving resistance, provided that the different contributions depend differently with respect to speed and other measurable quantities. The regression method is a very powerful tool for detecting even very small effects, provided that there are no systematic errors in the measurements. A serious limitation with the coastdown method is that it is not possible to separate components which have identical dependence on measurable quantities. One example of this is some components among the transmission losses, which may be expected to be proportional to the square of the vehicle speed. They will be indistinguishable from the air resistance and, hence, will be accounted for as an additional (small) air resistance. Similarly, the constant term in models (6.12) and (6.13) will include both transmission losses and losses in the tyres. Another limitation of the coastdown method is that it is not well suited for determining the mathematical form of a model. This should instead be based on physical principles and/or computer simulations The coastdown methodology elaborated in this project The objective of this project has been to design the coastdown method in a way that produces reliable results. We strongly believe that the coastdown method as designed in this study can be used to obtain reliable and accurate estimates of rolling resistance. The study shows that already a very small amount of measurements is enough to yield a reasonable (if not reliable) estimate of the rolling resistance. Moreover, the seemingly threatening high frequency fluctuations in acceleration affect the accuracy in results very little (see section 6.9.4). 71

72 However, the method is complex and a large number of possible error sources exist. In our study, we have investigated the influence of various errors in the result. The main lesson we have learnt from this work is the importance to avoid systematic errors in data. Better to use a smaller amount of reliable data than a large amount of less reliable measurements. All measurements of dubious quality should be discarded. We strongly recommend carrying out the checks proposed in section The temptation to make use also of less reliable data is, however, very high and we have ourselves not managed to avoid yielding for this temptation in some cases (measurement from some road strips should probably have been discarded, see section 8.2). In order to be able to make the complex measurements reliable there necessarily need to be routines developed based on measurements with some regularity. This reported study is based to some extent from the experience from a similar study (Hammarström, 2001). Errors may be categorized in the following classes: random (ordinary) errors (rapid fluctuations in acceleration) errors caused by meteorological conditions (wind, temperature) errors caused by shortcomings in road alignment data errors caused by malfunctioning of the on board measurement equipments other systematic errors Our experience is that the first category is not very important. In contrast, the third category has caused us a lot of problems, and, is the probable reason why the results (for the Volvo) are not more stable. It cannot be enough emphasised, the importance of measuring the longitudinal gradient with high accuracy and with a minimum of bias. A simple check can be done by comparing the gradients (or the corresponding road profiles) in opposite directions. Unfortunately there is no simple check method available for road surface conditions. Great care should, of course, also be taken to assure that data from the different measurement equipment are synchronized and consistent. One trivial mistake can destroy the whole result. A method to identify such errors may be to successively compute and compare results where measurements for one road are removed. Concerning the coastdowns, any measurements with dubious quality should be discarded. A simple way to identify errors is to plot velocity versus position for all coastdowns along a specific road strip. They should be very close to parallel. In a previous study by Hammarström (2001) the importance of uncorrelated variables was highlighted. For those terms in the model that we want to determine with high accuracy (in our case those containing IRI or MPD) a wide spread in values is strongly recommended. Other quantities (in our case curvature, gradient, crossfall, rut depth and temperature) may have been introduced as corrections but not with the explicit aim to determine these effects with high accuracy. For these it may be more appropriate (but not necessary) to instead aim at a low variation in the values Results The number of coastdowns measurements for the Volvo is indeed very large. In light of this we should expect even more stable results. The reason for this instability has not been fully 72

73 clarified but we suspect deficiencies in the road geometry (gradient) to be the main reason. From Table 8.3 and Table 8.4 it can be seen that reasonable accuracy can be obtained from a much smaller set of measurements. Checks of the measured road gradients indicate that the quality of this data could be better. This proved lack of accuracy in gradient data motivates the use of a including the gradient as a regression parameter. The use of such a parameter might improve the representativity for the estimated IRI and MPD parameters. Both the IRI and MPD parameters are reduced in such an analyse, Table The importance of limiting the meteorological wind speed during measurements is demonstrated by Table When limiting the wind speed to 0.5 m/s both IRI and MPD effects decrease. The relative decrease is bigger for MPD than for IRI. The total data set, the number of coastdowns, is reduced with approximately 1/3 In Table 8.26 results for different measures are presented. For roughness there are six measures and for macrotexture there are two measures. Even if small differences the biggest R 2 is reached by using IRI and MPD. The measurements have been done with the same tyre pressure at the measuring start of each test road section. The average tyre temperature and pressure will be a function of the speed and the road surface conditions per section. The tyre temperature could be expected to be a function of speed and road surface. The speed and tyre temperature effect will not be representative with coastdown measurements if normal driving is in a close to constant speed level. The drive wheels are not under normal driving conditions. If the coastdown technique is used for estimation of driving resistance measured values will include contributions from the transmission, both the gear box and the final gear box. If rolling resistance will be isolated from the other resistances one needs information about the resistance from the transmission. Information about such resistance is available in (Hammarström and Karlsson, 1987). The results for RST and, especially, RDT measurements are not very reliable. The reason for this is partly that not enough measurements were done but also, and more importantly, that the measurements were not performed with the same care as for the Volvo. This is true both concerning the planning of the measurement and their carrying through. The description in sections was not strictly followed. 73

74 PART 2: Comparison between coastdown measurements and vehicle simulations 11 Validation and comparison with vehicle simulations 11.1 Introduction In the previous sections an empirical method for establishing the relation between road surface conditions and rolling resistance was developed and applied to a car and to two heavier vehicles. We found that in general the rolling resistance is more dependent on the road texture than on road roughness for normal road conditions. There exists an alternative approach to estimate roughness effects: by simulation. At VTI a vehicle simulation program, VETO, has been developed. The dynamical behaviour of a vehicle running along a road profile can be simulated and the energy loss caused by road roughness and side forces can be estimated. Simulated results are based upon a mechanistic model describing the dynamics of the vehicle. In order to understand the behaviour of the simulation model results from simplified conditions are presented below (Hammarström, 2000b). The conditions are represented by a sinus profile and different constant driving speeds. The quarter car model used in the IRI model uses a speed of 80 km/h. From Table 4.1 we see that IRI increases with increasing amplitude and IRI increases with decreasing wave length until a maximum is attained at approximately 2 m wavelength. Table 11.1 IRI as a function of wave length and amplitude.* Amplitude Wavelength (m) (m) *Quarter car model. In VETO a mechanistic model of a half car vehicle, two wheel axles, is used. Energy damping losses in shock absorbers and in tyres are calculated and expressed as a driving resistance. In Table 11.2 additional driving resistance due to roughness, roughness resistance, as a function of speed and the sinus profile is presented. 74

75 Table 11.2 Roughness resistance for a car based on simulations. (VETO) Amplitude Wave length (m) (m) km/h km/h km/h km/h The additional driving resistance increases with increasing amplitude and decreasing wavelength. Increasing speed in most cases increases the additional driving resistance. Note the principal difference between IRI and energy losses. IRI increases with decreasing wavelength down to a 2m wavelength but the energy losses decreases in the whole observed interval. Are the empirical results presented in chapter 7 consistent with simulated results from VETO? The focus will be on: Total energy damping losses in tyres and shock absorbers (along a specific road segment) caused by road roughness (various drag forces) Total energy side force losses 11.2 Validation of VETO roughness subroutine In Part 1 an empirical model for roughness resistance based on coastdown measurements were estimated. A similar model can be created based on data from simulations. Simulations with VETO have been made based on: a vehicle description for the test vehicle (VOLVO 940) the same 28 road strips that were used for the car coastdown measurements road roughness profiles (with resolution 0.1 m) for the left and right wheel track constant speeds: 15.6, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85 and 90 km/h for each roughness profile and speed VETO simulations have been performed output data from VETO: IRI; damping losses in tyres; damping losses in shock absorbers. These damping losses have been recalculated into driving resistance The parameters in an IRI function in the same form as for measurements have been estimated: dcr(iri,v) = (a x IRI + b x IRI x (V 20)) 75

76 Results for the vehicle: a x m x 9.81=1.008, significant different from zero b x m x 9.81=0.0593, significant different from zero R 2 =0.809 Separate analyses have been performed for tyres and shock absorbers as well. Results for the tyres: a x m x 9.81=0.319, significant different from zero b x m x 9.81=0.0152, significant different from zero R 2 =0.324 Results for the shock absorbers: a x m x 9.81=0.689, significant different from zero b x m x 9.81=0.0441, significant different from zero R 2 =0.812 For these VETO simulations, the driving resistance contribution from the shock absorbers is, on average, 62 % and from the tyres 38 %. In Figure 11.1 the simulated effects are compared to the measured effects for different combinations of IRI (1, 2, 3 and 4) and speed (10, 15, 20 and 25 m/sec). VETO - measurements VETO (N) Coast down (N) Figure 11.1 Roughness resistance estimated from VETO simulations and from coastdown measurements. Each value corresponds to a (constant) velocity level and IRI. Velocities range from 10 to 25 m/s and IRI 1 to 4 mm/m. The absolute difference between coastdown and VETO is big. However there is a strong correlation (R 2 =0.99) between the two data sets. The conclusion should be that the vehicle dynamic part of VETO would be useful for predictions if a calibration is added. 76

77 11.3 Validation of VETO side force subroutine The side force routine in VETO is a general mechanistic expression for the influence of the side force on driving resistance. What is validated is the used parameter value for tyre stiffness. The estimated parameter value for SideQuad is equal to 1/CA in the expression for F side in section 3.1. In order to make a formal correct validation the stiffness of the tyres used on the Volvo should had been measured separately. The value used in VETO so far does not fulfil this demand. Anyway the value could be expected to have a representative size level. Comparison between estimated CA and the value used in VETO for cars: ECRPD: CA = (30303, 41667) VETO: CA = The value used in VETO for tyre stiffness is an old value not exactly valid for the tyres on the Volvo. The value is supposed to be in a representative size class. The conclusion is that the estimated ECRPD value is a value that could be valid for the Volvo tyres even if this has not been proved Discussion and conclusion Estimated IRI effects by measurements are much higher compared to simulated effects. What is not included in simulated effects is the deformation of the contact area between the tyre and the road surface. One way of estimate this additional effect could be by using the correction function for rolling resistance measured on a roller. The relation in rolling resistance between a drum and a flat surface is described in (Mitscke, 1982): F R,T /f R,R = (1 + (2 x r)/d) 0,5 where D is the diameter of the drum (m) F R,T is the rolling resistance on a drum (N) F R,E is the rolling resistance on a flat surface (N) With the correction function presented in (Mitschke, 1982) correction values of rolling resistance from flat to different wave lengths and amplitudes can be estimated, see Table Table 11.3 An analysis of possible roughness contributions from the tyre road crumple zone to driving resistance Wave length (m) Amplitude (m) Radius (m) IRI Correction

78 Thus, a wave length of 0,5 m and amplitude m would give a contribution to dcr(iri) equal to 0.039*(rolling resistance on flat surface). Increasing roughness will result in increased tyre temperature. Increased tyre temperature will result in increased tyre pressure. Increased tyre pressure will reduce rolling resistance. This effect is of interest when comparing measured values with simulated (VETO). In the simulation the tyre pressure is kept constant. An increased tyre pressure will influence the dynamic characteristics of the tyre. This will probably contribute to an overestimating roughness effect by simulation. This discussion needs further information about what methods used for estimating the tyre spring and damping effects. If these parameters have been measured after the tyre reaches an equilibrium temperature and without adjusting the tyre pressure the conclusion would be that the simulation in this respect is representative. Used spring and damping parameters for simulation of the tyre behaviour are not measured for the Volvo tyres. The expectation is that the size level of simulation parameters should not differ too much from the true values of the Volvo tyres. The additional IRI resistance calculated by VETO is much lower than the level estimated from measurements. However the R 2 value is high. The conclusion is that the VETO roughness routine might be used in order to formulate a function which can be calibrated based on coastdown measurements. One important matter for future work should be to explain and to eliminate the discrepancy between simulated results and measurements. 78

79 PART 3: A general driving resistance model 12 General driving resistance model 12.1 Introduction Driving resistance and fuel consumption need to be estimated for road traffic in general. The influence of road surface conditions on rolling resistance has, in the ECRPD project, been estimated based on field measurements with only three test vehicles. The ultimate goal is, however, a general model for driving resistance estimation valid for all type of road vehicles and tyres. One of the main objectives of the ECRPD project has been to develop and implement a general model in VTI s vehicle simulation program, VETO. In this chapter we investigate the possibility to generalize the previous estimated models into a general one. The road surface does not only influence rolling resistance but also vehicle speed. Hence, the vehicle speed effect needs also to be described in the final model A general model for road surface effects on driving resistance The objective for ECRPD is a general model for all road vehicles. Important questions then are: if estimated effects will be used even if not significantly different from zero if estimated additional road surface driving resistances depend on tyre model, expressed by the rolling resistance on a smooth surface, and, if so, to what extent if effects have been proved for one test vehicle but not for the other, how to estimate effects for the other type of vehicles if effects have been proved for one test vehicle, how to estimate effects for other road vehicles of the same type if parameter values are dependent of the tyre load if simulated values, IRI effects, by VETO are possible to use even if the absolute values are most different from measured. The total rolling resistance expression for use in the general model: Cr = Cr 01 + Cr 02 x V + dcr(iri) + dcr(mpd) dcr(iri) = C 2 x IRI + C 3 x IRI x (V 20) dcr(mpd) = C 4 x MPD + C 5 x MPD x (V 20) Cr: expression for total rolling resistance (not including the side force resistance) when multiplied with Fz. Cr 01 and Cr 02 : parameter for rolling resistance on a smooth road surface dcr(iri): function for additional rolling resistance caused by roughness dcr(mpd): function for additional rolling resistance caused by macrotexture 79

80 C 2 and C 3: parameters for describing additional rolling resistance from IRI C 4 and C 5 : parameters for describing additional rolling resistance from MPD This expression will replace the existing rolling resistance model in VETO. Since the temperature correction term is excluded Cr will represent a temperature of 25 C at least for cars. The reason to split Cr 0 into Cr 01 and Cr 02 is because this is a frequent way to express rolling resistance on a smooth surface. In Part 1 of this report models for three vehicles are presented: a car; a van and a truck. The estimated results represent an ambient temperature of 25 C when a temperature correction term is included in the rolling resistance function. If no such term is included results represents an average temperature for the measuring conditions. The ambient temperature is included in the car model but not in the other models. Meteorological wind is handled in a similar way. If the wind is included in the model then estimated parameters represent zero wind conditions. If not included estimated parameters include the wind conditions during measurements. The meteorological wind is included in the car model but not in the other models. Even if effects from ruts have been proved significantly different from zero these are not included in the model because of high correlations between rut depth and IRI. The analysis (for the Volvo) also has proved an effect from the side force. Since the estimated effect is not very stable the existing model in VETO for the side force is used. The existing VETO model should be valid for all type of road vehicles. An advantage with the existing VETO side force model is that the tyre stiffness is expressed as a function of Fz increasing the possibility to be general concerning tyre load. For the Volvo all estimated parameter values are significantly different from zero. No estimated road surface parameters for the RST are significantly different from zero. One should also notice that, for the RST and for the RDT, no speed terms for IRI and MPD were included in the model. The absence of the speed terms complicate comparisons with models including a speed term as for the Volvo. For the RDT the whole estimated IRI confidence interval is positive, i.e., a wrong sign makes it doubtful to use any estimated parameter values from the RDT. Even if estimated parameters are not significantly different from zero the confidence interval can be useful for the choice of alternative values. Different tyres per vehicle type can be expected to have different IRI and MPD effects compared to the tyres used in this study. One important question is if such expected effects are functions of Cr 0 and to what extent. The additional driving resistance caused by roughness includes contributions both from tyres and from shock absorbers. The tyre roughness effect on driving resistance is depending on the spring and damping characteristics of the tyre. If these characteristics are correlated with Cr 0 is not known. Another tyre than used in the study can mainly be expected to influence the tyre additional roughness effect and not the damping effects in the shock absorbers. In the general 80

81 model IRI effects for all vehicle types will be estimated by the use of estimated parameters independent of the Cr 0 choice. In order to generalize the measured MPD-results in ECRPD one needs to know if dcr(mpd) is dependent of Cr 0. Rolling resistance has been measured for 50 tyres on a drum. 12 Measurements have been performed: at 80 and 100 km/h at a smooth ( Smooth sandpaper surface, MPD 0 ) and a rough surface ( Roughtextured surface, MPD 1 ). Let dcr(mpd) i denote additional macro texture effect for tyre (i). Based on rolling resistance data for a set of tyres dcr(mpd) i has been estimated per tyre by: where dcr(mpd) i = Cr 1 (i) Cr 0 (i) Cr 0 (i): rolling resistance parameter for tyre (i) on a smooth sandpaper surface Cr 1 (i): rolling resistance parameter for tyre (i) on a rough textured surface Based on data for all tyres parameter values, a and b, have been estimated per speed level: dcr(mpd) i = a + b x Cr 0 (i) (12.1) In Table 12.1 the result of the analysis is presented. Table 12.1 Estimated parameter values for eq (12.1). Km/h a* b* R *Significantly different from zero. The estimated parameter values are significantly different from zero and the R 2 is at most With the estimated functions one can estimate the relative change in dcr(mpd) in parallel to a relative change in Cr 0. Relative increases in Cr 0 give relative changes in dcr(mpd): +14% in Cr 0 gives 4% in dcr(mpd) +29% in Cr 0 gives 9% in dcr(mpd) There is no information available if the relative change in dcr(mpd) with Cr 0 depends on MPD 0 and MPD 1. Based on this analysis the proposal is to let dcr(mpd), in the general model, be independent of Cr 0 for all vehicle types. This approach can be compared with HDM-4. In HDM-4 a change in Cr 0 will give an (almost) equal relative change in the IRI and MPD-effects. 12 Data from Ulf Sandberg, VTI. 81

82 In ECRPD estimated parameter values, IRI and MPD, for heavier vehicle types than cars have deficiencies. The choice of suitable parameter values then need to be based on different sources in addition to ECRPD. Available information about relative effects: IRI: - in HDM-4 the HDV effect is bigger compared to the car effect - in ECRPD the HDV (RST) effect at least for speeds <20 m/sec is bigger than for the car - In VETO the effects for HDV (heavy truck with trailer) at least for speeds <20 m/sec are higher than for the car - in ECRPD the HDV (RST) effect is bigger than in HDM-4 - in (Sandberg,1997) HDV effects are bigger than for cars. MPD: - in HDM-4 the HDV effect is bigger than for the car - in ECRPD the HDV (RST) effect is approximately the same as for the car - in ECRPD the HDV (RST) effect is bigger than in HDM-4 Selection of parameter values for HDV s in the general model: IRI: the values for the RST MPD: the same values as for the car. From the literature one can conclude that at least Cr 0 is dependent of the tyre load (Fz). In (Sturm and Hausberger,2005) the tyre load effect is expressed with a function Cr 0 = x (F z /1000) When Fz increases Cr 0 decreases. This expression is valid for HDV tyres with a dimension To what extent dcr(iri) and dcr(mpd) are functions of vehicle masses is not at our knowledge. For IRI one possibility could be to use VETO for an IRI analysis. Since available data on this effect is judged being not enough for acceptable representativity it is not included in our present general model. Standardized rolling resistance measurements include adjustments to one reference temperature. In the ECRPD study such a function for adjustments has been estimated. The estimated functions for the car are used for ambient air temperature adjustments. Proposed parameter values are presented in table Table 12.2 Parameter values in the general model.* Vehicle Cr 01 Cr 02 C 2 C 3 C 4 C 5 Pc/van E E LDV Bus Heavy truck *Cr = Cr 01 + Cr 02 x V + dcr(iri) + dcr(mpd); dcr(iri) = C 2 x IRI + C 3 x IRI x (V 20); dcr(mpd) = C 4 x MPD + C 5 x MPD x (V 20) 82

83 12.3 Vehicle speed The literature includes speed effects from IRI, from ruts and from weather conditions. There is no information available about MPD and speed. In the general model the effect of IRI will be described based on data in section Discussion and conclusion A change in crossfall will influence the side force and also the driving resistance. Another aspect of changed crossfall is a change in drainage at rainfalls. A change in drainage will influence the amount of water on the road surface and then also water driving resistance. The measurements have been done with the same tyre pressure at the measuring start of each test road section. The average tyre temperature and pressure will be a function of the speed and the road surface conditions per section. The tyre temperature could be expected to be a function of speed and road surface (see Appendix F). The speed and tyre temperature effect will not be representative with coastdown measurements if normal driving is in a close to constant speed level. There is a proved decrease in vehicle speed when IRI and ruts increase in parallel to a rolling resistance effect. The dcr(iri) function increase with increasing IRI and increasing V. The influence on driving speed will influence not only dcr(iri). The resulting effect of increasing IRI could be decreasing total driving resistance despite increased rolling resistance. In the basic model used in ECRPD the IRI effects (dcr(iri)) have been modelled as a linear function of IRI and speed. Based on the data simulated with VETO a polynomial approach has been compared to a linear. The results indicate: that a polynomial approach for IRI just gives minor improvements in R 2 that a polynomial approach for the speed gives a more than minor improvements in R 2. 83

84 13 References Arnberg,W.,A., Burke,M.,W., Magnusson,G., Oberholtzer,R., Råhs,K. och Sjögren,L. The Laser RST: Current Status. PM september Statens väg- och trafikinstitut. Linköping Bennett, C., R. and Greenwood, I., D. Modelling Road User and Environmental Effects in HDM-4. No 7 in the Highway Development and Management Series. Version 3.0-December 9, Fraggstedt, M. Power Dissipation in Car Tyres. Licentiate Thesis, TRITA-AVE 2006:26 ISSN Royal Institute of Technology. Stockholm. Gent, A., N. and Walter, J., D. The pneumatic tire. DOT contract DTNH22-02-P Published by the National Highway Traffic Safety Administration. US Department of Transportation, Washington Hammarström, U. and Karlsson, B. VETO a computer program for calculation of transport costs as a function of road standard. VTI meddelande 501. Swedish Road and Traffic Research Institute. Linköping Hammarström, U. Bränsleförbrukning och luftmotstånd vid kökörning. VTI meddelande Statens väg- och transportforskningsinstitut. Linköping. 2000a. Hammarström, U. PMS fordonskostnader. VTI notat Statens väg- och transportforskningsinstitut. Linköping. 2000b. Hammarström, U. Exhaust emission variations for short engine stops and driving time for petrol cars with and without catalyst. VTI meddelande Swedish National Road and Transport Research Institute. Linköping Hammarström, U. Fuel consumption and coastdown measurements for different road surfaces. VTI not published. Statens väg- och transportforskningsinstitut. Linköping IERD. Integration of the Measurement of Energy Usage into Road Design. Contract No: /Z/02-091/2002. Commission of the European Communities Directorate-General for Energy and Transport Ihs, A. och Velin, H. Vägytans inverkan på fordonshastigheter. VTI notat Statens väg- och transportforskningsinstitut ISO. Passenger car, truck, bus and motorcycle tyres Methods of measuring rolling resistance. ISO Mitscke, M. Dynamik der Kraftfahrzeuge. Band A: Antrieb und Bremsung. Springer Verlag. Berlin Heidelberg New York

85 Popov, A.,A., Cole,D.,J., Cebon, D. and Winkler, C., B. Laboratory Measurement of Rolling Resistance in Truck Tyres under Dynamic Vertical Load. November 27, 2002.( Sandberg, U. Influence of Road Surface Texture on Traffic Characteristics Related To Environment, Economy and Safety. A state of the art Study Regarding Measures and Measuring Methods. VTI notat 53A Statens väg- och transportforskningsinstitut. Linköping Sandberg, U. Vägytans inverkan på trafikbulleremission och rullmotstånd. Slutrapport för projektet: Kunskapsinsamling om lågbullerbeläggningar (Vägverket nr BY 20A 2006:6862/VTI projekt nr 50588). Statens väg- och transportforskningsinstitut. Linköping Sturm, P., J. and Hausberger, S. Emissions and fuel consumption from heavy duty vehicles. COST346 final report. Graz University of Technology. Institute for Internal Combustion Engines and Thermodynamics. Graz Wallman, C.-G, Möller, S., Blomqvist, G., Gustafsson, M., Niska, A., Öberg, G., Berglund, C.-M. and Karlsson, B., O. Tema Vintermodell. Etapp 2. Huvudrapport. VTI rapport 531. Statens väg- och transportforskningsinstitut. Linköping Vägverket. Metodbeskrivning 111:1998. Bestämning av jämnhet i längsled och tvärled samt tvärfall hos ett vägobjekt med mätbil. Funktionella egenskaper. Publikation 1998:52. Vägverket. Borlänge Vägverket. VViS. Väg Väder informations System. Broschyr. Vägverket. Borlänge. 85

86 Appendix A Description of test vehicles Volvo RST RDT Model Volvo 940 Chevrolet CG21305 VAN Scania R143 MI 4x21 Förl Year Weight: max gross veh [kg] Weight: tjänstevikt []kg] Weight: max load [kg] Operative weight: during measurements [kg] Fuel tank [liter] Transmission Rear wheel drive Rear wheel drive Rear wheel drive Gear box manual automatic manual Width [m] (2.50)* 2.4 (3.15)* Height [m] Length [m] Projected vertical area ** 7.6** [m^2] Air resistance coeff 0.37 No info No info Track width [m] No info Distance between axles [m] Number of axles Number of wheels Inertial moment per wheel [kgm^2] Wheel circumference [m] Tyres: front Michelin Green Energy, RadialxSE, 185/65 R15 88T MXT KUMHO 791 Touring A/S Radial tubeless P235/75R15 105S M+S Tyres: back Michelin Green Energy, RadialxSE, 185/65 R15 88T MXT KUMHO 791 Touring A/S Radial tubeless P235/75R15 105S M+S Tyres: pressure, front [bar] Tyres: pressure, back [bar] Max effect [kw] (ISO) *Width including measuring equipment. **Excluding measuring equipment. FIRESTONE, HP-3000, 12.00R20 Tubetype Regroovable BRIDGESTONE, R164, 445/65R22.5 Regroovable, V-steel rib 86

87 Appendix B Description of the selected road strips 1. Road strips used in the Volvo measurements Table B1: Road characteristics for the Volvo measurements Direction Length [m] Speed limit [km/h] IRI [mm/m] MPD [mm] Longitudinal gradient [%] Crossfall [%] Trace [mm] Curvature [10000/m] ID Name Min Max Mean Min Max Mean Min Max Mean Min Max Mean Min Max Mean Min Max Mean 1 Flygrakan Flygrakan StoraAska StoraAska Vikingstad Vikingstad Fornåsa Fornåsa Västerlösa Västerlösa Vattenskidklubben Vattenskidklubben MaspelösaA MaspelösaA MaspelösaB MaspelösaB MaspelösaC MaspelösaC Brokind Brokind Hundklubben Hundklubben Hycklinge Hycklinge Kisa Kisa Rimforsa Rimforsa Quantities have been computed from data aggregated to 25 meter intervals. When the length of a road strip is not a multiple of 25 meter the last part has been truncated. Note that the speed limit differs in the forward and backward directions for two road sections: Brokind and Kisa. 87

88 Table B2 Correlations between road quantities for the Volvo measurements. Based on 25 meter intervals. Only correlations significantly different from zero (95%). Correlations IRI MPD Gradient Crossfall Trace Curvature FRMS RMS1 RMS2 RMS3 RMS4 RMS5 RMS6 IRI 1 MPD Gradient 1 Crossfall Trace Curvature FRMS RMS RMS RMS RMS RMS RMS Table B3 Correlations between road properties. Based on averages over entire road strips. Correlation IRI MPD Gradient Crossfall Trace Curvature FRMS RMS1 RMS2 RMS3 RMS4 RMS5 RMS6 IRI 1 MPD 1 Gradient 1 Crossfall Trace Curvature 1 FRMS RMS RMS RMS RMS RMS RMS

89 2. Road strips used in the RST measurements Table B4: Road characteristics for the RST measurements Direction Length [m] Speed limit [km/h] IRI [mm/m] MPD [mm] Longitudinal gradient [%] Crossfall [%] Trace [mm] Curvature [10000/m] ID Name Min Max Mean Min Max Mean Min Max Mean Min Max Mean Min Max Mean Min Max Mean 19 Brokind Brokind Hundklubben Hundklubben Hycklinge Hycklinge Kisa Kisa Rimforsa Rimforsa Horn Horn Table B5 Correlations between road quantities for the RST measurements. Based on 25 meter intervals. Only correlations significantly different from zero (95%). Correlations IRI MPD Gradient Crossfall Trace Curvature FRMS RMS1 RMS2 RMS3 RMS4 RMS5 RMS6 IRI 1 MPD Gradient 1 Crossfall 1 Trace Curvature FRMS RMS RMS RMS RMS RMS RMS

90 Table B6 Correlations between road properties for the RST measurements. Based on averages over entire road strips. Correlations IRI MPD Gradient Crossfall Trace Curvature FRMS RMS1 RMS2 RMS3 RMS4 RMS5 RMS6 IRI 1 MPD 1 Gradient 1 Crossfall 1 Trace 1 Curvature 1 FRMS RMS RMS RMS RMS RMS RMS Road strips used in the RDT measurements Table B7: Road characteristics for the RDT measurements Direction Length [m] Speed limit [km/h] IRI [mm/m] MPD [mm] Longitudinal gradient [%] Crossfall [%] Trace [mm] Curvature [10000/m] ID Name Min Max Mean Min Max Mean Min Max Mean Min Max Mean Min Max Mean Min Max Mean 1 Flygrakan Flygrakan BetongNorrut BetongSöderut AsfaltNorrut AsfaltSöderut

91 Table B8 Correlations between road quantities for the RDT measurements. Based on 25 meter intervals. Only correlations significantly different from zero (95%). Correlations IRI MPD Gradient Crossfall Trace Curvature FRMS RMS1 RMS2 RMS3 RMS4 RMS5 RMS6 IRI 1 MPD Gradient 1 Crossfall 1 Trace Curvature FRMS RMS RMS RMS RMS RMS RMS Table B9 Correlations between road properties for the RDT measurements. Based on averages over entire road strips. Correlations IRI MPD Gradient Crossfall Trace Curvature FRMS RMS1 RMS2 RMS3 RMS4 RMS5 RMS6 IRI 1 MPD 1 Gradient 1 Crossfall 1 Trace 1 Curvature 1 FRMS RMS RMS RMS RMS RMS RMS

92 Appendix C Description of the coastdowns 1. Coastdown measurements with the Volvo Table C1 Statistics for the coastdown measurements Road ID # of coast downs Air temp [ C] Wind speed [m/s] Air pressure [mbar] Mean init velocity [km/h] Mean velocity [km/h] Mean accel [m/s 2 ] Vehicle weight [kg] Average Table C2 Correlations* between meteorological data and road variables Correlations Airtemp AirPressure WindSpeed IRI MPD Grad Cross Trace * Only correlations significantly different from zero (95%). Based on 25m aggregations. 92

93 Table C3 Correlations* between meteorological data and acceleration Airtemp AirPressure WindSpeed Adjusted dv/dt * Only correlations significantly different from zero (95%). Based on 25m aggregations. Table C4 Correlations* between road variables and acceleration IRI MPD FRMS RMS1 RMS2 RMS3 RMS4 RMS5 RMS6 Curve Grad Cross Trace Adjusted dv/dt * Only correlations significantly different from zero (95%). Based on 25m aggregations. Table C5 Correlations* between meteorological data Airtemp AirPressure WindSpeed Airtemp 1 AirPressure WindSpeed * Only correlations significantly different from zero (95%). Based on 25m aggregations Coastdown measurements with the RST Table C6 Statistics for the coastdown measurements.* # of coast Air temp Wind speed Air pressure Road ID downs [ C] [m/s] [mbar] Mean init velocity [km/h] Mean velocity [km/h] Mean accel [m/s 2 ] Vehicle weight [kg] Average *Wind speed on a height of 10 m Table C7 Correlations* between meteorological data and road variables Air temp Air pressure Wind speed IRI MPD Grad Cross 0.26 Trace 0.47 *Only correlations significantly different from zero (95%). Based on 25m aggregations. 93

94 Table C8 Correlations* between meteorological data and acceleration Airtemp AirPressure WindSpeed Adjusted dv/dt 0.34 *Only correlations significantly different from zero (95%). Based on 25m aggregations. Table C9 Correlations* between road variables and acceleration IRI MPD FRMS RMS1 RMS2 RMS3 RMS4 RMS5 RMS6 Curve Grad Cross Trace Adjusted dv/dt *Only correlations significantly different from zero (95%). Based on 25m aggregations. Table C10 Correlations* between meteorological data Airtemp AirPressure WindSpeed Airtemp 1 AirPressure WindSpeed 1 *Only correlations significantly different from zero (95%). Based on 25m aggregations. 3. Coastdown measurements with the RDT Table C11 Statistics for the coastdown measurements.* # of coast Air temp Wind speed Air pressure Road ID downs [ C] [m/s] [mbar] Mean init velocity [km/h] Mean velocity [km/h] Mean accel [m/s 2 ] Vehicle weight [kg] Average *Wind speed road ID 2 on a height of 10 m. For other road ID on a height of 2 m Table C12 Correlations* between meteorological data and road variables Air temp Air pressure Wind speed IRI MPD Grad 0.07 Cross Trace *Only correlations significantly different from zero (95%). Based on 25m aggregations. Table C13 Correlations* between meteorological data and acceleration Air temp Air pressure Wind speed Adjusted dv/dt 0.07 *Only correlations significantly different from zero (95%). Based on 25m aggregations. Table C14 Correlations* between road variables and acceleration IRI MPD FRMS RMS1 RMS2 RMS3 RMS4 RMS5 RMS6 Curve Grad Cross Trace Adjusted dv/dt *Only correlations significantly different from zero (95%). Based on 25m aggregations. 94

95 95

96 Table C15 Correlations* between meteorological data Airtemp AirPressure WindSpeed Airtemp 1 AirPressure WindSpeed *Only correlations significantly different from zero (95%). Based on 25m aggregations. 96

97 Appendix D Instructions for coastdown measurements Log-book Regnr: Date Time Odometer reading Driver Tanked volume Tyre pressure(kpa) Km vf hf vb hb Road strip Comments Scheme Activity Wind speed prognose OK** (1)Full tank Comment. Logg book (2) Adjust cold tyre pressure(200;240) (3) Warming up to stabilized conditions >30 min (4) Next road strip from scheme logg book (5) Adjust hot tyre pressure(220+/-5;260+/- 10)* logg book (6)Wind speed OK? (7) Select initial speed from scheme (8) If more than one initial speed go to (6) (9) If more than one roads strip go to (4) (10) Road strip Flygrakan for control (90 km/h) logg book (11) Full tank logg book (12) Indoor parking *Front: kpa; rear: kpa; **Prognose x 0.5<1 m/s (note. See text as follows) Measurements indicate that the time from hot to cold tyres during parking is approximately 60 minutes. 97

98 Side position during coastdown: if clear tracks then take a position in the centre of these if not clear tracks then the right side should be 1 m away from the surface edge. Windows closed. No other use of the vehicle until the study is ended. Measurements only if average wind speed < 1 m/s (1 2 m height) Data until now (10 m height): : Prognose (10 m height): Weather observations normally for 10 m height. The wind speed for 1 2 m height is estimated by multiplying with , use 0.5 SMHI data is always saved for measuring time. This is the only source for air pressure. The road surface shall be dry. Other weather data should be in a narrow interval. Measurements constitute coastdowns from different speeds: neutral gear position in good time before each coastdown. Clutch pressed down.. 13 if speed is too low for the coastdown to last the entire road strip then assign a special code for the analysis. if traffic is supposed to influence air resistance of the test vehicle give a special code. Data until the code will be used for analysis. Manually inspect the breaks (put a hand them) every day in order to control there is no braking. 13 Pressed down or not should be of minor importance. Be consequent and use pressed down clutch during coastdown. 98

99 Select road sections in the table order. Each letter represents a group of road sections.* Serie 1 Serie 2 E1 A2 E2 A1 C1 D2 C2 D1 C3 B5 A1 B4 A2 B3 D1 B2 D2 B1 B1 C3 B2 C2 B3 C1 B4 E2 B5 E1 *Random order of the groups. Each series of measurements constitutes 7 coastdowns per road strip. For each coastdown the initial speed is selected from the table below. The choice of initial speeds depends on the speed limit for the road strip. Coastdown no. Speed lim. 70 km/h Speed lim. 90 km/h Every day there shall be one control measurement on the road section Flygrakan with initial speed 90 km/h. Warming up of the test vehicle: car 30 minutes before a test 14 (heavy vehicles demand 90 minutes). Take photos of everything. Road sections: Section Directions Group Road strip Hundklubben 1 2 A A1 70 Speed lim. Km/h 14 ISO First edition Passenger car, truck, bus and motorcycle tyres - Methods of measuring rolling resistance. 99

100 Stora Aska 1 2 A A2 70 Fornåsa 1 2 B B1 90 Maspelösa A 1 2 B B2 70 Maspelösa B 1 2 B B3 70 Maspelösa C 1 2 B B4 70 Vattenskidklub 1 2 B B5 90 ben Flygrakan 1 2 C C1 90 Vikingstad 1 2 C C2 70 Västerlösa 1 2 C C3 70 Brokind 1 2 D D1 70(S): 90(N) Rimforsa 1 2 D D2 90 Kisa 1 2 E E1 70 (N); 90(S) Hycklinge 1 2 E E

101 Appendix E Road surface quantities measured by the RST vehicle The following statistical road characteristics are measured by the RST vehicle as an average over 1 m: IRI, wavelength 0.25 m, unit (mm/m) RMS1, wavelength m, unit (mm) RMS2, wavelength 1 3 m, unit (mm) RMS3, wavelength 2 10 m, unit (mm) RMS4, wavelength m, unit (mm) RMS5, wavelength m, unit (mm) RMS6, wavelength m, unit (mm) MRMS, megatexture, wavelength m, unit m (mm) RRMS, coarse macrotexture, wavelength m, unit (mm) FRMS, fine macrotexture, wavelength m, unit (mm) MPD (mean profile depth), wavelength m, unit (mm) rut Depth, unit (mm) gradient, unit (%) crossfall, unit (%) curvature, unit 10000/m. The measures for roughness are measured in both wheel tracks. MPD is measured along four different tracks. Further description of the RST system and the various measures can be found in (Arnberg et. Al, 1991) and (Vägverket, 1998). The texture of the road is classified in different wavelength areas as follows: microtexture, wavelength m macrotexture, wavelength m megatexture, wavelength m In this study macrotexture and roughness are used to describe the road surface. The macrotexture is described by the measures: MPD, FRMS; RRMS and MRMS. The roughness is described by the measures: IRI and RMS 1 6. IRI and MRMS have a small part of the wavelengths overlapping. RMS6 includes the full band of wavelengths that RMS1 to RMS5 are covering plus wavelengths up to 100 metres. 101

102 Appendix F Tyre temperature and pressure Temp VF Temp HF Temp VB Temp HB Temp Luft Figure F1 Temperature [ C] as function of driving time [minutes] on the surface of the four tyres of the Volvo 940. VF=left front, HF=right front, VB=left back, HB=right back, TempLuft = Ambient temperature. During the first 80 minutes the vehicle was driven with speed 90 km/h. After 80 minutes the vehicle was resting Temp Luft Ringtryck VF Ringtryck HF Ringtryck VB Ringtryck HB Figure F2 Pressure [bar] as function of driving time [minutes] inside the four tyres of the Volvo 940. Same conditions as in Figure F2 102

103 RDT degrees C minutes Temp VF Temp HF Temp VB Temp HB Figure F3 Temperature [ C] as function of driving time [minutes] on the surface of the four tyres of the RDT. VF=left front, HF=right front, VB=left back, HB=right back. In parallel to coastdown measurements on E6. Standstill after 77 minutes. RDT bar Pressure VF Pressure HF Pressure VB Pressure HB minutes Figure F4 Pressure [bar] as function of driving time [minutes] inside the four tyres of the RDT. Same conditions as in Figure F3. In parallel to coastdown measurements on E6. Standstill after 77 minutes. 103

104 Appendix G A filtering method for the acceleration A simple filtering method for the acceleration that has been used in this study may be of some general interest. It very efficiently eliminates the high frequency fluctuations without much affecting the original signal. From the perturbation study in section it turned out that this filtering had little effect on the regression results. It may however be useful for other purposes. The filtering can be defined by repeated averaging: For j=0, N-1 End For i=j+1,m End a j ( a + a )/ 2 =, j+ 1 j i i i 1 0 where N denotes the total number of iterations, a, i = 1, K, M denotes the computed (by N differentiation) acceleration values (= a i ), and a i denotes the corresponding filtered accelerations to the N:th degree. (To avoid displacements of the acceleration signal, the averaging can be appropriately applied alternately backwards and forwards, i.e. replacing index i-1 with i+1 in every second iteration.) In experiments, the typical high frequency fluctuations that arise in the acceleration have been very efficiently reduced by this filter without seriously distorting the true curve. However, rather large values for N may be needed (N in the order of 20 to 30 has been found appropriate in our application). In Fig H1 the result is shown for various values for the iteration number N. i Acceleration unfiltered Degree = Acceleration [m/s2] Distance [m] -3-4 Degree =