Estimating the Effects of Pavement Condition on Vehicle Operating Costs (2012)

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27 This chapter describes the research approach used for developing the appropriate models to estimate the effects of pavement condition on tire wear. The most recent tire wear model found in the literature is the mechanistic–empirical model found in HDM 4 (Bennett and Greenwood, 2003b). This model was calibrated to US conditions using truck tire wear data collected from NCAT and from field trials con- ducted in this project for a passenger car. HDM 4 Tire Wear Model The general form of the tire consumption model is the following: TC NW EQNT MODFAC =  ( . )4 1 where: TC = Tire consumption per vehicle (%/km) Nw = Number of wheels EQNT = Equivalent new tire (%/km) MODFAC = Tire life modification factor Tables 4-1 through 4-3 summarize the HDM 4 tire wear model (Bennett and Greenwood, 2003b). Tire wear is a func- tion of the normal, lateral, and circumferential forces applied on the tire. The latter include the aerodynamic, gradient, and rolling resistance forces. These forces are functions of vehi- cle characteristics, pavement conditions, and climate. Ben- nett and Greenwood (2003b) noted that, when testing the model, the values for C0tc (tire wear rate constant) were found to be too low and resulted in an unreasonably high tire life. Therefore, an interim model was adopted for HDM 4. A con- stant was added to the EQNT equation in Table 4-1, which becomes as follows: EQNT TWT VOL = × +   1 10 0 0027 4 2. ( . ) where: EQNT = Equivalent new tire (%/km) TWT = Total tire wear (dm3/1000 km) VOL = Tire volume (dm3) Data Collection Articulated Truck Tire Wear: NCAT Test Track Data Four tractor-trailer assemblies applied traffic to the NCAT track. Each tractor (13.6 metric tons or 30,000 lbs) towed three 2-axle trailers, each loaded to 18.2 metric tons (40,000 lbs) resulting in a GVW of 68 metric tons (150,000 lbs) (Brown et al., 2002). The truck configuration is shown in Figure 4-1; this configuration applies approximately 10 equivalent single- axle loads (ESALs) per pass. The tractor-trailer assemblies were driven at 72 km/h (45 mph) around the track for 18 hours a day, 6 days a week, for 2 years. Figure 4-2 shows the NCAT track configuration. The track consists of two tangent sections connected by two spiral curves. The north–south straight sections on the NCAT track are precisely 0.8 km (2,600 ft long: 13 sections of 200 ft in each direction), connected with two spiral sec- tions approximately 0.6 km (2,000 ft in length: 10 sections of 200 ft in each direction). The east curve profile travels down a -0.5% grade, while the west curve profile travels up a +0.5% grade. The maximum superelevation of both curves is 15%. The profiles of both the north and south straight sections are level with 2% normal cross slopes. Thus, of each duty cycle, about 60% is on level pavement (with 2% cross slope), 15% on up grade, and 15% on down grade (with 15% superelevation). Figures 4-3 and 4-4 show the pavement roughness and mean profile texture, respec- tively, provided by NCAT. The data collected by NCAT showed that the average life of truck tires are 148,563 km (92,852 mi) for drive/trailer C h a p t e r 4 Tire Wear Model

tires and 75,906 km (47,442 mi) for steer tires. These data were converted to tire wear rates assuming standard truck tires with tread depth of 23.8 mm initially (0.94 in.), and that the tires were replaced when the tread depth was 3.2 mm or 0.13 in. (according to tire manufacturers recommendation). The cumulative distribution of tire wear for each tire type was calculated, as shown in Figure 4-5. The range of data (25th to 75th percentile) is taken as the useful range, as shown in Figure 4-6. These data reveal that the range in truck tire wear rates is 0.0006%/km to 0.0021%/km (0.0009%/mi to 0.0034%/mi). Passenger Cars: Field Trials To validate the HDM 4 tire wear model for passenger cars, field tests were conducted using vehicles driven over long distances. Two different roads (I-69 and M-99) from the sections used during the fuel consumption field tests were selected based on the variability level of their pave- ment conditions (i.e., roughness, gradient, texture, and pave- ment type). Information on passenger car tire life collected from tire manufacturers was used to estimate the minimum length of test sections sufficient to establish tire wear rates. Table 4-4 summarizes the conditions of the test sections. Five field tests were conducted on M-99 (Trials 1 through 5) and two tests were conducted on I-69 (Trials 1 and 2). Measure- ments were repeated for Trial 1 on I-69 (Measurements 1 through 3). A 2008 Chevrolet Malibu (1.69 metric tons or 3,732 lb) with front-wheel drive and typical passenger car (radial) tires was used in the field tests (model P215/60R17). The tire pressure was kept at the manufacturer’s recommended value (207 kPa or 30 psi). Tire wear was investigated in the left front (LF), the right rear (RR), and the left rear (LR) tires. The initial tread depths at time of testing were 7.14 mm (9/32 in.) for the LF tire, 5.55 mm (7/32 in.) for the RR tire, and 7.23 mm (9/32 in.) for the LR tire. Test tires were driven only on the test sections; replacements tires were used while driving between the laboratory (where the measurement apparatus is) and the test sections. For tire tread depth mea- surement, the tires were mounted on a tire balancer, which allowed the tires to freely rotate so that measurements could be made at multiple points around the tire circumferences. A laser-based data acquisition system with accuracy of 4 microns, which was attached to the balancer, was used to measure tread depth. The vehicle’s tire tread depth (TD0) and pressure (P0) were measured before the start of the tests and after the 28 Name Description Unit Number of equivalent new tires (EQNT) 10 × VOL TWTEQNT = %/km VOL = Tire volume dm3 Total change in tread wear (TWT) CFT 2 + LFT 2 TWT = C0tc + Ctcte NFT TWT = C0tc + Ctcte × TE × dm3/1000 km C0tc = Tread wear rate constant (Table 4-3) dm3/1000 km Ctcte = Tread wear coefficient (Table 4-3) dm3/MNm The tire energy (TE) CFT 2 + LFT 2 TE NFT = MNm/1000 km The circumferential force on the tire (CFT) (1+CTCON * dFUEL) * (Fa + Fr + Fg) CFT NW = N CTCON = Incremental change of tire consumption related to congestion ratio dFUEL = Incremental change of fuel consumption related to congestion ratio Fa = Aerodynamic forces N Fr = Rolling resistance forces N Fg = Gradient forces N The lateral force on the tire (LFT ) Fc LFT NW = N Fc = Curvature forces N Nw = Number of wheels dimensionless The normal force on the tire (NFT) M * g NFT NW = N M = Vehicle mass kg g = Gravity m/s2 Table 4-1. HDM 4 tire consumption model.

29 Name Description Unit Aerodynamic forces (Fa) 2*****5.0 υρ AFCDCDmultFa = N CD Drag coefficient dimensionless CDmult CD multiplier dimensionless AF Frontal area m2 Mass density of the air kg/m3 Vehicle speed m/s Gradient forces (Fg) Fg = M * GR * g N M Vehicle weight kg GR Gradient radians g Gravity m/s2 Curvature forces (Fc) − = −3 22 10* * ** * ,0max CsNw egM R M Fc υ N R curvature radius m Superelevation (e) e = max(0,0.45−0.68* Ln(R)) m/m Nw Number of wheels dimensionless Tire stiffness (Cs) ++= 2 *2*10* Nw M a Nw M aaKCSCs kN/rad KCS Calibration factor factor a0 to a2 Model parameter (Table 3-28) dimensionless Rolling resistance (Fr) (( 2*13*12*1*11**2 υbMbCRNwbFCLIMCRFr ++= N CR1 Rolling resistance tire factor factor Rolling resistance parameters (b11, b12, b13) = = = 2/*012.012 /064.0 /067.0 12 *3711 DwNwb tireslatestDw tiresoldDw b Dwb factors Dw Diameter of wheel Rolling resistance surface factor (CR2) [ DEFaIRIaTdspaaKcr *3*2*102 +++= factor Kcr2 Calibration factor factor a0 to a3 Model coefficient (Table 3-28) dimensionless Tdsp Texture depth using sand patch method mm IRI International roughness index m/km DEF Benkelman Beam rebound deflection mm Climatic factor (FCLIM) FCLIM = 1 + 0.003*PCTDS + 0.002* PCTDW dimensionless )) ] Table 4-2. HDM 4 tractive forces model. vehicle was finished with the loops (TDfinal and Pfinal). The tire wear was calculated as the difference between TD0 and TDfinal. Because the accuracy of the measurement is highly sensitive to tire pressure, it was ensured that P0 and Pfinal were the same prior to computing the difference tread depth. The tread depth was measured in two different positions along the cross section of the tire as shown in Figure 4-7. For each position, the tread depth was also measured in 30 different cells along the longitudinal direction of the tire as shown in Figure 4-8. Table 4-5 summarizes the data collected from tire man- ufacturers. Based on these data, a passenger car tire incurs 0.1 mm (0.004 in.) of tread wear after the vehicle is driven at constant speed for 1,040 km (650 mi). However, according to the Uniform Tire Quality Grading Standards (UTQGS), the vehicle should be driven for at least 2560 km (1,600 mi) to measure a reliable tire wear value. Based on the detailed statistical analysis conducted as part of this study (Appen- dix B), the selected distance travelled by the vehicle during the field tests was 4,000 km (2,500 mi). The accumulated tire wear data for all trials were first normalized to 4,000 km (2,500 mi) for comparison pur- poses. The data for all cells were used to allow calculat- ing the cumulative distribution of the tire wear across the

30 Figure 4-1. NCAT test track vehicle. Source: NCAT (2010) Figure 4-2. NCAT track layout and configuration. Source: NCAT (2010) Vehicle type C0tc (dm3/1000 km) Ctcte (dm3/MNm) Motorcycle 0.00639 0.0005 Small car 0.02616 0.00204 Medium car 0.02616 0.00204 Large car 0.02616 0.00204 Light delivery car 0.024 0.00187 Light goods vehicle 0.024 0.00187 Four-wheel drive 0.024 0.00187 Light truck 0.024 0.00187 Medium truck 0.02585 0.00201 Heavy truck 0.03529 0.00275 Articulated truck 0.03988 0.00311 Mini bus 0.024 0.00187 Light bus 0.02173 0.00169 Medium bus 0.02663 0.00207 Heavy bus 0.03088 0.00241 Coach 0.03088 0.00241 Source: Bennett and Greenwood (2003b) Table 4-3. Tread wear rate constants. longitudinal direction, as shown in Figure 4-9. The data in the 25th to 75th percentile range were used to perform the calibration of the HDM 4 model; these data are shown in Figure 4-10. Calibration of the HDM 4 Tire Wear Model When the HDM 4 model was developed, it was calibrated using tire replacement data. Therefore, the following assump- tions were made during the calibration: • For passenger cars: The average wear rates of the front and rear tire were used for calculating overall tire wear rate, because tires are generally rotated every 6 months or so. • For trucks: Only tire wear data for drive or trailer tires were used.

31 Source: Data provided by NCAT 0 2 4 6 8 10 12 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 IR I ( m/ km ) Sections East North West South Figure 4-3. NCAT track roughness data. Figure 4-4. NCAT track texture data. Source: Data provided by NCAT 0 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 1011 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 M ea n Pr of ile D ep th (m m) Sections East North West South Figure 4-5. Cumulative distribution of tire wear data collected from NCAT. 1%/km = 1.6%/mi 0 25 50 75 100 0.5 1.5 2.5 3 3.5 More Ti re W ea r R at e D ist ri bu tio n (% ) Tire Wear Rate (%/km) x 10-3 Drive or Trailer Steer Cumulative -Drive or Trailer Cumulative -Steer 1 2

32 Road Start End Pavement Type Texture Depth (mm) IRI Range (m/km) Length (km) Speed (km/h)AC PCC M-99 S Bishop Rd Holt Hwy X 0.25–2.7 0.8–4.8 3.6 80 M-99 S Holt Hwy Columbia Hwy X 6.4 80 M-99 N Columbia Hwy Holt Hwy X 0.23–1.85 0.5–4.1 6.4 80 M-99 N Holt Hwy Diamondale Rd X 1.6 80 M-99 N Diamondale Rd Waverly Rd X 0.8 80 M-99 N Waverly Rd Bishop Rd X 2.1 80 I-69E Airport Rd Francis Rd X 0.3–0.75 0.8–3.8 4.8 96 I-69W Francis Rd Airport Rd X 0.2–1.25 1.1–3.1 4.8 96 1 in. = 25.4 mm; 1 m/km = 63.4 in./mi; 1 mi = 1.6 km; 1 mph = 1.6 km/h Table 4-4. Tire wear field test matrix. Because tire wear data were collected only for articulated trucks and passenger cars, the calibration was only per- formed for these two vehicle classes. The passenger car tire wear data obtained on I-69 and the NCAT truck tire wear data were used to calibrate the HDM 4 passenger car and articulated truck tire wear models, respectively. The calibration procedure was as follows: 1. The road surface calibration factor Kcr2 (Table 4-1) was assigned the same value obtained during the calibration of the HDM 4 fuel consumption model (Table 3-1). 2. The constant from Equation 4.2 (0.0027) was removed. 3. The optimal values for C0tc was calculated using the data obtained from tire manufacturers for passenger cars and articulated trucks (Table 4-5). 4. The optimal values for Ctcte were estimated by minimiz- ing the SSE between the observed field values and those predicted using the HDM 4 model. 5. The optimal values for C0tc and Ctcte for the remaining vehicle classes were estimated using Equations 4.3 and 4.4 and assuming that the ratios between the values reported 0 0.5 1 1.5 2 2.5 Steer Drive or Trailer Ti re W ea r R at e (% /km ) x 10 -3 Figure 4-6. Tire wear data used for calibration. in the HDM 4 (Table 4-5) between vehicle categories are acceptable: • For small and large cars, vans, SUVs, light trucks, mini- buses, and light buses: C C C Ctcnew tc old tc old tc ne 0 0 0 0= ( ) ×Passenger Car w tcte new tcte old tcte C C C Passenger Car( ) = ( . )4 3 old tcte newC Passenger Car Passenger Car( ) × ( ) • For medium and heavy trucks, medium and heavy buses, and coaches: C C C Ctcnew tc old tc old0 0 0 0= ( ) ×Articulated Truck tcnew tcte new tcteC C Articulated Truck( ) = ( . )4 4 old tcte old tcte new C C Articulated Truck Arti( ) × culated Truck( ) Where: Cnew 0tc = Calibrated tread wear rate constant Cold 0tc = Current HDM 4 tread wear rate constant Cnew tcte = Calibrated tread wear rate coefficient Cold tcte = Current HDM 4 tread wear rate coefficient Table 4-6 summarizes the new coefficients for the tire wear model. For example, the C0tc and Ctcte values for heavy trucks are: C tcnew0 0 03529 0 04328 0 03988HeavyTruck( ) = × = . . . 0 03829 1000 0 002 . . dm km HeavyTruck 3 Ctctenew ( ) = 75 0 00153 0 00311 0 00135 × = . . . dm MNm3 While, the I-69 tire wear data were used to calibrate the current HDM 4 tire wear model, the M-99 tire wear data were used to validate the newly calibrated HDM 4 model. Figure 4-11 presents the results of the calibration and valida- tion processes.

Vehicle Class Tire Informationa Tire Life New Tire Tread Depth [mm (in.)] Tire Tread Depth Limit [mm (in.)] Tire Volume [dm3 (ft3)] New Tire [km (mi)] After First Recap [km (mi)] After Second Recap [km (mi)] Passenger cars 7.94 (10/32) 1.6 (2/32) 1.4(0.049) 64,000a (40,000) No recaps Heavy trucks 23.81 (30/32) 3.2 (4/32) 8 (0.283) 160,000a (100,000) 128,000a,b,c (80,000) 64,000a,b,c (40,000) aTire manufacturers bTire Retread and Repair Information Bureau (TRIB) cThese values are not considered in calculating the average tire wear rate 1 mi = 1.6 km Table 4-5. Tire tread depth and life data. Figure 4-7. Locations of tread depth measurements of the tire cross section. Figure 4-8. Locations of tread depth measurements in the longitudinal direction.

34 LF position 1 LF position 2 RR position 1 RR position 2 (a) I-69 Trial 1: Reading 1 (c) I-69 Trial 1: Reading 3 0 25 50 75 100 0 0.1 0.2 0.3 0.4 0.5 Pe rc en til es (% ) Accumulated Tire Wear (mm) 0 25 50 75 100 Pe rc en til es (% ) 0 0.1 0.2 0.3 0.4 0.5 Accumulatcd Tire Wear (mm) (b) I-69 Trial 1: Reading 2 (d) I-69 Trial 2 Pe rc en til es (% ) 0 0.1 0.2 0.3 0.4 0.5 0 25 50 75 100 Accumulated Tire Wear (mm) Pe rc en til es (% ) 0 25 50 75 100 0 0.1 0.2 0.3 0.4 0.5 Accumulatcd Tire Wear (mm) (e) M-99 Trial 0 25 50 75 100 Pe rc en til es (% ) 0 0.1 0.2 0.3 0.4 0.5 Accumulatcd Tire Wear (mm) Figure 4-9. Cumulative distribution of tire wear data for a passenger car.

35 (a) I-69 Trial 1: Reading 1 0 0.5 1 1.5 2 2.5 LF position 1 LF position 2 RR position 1 RR position 2 Ti re W ea r R at e (% / k m) x 10 - 3 (b) I-69 Trial 1: Reading 2 0 0.5 1 1.5 2 2.5 LF position 1 LF position 2 RR position 1 RR position 2 Ti re W ea r R at e (% / k m) x 10 - 3 (c) I-69 Trial 1: Reading 3 LF position 1 LF position 2 RR position 1 RR position 2 0 0.5 1 1.5 2 2.5 Ti re W ea r R at e (% /km ) x 10 - 3 (d) I-69 Trial 2 LF position 1 LF position 2 RR position 1 RR position 2 0 0.5 1 1.5 2 2.5 Ti re W ea rR at e (% /km ) x 10 - 3 (e) M-99 Trial LF position 1 LF position 2 RR position 1 RR position 2 0 0.5 1 1.5 Ti re W ea r R at e (% /km ) x 10 - 3 Figure 4-10. Tire wear data used for calibration for a passenger car.

36 Vehicle Type C0tc (dm3/1000 km) Ctcte (dm3/MNm) Small car 0.01747 0.001 Medium car 0.01747 0.001 Large car 0.01747 0.001 Van 0.01602 0.00092 Four-wheel drive 0.01602 0.00092 Light truck 0.01602 0.00092 Medium truck 0.02999 0.00099 Heavy truck 0.03829 0.00135 Articulated truck 0.04328 0.00153 Mini bus 0.01747 0.00092 Light bus 0.01747 0.00092 Medium bus 0.02999 0.00099 Heavy bus 0.03829 0.00135 Coach 0.03829 0.00135 Table 4-6. Calibrated tread wear rate constants and coefficients. (a) Medium Car (b) Articulated Truck 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 I-69 Trial 1 Reading 1 I-69 Trial 1 Reading 2 I-69 Trial 1 Reading 3 I-69 Trial 2 M-99 Trial M ea su re d Ti re W ea r R at e (% /km ) x 10 - 3 Pr ed ic te d Ti re W ea r R at e (% /km ) x 10 - 3 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Drive or Trailer M ea su re d Ti re W ea r R at e (% /km ) x 10 - 3 Pr ed ic te d Ti re W ea r R at e (% /km ) x 10 - 3 HDM 4 (after calibration) Average 25-75 25 percentile 75 percentile Figure 4-11. Comparison between the calibrated HDM 4 predictions and measurements. wear as a function of IRI for the different speeds shown in Figure 4-12, generated at 17°C (62.6°F) when the mean pro- file depth is 1 mm (0.04 in.) and grade is 0%, indicates the following: • The effect of roughness on tire wear increases as speed increases. Table 4-7 lists the change in tire wear caused by change of IRI from the baseline condition of IRI = 1 m/km (63.4 in./mi) for all vehicle classes at 56, 88, and 112 km/h (35, 55, and 70 mph). • Roughness will affect passenger car tires more than articu- lated truck tires. However, because trucks have more tires than passenger cars, the total effect of roughness per vehicle will be greater. Summary The information presented showed that the calibrated HDM 4 tire wear model adequately predicts tire wear of passenger cars and articulated trucks. The calibrated model is presented in Tables 4-8 through 4-11; the new default values for vehicle and tire characteristics are summarized in Table 4-12. (b) Articulated truck 1 1 2 3 4 5 6 1.02 1.04 1.06 1.08 A dju stm en t fa cto r IRI (m/km) (a) Passenger car 1 2 3 4 5 6 1 1.02 1.04 1.06 A dju stm en t fa cto r IRI (m/km) 56 km/h (35 mph) 88 km/h (55 mph) 112 km/h (70 mph) Figure 4-12. Effect of roughness on tire wear estimated using calibrated HDM 4. Effect of Roughness on Tire Wear The calibrated HDM 4 provides an accurate estimate of the roughness effect on rolling resistance and thus on tire wear, since it is a function of rolling resistance. The change in tire

37 Speed Vehicle Class (Number of Wheels) Baseline Conditions (%/km)a Baseline Conditions (%/mi)a Adjustment Factors from the Baseline (Fraction per Tire) IRI (m/km) 1 2 3 4 5 6 56 km/h (35 mph) Medium car (4) 0.0013 0.0021 1.01 1.01 1.02 1.02 1.03 Van (4) 0.0011 0.0017 1.00 1.01 1.01 1.02 1.02 SUV (4) 0.0011 0.0017 1.01 1.02 1.03 1.04 1.05 Light truck (4) 0.0012 0.0020 1.01 1.02 1.03 1.04 1.05 Articulated truck (18) 0.0006 0.0010 1.01 1.01 1.02 1.02 1.03 88 km/h (55 mph) Medium car (4) 0.0014 0.0022 1.01 1.02 1.03 1.04 1.05 Van (4) 0.0013 0.0021 1.01 1.01 1.02 1.03 1.04 SUV (4) 0.0013 0.0021 1.01 1.03 1.05 1.06 1.08 Light truck (4) 0.0018 0.0029 1.01 1.02 1.04 1.05 1.06 Articulated truck (18) 0.0007 0.0012 1.01 1.02 1.03 1.04 1.05 112 km/h (70 mph) Medium car (4) 0.0015 0.0025 1.01 1.03 1.04 1.06 1.08 Van (4) 0.0018 0.0028 1.01 1.02 1.03 1.04 1.04 SUV (4) 0.0017 0.0027 1.02 1.04 1.06 1.08 1.10 Light truck (4) 0.0029 0.0046 1.01 1.02 1.04 1.05 1.06 Articulated truck (18) 0.0009 0.0015 1.01 1.02 1.03 1.04 1.06 a percentage of new tire volume Table 4-7. Effect of roughness on tire wear. Table 4-8. HDM 4 tire consumption model. Name Description Unit Number of equivalent new tires (EQNT) 10 × VOL TWT EQNT = % new tire/km VOL = Tire volume dm3 Total change in tread wear (TWT) CFT 2+ LFT 2 TWT = C0tc + Ctcte × NFT TWT = C0tc + Ctcte × TE dm3/1000 km C0tc = Tread wear rate constant (Table 4-12) dm3/1000 km Ctcte = Tread wear coefficient (Table 4-12) dm3/MNm Tire energy (TE) CFT 2 + LFT 2 TE = NFT MNm/1000 km Circumferential force on the tire (CFT) (1 + CTCON* dFUEL) * (Fa + Fr + Fg) CFT = NW N CTCON = Incremental change of tire consumption related to congestion ratio dFUEL = Incremental change of fuel consumption related to congestion ratio Fa = Aerodynamic forces N Fr = Rolling resistance forces N Fg = Gradient forces N Lateral force on the tire (LFT) Fc LFT NW = N Fc = Curvature forces N Nw = Number of wheels dimensionless Normal force on the tire (NFT) M * g NFT = NW N M = Vehicle mass kg g = Gravity m/s2

38 Table 4-9. HDM 4 tractive forces model. [ Name Description Unit Aerodynamic forces (Fa) 20.5* * * *Fa CD AFρ υ= N CD Drag coefficient (Table 4-12) dimensionless AF Frontal area (Table 4-12) m2 Mass density of the air (default = 1.2) kg/m3 Vehicle speed m/s Gradient forces (Fg) Fg = M * GR * g N M Vehicle weight (Table 4-12) kg GR Gradient radians g Gravity m/s2 Curvature forces (Fc) − = −3 22 10* * ** * ,0max CsNw egM R M Fc υ N R Curvature radius (Default = 3000) m Superelevation (e) e = max(,0.045 − 0.68 * Ln(R)) m/m Nw Number of wheels (Table 4-12) dimensionless Tire stiffness (Cs) 2 0 1* 2*M MCs a a a Nw Nw = + + kN/rad a0 to a2 Model parameter (Table 4-10) dimensionless Rolling resistance (Fr) Fr = CR2*(b11* Nw + CR1*(b12*M + b13*υ2)) N CR1 Rolling resistance tire factor (Table 4-12) factor Rolling resistance parameters (b11, b12, b13) 2 11 37* 12 0.064 / 13 0.012* / b Dw b Dw b Nw Dw = = = factors Dw Diameter of wheel Rolling resistance surface factor (CR2) IRI + a3 * DEF]aTdspaaKcr *2*102 ++= factor Kcr2 Calibration factor (Table 4-12) factor a0 to a3 Model coefficient (Table 4-11) dimensionless Texture depth using sand patch method (Tdsp) Tdsp = 1.02 * MPD + 0.28 mm MPD Mean Profile Depth mm IRI International roughness index m/km DEF Benkelman Beam rebound deflection mm Table 4-10. Final parameters for tire stiffness (Cs) model. Coefficient 2500 kg > 2500 kg Bias Radial Bias Radial a0 30 43 8.8 0 a1 0 0 0.088 0.0913 a2 0 0 0.0000225 0.0000114 Source: Bennett and Greenwood (2003b) Table 4-11. Final parameters for rolling resistance coefficient (CR2) model. Surface Type 2500 kg > 2500 kg a0 a1 a2 a3 a0 a1 a2 a3 Asphalt 0.5 0.02 0.1 0 0.57 0.04 0.04 1.34 Concrete 0.5 0.02 0.1 0 0.57 0.04 0.04 0 Source: Bennett and Greenwood (2003b)

39 Table 4-12. HDM 4 new default values—vehicle and tire characteristics. Vehicle Class Number of Axles Nw M (tons) Kcr2 CD AF (m2) WD Tire Type CR1 b11 b12 b13 C0tc (dm3/1000 km) Ctcte (dm3/MNm) VOL (dm3) VEHF AC Small car 2 4 1.9 0.5 0.42 1.9 0.62 Radial 1 22.2 0.11 0.13 0.01747 0.001 1.4 2 Medium car 2 4 1.9 0.5 0.42 1.9 0.62 Radial 1 22.2 0.11 0.13 0.01747 0.001 1.4 2 Large car 2 4 1.9 0.5 0.42 1.9 0.62 Radial 1 22.2 0.11 0.13 0.01747 0.001 1.4 2 Van 2 4 2.54 0.67 0.5 2.9 0.7 Radial 1 25.9 0.09 0.10 0.01602 0.00092 1.6 2 Four-wheel drive 2 4 2.5 0.58 0.5 2.8 0.7 Radial 1 25.9 0.09 0.10 0.01602 0.00092 1.6 2 Light truck 2 4 4.5 0.99 0.6 5 0.8 Radial 1 29.6 0.08 0.08 0.01602 0.00092 1.6 2 Medium truck 2 6 6.5 0.99 0.6 5 0.8 Bias 1.3 29.6 0.08 0.11 0.02999 0.00099 6 1 Heavy truck 3 10 13 1.1 0.7 8.5 1.05 Bias 1.3 38.85 0.06 0.11 0.03829 0.00135 8 1 Articulated truck 5 18 13.6 1.1 0.8 9 1.05 Bias 1.3 38.85 0.06 0.20 0.04328 0.00153 8 1 Mini bus 2 4 2.16 0.67 0.5 2.9 0.7 Radial 1 25.9 0.09 0.10 0.01747 0.00092 1.6 2 Light bus 2 4 2.5 0.99 0.5 4 0.8 Radial 1 29.6 0.08 0.08 0.01747 0.00092 1.6 2 Medium bus 2 6 4.5 0.99 0.6 5 1.05 Bias 1.3 38.85 0.06 0.07 0.02999 0.00099 6 1 Heavy bus 3 10 13 1.1 0.7 6.5 1.05 Bias 1.3 38.85 0.06 0.11 0.03829 0.00135 8 1 Coach 3 10 13.6 1.1 0.7 6.5 1.05 Bias 1.3 38.85 0.06 0.11 0.03829 0.00135 8 1