**2.2. Go-kart used power analysis based on Rotax max challenge series**

The MicroMax Rotax Max Challenge category according to **Table 1** is a category for children aged 8–10. In this category of go-karts, maximum engine power is 6 kW with engine power/ rpm curve shown in **Figure 4**.

The chassis of this category is the so-called "small frame" with a wheelbase of 950 mm, with brakes only on the rear axle. Maximum race distance for this category is 14 km, which translates to a maximum race time of 12 min and 54.576 s.

The data for the analysis were collected during official races and trainings on the following tracks:


Two lap times from the session on August 12, 2015, on Speedworld track with the configuration of 1120 m shown in **Figure 5** were selected:

Based on **Figure 6**, the average levels of power used for laps were calculated:

The maximum power was determined for both laps at the same level, that is, 6 kW.

**Figure 5.** Race data from MicroMax category during Speedworld session on August 12, 2015, and track configuration

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Further laps were selected from the following sessions on the following tracks:

**Figure 6.** The power usage diagram for lap (i) and (ii) on Speedworld track, session on August 12, 2015.

• Gokart Stadion session on June 21, 2015, data from two laps:

**i.** 5.58 (kW)

Off Camber Data tool.

**ii.** 5.64 (kW)

**iii.** 41,232 (s)—the fastest lap

**iv.** 41,760 (s)—the slowest lap


The power usage diagram for lap (i) and (ii) is shown in **Figure 6**.

**Figure 4.** Rotax engine power/rpm curve for different categories [10].

**Figure 5.** Race data from MicroMax category during Speedworld session on August 12, 2015, and track configuration Off Camber Data tool.

Based on **Figure 6**, the average levels of power used for laps were calculated:

**i.** 5.58 (kW)

**2.2. Go-kart used power analysis based on Rotax max challenge series**

rpm curve shown in **Figure 4**.

tracks:

110 Green Electronics

• Speedworld

• Go-kart Stadion • Pannónia Ring

lates to a maximum race time of 12 min and 54.576 s.

tion of 1120 m shown in **Figure 5** were selected:

**Figure 4.** Rotax engine power/rpm curve for different categories [10].

The power usage diagram for lap (i) and (ii) is shown in **Figure 6**.

**i.** 49,940 (s)—the fastest one **ii.** 50,577 (s)—the slowest one

The MicroMax Rotax Max Challenge category according to **Table 1** is a category for children aged 8–10. In this category of go-karts, maximum engine power is 6 kW with engine power/

The chassis of this category is the so-called "small frame" with a wheelbase of 950 mm, with brakes only on the rear axle. Maximum race distance for this category is 14 km, which trans-

The data for the analysis were collected during official races and trainings on the following

Two lap times from the session on August 12, 2015, on Speedworld track with the configura-

**ii.** 5.64 (kW)

The maximum power was determined for both laps at the same level, that is, 6 kW.

Further laps were selected from the following sessions on the following tracks:


**Figure 6.** The power usage diagram for lap (i) and (ii) on Speedworld track, session on August 12, 2015.


The average power value used during laps and the maximum power achieved in the MicroMax category were summarized in **Table 2**.

**Lap (i) Lap (ii) Lap (iii) Lap (iv) Lap (v) Lap (vi)**

July 12, 2015

9.15 9.12 8.91 8.95 9.29 9.21

11 11 11 11 11 11

13.70 13.41 13.64 14.00 13.45 13.75

17 17 17 17 16.99 17

19, 2015

17.63 18.44 17.22 16.71 — —

22 21.99 22 21.99 — —

19.05 18.80 20.16 19.59 20.79 20.16

24.99 25 25 25 24.99 25

**Table 3.** Summarized sessions and laps information with average power used and maximum power on the lap for rest

of Rotax max challenge categories, that is, MiniMax, JuniorMax, SeniorMax and DD2 [17].

Pannónia Ring May

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1, 2016

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29, 2016

Session Speedworld August 14, 2015 Motodrom Vysoke Myto

Session Speedworld May 21, 2015 Pannónia Ring September

Lap time (s) 46,520 47,224 49,315 50,165 49,252 50,027 Fastest/slowest lap Fastest Slowest Fastest Slowest Fastest Slowest

Session Pannónia Ring May 29, 2016 Tor Radom May 22, 2016 Tor Bydgoszcz May

Lap time (s) 47,152 48,356 32,480 33.34 46,331 46,821 Fastest/slowest lap Fastest Slowest Fastest Slowest Fastest Slowest

Lap time (s) 44,086 45,597 45,786 46,532 — — Fastest/slowest lap Fastest Slowest Fastest Slowest — —

Session Speedworld August 29, 2015 7 Laghi Kart May 16, 2016 Pannónia Ring May

Lap time (s) 56,173 57,048 49,568 51,918 45,455 46,527 Fastest/slowest lap Fastest Slowest Fastest Slowest Fastest Slowest

**MiniMax**

(kW)

(kW)

(kW)

(kW)

(kW)

(kW)

**DD2**

(kW)

(kW)

**SeniorMax**

**JuniorMax**

Average power used

Average power used

Average power used

Average power used

Maximum power

Maximum power

Maximum power

Maximum power

Maximum power of electric motors for MicroMax category was defined on the level of Pmax = 6 kW. Average power value used during the lap with the highest power requirements POmax = 5.83 kW.

Knowing that the maximum race time is tRmax = 12: 54,576, the work done by the MicroMax go-kart drive systems according to Eq. (2) WRmax:

$$\mathbf{W}\_{\text{Rmax}} = \mathbf{P}\_{\text{Omax}} \times \mathbf{t}\_{\text{Wmax}} = 9.29 \times 0.239651 = 2.23 \text{ kWh}$$

Similar analyses and calculations were conducted for each Rotax Max Challenge category, and the results are presented in condensed form.

Knowing the value of average power used during a lap for each of the categories POmax and knowing maximum race time tRmax based on **Figure 3**, and Section 2.1. Analysis of race durations in the Rotax Max Challenge Poland Championships in 2016, we calculated the work done by a running go-kart during the race with maximum energy consumption WRmax. The results are presented in **Table 4**.

#### **2.3. eKart: initial definition of main parameters**

Based on the analysis of go-kart power usage presented in Section 2.2, the average power calculated based on Eq. (3) is assumed to be the minimum power that an eKart should generate. Maximum power for each category of eKarts is the maximum power achieved in a given age category for safety reasons. The engine power ranges for each eKart age category are shown in **Figure 7**.

Knowing the work done by a running go-kart during the race with maximum energy consumption for every Rotax Max Challenge category in **Table 4**, we can assume to conserve the same energy for each of the age categories of eKarts.

However, in order to calculate the practical value of energy stored in batteries in accordance with Eq. (1), it is assumed that n should be 120%.


**Table 2.** Average power used and maximum power of MicroMax category in six different laps of three sessions.


• Pannónia Ring session on September 20, 2015, data from two laps:

WRmax = POmax × tWmax = 9.29 × 0.239651 = 2.23 kWh

The average power value used during laps and the maximum power achieved in the MicroMax

Maximum power of electric motors for MicroMax category was defined on the level of Pmax = 6 kW. Average power value used during the lap with the highest power requirements

Knowing that the maximum race time is tRmax = 12: 54,576, the work done by the MicroMax

Similar analyses and calculations were conducted for each Rotax Max Challenge category,

Knowing the value of average power used during a lap for each of the categories POmax and knowing maximum race time tRmax based on **Figure 3**, and Section 2.1. Analysis of race durations in the Rotax Max Challenge Poland Championships in 2016, we calculated the work done by a running go-kart during the race with maximum energy consumption WRmax. The

Based on the analysis of go-kart power usage presented in Section 2.2, the average power calculated based on Eq. (3) is assumed to be the minimum power that an eKart should generate. Maximum power for each category of eKarts is the maximum power achieved in a given age category for safety reasons. The engine power ranges for each eKart age category are shown

Knowing the work done by a running go-kart during the race with maximum energy consumption for every Rotax Max Challenge category in **Table 4**, we can assume to conserve the

However, in order to calculate the practical value of energy stored in batteries in accordance

Average power used (kW) 5.58 5.64 5.81 5.83 5.64 5.78 Maximum power (kW) 6 6 6 6 6 6

**Table 2.** Average power used and maximum power of MicroMax category in six different laps of three sessions.

**Lap (i) Lap (ii) Lap (iii) Lap (iv) Lap (v) Lap (vi)**

**v.** 50,626 (s)—the fastest lap **vi.** 52,015 (s)—the slowest lap

POmax = 5.83 kW.

112 Green Electronics

in **Figure 7**.

category were summarized in **Table 2**.

go-kart drive systems according to Eq. (2) WRmax:

and the results are presented in condensed form.

**2.3. eKart: initial definition of main parameters**

same energy for each of the age categories of eKarts.

with Eq. (1), it is assumed that n should be 120%.

results are presented in **Table 4**.

**Table 3.** Summarized sessions and laps information with average power used and maximum power on the lap for rest of Rotax max challenge categories, that is, MiniMax, JuniorMax, SeniorMax and DD2 [17].


**Table 4.** Work done by running go-kart during the race with maximum energy consumption for every Rotax Max Challenge category.

**Figure 7.** Power range of eKart drive system for different age categories.

$$\mathbf{E}\_A = \mathbf{W}\_{\text{max}} \times 120\% \tag{4}$$

This assumption was stated because of the necessity to provide energy for additional formation laps and potentially higher consumption during rain races. On average, a rain race is longer than a race in normal conditions by 18% (**Figure 3**).

It was assumed that eKarts will be equipped with Li-ion batteries due to their best energy-toweight ratio [11]. Degradation of Li-ion depends on the conditions, but it is up to 10% less capacity already at 300 charging-discharging cycles and 20% at about 1000 cycles [12, 13]. Therefore, it was proposed that the batteries should have 20% larger capacity than the expected EA energy needed for an eKart race. Such a solution in addition will provide optimum, fast loading and braking capability from the first lap. The above can be described as:

$$Q\_{\oplus} = 120 \,\%\,\text{\*}\,\text{E}\_A \tag{5}$$

Therefore, we can rewrite **Table 4** for the eKart categories as following in **Table 5**.

train system and weight of the fuel for the race shown in **Table 1**.

technology nowadays and in 3-year time for given age categories.

**Table 5.** Capacity of batteries for different age categories of eKarts.

Average power used by eKart

Work expected to be done during the race, WRmax (kWh)

Energy stored in batteries, E<sup>B</sup>

on lap, POmax (kW)

(kWh)

An additional guideline for the selection of detailed electrical system parameters was the current weight of the go-kart in each age category. It was assumed that the weight of the eKart drive train system and the batteries should not exceed the weight of the current kart drive

**Figure 8.** Maximum weight of drive train unit of eKart with batteries compared to potential mass of the batteries in Li-ion

**MicroMax MiniMax JuniorMax SeniorMax DD2**

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5.83 9.29 14.00 18.44 20.79

1.25 2.23 3.62 5.42 5.79

1.50 2.68 4.34 6.50 6.95

Expected race time, tRmax (min:s) 12:54,576 14:22,744 15:31,520 17:39,315 16:41,609

Expected race time, tRmax (h) 0.21516 0.23965 0.25876 0.2942 0.2783

Capacity of batteries, QB (kWh) 1.75 3.12 5.07 7.59 8.11

where QB—battery capacity (kWh).


**Table 5.** Capacity of batteries for different age categories of eKarts.

E*<sup>A</sup>* = *WR*max × 120% (4)

**8–10 10–13 13–16 15+ 15+ gears**

POmax (kW) 5.83 9.29 14.00 18.44 20.79

Rmax (mins:s) 12:54,576 14:22,744 15:31,520 17:39,315 16:41,609

**Table 4.** Work done by running go-kart during the race with maximum energy consumption for every Rotax Max

Rmax (h) 0.21516 0.23965 0.25876 0.2942 0.2783 WRmax (kWh) 1.25 2.23 3.62 5.42 5.79

t

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t

Challenge category.

This assumption was stated because of the necessity to provide energy for additional formation laps and potentially higher consumption during rain races. On average, a rain race is

It was assumed that eKarts will be equipped with Li-ion batteries due to their best energy-toweight ratio [11]. Degradation of Li-ion depends on the conditions, but it is up to 10% less capacity already at 300 charging-discharging cycles and 20% at about 1000 cycles [12, 13]. Therefore, it was proposed that the batteries should have 20% larger capacity than the expected EA energy needed for an eKart race. Such a solution in addition will provide optimum, fast loading and

*QB* = 120 % × E*<sup>A</sup>* (5)

longer than a race in normal conditions by 18% (**Figure 3**).

**Figure 7.** Power range of eKart drive system for different age categories.

braking capability from the first lap. The above can be described as:

where QB—battery capacity (kWh).

**Figure 8.** Maximum weight of drive train unit of eKart with batteries compared to potential mass of the batteries in Li-ion technology nowadays and in 3-year time for given age categories.

Therefore, we can rewrite **Table 4** for the eKart categories as following in **Table 5**.

An additional guideline for the selection of detailed electrical system parameters was the current weight of the go-kart in each age category. It was assumed that the weight of the eKart drive train system and the batteries should not exceed the weight of the current kart drive train system and weight of the fuel for the race shown in **Table 1**.

Based on battery capacity QB (6), we analyzed the options for designing eKarts for each category, within the limits of the maximum mass of the drivetrain system and the battery. We took into consideration the energy density of today's most efficient Li-ion battery technology (250 Wh/kg) and the technology expected in 3 years time (350 Wh/kg). The analysis is shown in **Figure 8**.
