A comparative analysis of several vehicle emission models for road freight transportation

Transportation Research Part D 16 (2011) 347–357

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Transportation Research Part D journal homepage: www.elsevier.com/locate/trd

A comparative analysis of several vehicle emission models for road freight transportation Emrah Demir a, Tolga Bektasß a,⇑, Gilbert Laporte b a School of Management and Centre for Operational Research, Management Science and Information Systems University of Southampton, Southampton, Highfield SO17 1BJ, UK b Centre on Enterprise Networks, Logistics, and Transportation HEC Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, Canada H3T 2A7

a r t i c l e

i n f o

Keywords: Fuel consumption Emission models Vehicle routing Freight transportation modeling

a b s t r a c t Reducing greenhouse gas emissions in freight transportation requires using appropriate emission models in the planning process. This paper reviews and numerically compares several available freight transportation vehicle emission models and also considers their outputs in relations to field studies. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Green logistics, aiming at minimizing the harmful effects of transportation on the environment, has gained in importance. In particular, an explicit consideration is given to reducing levels of CO2 through better operational level planning. Measuring and reducing emissions requires good estimations to be fed into planning activities, which in turn require estimation models to be incorporated into the planning methods.1 The choice of the type and the nature of emission functions are important for deriving accurate estimates in the planning of transportation activities. There exists a variety of analytical emission models that differ in the ways they estimate fuel consumption or emissions, or in the parameters they take into account in the estimations. In this context, Ardekani et al. (1996), for example, divide models into urban (vehicle speed is less than 55 km/h) and highway (vehicle speed is at least 55 km/h) fuel consumption models, whereas Esteves-Booth et al. (2002) consider three types of emission models based on emission factors, average speeds, and mode. Here we compare a number of such models, and assess their respective strengths and weaknesses.

2. Fuel consumption models 2.1. Model 1: An instantaneous fuel consumption model An instantaneous fuel consumption model, or instantaneous model for short, is developed by Bowyer et al. (1985) as an extension of Kent et al.’s (1982) power model. It uses vehicle characteristics such as mass, energy, efficiency parameters, drags force and fuel consumption components associated with aerodynamic drag and rolling resistance, and approximates

⇑ Corresponding author. E-mail address: [email protected] (T. Bektasß). For example, Jabali et al. (2009) investigate reducing CO2 emissions in road-based freight transportation, Bauer et al. (2010) consider emissions in rail transportation, and Fagerholt et al. (2010) look at reducing emissions in shipping. 1

1361-9209/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.trd.2011.01.011

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the fuel consumption per second. The model assumes that changes in acceleration and deceleration levels occur within 1 s time interval and takes the form

( ft ¼

a þ b1 Rt v þ ðb2 Ma2 v =1000Þ for Rt > 0 ; a for Rt 6 0

ð1Þ

where ft is the fuel consumption per unit time (mL/s), Rt is the tractive force (kN = kilonewtons) required to move the vehicle and calculated as the sum of drag force, inertia force and grade force as Rt = b1 + b2v2 + Ma/1000 + gMx/100,000. Furthermore, a is the constant idle fuel rate (in mL/s, typically between 0.375 and 0.556), b1 is the fuel consumption per unit of energy (in mL/kJ, typically between 0.09 and 0.08), b2 is the fuel consumption per unit of energy-acceleration (in mL/ (kJ m/s2), typically between 0.03 and 0.02), b1 is the rolling drag force (in kN, typically between 0.1 and 0.7), and b2 is the rolling aerodynamic force (in kN/(m/s2), typically between 0.00003 and 0.0015). In addition, x is the percent grade, a is the instantaneous acceleration (m/s2), M is the weight (kg), and v is the speed (m/s). Using Model 1, the amount of fuel consumption Ft(mL/s) for a journey of duration t0 can be calculated as:

Ft ¼

Z

t0

ft dt:

ð2Þ

0

The instantaneous model operates at a microscale level and is better suited for short trip emission estimations. The model does not make use of macro-level data such as the number of stops but is able to take into account acceleration, deceleration, cruise and idle phases. Using data from special on-road experiments in Melbourne, Bowyer et al. (1985) showed it is able to approximate fuel consumption of individual vehicles within a 5% error margin for short trips, and dynamometer tests suggested that its accuracy is within 10% for a variety of on-road experiments (Esteves-Booth et al., 2002). 2.2. Model 2: A four-mode elemental fuel consumption model A four-mode elemental model is described by Bowyer et al., in a refinement of Akçelik (1982) estimates fuel consumption for idle, cruise, acceleration and deceleration. The model includes the same parameters as Model 1 but introduces new considerations such as initial speed, final speed and energy-related parameters. It requires data related to the distance, cruise speed, idle time and average road grade as inputs. A vehicle is said to be in an idle mode when the engine is running but the speed is below 5 km/h. More accurate estimations can be made if the initial and final speeds for each acceleration and deceleration cycles are known. The model consists of four functions, Fa, Fd, Fe and Fi, corresponding to fuel consumption estimations (mL) for acceleration, deceleration, cruise and idle modes. 2.2.1. Acceleration fuel consumption The following can be used to calculate the amount of fuel consumption over the acceleration phase of a vehicle from an initial speed vi to a final speed vf

n     o F a ¼ max at a þ C þ k1 B v 2i þ v 2f þ b1 MEk þ k2 b2 ME2k þ 0:0981b1 Mx xa ; ata :

ð3Þ

where Ek denotes the change in kinetic energy per unit distance during acceleration and is calculated as   p v 2f  v 2fi =xa . The integration coefficients are k1 = 0.616 + 0.000544vf  0.0171 vi and k1 = 1.376 +

Ek ¼ 0:3858104

0.00205vf  0.0053vi. When the travel distance xa and the travel time ta are not known, they can be estimated as xa = ma(p vi + vf)ta/3600 where ma = 0.467 + 0.00200vf  0.00210vi and ta = (vf  vi)/(2.08 + 0.127 (vf  vi)  0.0182vi. C is the function parameter (in mL/km, typically between 21 and 100), and B is the function parameter – in (mL/km)/(km/h)2 and typically between 0.0055 and 0.018). 2.2.2. Deceleration fuel consumption The following can be used to calculate the amount of fuel consumption during the deceleration phase from an initial speed vi to a final speed vf:

n     o F d ¼ max at d þ kx C þ ky k1 B v 2i þ v 2f þ ka b1 MEk þ 0:0981kx b1 Mx xd ; at d ; 0:75 kx ka

3:81 kx ð2

ð4Þ 3:81 kx Þ

where kx = 0.046 + 100/M + 0.00421vi + 0.00260vf + 0.05444x, ky = , ¼  and kx1 = 0.621 + 0.000777vi  p 0.018 vf. If xa and ta are not known, they are estimated as for Eq. (3), although the coefficients change slightly. In addition, kx, ky and ka are the energy-related parameters. 2.2.3. Cruise fuel consumption This can be estimated using;

n o F c ¼ max fi =v c þ C þ Bv 2c þ kE1 b1 MEkþ þ kE2 b2 ME2kþ þ 0:0981kG b1 M x; fi =v c xc ;

ð5Þ

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where fi denotes the idle fuel rate (mL/h), vc is the average cruise speed (km/h), and xc is the travel distance (km). The change in positive kinetic energy per unit distance during the cruise mode is calculated as Ek+ = max{0.258–0.0018vc, 0.10} and the other parameters are set to kE1 ¼ maxf12:5=v c ; þ0:000013v 2c ; 0:63g, kE2 = 3.17, and kG = 1–2.1 Ek+ for x < 0, and 1–0.3 Ek+ for x > 0 with kE1, kE2 and kG the calibration parameters. 2.2.4. Fuel consumption while idle To estimate this we use;

F i ¼ ati ;

ð6Þ

where ti is the idle time (s), and a is the idle fuel rate (mL/s). The fuel consumption Ft (mL) using the elemental model can be calculated as:

Ft ¼

Z

ta

F a dt þ 0

Z

td

0

F d dt þ

Z 0

tc

F c dt þ

Z

ti

F i dt:

ð7Þ

0

The elemental model assumes minimum loss of driving information, and hence minimum loss of accuracy in fuel consumption estimates. It is better suited for estimation of fuel consumption for short distance trips, but its large number of parameters and the existence of four functions can make it difficult to implement. Bowyer et al. experimented with Model 2 and compared it against the instantaneous model. Their results suggest that the elemental model can predict fuel consumption within a 1% error margin. If the initial and final speeds are known, the model yields more accurate estimates for fuel consumption, and provides results very similar to those of the instantaneous model. 2.3. Model 3: A running speed fuel consumption model The running speed fuel consumption model is an aggregated form of the elemental model and was introduced by Bowyer et al. (1985) to calculate fuel consumption during periods when a vehicle is running and is in an idle mode. The model is:

n o F s ¼ max ati þ ðfi =v r þ c þ Bv 2r þ kE1 b1 MEkþ þ kE2 b2 ME2kþ þ 0:0981kG b1 MxÞxs ; ats ;

ð8Þ

where Fs is the fuel consumption (mL), xs is the total distance, vr is the average running speed (km/h), ts and ti the travel and idle time. Average speed is calculated as ts = 3600xs/(ts  ti). Furthermore, Ek+ = max{0.35–0.0025vr, 0.15}, k1 = max{0.675– 1.22/vr, 0.5}, k2 = 2.78 + 0.0178vr. The model is an extension of the instantaneous model and can be viewed as an aggregation of the elemental model. Acceleration, deceleration and cruise modes are considered together within a single function. It does not take into account the idle mode of a vehicle, but it can be used to estimate fuel consumption in a variety of traffic situations, ranging from short to long distance trips, although it is more useful for the latter. 2.4. Model 4: A comprehensive modal emission model A comprehensive emissions model for heavy-good vehicles was developed in Barth et al. (2000, 2005) and Barth and Boriboonsomsin (2008). It follows, the model of Ross (1994), consisting of three modules; engine power, engine speed and fuel rate. 2.4.1. The engine power module The power demand function for a vehicle is obtained from the tractive power requirements Ptract(kW) placed on the vehicle at the wheels:

Ptract ¼ ðMa þ Mg sin h þ 0:5C d qAv 2 þ MgC r cos hÞv =1000;

ð9Þ 3

where v is the speed (m/s), and M is the weight (kg), with q is the air density in kg/m (typically 1.2041), A is the frontal surface area in m2 (typically between 2.1 and 5.6), and g is the gravitational constant in m/s2 (typically 9.81). In addition, Cd is the coefficient of aerodynamic drag (typically 0.7), and Cr the coefficient of rolling resistance (typically 0.01). To translate the tractive requirement into engine power requirement, the following is used:

P ¼ Ptract =gtf þ Pacc ;

ð10Þ

where P is the second-by-second engine power output (kW), gtf is the vehicle drive train efficiency (typically 0.4), and Pacc the engine power demand associated with running losses of the engine and the operation of vehicle accessories such as usage of air conditioning (typically 0). 2.4.2. The engine speed module Engine speed is approximated in terms of vehicle speed as

N ¼ SðRðLÞ=RðLg ÞÞv ;

ð11Þ

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where N is the engine speed (in rpm, typically between 16 and 48), S is the engine-speed/vehicle-speed ratio in top gear Lg, R(L) is the gear ratio in gear L = 1, . . . , Lg, v is the vehicle speed (m/s), and g is the efficiency parameter for diesel engines (typically 0.4). 2.4.3. The fuel rate module The fuel rate (g/s) is given by the expression

FR ¼ /ðkNV þ P=gÞ=44;

ð12Þ

where u is fuel-to-air mass ratio, k is the engine friction factor (typically 0.2), and V is the engine displacement (in liters, typically between 2 and 8). The comprehensive emissions model is similar to the instantaneous fuel consumption model but to for accuracy it requires detailed vehicle-specific parameters to estimation such as the engine friction coefficient, and the vehicle engine speed. Barth et al. (2005) have tested the under a variety of traffic scenarios for 23 vehicle technology categories and cycles. 2.5. Model 5: Methodology for calculating transportation emissions and energy consumption (MEET) Hickman et al. (1999) work on emission factors for road transportation (INFRAS, 1995) describes a methodology called MEET, used for calculating transportation emissions and energy consumption for heavy-good vehicles. This methodology includes a variety of estimating functions, which are primarily dependent on speed and a number of fixed and predefined parameters for vehicles of weights ranging from 3.5 to 32 tonnes. For vehicles weighing less than 3.5 tonnes, the fuel consumption is estimated using a speed dependent function of the form e = 0.0617v2  7.8227v + 429.51. For other classes of vehicles, MEET suggests the use of:

 ¼ K þ av þ bv 2 þ cv 3 þ d=v þ e=v 2 þ f =v 3 ;

ð13Þ

where e is the rate of emissions (g/km) for an unloaded goods vehicle on a road with a zero gradient and v the average speed of the vehicle (km/h). Emission factors and functions refer to standard testing conditions (i.e., zero road gradient and empty vehicles) and are typically calculated as a function of the average vehicle speed. Depending on the vehicle type, a number of corrections may be needed to allow for the effects of road gradient and vehicle load on the emissions, once a rough estimate has been produced; the following is used to take the effect of road gradient into account:

GC ¼ A6 v 6 þ A5 v 5 þ A4 v 3 þ A2 v 2 þ A1 v þ A0 ;

ð14Þ

where GC is the road gradient correction factor. The following is used to take the load factor into account:

LC ¼ k þ nc þ pc2 þ qc3 þ r=v þ s=v 2 þ t=v 3 þ u=v ;

ð15Þ

where LC is the load correction factor. MEET suggests estimating CO2 emissions (g) as:

F ¼   GC  LC  Distance:

ð16Þ

MEET is based on on-road measurements and parameters are extracted from real-life experiments. The main deficiency of the model is its use of fixed vehicle-specific parameter settings for any vehicle in a given weight class. 2.6. Model 6: Computer programme to calculate emissions from road transportation (COPERT) model COPERT was developed by Ntziachristos and Samaras (2000) and estimates emissions for all major air pollutants as well as greenhouse gases produced by various vehicle categories (e.g., passenger cars, light duty vehicles, heavy duty vehicles, mopeds and motorcycles). Similar to Model 5, it uses a number of functions, which are specific to vehicles of different weights, to estimate fuel consumption. For example, the function for a vehicle with weight less than is 0.0198v2  2.506 v + 137.42. The model is also based on on-road measurements, like Model 5 but does not take road gradient and acceleration into account, but t can differentiate between two speed ranges for each vehicle class. 3. Simulations Fuel consumption depends on a number of factors that can be grouped into four categories: vehicle, driver, environmental conditions and traffic conditions. Using three of these four categories, Table 1 compares comparison of the six models. Driver-related factors are difficult, if not impossible, to integrate into estimation models. The table shows that all models consider vehicle load, speed and acceleration, although the way in which they incorporate them varies, especially for vehicle load. Models 1–4 are similar in their consideration of detailed and technical vehicle-specific parameters, such as vehicle shape (frontal area), and road conditions (gradient, surface resistance), while 5 and 6 present simpler estimations through a predefined set of parameters for a number of vehicle classes. Model 5 is, to some extent, able to take into account factors of

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E. Demir et al. / Transportation Research Part D 16 (2011) 347–357 Table 1 Comparison of Models 1–6 regarding factors affecting fuel consumption. Factors Vehicle related Total vehicle mass Engine size Engine temperature Oil viscosity Gasoline type Vehicle shape The degree of use of auxiliary electric devices

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

 

 

 

 





  

 

 

   

Environment related Roadway gradient Wind conditions Ambient temperature Altitude Pavement type Surface conditions

     

     

     

     



Traffic related Speed Acceleration

 

 



 









load and gradient through the correction factors, but this is not so for 6. No model explicitly considers driver-related factors or some vehicle related factors such as transmission type, or tire pressure, largely because quantifying such them is difficult. Numerically experiments are used to compare the models under different scenarios. In all the experiments, we assume a single vehicle driven on a 100 km road, and vary vehicle speed, load, acceleration and road gradient.  Vehicle speed: Countries impose different restrictions on driving speed and here the lower and upper speed limits are set to 20 km/h and 110 km/h.  Vehicle load: The gross vehicle weight rating (GVWR) is the maximum allowable mass of a road vehicle or trailer when loaded, including the weight of the vehicle itself plus fuel, passengers, cargo, and trailer weight. Commercial trucks are usually classified; Classes 1 and 2 or referred light duty, 3–5 as medium duty, and 6–8 as heavy duty. Here we consider a vehicle from each group. The load factors used for light duty vehicles are 0% (unloaded), 10% and 20%. The load factors used for medium duty vehicles are 0%, 15% and 30%. Finally, the load factors used for heavy duty vehicles are 0%, 30%, 60% and 90%.  Acceleration: While there are two types of acceleration: average acceleration which denotes the change in velocity divided by the change in time and instantaneous acceleration which corresponds to the acceleration at a specific point in time, i.e. only consider the latter.  Road slope: The gradient of a road affects the resistance of a vehicle to traction, as the power employed during the driving operation determines the amount of fuel consumption. Road gradient factors are set to ±0.57 and ±1.15 degrees for the road. The experiments are based on scenarios generated by varying values of these four parameters and are summarized in Table 2. For scenarios 1–14, there are ten possible speed values, ranging from 20 km/h to 110 km/h in increments of 10 km/h, as well as the three types of vehicle (i.e., light, medium, heavy) giving 432 possibilities. Only selections from this set are presented. In scenarios 15–18, vehicle speed is kept constant at either 50 km/h or 70 km/h, but load is gradually changed from 0% to 10% in Scenarios 15 and 17 and from 0% to 30% in the other two. Models 1–3 give fuel consumption in mL per time or distance. Model 4 estimates fuel consumption in gram fuel per time or distance, and Models 5 and 6, CO2 emissions in grams per unit of distance. For comparative purposes, these outputs are converted to the estimated fuel usage (in L) for the 100 km road segment. 3.1. Results Tables 3–5, present results for scenarios 1–14 in Table 3 for three levels of speed: 50 km/h, 70 km/h and 100 km/h and provide, for each scenario, the fuel consumption (L) estimated by each model. From Tables 3–5, it can be seen that there is a considerable increase in fuel consumption with respect to the changes in vehicle speed, with Model 1 the most sensitive among all those tested. With this model, the difference in fuel requirements is about 146% when speed is increased from 50 km/h to 100 km/h; whereas Models 2 and 4 show very similar results for each of three speed levels. The models based on on-road measurements, Model 5 and 6 yield similar fuel consumption. Scenarios 1–3 show that fuel consumption depends on vehicle load with all models sensitive to changes in load and acceleration. Models 1–4 are also sensitive to changes in deceleration rates, but this less so for Models 5 and 6. Similar conclusions can be made for changes in road gradient; all models, with the exception of 6, show an increase in fuel consumption when there is an increase in gradient.

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E. Demir et al. / Transportation Research Part D 16 (2011) 347–357

Table 2 Setting of parameters in the 18 predefined scenarios. Scenario

Speed (km/h)

Load (kg)

Acceleration (km/h/s)

Road gradient (degrees)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

20–110 20–110 20–110 20–110 20–110 20–110 20–110 20–110 20–110 20–110 20–110 20–110 20–110 20–110 50 50 70 70

0% 15% 30% 15% 15% 15% 15% 15% 15% 15% 15% 15% 15% 15% 0–10% 0–30% 0–10% 0–30%

0 0 0 0.01 0.02 0.01 0.02 0 0 0 0 0.01 0.01 0.01 0 0 0 0

0 0 0 0 0 0 0 0.57 1.15 0.57 1.15 0.57 0.57 0.57 0 0 0 0

Table 3 Fuel consumption with speed of 50 km/h for scenarios 1–14. Scenario

Model 1

Model 2

Model 3

Model 4

Mode 5

Model 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14

19.79 22.08 25.08 37.80 47.62 19.40 21.74 28.09 34.09 16.08 10.07 43.81 31.79 25.41

16.52 18.24 20.34 11.58 17.04 17.44 17.80 23.94 29.64 14.35 10.46 15.24 8.20 23.21

31.90 35.53 39.88 40.33 43.37 34.89 35.53 40.94 46.34 32.32 29.11 45.73 37.12 40.30

15.44 18.14 21.74 19.62 21.52 18.77 17.79 24.27 30.41 12.00 5.87 25.76 13.48 24.90

10.35 13.15 17.39 16.42 19.98 13.68 13.15 13.78 14.37 12.52 11.92 17.21 15.64 14.34

10.65 10.65 21.28 14.49 16.81 11.30 10.65 10.65 10.65 10.65 10.65 14.49 14.49 11.30

Table 4 Fuel consumption with speed of 70 km/h for scenarios 1–14. Scenario

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14

28.64 32.23 36.96 48.21 51.26 25.93 26.06 38.23 44.24 26.22 20.22 54.22 42.21 31.94

17.06 18.86 21.09 15.98 19.68 16.41 17.36 24.63 30.40 14.52 10.18 20.37 11.44 22.29

34.63 38.61 43.38 43.60 44.51 36.73 36.81 44.02 49.42 35.40 32.19 49.00 40.39 42.14

15.95 18.40 21.63 21.33 22.04 17.88 17.63 24.54 30.67 12.26 6.13 27.47 15.20 24.01

11.35 14.42 18.06 19.98 21.03 13.44 13.38 15.11 15.76 13.73 13.07 20.93 19.02 14.08

13.30 13.20 21.28 17.00 17.69 11.67 11.76 13.20 13.20 13.20 13.20 17.00 17.00 11.67

We present the results for the remaining scenarios 15–18 in Table 6. To look at potential difference in impact according to vehicles and infrastructure characteristics, we focus on Models 2 and 4 basically because they encapsulate the features of the other models.

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E. Demir et al. / Transportation Research Part D 16 (2011) 347–357 Table 5 Fuel consumption with speed of 100 km/h for scenarios 1–14. Scenario

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14

48.78 55.16 63.45 59.92 58.73 47.06 41.94 61.17 67.17 49.16 43.15 65.92 53.91 53.06

21.72 24.04 26.91 24.54 24.54 19.97 19.71 29.86 35.69 19.29 14.55 30.10 19.30 25.98

41.14 45.85 51.50 47.29 46.86 43.34 41.78 51.25 56.66 42.64 39.43 52.70 44.08 48.75

15.92 22.51 25.86 23.67 23.55 20.76 19.70 28.65 34.78 16.38 10.24 29.80 17.53 26.89

17.89 22.72 27.75 24.87 24.22 19.45 17.68 23.81 24.85 21.63 20.60 26.06 23.67 20.38

18.70 18.70 27.31 19.79 19.47 16.81 15.62 18.70 18.70 18.70 18.70 19.79 19.79 16.81

Table 6 Fuel consumption for scenarios 15–18. Scenario

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

15 16 17 18

20.49 22.05 29.75 32.20

17.05 18.19 16.87 18.07

33.03 35.42 35.88 38.50

16.26 18.11 16.70 18.37

12.87 14.57 14.12 15.57

10.65 14.90 13.21 16.44

3.1.1. Effect of changes in vehicle type To examine the effects by vehicle type, light duty (LD), medium duty (MD) and heavy duty (HD), we assume a 0% load factor, zero acceleration and zero road gradient. Fig. 1 shows the effect of different types of vehicles on fuel consumption as estimated by Model 4. Each figure shows fuel consumption at varying speeds for the vehicles types. Model 2 yields similar results to those seen in Fig. 1. For low speed values fuel consumption is high because of inefficiencies in the usage of fuel that decrease as speed increases to a point, and then starts to increase due to aerodynamic drag. Fig. 1 also indicates that heavy vehicles consume significantly more fuel than the other types, mainly due to their weight. Looking at the effect of vehicle weight on fuel

Fig. 1. Fuel consumption for three types of vehicle under various speed levels estimated in Model 4.

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E. Demir et al. / Transportation Research Part D 16 (2011) 347–357

consumption for a medium duty vehicle, light and heavy vehicles are not considered because they exhibit similar patterns in terms of fuel consumption, with only actual consumption values being different, indicated that vehicle weight has a significant the effect on fuel consumption are similar to that seen in Fig. 1. Comparing Models 2 and 4, the latter is more sensitive to the changes in load. Optimal vehicle speed turns out to be around 55 km/h for an unloaded medium duty vehicle using Models 2 and 4.

Fig. 2. Fuel consumption with a 0.01 m/s2 acceleration as estimated by Models 2 and 4.

Fig. 3. Fuel consumption with a 0.01 m/s2 deceleration as estimated by Models 2 and 4.

E. Demir et al. / Transportation Research Part D 16 (2011) 347–357

355

Fig. 4. Effects of positive grades on fuel consumption as estimated by Model 4.

3.1.2. Effect of changes in acceleration and deceleration rates For the effects of acceleration on fuel consumption, the vehicle accelerates at 0.01 m/s2 with fixed speeds ranging from 20 km/h up to 100 km/h in increments of 10 km/h. For each initial speed, we assume that the vehicle accelerates up to 110 km/h using the specified rate. For deceleration, we consider a rate of 0.01 m/s2 with initial speeds ranging from 30 km/h to 100 km/h, again in increments of 10 km/h. For each initial speed, the vehicle is assumed to slow down to 20 km/h at the specified rate. The results are given in Fig. 2 for acceleration and in Fig. 3 for deceleration, for a medium vehicle. The speed values on the x-axis of these figures are the starting speeds. The results shown are unlike the ones presented earlier because fuel consumption does not exhibit a parabolic shape, in part because travel time decreases as speed increases. This analysis also shows that Model 2 is sensitive to acceleration at relatively low levels of speed, whereas Model 4 is not.

3.1.3. Changes in road gradient To test the significance of road gradient, two positive gradient values on the 100 km road segment as 0.57 and 1.15 degrees, and two negative values as 0.57 and 1.15 degrees are considered. We assume that a medium duty vehicle travels at an average speed. Fig. 4 shows the effect of positive grades on fuel consumption obtained with Model 4; experiments with negative grades yield similar conclusions. A positive road gradient leads to an increase in fuel consumption compared to a negative gradient. With Model 4 more sensitive to the changes in negative gradients as compared to Model 2.

3.1.4. Changes in resistance and drag Rolling resistance occurs when a round object, such as a tire, rolls on a flat surface. It is responsible for over half of energy for the vehicle motion. The power required to overcome aerodynamic drag is higher at highway speeds. Aerodynamic drag is the force on an object that resists its motion through air and about a third of the energy produced by the engine of a goods vehicle is used to overcome aerodynamic drag. The rest of the energy requirement is related to climbing. Rolling resistance ranges from 0.010 to 0.15, and aerodynamic drag ranges from 0.6 to 0.8 (Genta, 1997). We set the vehicle speed at 70 km/h and assume 15% of the empty weight of a medium duty vehicle – see Table 7 obtained using Model 4.2 The results indicate that resistance and drag both have significant effects on fuel consumption. In particular, if the rolling resistance goes down from 0.015 to 0.010, we can expect savings up to 14% in fuel consumption. Similarly, if the aerodynamic drag is reduced from 0.80 to 0.06, we can expect to achieve a saving of around 8.6%.

2

Model 2 does not allow a direct input of resistance and drag as parameters in the estimation.

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E. Demir et al. / Transportation Research Part D 16 (2011) 347–357 Table 7 Effect of changes in rolling resistance and aerodynamic drag consumption. Rolling resistance

Model 4

Aerodynamic drag

Model 4

0.010 0.011 0.012 0.013 0.014 0.015

18.40 19.02 19.63 20.24 20.86 21.47

0.60 0.65 0.70 0.75 0.80

17.57 17.99 18.40 18.82 19.23

Table 8 Comparison of the fuel consumption measured with on-road fuel consumption. On road

Vehicle weight (kg)

Average speed

Model 1

Model 2

Model 3

Model 1

Model 5

Model 6

30.3

15,000

38.8

37.73 (25%)

32.26 (6%)

51.12 (69%)

34.93 (15%)

19.18 (37%)

24.10 (21%)

43.6

50,000

64.2

76.58 (76%)

65.75 (51%)

85.61 (96%)

61.73 (42%)

33.85 (22%)

41.17 (6%)

53.0

60,000

53.7

61.42 (16%)

73.75 (39%)

96.27 (82%)

70.79 (34%)

36.44 (31%)

44.21 (17%)

3.2. Discussion Measurements of on-road fuel consumption of vehicles are typically carried out using such methods as engine and chassis dynamometer tests, tunnel studies, remote censoring and on-board instrumentation readings. Here we compare our results analysis from the simulations entailing Models 1–6 with measurements carried out by Erlandsson et al. (2008) who conducted on-road measurements of 15, 50 and 60 tonnes, heavy-goods vehicles. In these experiments, the average speeds were set to 38.8, 64.2 and 53.7 km/h for the three classes of vehicles. The tests were executed on a highway segment of 100 km, with the other parameters those used in Scenario 1. Table 8 shows the results obtained using Models 1–6 in absolute terms (L) as well as the percentage difference from on-road fuel consumption measurements. As seen there are large discrepancies between the results yielded by the models and those of the on-road measures. Model 4 seems to provide the best estimation for a vehicle with weight of around 15,000 kg. However, for heavier vehicles Model 6 yields better estimations. Models 5 and 6 underestimate emissions for this particular data set in all cases, whereas the remaining models overestimate them; Model 3’s results, for example, quite far off to the on-road measurements. 4. Conclusions The study has compared a number of models that have been developed to look at the fuel consumption and greenhouse gas emissions associated with road freight transportation. The models produce somewhat different results in simulations using broadly realistic assumptions, but overall are consistent with expectations; e.g. fuel consumption varies with size of vehicle, the gradient of the road track, and speed. When comparing the modeled results with comparable data from actual, road use data, the models vary in their performance. Acknowledgements The authors thank two anonymous referees for their constructive comments. This work was partially supported by a Pump-Priming grant from the School of Management at the University of Southampton and by the Canadian Natural Sciences and Engineering Research Council under grant 39682-10. This support is gratefully acknowledged. References Akçelik, R., 1982. Progress in Fuel Consumption Modelling for Urban Traffic Management. Australian Road Research Board Report 124, Canberra. Ardekani, S., Hauer, E., Jamei, B., 1996. Traffic impact models. In: Traffic Flow Theory. US Federal Highway Administration, Washington, DC, pp. 1–7. Barth, M., Boriboonsomsin, K., 2008. Real-world CO2 impacts of traffic congestion. Transportation Research Record 2058, 63–71. Barth, M., An, F., Younglove, T., Scora, G., Levine, C., Ross, M., Wenzel, T., 2000. Comprehensive Modal Emission Model (CMEM), Version 2.0 Users Guide. Technical Report. (accessed on 20.01.11). Barth, M., Younglove, T., Scora, G., 2005. Development of a Heavy-Duty Diesel Modal Emissions and Fuel Consumption Model. Technical Report. UC Berkeley: California Partners for Advanced Transit and Highways, San Francisco. Bauer, J., Bektasß, T., Crainic, T.G., 2010. Minimizing greenhouse gas emissions in intermodal freight transport: an application to rail service design. Journal of the Operational Research Society 61, 530–542. Bowyer, D.P., Biggs, D.C., Akçelik, R., 1985. Guide to fuel consumption analysis for urban traffic management. Australian Road Research Board Transport Research 32.

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