a) Theoretical determination of Fuel Consumption
On the basis of initial drive data it is possible to make relatively precise estimations of the fuel consumption mathematically, in the early development stages of a vehicle. In addition, parametric variations can be undertaken without additional expense.
In order to undertake this however, an engine map which contains the lines of a constant specific fuel consumption be (see figure) is a prerequisite.
From the force demand at the speed which is to be analyzed (constant velocity in the plane):
Eq. 3-19
considering the torque loss Mloss, the engine torque demand Mengdemed can be determined according to the relation:
Eq. 3-20
The engine mean effective pressure pae is then given by:
Eq. 3-21
Eq. 3-22
The engine speed can be calculated from the driving speed as follows:
Eq. 3-23
The corresponding operating point in the engine map can now be clearly determined. For this operating point, the specific fuel consumption can be read from the map. Using the power demand and the fuel density the temporal fuel consumption can be determined:
conversion factor Eq. 3-24
The track fuel consumption results from the relation:
conversion factor Eq. 3-25
If the fuel consumption for a driving cycle is to be calculated, apart from the steady-state phases, the transient driving conditions have also to be taken into account. Similar to the determination of the energy demand, the speed characteristic is divided into small time intervals. In these intervals, the acceleration can be assumed as constant and the actual driving speed can be averaged. The traction force demand in the respective intervals for a drive in the plane is then given by:
Eq. 3-26
When considering the losses in the drive train, we obtain the effective fuel consumption from the engine map. The amount of fuel consumed in each interval can be determined by the time interval Δti:
Eq. 3-27
The track fuel consumption in order to drive through such a cycle results from the sum of the individual fuel consumption values:
Eq. 3-28
Since the time intervals selected have to be as small as possible, a fuel consumption calculation of this sort becomes meaningful only when supported by a computer. Sufficiently precise results can then be achieved. One of the limitations encountered here results from the fact that only engine maps for stationary operating points are included, hence leading to the results for transient driving conditions being only partly (although with a good approximation) applicable.