**2. Model of go-kart energy usage**

In order to determine energy requirements, the model assumes that the energy stored in batteries EB must provide the possibility to finish a maximum duration race (based on the Rotax Max Challenge 2016 Cup) with the go-kart using maximum power, which was experimentally derived on different racetracks in Poland and Europe:

$$\mathbf{E}\_{\rm g} = \mathbf{W}\_{\rm gmax} \times \mathbf{n} \tag{1}$$

The model assumes that the energy used on one lap PO is equal to the sum of instantaneous

where PO—average power value used during lap (kW), Pch—instantaneous power (kW), NO—

In the presented approach, it was assumed that Pch—instantaneous power is calculated based on instantaneous engine rpm and the engine power/rpm specification curve presented in **Figure 4**. Due to the permanent coupling of the engine with the drive axle, in the course of the analysis, braking periods during the lap were identified and excluded from the calculation of average power. Based on observations and analysis, it was assumed that braking is a decrease in engine speed of at least 300 rpm with at least three measuring periods, that is, over 0.3 s and

is associated with a significant decrease in vehicle speed, that is, at least 2 km in 0.1 s.

**2.1. Analysis of race durations in the Rotax max challenge Poland championships in** 

rounds of the Rotax Max Challenge Poland Championships in 2016.

**Figure 3.** Race durations in Rotax Max Challenge Poland Championships 2016 for given categories.

Championships in 2016 are shown separately.

Following Eq. (2), it was necessary to analyze the duration of races tRmax to calculate the work performed by the power train. This analysis is based on the duration of go-kart races in the 12

The analysis allowed us to determine maximum race times for the drivers who had completed full races in each of the age categories. **Figure 3** shows the time intervals in which the drivers finished the races of the given round of the Rotax Max Challenge Poland Championships in 2016. The data for wet races of the first round of the Rotax Max Challenge Poland

*NO P* \_\_\_\_\_\_\_*ch NO*

Vehicle Dynamics and Green Electronic Differential for eKart

http://dx.doi.org/10.5772/intechopen.72892

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power calculations in tenths of a second of the lap.

*PO* <sup>=</sup> <sup>∑</sup>*<sup>i</sup>*=0

**2016**

number of measurements (measurement in 0.1-s intervals).

where EB—energy stored in batteries (kWh), WRmax—work done by running go-kart during the race with maximum energy consumption (kWh), n—coefficient of securing sufficient level of energy (%).

In simplified terms, it was assumed that WRmax is the work done by the combustion engine of a go-kart of average power POmax throughout the maximum duration of the race tRmax.

$$\mathcal{W}\_{\text{Rmax}} = \mathcal{P}\_{\text{Omax}} \times t\_{\text{Rmax}} \tag{2}$$

where tRmax—the maximum duration of the race based on an analysis of the Rotax Max Challenge 2016 Polish Championships (s), POmax—average power used by go-kart during a lap with the highest power usage (kW).

POmax was obtained by selecting the highest value from the calculated average power POs, for six different cases of go-kart racing in a given age category. We chose the shortest and longest run times on three racetracks with different characteristics.

The model assumes that the energy used on one lap PO is equal to the sum of instantaneous power calculations in tenths of a second of the lap.

$$P\_O = \frac{\sum\_{i=0}^{M\_b} P\_{ab}}{N\_0} \tag{3}$$

where PO—average power value used during lap (kW), Pch—instantaneous power (kW), NO number of measurements (measurement in 0.1-s intervals).

In the presented approach, it was assumed that Pch—instantaneous power is calculated based on instantaneous engine rpm and the engine power/rpm specification curve presented in **Figure 4**. Due to the permanent coupling of the engine with the drive axle, in the course of the analysis, braking periods during the lap were identified and excluded from the calculation of average power. Based on observations and analysis, it was assumed that braking is a decrease in engine speed of at least 300 rpm with at least three measuring periods, that is, over 0.3 s and is associated with a significant decrease in vehicle speed, that is, at least 2 km in 0.1 s.
