Vehicle design is a very complex domain since it involves a lot of attributes, like: interior space, dynamic performance, active and passive safety, connectivity, etc.. The same principles apply to either electric vehicles or conventional vehicles (with internal combustion engines) design.

In a series of articles we are going to focus on the high level design of an electric vehicle drive unit and battery pack. The same calculation methods can be applied whether we design an electric vehicle from scratch or if we do a conversion from a conventional vehicle.

The current article is an introduction, the full content being:

- EV design – introduction
- EV design – energy consumption
- EV design – battery
- EV design – electric motors
- EV design – mode management
- EV design – vehicle systems and components
- EV design – simulation model
- EV design – simulation results and evaluation

### EV market analysis

The entry point in the electric vehicle design are the performance parameters. In our case we are going to focus on:

- top speed
- 0-100 kph acceleration time
- range

In order to come up with suitable parameters, we can study the current market of electric vehicles and also some statistical data. In the table below you can find a list of some electric vehicles and their main parameters.

Vehicle | Range[km] | BatteryType | Batterycapacity [kWh] | BatteryVoltage [V] | Motor MaxPower [kW] | Motor MaxTorque [Nm] | MotorType | TopSpeed [kph] | Time0-100 kph [s] |

BMW i3 | 257 | Li-ion | 42.2 | 360 | 127 | 250 | PM Sync. | 150 | 7.3 |

Mitsubishi I-miev | 160 | Li-ion | 16 | 330 | 49 | 196 | PM Sync. | 130 | 12.1 |

Kia Soul EV | 249 | Li-ion | 30 | 375 | 81.4 | 285 | PM Sync. | 145 | 11 |

Nissan Leaf | 273 | Li-ion | 40 | 350 | 110 | 320 | AC Sync. | 146 | 7.9 |

Renault Zoe | 303 | Li-ion | 41 | 400 | 80 | 225 | AC Sync. | 137 | 11.4 |

Tesla Model S 75D | 375 | Li-ion | 75 | 350 | 305 | 525 | AC Sync. | 228 | 4.2 |

*Sync. (Synchronous)

Source: bmw.co.uk, mitsubishi-cars.co.uk, kia.co.uk, media.nissan.eu, renault.co.uk, teslamotors.com

**Note**: The table data might not be up to date since vehicle manufacturers release new models with different parameters

From the vehicle models summarised in the table we can extract some trends in electric vehicle design:

- battery chemistry:
**Lithium-ion (Li-ion)** - electric motor type:
**PM or AC/Induction synchronous** - range:
**above 200 km**

Regarding electric vehicles, government studies are also a good source for daily commute distances. Depending on country, the daily average commuting can vary between 11 miles in UK up to 40 miles in US.

If, for example, we want to design an electric vehicle which can sustain a week’s commuting in the US, without any charge, its range should be around 270 miles.

### Electric vehicle conversion

In our case we are going to focus on the the **conversion** of a sports car with internal combustion engine into an **fully electric vehicle**. The model of choice will be **16MY Jaguar F-type**, with the main parameters defined in the table below:

Engine | 3-litre V6 DOHC V6, aluminium-alloy cylinder block and heads | |

Maximum torque [Nm] | 450 | |

Engine speed @ maximum torque [rpm] | 3500 | |

Maximum power [HP] | 340 | |

Engine speed @ maximum power [rpm] | 6500 | |

Transmission type | automatic, ZF8HP, RWD | |

Gear ratio | 1^{st} | 4.71 |

2^{nd} | 3.14 | |

3^{rd} | 2.11 | |

4^{th} | 1.67 | |

5^{th} | 1.29 | |

6^{th} | 1.00 | |

7^{th} | 0.84 | |

8^{th} | 0.67 | |

Final drive (i_{0}) | 3.31 | |

Tire symbol | 295/30ZR-20 | |

Vehicle mass (kerb) [kg] | 1741 | |

Aerodynamic drag, C_{d} [-] | 0.36 | |

Frontal area, A [m^{2}] | 2.42 | |

Top speed [kph] | 260 | |

Acceleration time 0-100 kph [s] | 5.3 |

From data available on-line, we can also extract the static engine torque values at full load, function of engine speed:

Engine speed points (full load) [rpm] | 1000 | 2020 | 2990 | 3500 | 5000 | 6500 |

Engine static torque points (full load) [Nm] | 306 | 385 | 439 | 450 | 450 | 367 |

The engine torque and power at full load is plotted in the image below:

The high level requirements of the electric vehicle is to have the same (or better) **dynamic performance** compared with the internal combustion engine version.

Based on the analysis of the current EV market and the performance parameters of the base vehicle (internal combustion engine), in the table below, we are going to summarise the **high level requirements of our electric vehicle conversion**.

Battery | Nominal voltage [V] | 400 |

Chemistry | Lithium-ion | |

Powertrain | Electric motor type | PM Synchronous |

Vehicle | Range [km] | 250 |

Top speed [kph] | 260 | |

Time 0-100 kph [s] | 5.3 | |

Kerb weight [kg] | 1741 |

In order to achieve the required performance, the electric vehicle will be all-wheel drive (AWD), with an drive unit on each axle. The **drive unit** will contain the power electronics (inverter), electric motor, transmission (fixed gear) with decoupling element (clutch / dog clutch) and differential.

### Traction force calculation

One key requirement of our battery electric vehicle conversion is to reach 100 kph from standstill in 5.3 seconds. From this requirement, knowing the vehicle weight, we can calculate what is the total traction force and torque. Also, we can check if the wheel (tire) friction can sustain the required traction force.

The input data in our calculation is:

- vehicle total weight (vehicle kerb weight x mass factor + driver weight):
**1908 kg** - vehicle initial speed:
**0 kph** - vehicle final speed:
**100 kph** - vehicle initial time:
**0 s** - vehicle final time:
**5.3 s** - tire radius:
**0.33565 m** - tire friction coefficient:
**1.0** - gravitational acceleration:
**9.81 m/s**^{2}

According to Newton’s second law of motion:

\[F = m \cdot a \tag{1}\]From (1) we can write the equation of the **required traction force** as:

where:

F_{t} [N] – total traction force

m_{v} [kg] – total vehicle mass

v_{f} [m/s] – final speed

v_{i} [m/s]– initial speed

t_{f} [s] – final time

t_{i} [s] – initial time

Replacing the input data into equation (2), gives the total traction force required to achieve 0-100 kph in 5.3 s:

\[F_{t} = 1908 \cdot \left ( \frac{27.78-0}{5.3-0} \right ) = 10000.8 \text{ N}\]The total required traction torque can be calculated as:

\[T_{t} = F_{t} \cdot r_{w} \tag{3}\]where:

T_{t} [N] – total traction torque

r_{w} [m] – wheel radius

Replacing the input data into equation (3), gives the total traction torque required to achieve 0-100 kph in 5.3 s:

\[T_{t} =10000.8 \cdot 0.33565 = 3356.77 \text{ Nm} \]In terms of friction, we can calculate the **available friction force** as:

where:

F_{f} [N] – friction force

G_{v} [N] – vehicle weight

g [m/s^{2}] – gravitational acceleration

μ_{f} [-] – friction coefficient (wheel-road)

Replacing the input data into equation (4), gives the available friction force:

\[F_{f} = 1908 \cdot 9.81 \cdot 1 = 18717.48 \text{ N}\]Since the available friction force is bigger than the total traction force, assuming that there is no slip between the wheels and road, the total traction force can be applied at the wheels in order to achieve the 0-100 kph acceleration time.

In the next article we are going to focus on the energy consumption of the vehicle over a standard homologation cycle. This will serve as a basis for the high level design of the battery.

## Vaishnav G

If the coefficient of friction is taken 0.2, the frictional force would sum up to be 3743.5 N. With the traction torque equal to 3356.77 N-m, you can see it is quiet close to the friction force. so there is a chance of weak grip or even slipping of tyres. Larger the coefficient of friction, better would be the hold of the vehicle to the ground.

## Krishna

Taking “coefficient of friction is 0.2”, is quite un-realistic for Tyre to road contact. Friction values of around 0.4-0.5 (wet conditions) and 0.7-0.8 (dry conditions) are reasonable.

## MM

Hello , is it correct to put friciton coefficient as 1? Is int it 0.1-0.2