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

Chapter: Chapter 3 - Fuel Consumption Model

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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
×
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Suggested Citation:"Chapter 3 - Fuel Consumption Model." National Academies of Sciences, Engineering, and Medicine. 2012. Estimating the Effects of Pavement Condition on Vehicle Operating Costs. Washington, DC: The National Academies Press. doi: 10.17226/22808.
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8The most recent VOC model found in the literature review is the HDM 4. It incorporates a mechanistic–empirical model of fuel consumption. This chapter describes the cali- bration of the HDM 4 fuel consumption model using data from instrumentation on board vehicles driven on roads of known condition. HDM 4 Fuel Consumption Model The general form of the HDM 4 fuel consumption model is expressed conceptually by Equation 3.1 (Bennett and Greenwood, 2003b). ( ) ( ) ( )( ) = + = υ ∗ α ξ ∗ + , 1000 max , 1 (3.1) IFC f P P P Ptot dFuel tr accs eng where: IFC = Instantaneous fuel consumption (mL/km) u = Vehicle speed (m/s) Ptr = Power required to overcome traction forces (kW) Paccs = Power required for engine accessories (e.g., fan belt, alternator etc.) (kW) Peng = Power required to overcome internal engine friction (kW) a = Fuel consumption at idling (mL/s) x = Fuel-to-power efficiency factor (mL/kW/s) = + −( )   ξb tot eng ehp P P P 1 max xb = Base fuel-to-power efficiency (depends on the technology type: gasoline versus diesel) Pmax = Rated engine power (kW) ehp = Proportionate decrease in efficiency at high out- put power (dimensionless) Ptot = Total power (kW) dFuel = Excess fuel conception due to congestion as a percentage The engine efficiency decreases at high levels of output power, resulting in an increase in the fuel efficiency factor x. The total power required is divided into tractive power, and engine drag and vehicle accessories power. The total require- ment can be calculated by two alternative methods depending on whether the tractive power is positive or negative as shown in Table 3-1. Table 3-2 shows parameters for the engine speed model that feeds into the engine and accessories power equa- tion. The tractive power is a function of the aerodynamic, gradient, curvature, rolling resistance, and inertial forces. The aerodynamic forces are expressed as a function of the air density and the aerodynamic vehicle characteristics, and are given in Table 3-3. The gradient forces are a function of vehicle mass, gradient, and gravity. The curvature forces are computed using the slip energy method. Table 3-4 shows parameters for the tire stiffness model. The rolling resistance forces are a function of vehicle characteristics, pavement con- ditions, and climate. Table 3-5 shows parameters for the roll- ing resistance model for asphalt and concrete pavements. The inertial forces are a function of the vehicle mass, speed, and acceleration. Table 3-6 shows the parameters for the effective mass ratio model. Field Trials and Data Collection The main objective of the field trials was to validate and cal- ibrate the HDM 4 fuel consumption model. During the field trials, the following data related to vehicle engine parameters, pavement surface characteristics, and environmental factors were collected: • Engine/vehicle parameters – Mass air flow rate (g/s) – Air-to-fuel ratio – Fuel rate (L/h) – Engine rotation (rev/min) – Fuel temperature (°C) C h a p t e r 3 Fuel Consumption Model

9 Name Description Unit Total power (Ptot) for 0, uphill/level for 0, downhill tr tot accs eng tr tot tr accs eng tr P P P P P edt P edtP P P P = + + ≥ = + + < kW edt Drive-train efficiency factor factor Engine and accessories power (Pengaccs = Peng + accsP ) ( ) RPMIdleRPM RPMIdleRPM aPaccsaPaccsaPaccs PKPeaPengaccs − −−+ = 100 *1_0_(1_ max** kW KPea Calibration factor Pmax Rated engine power kW Paccs_a1 −= = −= −+−= α ξ ξ c PKPeab PctPeng PKPeaehpa a cabb aPaccs b b max** 100 100 max**** *2 **4 1_ 2 2 factor ξb Base fuel-to-power efficiency (depends on the technology type: gasoline versus diesel) mL/kW/s ehp Proportionate decrease in efficiency at high output power dimensionless α Fuel consumption at idling mL/s Paccs_a0 Ratio of engine and accessories drag to rated engine power when traveling at 100 km/h dimensionless PctPeng Percentage of the engine and accessories power used by the engine (Default = 80%) % Engine speed (RPM) ( ) 20 1* 2* 3* max 20, RPM a a SP a SP a SP SP υ = + + + = rev/min Vehicle speed m/s a0 to a3 Model parameter (Table 3-2) dimensionless RPM100 Engine speed at 100 km/h rev/min RPMIdle Idle engine speed rev/min Tractive power ( trP ) 1000tr Fa Fg Fc Fr Fi P υ + + + += kW Fa Aerodynamic forces N Fg Gradient forces N Fc Curvature forces N Fr Rolling resistance forces N Fi Inertial forces N 3 Table 3-1. HDM 4 fuel consumption model. Vehicle Type Engine Speed a0 a1 a2 a3 Motorcycle 162 298.86 4.6723 0.0026 Small car 1910 12.311 0.2228 0.0003 Medium car 1910 12.311 0.2228 0.0003 Large car 1910 12.311 0.2228 0.0003 Light delivery car 1910 12.311 0.2228 0.0003 Light goods vehicle 2035 20.036 0.356 0.0009 Four wheel drive 2035 20.036 0.356 0.0009 Light truck 2035 20.036 0.356 0.0009 Medium truck 1926 32.352 0.7403 0.0027 Heavy truck 1905 12.988 0.2494 0.0004 Articulated truck 1900 10.178 0.1521 0.00004 Mini bus 1910 12.311 0.2228 0.0003 Light bus 2035 20.036 0.356 0.0009 Medium bus 1926 32.352 0.7403 0.0027 Heavy bus 1926 32.352 0.7403 0.0027 Coach 1926 32.352 0.7403 0.0027 Source: Bennett and Greenwood (2003b) Table 3-2. Engine speed model parameters for the HDM 4 model. – Calculated power (kW) – Calculated efficiency (%) – Vehicle speed (km/h) • Environmental variables – Ambient temperature (°C) – Maximum relative humidity (%) – Minimum relative humidity (%) – Wind speed (km/h) • Pavement surface characteristics – Roughness (IRI) – Grade (%) – Texture depth (mm) – Pavement type Since the goal of the study was to estimate the effect of roughness on fuel consumption, the repeatability and accuracy

10 Name Description Unit Aerodynamic forces (Fa) 2*****5.0 υρ AFCDCDmultFa = N CD Drag coefficient dimensionless CDmult CD multiplier dimensionless AF Frontal area m2 ρ Mass density of the air kg/m3 υ Vehicle speed m/s Gradient forces (Fg) gGRMFg **= 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) ( )RLne *68.045.0,0max −= 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 3-4) 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 factor Rolling resistance surface factor (CR2) DEFaIRIaTdspaaKcrCR *3*2*1022 +++= dimensionless Kcr2 Calibration factor factor a0 to a3 Model coefficient (Table 3-5) dimensionless Tdsp Texture depth using sand patch method mm IRI International roughness index m/km DEF Benkelman Beam rebound deflection mm Climatic factor (FCLIM) PCTDWPCTDSFCLIM *002.0*003.01 ++= factor PCTDS Percentage driving on snow PCTDW Percentage driving on wet surface Inertial forces (Fi) a a aaMFi * 2 arctan*10* 3+= υ N a0 to a2 Model parameter (Table 3-6) dimensionless Table 3-3. HDM 4 tractive forces 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 KCS 1 1 1 1 Source: Bennett and Greenwood (2003b) Table 3-4. Tire stiffness (Cs) model parameters for the HDM 4 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) Table 3-5. Parameters for rolling resistance (CR2) model in the HDM 4 model for asphalt and concrete pavements.

11 Vehicle Type Effect Mass Ratio Model Coefficients a0 a1 a2 Motorcycle 1.1 0 0 Small car 1.14 1.01 399 Medium car 1.05 0.213 1260.7 Large car 1.05 0.213 1260.7 Light delivery car 1.1 0.891 244.2 Light goods vehicle 1.1 0.891 244.2 Four-wheel drive 1.1 0.891 244.2 Light truck 1.04 0.83 12.4 Medium truck 1.04 0.83 12.4 Heavy truck 1.07 1.91 10.1 Articulated truck 1.07 1.91 10.1 Mini bus 1.1 0.891 244.2 Light bus 1.1 0.891 244.2 Medium bus 1.04 0.83 12.4 Heavy bus 1.04 0.83 12.4 Coach 1.04 0.83 12.4 Source: Bennett and Greenwood (2003b) Table 3-6. Effective mass ratio model parameters for the uncalibrated HDM 4 model. of the measurements are considered a key criterion for data interpretation. Therefore, preliminary tests were conducted to validate the accuracy and repeatability of the equipment that were used during field tests. The data acquisition sys- tem was able to access and log data from the vehicle’s engine control unit (ECU) via an on-board diagnostic (OBD) connector. Testing of the Accuracy and Precision of Test Equipment Repeatability/Precision Two different tests were conducted at two different loca- tions (Flint and Lansing areas in Michigan) using two differ- ent vehicles (a 2008 Mercury Sable and a 2008 Chevy Impala) to measure the repeatability of the instrument. During both tests, the outdoor conditions for the identified sections were measured using a portable weather station. The tire pressure during the runs was maintained at 207 kPa (30 psi). The first section was a loop of 32 km or 20 mi (I-69E, I-496N and I-75S). The start and end points of each run were marked by distinct flags and road markers. The data acquisition system was connected to the vehicle during the test. Five runs were made on the pavement: three runs (Runs 1 through 3) at a speed of 105 km/h (65 mph) and two runs (Runs 4 and 5) at a speed of 96 km/h (60 mph). Cruise control was engaged to reduce the acceleration and deceleration cycles. The results of the repeatability test are summarized in terms of correlations in Tables 3-7 and 3-8. The correlation between Runs 1 through 3 was almost perfect (r ≈ 0.98 and 0.02% error). Also, Runs 4 and 5 were highly correlated (r ≈ 0.9 and 0.05% error). The second section selected was a 14 km (8.8 mi) stretch along I-69 (E and W). The speed for the runs was 105 km/h (65 mph). The start and end points of each run were also marked by distinct flags and road markers. Two runs were made on this section. The repeatability test results are sum- marized in terms of correlations in Table 3-9. The correlation between Runs 1 and 2 was also almost perfect (r ≈ 0.92 and 0.02% error). Based on these results, it was concluded that the instru- ment was reliable enough to determine the changes in fuel consumption due to minor changes of surface conditions. Run 1 Run 2 Run 3 Run 1 Pearson Correlation 1.00 0.99** 0.98** Sig. (2-tailed) 0.00 0.00 N 638 633 638 Run 2 Pearson Correlation 0.99** 1.00 0.97** Sig. (2-tailed) 0.00 0.00 N 633 633 633 Run 3 Pearson Correlation 0.98** 0.97** 1.00 Sig. (2-tailed) 0.00 0.00 N 638 633 638 ** Correlation is significant at the 0.01 level (2-tailed). Table 3-7. Correlations for Runs 1 through 3. Run 4 Run 5 Run 4 Pearson Correlation 1.00 0.91** Sig. (2-tailed) 0.00 N 747 745 Run 5 Pearson Correlation 0.91** 1.00 Sig. (2-tailed) 0.00 N 745 745 ** Correlation is significant at the 0.01 level (2-tailed). Table 3-8. Correlations for Runs 4 and 5. Run 1 Run 2 Run 1 Pearson Correlation 1.00 0.924** Sig. (2-tailed) 0.00 N 4733 4733 Run 2 Pearson Correlation 0.924** 1.00 Sig. (2-tailed) 0.00 N 4733 4733 ** Correlation is significant at the 0.01 level (2-tailed). Table 3-9. Correlations for Runs 1 and 2.

12 Table 3-10 summarizes the results of the paired t-test that was conducted. A paired samples t-test failed to reveal a statistically reliable difference between the mean fuel consumption mea- sured using Graphtec (mean = 102.38 mL/km, standard devia- tion = 13.09 mL/km) and AutoTap (mean = 102.24 mL/km, standard deviation = 13.08 mL/km), t(19) = 0.34, p = 0.74, a = 0.05. The maximum difference is 2.56%. Previous studies indi- cated that a pavement surface with an IRI range of 1 to 5 m/ km contributes to a change in fuel consumption of 3% to 5%. Therefore, this level of error was judged as acceptable. Field Trials Five different locations near Lansing, Michigan, were selected for field trials to reflect a wide range of pavement conditions (i.e., roughness, gradient, texture, and pavement type). Table 3-11 shows the field test matrix. Both asphalt and concrete pavements were included; IRI values for the test sec- tions ranged from 0.8 to 8.5 m/km (51 to 539 in./mi); mean profile depth (MPD) values ranged from 0.2 to 2.7 mm (0.01 to 0.1 in.); grade ranged from -3.4% to 3.1%; and five speeds were considered. The tests were conducted during both winter wet and summer dry conditions. The actual weather conditions (temperature and wind speed), summarized in Table 3-12, were recorded using a portable weather station. Tests were repeated when changes of more than 3°C (5°F) in ambient temperature were recorded. The pavement and weather test Data Acquisition System Accuracy/Calibration The calibration of the data acquisition system was conducted by comparing the OBD fuel consumption data to direct fuel meter measurements. The fuel measurement tests were con- ducted using a fuel meter. An instrumented van was driven under the same environmental, operating, and pavement con- ditions using both data acquisitions systems for 20 s at highway speed. Figure 3-1 summarizes the data collected using both data acquisition systems (Graphtec fuel meter and OBD AutoTap). y = x R2 = 0.96 SSE = 1.88 ml/km 60 80 100 120 140 60 80 100 120 140 Fu el C on su m pt io n C ol le ct ed U si ng A ut oT ap (m l/k m ) Fuel Consumption Collected Using Graphtec (ml/km) Figure 3-1. Comparison between data collected using AutoTap and Graphtec. Paired Differences t df Significance Mean (mL/km) Standard Deviation (mL/km) Standard Error Mean 95% Confidence Interval of the Difference (mL/km) Lower Upper FC_Graphtec– FC_AutoTap 0.14 1.88 0.42 0.74 1.02 0.34 19 0.74 FC: Fuel Consumption Table 3-10. Paired samples t-test results. Day Road Start End Pavement Type Length (km) IRI range (m/km) MPD (mm) Grade (%) Speed limit (km/h) Operating Speed (km/h) AC PCC 56 72 88 96 112 1 Creyts Rd Lansing Rd Millett Hwy X 1.5 1.28–8.5 0.2–2.0 ( 1.6) – 0.7 72 1 Creyts Rd Millett Hwy Mount Hope X 1.6 1.7–7 ( 0.5) 2.3 72 2 Waverly Rd Willow Hwy Tecumseh River Rd X 0.8 3.5–6 0.2–1.0 ( 3.1) – 1.9 72 2 Waverly Rd Tecumseh River Rd Delta River Dr X 0.8 3.25–6 ( 0.27) 3.1 72 2 I-69E Airport Rd Francis Rd X 7.6 0.8–3.8 0.3–0.8 ( 0.9) – 1.4 112 2 I-69W Francis Rd Airport Rd X 7.6 1.1–3.1 0.2–1.3 ( 1.4) – 0.9 112 2 M-99S Holt Hwy Columbia Hwy X 6.4 0.8–4.8 0.2–2.7 ( 3.4) – 2.1 88 2 M-99S Bishop Rd Holt Hwy X 3.6 ( 2.5) – 1.8 88 2 M-99N Columbia Hwy Holt Hwy X 6.4 0.5–4.1 0.2–1.9 ( 3.2) – 3.1 88 2 M-99N Dimondale Rd Waverly Rd X 0.8 ( 0.9) – 2.5 88 2 M-99N Waverly Rd Bishop Rd X 2.1 ( 1.8) – 1.4 88 Note: All tests were repeated. 1 km = 0.63 mi; 1 mm = 0.04 in.; 1 m/km = 63.4 in./mi; 1 km/h = 0.63 mph. Table 3-11. Field test matrix.

13 Variables Winter Summer 11/24/2008 11/25/2008 06/05/2009 06/06/2009 06/07/2009 Ambient temperature (°C) 0–2 1–3 28.9–29.2 27.2–28.3 22.5–25.2 Wind speed (m/s) 1.7–2.4 0.4–1 2.1 – 2.9 1.4–2.4 1.7–2.4 Table 3-12. Recorded weather conditions. conditions were considered typical of those encountered in the United States. The pavement conditions data (raw profile and texture depth) were collected by the Michigan Department of Trans- portation using a Rapid Travel Profilometer (ASTM E950-98) and a Road Surface Analyzer (ASTM E1845-09). In addition, slope data surveys were collected using a high- precision global positioning system (GPS). The sampling rate was every 1 s at highway speed (i.e., every 30.5 m or 100 ft). The average error of the measurement was 12.7 mm per 0.5 km (0.5 in. per 0.3 mi), i.e., 0.003% (about twice the error of the total station). Six different vehicles that represent typical vehicles in the United States—medium car, sport utility vehicle (SUV), van, light truck (gas and diesel), and articulated truck (Figure 3-2)—were used. Table 3-13 lists the characteristics of the (e) Articulated Truck (a) Medium Car (c) Van (b) SUV (d) Light Truck Figure 3-2. Vehicles used in field trials.

14 vehicles used in field trials. Tests for trucks were conducted using loaded (Figure 3-3) and unloaded (Figure 3-2e) trucks. The light truck was loaded with two concrete blocks weigh- ing a total of 2.82 metric tons (6,210 lb), in accordance with the recommended payload. Both blocks were tightly secured to the truck bed. The trailer of the heavy truck was loaded with steel sheets (21.32 metric tons or 47,000 lb) also tightly secured to the trailer. The gross vehicle weight (GVW) was about 36.3 metric tons (80,000 lb), which is the maximum GVW allowed in the United States. Characteristics Vehicle Class Medium Car SUV Van Light Truck Heavy Truck Make Mitsubishi Chevrolet Ford GMC International Model Galant Tahoe E350 W4500 9200 6x4 Year 2008 2009 2008 2006 2005 Drag coefficient 0.4 0.5 0.5 0.6 0.8 Frontal area (m2) 1.9 2.9 2.9 4.2 9 Tare weight (t) 1.46 2.5 2.54 3.7 13.6 Maximum allowable load (t) – – – 2.9 22.7 GVW (t) – – – 6.6 36.3 Weight of the load (t) – – – 2.8 21.3 Gas type Gas Gas Gas Gas/Diesel Diesel Tire diameter (m) 0.38 0.4 0.4 0.4 0.57 Tire pressure in kPa (psi) 242 (35) 269 (39) 297 (43) 393 (57) 759 (110) Tire type radial radial radial radial bias Cargo length (m) – – – 4.88 15.85 Other – 4WD 15 seats – Flat bed Table 3-13. Characteristics of the vehicles used in the field trials. (a) Loading of Light Truck (b) Loaded Light Truck (c) Loading of Heavy Truck (d) Loaded Heavy Truck Figure 3-3. Truck loading conditions.

15 Each vehicle had a data logger (scanner) connected to the OBD connector and the vehicle was driven at different speeds on cruise control to reduce the acceleration and deceleration cycles. Multiple and repeated runs were performed. In order to understand the effect of cruise control on the collected data, all the tests were conducted at constant speed with and without cruise control. The start and end points of data log- ging were marked by distinct flags and road markers. Figure 3-4 shows example data collected during runs at 56 km/h (35 mph) except for section I-69 east and west where the speed was 88 km/h (55 mph). Calibration of the HDM 4 Model The data acquisition system collects the mass airflow rate (MAF) in grams per second and the air-to-fuel ratio. Equa- tion 3.2 is used to convert these data to instantaneous fuel consumption in terms of milliliters per kilometer. IFC MAF g = ∗ ∗ ∗ 1000 14 7 3 2 υ ρ. ( . ) where: IFC = Instantaneous fuel consumption (mL/km) u = Vehicle speed (m/s) MAF = Mass air flow (g/s) 14.7 = Air-to-fuel ratio rg = Density of gasoline (g/mL) = 0.74 The predicted and measured engine speeds are plotted in Figure 3-5 for the medium car, van, SUV, light truck, and articulated truck. The plots show that the HDM 4 model overpredicts the engine speed of the vehicle; it will therefore overpredict the engine and accessories power and overesti- mate the fuel consumption. Consequently, when calibrat- ing the fuel consumption model, the tractive power (i.e., the effect of pavement conditions) will be underestimated. Therefore, the HDM 4 engine speed model had to be cali- brated first, before calibrating the fuel consumption model. Calibration of the HDM 4 Engine Speed Model The engine speed model expressed in terms of revolutions per minute (rpm) was calibrated for all vehicle classes using the data collected during the field tests. Vehicles were classi- fied into categories listed in Table 3-14. Figure 3-5 show the results of the calibration for both winter and summer field test data. Note that the HDM 4 engine speed model has a discontinuity at idle speed. It was observed that the engine speed model calibrated using winter data could be used to predict the engine speed in the summer for all vehicle classes except for the light truck because the engine of the light truck used in the winter tests misfired. Therefore, only summer test data were used to calibrate the HDM 4 engine speed model for the light truck. 1 km = 0.63 mi, 1,000 mL = 0.26 gal. (a) Creyts Road (3.2 km) (b) Waverly Road (1.6 km) (c) I-69E (7.6 km) (d) I-69W (7.6 km) (e) M-99N (10 km) (f) M-99S (10 km) 0 200 400 600 F ue l c on su m pt io n (m L ) 0 200 400 F u el c on su m pt io n (m L ) 0 200 400 600 800 1000 F u el c on su m pt io n (m L ) 0 200 400 600 800 1000 F ue l c on su m pt io n (m L ) 0 500 1000 1500 2000 F u el c on su m pt io n (m L ) 0 500 1000 1500 2000 F u el c on su m pt io n (m L ) Medium Car Van SUV Gas Truck Diesel Truck Figure 3-4. Examples of collected data.

16 (a) Calibration Procedure for Medium Car (b) Measured versus Predicted Engine Speed for Medium Car (c) Calibration Procedure for Van (d) Measured versus Predicted Engine Speed for Van (e) Calibration Procedure for SUV (f) Measured versus Predicted Engine Speed for SUV y = -0.0007x3 + 0.2006x2 + 0.868x + 720.05 R2 = 0.99 0 500 1000 1500 2000 2500 3000 0 20 40 60 80 100 120 E ng in e S pe ed ( rp m ) Speed (km/h) 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 ) m pr( dee p S enign E detcider P Measured Engine Speed (rpm) y = 0.0033x3 - 0.2845x2 + 7.3118x + 595.73 R² = 0.96 0 500 1000 1500 2000 2500 3000 0 20 40 60 80 100 120 E ng in e S pe ed ( rp m ) Speed (km/h) 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 ) mpr( deepS enign E detciderP Measured Engine Speed (rpm) y = 0.0019x3 - 0.1331x2 + 3.6701x + 982.37 R2 = 0.99 0 500 1000 1500 2000 2500 3000 3500 0 20 40 60 80 100 120 E ng in e S pe ed ( rp m ) Speed (km/h) 0 500 1000 1500 2000 0 500 1000 1500 2000 ) m pr( dee p S enign E detcider P Measured Engine Speed (rpm) measured engine speed-Winter condition engine speed (HDM 4) measured engine speed-Summer condition calibrated model Figure 3-5. Calibration of HDM 4 engine speed model for all vehicle classes.

17 (g) Calibration Procedure for Light Truck (h) Measured Versus Predicted Engine Speed for Light Truck (i) Calibration Procedure for Articulated Truck (j) Measured Versus Predicted Engine Speed for Articulated Truck y = -0.0018x3 + 0.3798x2 - 3.0722x + 550.08 R2 = 0.99 0 500 1000 1500 2000 2500 3000 0 20 40 60 80 100 120 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 P re di ct ed E ng in e S p ee d (r p m ) Measured Engine Speed (rpm) y = 6E-05x3 + 0.2077x2 - 5.3791x + 799.6 R2 = 0.99 0 500 1000 1500 2000 2500 3000 0 20 40 60 80 100 Speed (km/h) 0 500 1000 1500 2000 0 500 1000 1500 2000 P re di ct ed E ng in e S p ee d (r p m ) Measured Engine Speed (rpm) measured engine speed-Winter condition engine speed (HDM 4) measured engine speed-Summer condition calibrated model E ng in e S pe ed ( rp m ) E ng in e S pe ed ( rp m ) Speed (km/h) Figure 3-5. (Continued). Categories Vehicle Classes Vehicle Used Passenger car • Small car • Medium car • Large car • Mini bus • Medium car Light commercial vehicle • Light delivery vehicle • Light goods vehicle • Van Four-wheel drive • Four-wheel drive • SUV Light truck • Light truck • Light bus • Light truck Heavy truck • Medium truck • Heavy truck • Articulated truck • Medium bus • Heavy bus • Coach • Articulated truck Table 3-14. Vehicle classification used in the engine speed model calibration.

18 • Kcr2, which modifies the tractive power; • KPea, which modifies the accessories and engine power. The calibration procedure determines the coefficients required to minimize the sum of squared errors (i.e., sum of squared differences between the observed field values and those predicted using HDM 4 model). The methodology used is according to the HDM 4 calibration guide (Bennett and Greenwood, 2003a) and is summarized as follows: 1. A random value is assigned to Kcr2, and then the value of KPea yielding the lower least squared value is determined. 2. This process is continued iteratively until the lowest sum of the squared errors (SSE) is obtained. The data collected during the field tests were used to cali- brate the HDM 4 fuel consumption model. It was observed that, for light vehicles (medium car, SUV, and van), the fuel consumption with and without cruise control were compa- rable. On the other hand, there was a noticeable difference between the fuel consumption of heavier vehicles (light and articulated trucks) with and without cruise control. This is illustrated in Figure 3-6 which shows the measured and predicted fuel consumption with cruise control for van and light truck. The figure shows that, with the cruise control engaged, low consumption was underestimated, and the high consumption was overestimated for the light truck but not for the van. Figure 3-7, which shows measured ver- sus predicted fuel consumption for the articulated truck with and without cruise control engagement, confirms that the HDM 4 predictions agree only with the measure- Table 3-15 lists the engine speed model coefficients for winter and summer conditions. These coefficients were used for the calibration of the HDM 4 fuel consumption model. Table 3-16 lists the recommended coefficients for the HDM 4 engine speed model. Calibration of HDM 4 Fuel Consumption Model The HDM 4 fuel consumption model provides the follow- ing two coefficients for calibration (Bennett and Greenwood, 2003a): Vehicle Class Engine Speed Coefficients Winter Condition Summer Condition a0 a1 a2 a3 a0 a1 a2 a3 Small car 823.78 4.6585 0.2702 0.0012 720.05 0.868 0.2006 0.0007 Medium car 823.78 4.6585 0.2702 0.0012 720.05 0.868 0.2006 0.0007 Large car 823.78 4.6585 0.2702 0.0012 720.05 0.868 0.2006 0.0007 Light delivery car 595.73 7.311 0.2845 0.0033 671.98 6.7795 0.3018 0.0062 Four-wheel drive 943.51 0.0861 0.0069 0.0007 982.37 3.6701 0.1331 0.0019 Light truck 797.01 25.028 0.9112 0.0049 550.08 3.0722 0.3798 0.0018 Mini bus 823.78 4.6585 0.2702 0.0012 720.05 0.868 0.2006 0.0007 Light bus 797.01 25.028 0.9112 0.0049 550.08 3.0722 0.3798 0.0018 Medium truck – – – – 799.6 5.3791 0.2077 0.00006 Heavy truck – – – – 799.6 5.3791 0.2077 0.00006 Articulated truck – – – – 799.6 5.3791 0.2077 0.00006 Medium bus – – – – 799.6 5.3791 0.2077 0.00006 Heavy bus – – – – 799.6 5.3791 0.2077 0.00006 Coach – – – – 799.6 5.3791 0.2077 0.00006 Table 3-15. Estimated coefficients for engine speed model. Vehicle Class Engine Speed Coefficients a0 a1 a2 a3 Small car 720.05 0.868 0.2006 0.0007 Medium car 720.05 0.868 0.2006 0.0007 Large car 720.05 0.868 0.2006 0.0007 Light delivery car 595.73 7.311 0.2845 0.0033 Light goods vehicle 595.73 7.311 0.2845 0.0033 Four-wheel drive 982.37 3.6701 0.1331 0.0019 Light truck 550.08 3.0722 0.3798 0.0018 Mini bus 720.05 0.868 0.2006 0.0007 Light bus 550.08 3.0722 0.3798 0.0018 Medium truck 799.6 5.3791 0.2077 0.00006 Heavy truck 799.6 5.3791 0.2077 0.00006 Articulated truck 799.6 5.3791 0.2077 0.00006 Medium bus 799.6 5.3791 0.2077 0.00006 Heavy bus 799.6 5.3791 0.2077 0.00006 Coach 799.6 5.3791 0.2077 0.00006 Table 3-16. Recommended coefficients for engine speed model.

19 ments without cruise control for the heavier vehicles. The HDM 4 overpredicts fuel consumption in the high range (above 200 mL/km) and underpredicts fuel consumption in the low range (less than 200 mL/km). The reason can be explained as follows: During testing, when the vehicle was driven over a steep positive slope, the cruise control disengaged and the vehicle speed decreased resulting in a decrease in fuel consumption. However, for a vehicle driven over a steep negative slope, the HDM 4 model yields nega- tive tractive power, indicating that the vehicle requires no traction force from the engine, and predicts lower fuel con- sumption. This did not occur during the tests; instead the speed increased. For some vehicles, it was difficult to maintain constant speed without cruise control especially when the roads are very rough. For calibration purposes, data collected during the tests with cruise control were used for light vehicles; the data collected during tests without cruise control were used for light and heavy trucks. Figure 3-8 shows the results after calibration of the HDM 4 fuel consumption model for all vehicle classes. Table 3-17 lists the calibration coef- ficients and the corresponding errors. Statistical analysis showed that there is no difference between the observed and the estimated fuel consumption at 95 percent confi- dence level. Effect of Roughness and Texture on Fuel Consumption To verify that the calibrated HDM 4 model is able to cor- rectly predict the effects of pavement conditions on fuel consumption, a more detailed analysis was conducted. The analysis assumes that there is no interaction between the effects of roughness and surface texture and that, in most cases, PCC and AC pavements exhibit similar trends in how fuel con- sumption increases with greater pavement roughness. (a) Van (b) Light Truck 0 20 40 60 80 100 120 140 0 2 4 6 8 10 F ue l C on su m pt io n (m L /k m ) Distance (km) ` 0 50 100 150 200 250 300 350 0 2 4 6 8 10 F ue l C on su m pt io n (m L /k m ) Distance (km) ` Predicted Fuel Consumption Measured Fuel Consumption Figure 3-6. Predicted and measured fuel consumption (with cruise control) versus distance. (a) With Cruise Control (b) Without Cruise Control 0 10 0 20 0 30 0 40 0 0 1 00 20 0 3 00 400 Pr ed ic te d Fu el R at e (m L/ km ) Measured Fuel Rate (mL/km) 0 10 0 20 0 30 0 40 0 0 1 00 200 300 40 0 Pr ed ic te d Fu el R at e (m L/ km ) Measured Fuel Rate (mL/km) Figure 3-7. Measured versus estimated fuel consumption for heavy truck.

20 (a) Medium Car (b) SUV (c) Van (d) Light Truck (e) Articulated Truck R 2 = 0.90 SSE = 4.09 0 20 40 60 80 10 0 0 2 0 4 0 6 0 8 0 1 00 C al ib ra te d Fu el Ra te (m L/ km ) Measured Fuel Rate (mL/km) R 2 = 0.83 SSE = 9.58 0 50 10 0 15 0 20 0 0 5 0 100 150 200 C al ib ra te d Fu el Ra te (m L/ km ) Measured Fuel Rate (mL/km) R 2 = 0.8 9 SSE = 4.19 0 40 80 12 0 0 4 0 8 0 1 20 C al ib ra te d Fu el Ra te (m L/ km ) Measured Fuel Rate (mL/km) R 2 = 0.82 SSE = 10.1 6 0 10 0 20 0 30 0 0 100 20 0 3 00 C al ib ra te d Fu el Ra te (m L/ km ) Measured Fuel Rate (mL/km) R 2 = 0.8 8 SSE = 5.29 0 10 0 20 0 30 0 40 0 0 100 200 30 0 4 00 C al ib ra te d Fu el Ra te (m L/ km ) Measured Fuel Rate (mL/km) Figure 3-8. Measured versus estimated fuel consumption using HDM 4 model. Vehicle Class Kcr2 KPea SSE (mL/km) Number of Data Points Considered Medium car 0.5 0.25 4.09 456 SUV 0.58 0.56 9.58 250 Light truck 0.99 0.61 10.16 356 Van 0.67 0.49 4.19 352 Articulated truck 1.1 0.35 5.29 456 Table 3-17. Calibration coefficients and statistical performance. The effects of roughness and texture on fuel consumption were estimated using a detailed analysis that induced the fol- lowing operations: 1. Range discretization: The grade data were divided into equal ranges. A width of the discretization interval of 0.1% was selected (based on the sensitivity of fuel consumption to the grade). 2. Analysis of covariance (ANCOVA): The grade was treated as a fixed factor, IRI and texture as covariate variables, and the fuel consumption as the dependent variable. The groups that have at least 3 points were selected for use in this analysis. A 95% confidence level is generally suitable

21 for scientific research. Lower confidence levels would lead to perhaps too many variables that are statistically signifi- cant and greater confidence would require more data to generate intervals of usable lengths. First, separate analyses were conducted for summer and winter conditions and for asphalt and concrete pavement sections. The results in terms of the effect of roughness and texture were similar for both pavement types. There- fore, the data from all pavement sections were combined. 3. Linear regression analysis: A linear function was fitted to the data within each group of grade. The quality of fit analysis for all vehicle classes is presented in Table 3-18. The lack of fit test showed that the selected models fit the data very well (p-value is more than 0.05). The results from the analysis showed that the effect of rough- ness is statistically significant for all vehicle classes. On the other hand, the effect of surface texture was only statistically significant for the articulated truck at low speed (56 km/h or 35 mph), although the p-value is close to 0.05 for higher speed. Roughness Table 3-18 shows that the effect of roughness is statistically significant (p-value is less than 0.05). Therefore, focus was also placed on the accuracy of the calibrated model to predict the effect of roughness. Figure 3-9 shows the change in fuel consumption (from the baseline condition of IRI = 1 m/km) as a function of IRI using the current and calibrated HDM 4 models and regression from the measured field test data. Fig- ure 3-9a shows that the current HDM 4 underpredicts the effect of roughness on fuel consumption. Figure 3-9b shows that the calibrated HDM 4 model predicts the effect of rough- ness on fuel consumption reasonably well. Vehicle Class Speed (km/h) Summer Winter Significance (p-value)* Number of Data Points Significance (p-value)* Number of Data Points IRI MPD Grade Lack of Fit IRI MPD Grade Lack of Fit Medium car 56 0.00 0.54 0.00 0.77 136 0.00 0.81 0.00 0.61 136 72 0.00 0.22 0.00 0.78 146 0.00 0.13 0.00 0.56 146 88 0.00 0.90 0.00 0.75 136 0.00 0.84 0.00 0.78 136 Van 56 0.00 0.35 0.00 0.96 136 0.00 0.83 0.00 0.79 136 72 0.00 0.38 0.00 0.68 146 0.00 0.21 0.00 0.97 146 88 0.00 0.29 0.00 0.77 136 0.00 0.22 0.00 0.78 136 SUV 56 0.00 0.20 0.00 0.75 136 0.00 0.61 0.00 0.86 136 72 0.00 0.40 0.00 0.86 146 0.00 0.83 0.00 0.91 146 88 0.00 0.70 0.00 0.71 136 0.00 0.35 0.00 0.88 136 Light truck 56 0.00 0.50 0.00 0.79 136 0.00 0.96 0.00 0.75 136 72 0.00 0.60 0.00 0.75 146 0.00 0.40 0.00 0.86 146 88 0.00 0.10 0.00 0.77 136 0.00 0.72 0.00 0.71 136 Articulated truck 56 0.00 0.03 0.00 0.79 137 No tests were conducted in winter. 72 0.00 0.06 0.00 0.97 146 88 0.00 0.07 0.00 0.78 137 *If higher than 5%, the mean difference is considered statistically not significant. Table 3-18. Analysis of covariance results for all vehicles. (a) Current HDM 4 model 1 m/km = 63.4 in./mi 0 2 4 6 8 10 12 14 1 2 3 4 5 6 C ha ng e in F ue l C on su m pt io n (% ) IRI (m/km) Medium car Medium car - Regression SUV SUV - Regression Van Van - Regression Light truck Light truck - Regression Articulated truck Articulated truck - Regression (b) Calibrated HDM 4 Model 0 2 4 6 8 10 12 14 1 2 3 4 5 6 C ha ng e in F ue l C on su m pt io n (% ) IRI (m/km) Medium car - HDM 4 Medium car - Regression SUV - HDM 4 SUV - Regression Van - HDM 4 Van - Regression Light truck - HDM 4 Light truck - Regression Articulated truck - HDM 4 Articulated truck - Regression Figure 3-9. Effect of roughness on fuel consumption at 88 km/h (55 mph).

22 The sensitivity analyses for the current and calibrated mod- els (Figures 3-9a and 3-9b, respectively) at 88 km/h (55 mph) show the following increase in fuel consumption as a result of increasing IRI from 1 to 3 m/km at 30°C (86°F) when the MPD is 1 mm (0.04 in.) and grade is 0%: • For medium car: 2.6% and 4.8% for the current and cali- brated models, respectively. • For SUV: 0.8% and 4.1% for the current and calibrated models, respectively. • For van: 0.8% and 1.8% for the current and calibrated models, respectively. • For light truck: 0.5% and 1.6% for the current and cali- brated models, respectively. • For articulated truck: 0.9% and 2.9% for the current and calibrated models, respectively. Figure 3-10 shows the effect of roughness on fuel con- sumption for all vehicle classes at different speeds at 17°C (62.6°F) when the MPD is 1 mm (0.04 in.) and grade is 0%. Figure 3-10. Effect of roughness on fuel consumption estimated using calibrated HDM 4. 1 m/km = 63.4 in./mi. (a) Passenger car (b) Van (c) SUV 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1 2 3 4 5 6 A dj us tm en t F ac to rs IRI (m/km) 1 1.01 1.02 1.03 1.04 1.05 1.06 1 2 3 4 5 6 A dj us tm en t F ac to rs IRI (m/km) 1 1.02 1.04 1.06 1.08 1.1 1.12 1 2 3 4 5 6 A dj us tm en t F ac to rs IRI (m/km) 40 km/h (25 mph) 56 km/h (35 mph) 72 km/h (45 mph) 88 km/h (55 mph) 112 km/h (70 mph) (d) Light truck (e) Articulated truck 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1 2 3 4 5 6 A dj us tm en t F ac to rs IRI (m/km) 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1 2 3 4 5 6 A dj us tm en t F ac to rs IRI (m/km)

23 Source: adapted from Michelin (2003) 0 25 50 75 100 0 40 80 120 160 T ot al P o w er ( % ) Speed (km/h) Air DragInternal Friction Rolling Resistance Figure 3-11. Energy distribution in a passenger car versus speed. (a) 56 km/h (35 mph) (b) 88 kn/h (55 mph) 1 1.01 1.02 1.03 1.04 1.05 1.06 0.5 1 1.5 2 2.5 3 A dj us te m en t F ac to r Mean Profile Depth (mm) 1 1.01 1.02 1.03 1.04 1.05 1.06 0.5 1 1.5 2 2.5 3 A dj us te m en t F ac to r Mean Profile Depth (mm) 1 mm = 0.04 in. Medium car - HDM 4 Medium car - Regression SUV - HDM 4 SUV - Regression Van - HDM 4 Van - Regression Light truck - HDM 4 Light truck - Regression Articulated truck - HDM 4 Articulated truck - Regression Figure 3-12. Effect of surface texture on fuel consumption. Texture According to Sandberg (1990), road surface texture has a higher effect on rolling resistance at higher speeds. How- ever, the analysis of covariance showed that the effect of tex- ture on fuel consumption is statistically not significant at higher speeds. An explanation for these observations is that, at higher speeds, air drag becomes the largely predominant factor in fuel consumption such that the increase in rolling resistance due to texture will be masked by the increase in air drag. Figure 3-11 shows the mechanical power available by the engine as a function of the vehicle speed (no climb- ing, no acceleration) for passenger cars. At a constant speed of 100 km/h on a horizontal road, air drag represents 60% of energy loss while rolling resistance accounts for 25% and internal friction (drive line loss) for 15%. For a heavy truck operating at 80 km/h, approximately 12% of the fuel con- sumption is accounted for by the rolling resistance losses in the tires, which accounts for approximately 30% of the avail- able mechanical power from the engine. Figure 3-12 shows the change in fuel consumption (from the baseline condi- tion of MPD = 0.5 mm) as a function of texture using the calibrated HDM 4 model and regression. The results were generated for a vehicle speed of 56 and 88 km/h (35 and 55 mph) at 30°C (86°F) when IRI is 1 m/km (63.4 in./mi) and grade is 0%. The figure shows that the calibrated HDM 4 model predicts the effect of texture on fuel consumption reasonably well. Summary The analysis presented in this chapter shows that the HDM 4 fuel consumption model, after appropriate calibra- tion, adequately predicts the fuel consumption of five dif- ferent vehicle classes under different operating, weather, and pavement conditions. Also, because the key characteristics of representative vehicles used in the current HDM 4 model vary substantially from those used in the United States, the current model (i.e., without calibration) predicted lower fuel consumption than actually consumed. Table 3-19 sum- marizes the predictions using the current and the calibrated HDM 4 model. The analysis of covariance of the data collected during the field test showed that the effect of surface texture is statis- tically significant at 95 percent confidence interval only for heavier trucks and at low speed. An explanation of this obser- vation is that, at higher speeds, air drag becomes the largely predominant factor in fuel consumption. The increase in rolling resistance (i.e., fuel consumption) due to texture is masked by the increase in air drag due to speed. The calibrated HDM 4 fuel consumption model is listed in Tables 3-20 through 3-25.

Speed Vehicle Class Calibrated HDM 4 model Current HDM 4 model Base (mL/km) Adjustment factors from the base value Base (mL/km) Adjustment factors from the base value IRI (m/km) IRI (m/km) 1 2 3 4 5 6 1 2 3 4 5 6 56 km/h (35 mph) Medium car 70.14 1.03 1.05 1.08 1.10 1.13 81.83 1.01 1.03 1.04 1.05 1.06 Van 76.99 1.01 1.02 1.03 1.04 1.05 94.8 1.01 1.02 1.03 1.04 1.05 SUV 78.69 1.02 1.05 1.07 1.09 1.12 96 1.01 1.02 1.02 1.03 1.04 Light truck 124.21 1.01 1.02 1.04 1.05 1.06 159.1 1.01 1.01 1.02 1.02 1.03 Articulated truck 273.41 1.02 1.04 1.07 1.09 1.11 425 1.01 1.02 1.03 1.04 1.04 88 km/h (55 mph) Medium car 83.38 1.03 1.05 1.08 1.10 1.13 76.60 1.01 1.03 1.04 1.05 1.06 Van 96.98 1.01 1.02 1.03 1.04 1.05 98.04 1.01 1.02 1.03 1.04 1.05 SUV 101.29 1.02 1.04 1.07 1.09 1.11 103.12 1.01 1.02 1.02 1.03 1.04 Light truck 180.18 1.01 1.02 1.03 1.04 1.05 187.06 1.01 1.01 1.02 1.02 1.03 Articulated truck 447.31 1.02 1.03 1.05 1.06 1.08 420.09 1.01 1.02 1.03 1.04 1.04 112 km/h (70 mph) Medium car 107.85 1.02 1.05 1.07 1.09 1.12 87.64 1.01 1.03 1.04 1.05 1.06 Van 128.96 1.01 1.02 1.03 1.03 1.04 115 1.01 1.02 1.03 1.04 1.05 SUV 140.49 1.02 1.04 1.06 1.08 1.10 124 1.01 1.02 1.02 1.03 1.04 Light truck 251.41 1.01 1.02 1.02 1.03 1.04 250.5 1.01 1.01 1.02 1.02 1.03 Articulated truck 656.11 1.01 1.02 1.04 1.05 1.06 584.7 1.01 1.02 1.03 1.04 1.04 2352 mpg = mL/km Table 3-19. Effect of roughness on fuel consumption. = + Name Description Unit Fuel Consumption (FC) ( )1000 * max , * * 1FC Ptot dFuelα ξυ= + mL/km Vehicle speed m/s α Fuel consumption at idling (Table 3-22) mL/s Engine efficiency (ξ ) 1 max engtot b P P ehp P ξ − mL/kW/s ξb Engine efficiency (depends on the technology type: gasoline versus diesel) (Table 3-22) mL/kW/s Pmax Rated engine power (Table 3-22) kW ehp Engine horsepower (Table 3-22) hp dFuel Excess fuel consumption due to congestion as a ratio (default = 0) dimensionless Peng Power required to overcome internal engine friction (80 percent of the engine and accessories power) kW Engine and accessories power (Pengaccs = Peng + accsP ) * max* _ 1 ( _ 0 _ 1 * 100 engaccsP KPea P RPM RMPIdle Paccs a Paccs a Paccs a RPM RPMIdle = −+ − − kW KPea Calibration factor (Table 3-23) dimensionless Paccs_a1 −= = −= −+−= α ξ ξ c PkPeab PctPeng PkPeaehpa a cabb aPaccs b b max** 100 100 max**** *2 **4 1_ 2 2 Paccs_a0 Ratio of engine and accessories drag to rated engine power when traveling at 100 km/h (Table 3-23) dimensionless PctPeng Percentage of the engine and accessories power used by the engine (Default = 80%) % Engine speed (RPM) ( )vSP SPaSPaSPaaRPM ,20max *3*2*10 32 = +++= rev/min a0 to a3 Model parameter (Table 3-22) RPM100 Engine speed at 100 km/h rev/min RPMIdle Idle engine speed (Table 3-22) rev/min Total power (Ptot) for 0, uphill/level for 0, downhill tr tot accs eng tr tot tr accs eng tr P P P P P edt P edtP P P P = + + ≥ = + + < kW edt Drive-train efficiency factor (Table 3-22) dimensionless Tractive power ( trP ) * 1000tr Fa Fg Fc Fr Fi P υ + + + += kW Table 3-20. Calibrated HDM 4 fuel consumption model.

( ) Name Description Unit Aerodynamic forces (Fa) 20.5* * * *Fa CD AFρ υ= N CD Drag coefficient (Table 3-23) dimensionless AF Frontal area (Table 3-23) m2 Mass density of the air (Default = 1.2) kg/m3 Vehicle speed m/s Gradient forces (Fg) gGRMFg **= N M Vehicle weight (Table 3-23) kg GR Gradient radians g Gravity (Default = 9.81) m/s2 Curvature forces (Fc) − = −3 22 10* * ** * ,0max CsNw egM R M Fc υ N R curvature radius (Default=3000) m Superelevation (e) ( )( )RLne *68.045.0,0max −= m/m Nw Number of wheels (Table 3-23) dimensionless Tire stiffness (Cs) 2 0 1* 2* M M Cs a a a Nw Nw = + + kN/rad a0 to a2 Model parameter (Table 3-24) Rolling resistance (Fr) ( )22* 11* 1* 12* 13*Fr CR b Nw CR b M b υ= + + N CR1 Rolling resistance tire factor (Table 3-25) factor Rolling resistance parameters (b11, b12, b13) 2 11 37* 12 0.064 / 13 0.012* / b WD b WD b Nw WD = = = parameters WD Wheel diameter (Table 3-23) m Rolling resistance surface factor (CR2) DEFaIRIaTdspaaKcr *3*2*102 +++= factor Kcr2 Calibration factor (Table 3-23) factor a0 to a3 Model coefficient (Table 3-23) dimensionless Texture depth using sand patch method (Tdsp) 1.02* 0.28Tdsp MPD= + mm MPD Mean profile depth mm IRI International roughness index m/km DEF Benkelman Beam rebound deflection mm Inertial forces (Fi) 3 2 * 0 1*arctan * a Fi M a a acc υ = + N acc Vehicle acceleration m/s 2 a0 to a2 Model parameter (Table 3-23) dimensionless Table 3-21. Calibrated HDM 4 tractive forces model. Vehicle Class Fuel Type Engine Speed (rpm) RPMIdle α (mL/s) ξb (mL/kW/s) ehp (hp) Pmax (kW) edt Paccs_a0 PctPeng (%) a0 a1 a2 a3 Small car P 720.05 0.868 0.2006 0.0007 800 0.65 0.096 0.05 130 0.91 0.2 80 Medium car P 720.05 0.868 0.2006 0.0007 800 0.65 0.096 0.05 130 0.91 0.2 80 Large car P 720.05 0.868 0.2006 0.0007 800 0.65 0.096 0.05 130 0.91 0.2 80 Light delivery car P 589.6 0.5145 0.0168 0.0019 500 0.65 0.072 0.05 90 0.91 0.2 80 Light goods vehicle P 589.6 0.5145 0.0168 0.0019 500 0.65 0.072 0.05 90 0.91 0.2 80 Four-wheel drive P 982.37 3.6701 0.1331 0.0019 500 0.65 0.072 0.25 95 0.91 0.2 80 Light truck P 550.08 3.0722 0.3798 0.0018 500 0.7 0.062 0.1 150 0.86 0.2 80 Medium truck P 799.6 5.3791 0.2077 0.00006 833.7 0.8 0.059 0.1 200 0.86 0.2 80 Heavy truck D 799.6 5.3791 0.2077 0.00006 833.7 0.9 0.059 0.1 350 0.86 0.2 80 Articulated truck D 799.6 5.3791 0.2077 0.00006 833.7 0.9 0.059 0.1 350 0.86 0.2 80 Mini bus P 720.05 0.868 0.2006 0.0007 500 0.48 0.096 0.25 55 0.9 0.2 80 Light bus P 550.08 3.0722 0.3798 0.0018 589.6 0.48 0.062 0.1 100 0.86 0.2 80 Medium bus D 799.6 5.3791 0.2077 0.00006 833.7 0.7 0.059 0.1 200 0.86 0.2 80 Heavy bus D 799.6 5.3791 0.2077 0.00006 833.7 0.8 0.059 0.1 350 0.86 0.2 80 Coach D 799.6 5.3791 0.2077 0.00006 833.7 0.9 0.059 0.1 350 0.86 0.2 80 P = petroleum; D = diesel Table 3-22. Calibrated HDM 4 default values for engine and vehicle characteristics.

26 Vehicle Class Number of Axles CD AF (m2) NW M (tons) WD (m) Tire Type CR1 b11 b12 b13 Effect Mass Ratio Model Coefficients Kcr2 KPeaa0 a1 a2 Small car 2 0.42 2.16 4 1.9 0.62 Radial 1 22.2 0.11 0.13 1.05 0.213 1260.7 0.5 0.25 Medium car 2 0.42 2.16 4 1.9 0.62 Radial 1 22.2 0.11 0.13 1.05 0.213 1260.7 0.5 0.25 Large car 2 0.42 2.16 4 1.9 0.62 Radial 1 22.2 0.11 0.13 1.05 0.213 1260.7 0.5 0.25 Light delivery car 2 0.5 2.9 4 2.54 0.7 Radial 1 25.9 0.09 0.10 1.1 0.891 244.2 0.67 0.49 Light goods vehicle 2 0.5 2.9 4 2.54 0.7 Radial 1 25.9 0.09 0.10 1.1 0.891 244.2 0.67 0.49 Four-wheel drive 2 0.5 2.8 4 2.5 0.7 Radial 1 25.9 0.09 0.10 1.1 0.891 244.2 0.58 0.56 Light truck 2 0.6 5 4 4.5 0.8 Radial 1 29.6 0.08 0.08 1.04 0.83 12.4 0.99 0.61 Medium truck 2 0.6 5 6 6.5 0.8 Bias 1.3 29.6 0.08 0.11 1.04 0.83 12.4 0.99 0.61 Heavy truck 3 0.7 8.5 10 13 1.05 Bias 1.3 38.85 0.06 0.11 1.07 1.91 10.1 1.1 0.35 Articulated truck 5 0.8 9 18 13.6 1.05 Bias 1.3 38.85 0.06 0.20 1.07 1.91 10.1 1.1 0.35 Mini bus 2 0.5 2.9 4 2.16 0.7 Radial 1 25.9 0.09 0.10 1.1 0.891 244.2 0.67 0.49 Light bus 2 0.5 4 4 2.5 0.8 Radial 1 29.6 0.08 0.08 1.1 0.891 244.2 0.99 0.61 Medium bus 2 0.6 5 6 4.5 1.05 Bias 1.3 38.85 0.06 0.07 1.04 0.83 12.4 0.99 0.61 Heavy bus 3 0.7 6.5 10 13 1.05 Bias 1.3 38.85 0.06 0.11 1.04 0.83 12.4 1.1 0.35 Coach 3 0.7 6.5 10 13.6 1.05 Bias 1.3 38.85 0.06 0.11 1.04 0.83 12.4 1.1 0.35 Table 3-23. Calibrated HDM 4 default values for tire and vehicle characteristics. 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 3-24. Final parameters for tire stiffness (Cs) 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) Table 3-25. Final parameters for rolling resistance coefficient (CR2) model.

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Estimating the Effects of Pavement Condition on Vehicle Operating Costs Get This Book
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TRB’s National Cooperative Highway Research Program (NCHRP) Report 720: Estimating the Effects of Pavement Condition on Vehicle Operating Costs presents models for estimating the effects of pavement condition on vehicle operating costs.

The models address fuel consumption, tire wear, and repair and maintenance costs and are presented as computational software that is included in the print version of the report in a CD-ROM format. The CD-ROM is also available for download from TRB’s website as an ISO image. Links to the ISO image and instructions for burning a CD-ROM from an ISO image are provided below.

Appendixes A through D to the report provide further elaboration on the work performed in the project that developed NCHRP Report 720. The appendixes, which were not included with the print version of the report, are only available for download through the link below.

• Appendix A: Fuel Consumption Models,

• Appendix B: Tire Wear Models,

• Appendix C: Repair and Maintenance Models, and

• Appendix D: An Overview of Emerging Technologies.

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CD-ROM Disclaimer - This software is offered as is, without warranty or promise of support of any kind either expressed or implied. Under no circumstance will the National Academy of Sciences or the Transportation Research Board (collectively "TRB") be liable for any loss or damage caused by the installation or operation of this product. TRB makes no representation or warranty of any kind, expressed or implied, in fact or in law, including without limitation, the warranty of merchantability or the warranty of fitness for a particular purpose, and shall not in any case be liable for any consequential or special damages.

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