1. Introduction

2. Model and Assessment Methodology

2.1. Mission Load Profile: Route Analysis

The route is analyzed cosidering the overall length and the distance between stops. A trapezoidal profile is chosen to undertake transients and describe the speed variation between two consecutive simulation steps. The front part of the profile consists of a linear rise of the speed (acceleration) up to a determined value. The steady-state condition lasts for a duration compliant with the travel mission (distance between two consecutive stops of the coach). Then, the trail front represents the deceleration, where the speed linearly decreases to zero when the vehicle needs to stop.

Figure 2. Simplified transient profile: route analysis method.

Figure 2. Simplified transient profile: route analysis method.

A literature analysis about coaches suggests reasonable values for the acceleration in the corresponding velocity range [24] – summarized in Table 2. The acceleration is assumed 0.9 m/s² from 0 to 16.6 m/s (approximately 60 km/h). Above this threshold, the acceleration decreases up to 0.4 m/s² until the maximum speed 27.8 m/s is reached corresponding to 100 km/h. In the deceleration operations, the torque on the driving wheel is assumed to be null and the acceleration equal to - 0.9 m/s². This means that the deceleration is solely due to the brakes, thus neglecting the engine’s pumping operations.

2.2. Mission Load Profile: Drive Features

The coach power train and driveline are modeled according to the scheme in Figure 3, where the engine drives the rear wheels through the mechanical shaft. Moreover, the coach uses an electric generator for the ancillary services. For the sake of this work, the electric generator is assumed to be directly connected with the engine, adjoining an additional load to it. The model and the powertrain assumed for this study also require to consider speed range for each gear (Table 2).

Figure 3. Schematization of the powertrain and driveline of the coach.

Figure 3. Schematization of the powertrain and driveline of the coach.

2.3. Dynamic Coach Model: Torque-Velocity Correlation

The simplified dynamic modelling of the coach consists of the analysis of all forces acting on it during the whole mission. Despite its simplicity, this approach is suitable for predicting fuel consumption by determining the resultant force on the coach as a function of the route slope ($\alpha$). Moreover, the advantage of this methods stands in a small number of input parameters. Then, the model allows to simlate the flexibly of operation in routes featured by frequent start and stops and considerable slopes, whose effect is to increase the total resistance and then the fuel consumption.

In detail, the forces analysed are:

• the traction between wheels and the ground (F_m), responsible for the rolling friction and the forces parallel to the direction of the motion given by the velocity vector (v), with a direction $\alpha$(representing the route slope)
• the gravity load (P)
• the inertial load due to the acceleration of the coach. (F_i)
• the aerodynamic friction (D)
• the normal reaction force (N).

Equation (1) reports the vectorial equation of the particle model of the coach, where Fi, D and N are detailed in Equations (2), (3) and (4) respectively. The force diagram is shown in Figure 4.

$$\underset{\_}{F_m} +\underset{\_}{D}+\underset{\_}{F_i} +\underset{\_}{N}+\underset{\_}{P} =\underset{\_}{0}$$

(1)

$$\underset{\_}{F_i}=-m\underset{\_}{a}$$

(2)

$$\underset{\_}{D}=-{\displaystyle \frac{1}{2}}\varrho v^2{c}_{D}A{\displaystyle \frac{\underset{\_}{v}}{\left|\underset{\_}{v}\right|}}$$

(3)

$$\underset{\_}{P}=-m\underset{\_}{g}$$

(4)

Figure 4. Force diagrams: material point model (left), free body of driving wheels (center) and driven wheels (right) along a sloped path.

Figure 4. Force diagrams: material point model (left), free body of driving wheels (center) and driven wheels (right) along a sloped path.

Considering the extensive volume and mass of the coach, these forces are applied in different points of actions. Namely, the traction acts on a small area on the tires, thus being considered as a concentrated force in the corresponding point of of contact between the ground and the tire. The inertial and gravitational loads act on the whole volume of the coach, while the aerodynamic friction was distributed on its surface.

As a result, these considerations required knowing the exact position of the application point of every force to obtain the free-body diagram of the coach as well as its geometry, but the lack of such details imposed to model the coach as a material point (Figure 4, left). However, the need to assess the rolling friction on the wheels in the material point model required considering the free body diagram of the coach as an extended body to determine the weight distribution between the front and rear axle. As a result, the weight distribution was considered symmetric between the axles because the engine, transmission system, steering system, and tank were assumed to be located on the chassis in a way that made the weight distribution symmetric between the axles (Figure 3).

This assumption allowed imposing the equilibrium of the moments of all forces and torque that acted on the driving and the driven wheels about their corresponding rotation centers (O_r and O_f, for the rear driving wheel and front driven wheels respectively - see Figure 4, center and right). In Figure 4 center and right, each free body diagram represents the wheels placed on each axle. The forces due to the hinge in the rotation center are not reported because their moments about these points are null. The driving torque ($T_w$) contributes to the moment equilibrium of the driving wheels on the rear axle. The inertia of the wheels is neglected because it is assumed to be smaller compared to the whole mass of the coach. The equilibrium of the moments on the wheels determines $F_r$ and $F_f$ as in Equation (5) and Equation (6) respectively. The algebraic sum of the components of the forces $F_r$ and $F_f$ corresponds with the component of the force $F_m$ in the material point model - Equation (1). At the same time, the algebraic sum of the components of the vertical forces $P_r$ and $P_f$ matches with the component of the vertical force $N$ of the material point model - Equation(7) and Equation (8) in reference to Equation (1).

$$F_r={\displaystyle \frac{T_w}{r_r}}-P_r{f}_r$$

(5)

$$F_f=P_f{f}_f$$

(6)

$$P_r={\displaystyle \frac{mgcos\alpha }{2}}$$

(7)

$$P_f={\displaystyle \frac{mgcos\alpha }{2}}$$

(8)

Therefore, the combination of Equation (5) and Equation (6) with Equation (1) allows expressing the torque on the rear wheels as a dependence of the resistances. In detail, the assumption that front and rear wheels have the same radius $r$ and the same rolling friction coefficient $f_v$ leads to calculate the torque responsible of the motion of the rear wheels as in Equation (9). The friction coefficient is assumed equal to 0.015. Moreover, the same value of the radius for the rear and forward wheels implies that their angular velocity is the same (${\omega }_{\omega }$). As a result, the multiplication of the left and right hand sides of Equation (9) by the angular velocity ${\omega }_{\omega }$ allows expressing the power provided to the rear wheels (${\dot{W}}_w Eq. \left(10\right))$, as required for the motion of the coach with a linear speed equal to $v.$ In addition to the traction power, the ancillary functions add a further load, equal to a net power requirement named ${\dot{W}}_{an}$. The efficiency of power conversion is indicated by ${\eta }_{an}$. Finally, the resulting power required at the engine (${\dot{W}}_e, Eq. \left(11\right)$ in which ${\eta }_{dv}$ represents the overall efficiency of the driveline including the gearbox, the shaft and the differential) is given by the sum of the gross share of ${\dot{W}}_w$ and ${\dot{W}}_{an}$, corresponding to a total engine torque named $T_e$ - Equation (12), where the engine angular velocity ${\omega }_e$ is found as the product of the angular velocity of the wheels ${\omega }_w$ and the gear ratio of the whole driveline $z_{dv}$. The specific energy consumption of the engine is deducted from literature torque-angular velocity curves, available in the literature for the types of engine under consideration [25].

$$T_w=r\left(mg{f}_{v}cos\alpha +mgsen\alpha +{\displaystyle \frac{1}{2}}\varrho v^2{c}_{D}A+ma\right)$$

(9)

$${\dot{W}}_w=v\left(mg{f}_v\mathit{cos}\alpha +mgsen\alpha +{\displaystyle \frac{1}{2}}\varrho v^2{c}_{D}A+ma\right)$$

(10)

$${\dot{W}}_e={\displaystyle \frac{{\dot{W}}_w }{{\eta }_{dv}}}+{\displaystyle \frac{{\dot{W}}_{an} }{{\eta }_{an}}}$$

(11)

$$T_e={\displaystyle \frac{{\dot{W}}_e}{{\omega }_e}}={\displaystyle \frac{{\dot{W}}_e}{z_{dv}{\omega }_w}}$$

(12)

3. Case-Study

3.3. Design of Simulation Cases

The simulation is run under 4 cases, namely DI compression ignition engine fueled with standard diesel B0 (case 0, assumed as baseline for the validation of the proposed methodology), DI compression ignition engine fueled with synthetic diesel (case 1 synthetic diesel produced with electrolytic hydrogen and CO₂ from combustion flue gases, case 2 Fisher Tropsch synthetic diesel from wood gasification syngas coupled with CSS) and bio-diesel (case 3 FAME and case 4 HVO), and finally Spark Ignition engine fueled with hydrogen (case 5). Related GHG emissions are disaggregated in the W-t-T and T-t-W segments. Regarding Hydrogen, the T-t-W phase is carbon neutral, yet the production step brings to not negligible GHG emissions, depending on the process [31]. Considering hydrogen from an electrolytic pathway, GHG emissions are influenced from electricity carbon intensity [32]. Therefore, the W-t-T emission factor for hydrogen is referred to the electrolysis processes (average efficiency of 60%) and EU mix for grid CO₂ emissions as reported from energy bulletins related to 2022.

Table 5. Fuel properties, equivalence factors and CO₂ emissions (Type4 forecast 2025+, from JRC report [33]). Abbreviations: see the Nomenclature section.

Table 5. Fuel properties, equivalence factors and CO₂ emissions (Type4 forecast 2025+, from JRC report [33]). Abbreviations: see the Nomenclature section.

Case	Fuels	LHV MJ/kg	${\mathit{e}}_{\mathit{f},\mathit{W}\mathit{t}\mathit{T}}$ gCO2eq/MJfuel	${\mathit{e}}_{\mathit{f},\mathit{T}\mathit{t}\mathit{W}}$ gCO2eq/MJfuel	${\mathsf{\kappa }}_{\mathit{f}}$ MJWtT/MJTtW
0	Fossil Diesel B0	42.7	69.3	76.7	0.28
1	Syn. Diesel (e-fuel)	44.0	-42.4	74.1	1.57
2	Syn. Diesel (FT Wood gas+CCS)	44.0	-133.3	74.1	1.33
3	FAME (Rapeseed)	37.1	-24.6	79.6	1.13
4	HVO (Waste cooking oil)	44.4	-355.6	74.1	0.17
5	Hydrogen (electrolysis, EU electricity mix)	120.0	35.7	0	0.35

4. Results and Discussion

4.1. Travel Mission Simulation in the Base Case: Results and Validation

Figure reports the simulation profiles for torque and shaft speed required to accomplish the defined travel mission. The results revealed that the fuel consumption requested by the mission profile was 2.08 km/l for a speed of 41.5 km/h and appeared acceptable in comparison with the references that estimated a fuel consumption between 1.4 and 3.4 km/l. Furthermore, the validation indicated that the maximum power, torque, and rotating speed provided by the engine fell within the limit proposed for this engine since they were about 310 kW, 1950 Nm, and 1800 rpm, respectively. Therefore, these travel profiles obtained for the DI compression ignition engine and validated were taken as reference profiles to evaluate the energy and emission parameters for all alternative fuels.

Figure 5. Mission profile for the passenger coach: torque and shaft speed vs. travelled distance.

Figure 5. Mission profile for the passenger coach: torque and shaft speed vs. travelled distance.

4.2. Direct Fuel Consumption

Figure 6 reports the brake efficiency profiles, as well as the integral of the fuel consumption. In the top graph of Figure 6, the brake efficiency and fuel consumption are depicted for the reference DI compression ignition engine. In this case, the 100-km travel mission requires 38.6 kg of standard diesel oil, equivalent to 37.5 kg of synthetic diesel (cases 1 and 2), 44.4 kg of FAME biodiesel (case 3), and 37.1 kg of HVO biodiesel (case 4). Regarding the hydrogen spark ignition engine, the brake efficiency profiles and integral of the fuel consumption are shown in the bottom graph of Figure 6. For this application, the total fuel consumption requires 18.1 kg. The profile for the brake efficiency and subsequent instantaneous fuel consumption are referred to the engine map available at [25,26,27,28,29,30], as previously noted in Table 4. The integral of the fuel consumption obtained in the two simulation is set as the basis for the Well-to-Wheel energy and emissions assessment discussed in the next sub-section.

Figure 6. Brake efficiency profile and fuel consumption integral: DI compression ignition diesel-type ICE (top), DI spark ignition Hydrogen ICE (bottom).

Figure 6. Brake efficiency profile and fuel consumption integral: DI compression ignition diesel-type ICE (top), DI spark ignition Hydrogen ICE (bottom).

4.3. Well-to-Wheel Assessments

The methodology shown in sub-section 2.5 is applied to the cases from Table 5, based on the direct fuel consumption obtained from the 100-km travel mission simulation.

4.3.1. Primary Energy

Figure 7 compares the fuels from the point of view of the overall Well-to-Wheel primary energy consumption. In particular, the bar plot reports the primary energy consumption disaggregated into the direct consumption ascribed to the travel mission ${E_{mission}}_{100km}$ (in other words the energy related to the fuel consumption of the DI compression ignition ICE for the diesel-type fuels and DI spark ignition hydrogen ICE), and the primary energy consumption necessary upstream the fuel utilization in the coach engine. In Figure 7, the ${E_{mission}}_{100km}$ data series is identified as Tank-to-Wheel (T-t-W), likewise the nomenclature used for the emissions computation. This data series reflects the integral of fuel consumption, as already shown in Figure 6. For that all diesel-type fuels have the same indicator, while the hydrogen direct energy consumption is higher, because of the average brake efficiency exhibited in the profile at Figure 6 (bottom). To complete the Well-to-wheel energy assessment, the Well-to-Tank (W-t-T) primary energy consumption is calculated (orange data series from Figure 7) and summed to the previous data series to obtain $E_{WtW,100 km}$ – see Equation (20). The results show that the primary energy consumption in case 5 (hydrogen) exceeds by 40% case 0 (B0). In addition to the higher primary energy consumption calculated in the direct utilization, electrolytic hydrogen shows a higher κ_f ration compared to standard diesel (0.35 vs. 0.28). The least primary energy consumption is obtained in case 4 (HVO), where the W-t-T primary emission consumption is lower by -9% compared to the reference case 0. All others diesel-type alternative fuels (case 1, case 2 and case 3) exhibit higher W-t-T primary energy consumption, with mention to synthetic e-fuels (case 1, +101% with regard to reference).

Figure 7. Weel-to-Whell primary energy consumption comparison.

Figure 7. Weel-to-Whell primary energy consumption comparison.

4.3.2. GHG Emissions Assessment

Figure 8 compares the fuels from the point of view of the overall Well-to-Wheel equivalent GHG emissions. The bar plot reports the CO₂ emissions specific to the 100-km travel mission, disaggregated into W-t-T and T-t-W emissions.

Figure 8. Weel-to-Whell equivalent GHG emissions comparison.

Figure 8. Weel-to-Whell equivalent GHG emissions comparison.

As expected, the reference case 0 shows the higher impact in terms of W-t-W emissions, being both the W-t-T and the T-t-W components positive. Conversely. the alternative diesel-type fuels exhibit negative emissions in the W-t-T phase (namely the production and provision of the fuel). This happens because the alternative fuels of biologic origin (case 2, case 3 and case 4) involve the transformation of biomass, hence a zero or negative balance of carbon, and the RFNBOs (case 1) require CCS to provide CO₂ for synthetic hydrocarbon production [34]. In particular, the combination of a biological feedstock (wood) with CCS in a FT synthesis process, brings excellent results in terms of CO₂ emission reduction – see case 2. However, the best result for what concerns W-t-W GHG emissions is obtained with HVO, where the final net emission is -464 kg_CO2/_100km (vs. case 0, 240 kg_CO2/_100km). The performances obtained with hydrogen in case 5 are encouraging looking at the direct comparison with case 0, since there are no direct T-t-W CO₂ emissions and moderate W-t-T emissions due to the electric grid residual carbon footprint and electrolysis efficiency (-29% compared to case 0). The W-t-T emissions in case 5 can be eliminated whether hydrogen production is achieved with fully renewable electricity coming from a dedicated power plant. In this ultimate circumstance, hydrogen and synthetic diesel would be convenient against FAME. Nevertheless, the gap between case 4 and case 5 (HVO vs. hydrogen)

5. Conclusions

Nomenclature

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