# A Comparison of the Fuel Consumption and Truck Models in Different Production Scenarios
## 2 Materials and Methods
### Production Scheduling
#### 2.6.2. Haulage Profile  
Cycles Times  
Following equipment selection, performance was estimated using rimpull curves and retardation curves. These curves are used when the trucks are moving uphill and downhill, respectively, and are especially important to estimate the speed of the truck on a specific route considering parameters such as the Gross Vehicle Weight (GVW) and the Total Resistance (TR), which are given by:  
\[\text{GVW}=\text{Empty truck weight}+\text{Payload} \tag{1}\]  
\[\text{TR}=\text{Grade Resistance }(\text{GR})+\text{Rolling Resistance }(\text{RR}) \tag{2}\]  
where GR is the haul road slope; RR is the force resisting the movement and depends on the tire characteristics and the haul road surface. These parameters allow for determining the traction force (RF), which is the force available between the tire and the ground to propel the machine, according to [PERSON] et al. (2015), and is given by:  
\[\text{RF}=\text{GVW }\times\text{TR} \tag{3}\]  
When a truck is moving at a constant speed, the rimpull force and velocity can be calculated according to the rimpull-speed-gradeability curve extracted from the manufacturer's catalog. This is because the engine power is given by the following equation:  
\[\text{Engine Power}=\text{Thrust Force}\times\text{ Speed} \tag{4}\]  
A more detailed description of how the information was extracted from the rimpull curves can be found in each manufacturer's catalog. Figure 5a shows the information in terms of rimpull and speeds for each selected truck, where logically the larger trucks have greater load capacity, thrust, and higher maximum speeds. One limitation is that all trucks will reach a maximum speed of 50 km/h ([PERSON], 2017). Fuel consumption is strongly impacted by factors such as tire usage, age, vehicle maintenance, idling times, engine operating parameters, and transmission shift patterns. In addition, external factors related to weather such as temperature, humidity, wind effects, traffic, and driver behavior are also important ([PERSON], 2017; [PERSON], 2017). Fuel consumption in trucks can be calculated using the following equation ([PERSON], 2017):  
\[\text{FC}=\frac{\text{SFC}}{\text{FD}}\times(\text{LF}\times\text{P}) \tag{5}\]  
where SFC is the specific fuel consumption of the engine at maximum power (0.213-0.268 kg/(kg/kW\(\times\)h)), and FD is the fuel density (0.85 kg/L for diesel). Additionally, the following simplified equation can be used ([PERSON], 2017):  
\[FC=0.3\times(LF\times P) \tag{6}\] \begin{table}
\begin{tabular}{c|c c c c c c} \hline \hline
**Ramp Width** **(m)** & **Truck Model** & **Wheel Loader** & **Width** & **Empty Truck (m)** & **Gross Weight (kg)** & **Payload Vehicle (m\({}^{3}\))** & **Payload (tons)** \\ \hline
15 & 770G & 992 & 4.78 & 33,224 & 71,214 & 17.20 & 38 \\
25 & 777G & 994 & 6.10 & 70,753 & 163,360 & 42.00 & 93 \\
35 & 789D & 998 & 7.65 & 141,214 & 324,319 & 108.00 & 183 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mining truck and wheel specifications. where LF is the engine load factor and is defined as the ratio of the average payload to the maximum load in an operating cycle. At continuous operation using the recommended truck weight, the load factor is 30-40%. P is the truck power (kW). To achieve the best performance of the truck operation, P is determined by:  
\[P=\frac{1}{3.6}\times(RF\times V_{max}) \tag{7}\]  
where RF is the product of the rimpull (R) and the gravity acceleration (g). Vmax is the maximum velocity obtained. Figure 5b shows the fuel consumption in two situations: when the truck moves uphill, where fuel consumption is higher because the engine overcomes the gravity force, and when the truck moves downhill, where fuel consumption is minimal since the gravity force acts in the same direction. In addition, this graph shows that fuel consumption in larger trucks is exponentially higher compared to smaller trucks. In general, fuel consumption varies as the truck accelerates and then becomes constant as it increases speed.