0.0.1 Specifications
- We want to simulate accleration 0 - 60 kph (16.67 m/s)
- plot a graph of speed vs time and see if the time is actually 6.7s
- we use the data from the data sheet
0.0.2 Assumptions
- No incline
- Equilibrium at maximum speed
- Full electric vehicle → torque is constant
- Rolling resistance is constant and take maximum value for worst case scenario
- Tyre Class C1 w/ Fuel Efficiency class A [2]
- Negligble tyre deformation thoughout acceleration
- Road is dry
- Assume gear ratio is the same (not true but still)
0.0.3 Parameters
- Mass: $m = 2145 kg$ [1]
- Maximum torque $\mathcal{T}= 545 Nm$ [1] *3
- Maximum speed 112 mph $\dot{x}^{max}= 50.0685 m/s$ [1]
- Drag Factor $k_d=0.8233\frac{kg}{m}$
- Initial speed $\dot{x}_0=0 m/s$
- Tire diameter: $d=0.4953 m$ [2] *6
- $C_{rr}=0.0065$ [3], *4 *5
- Gear box ratio: $i=0.1$ [4] *8
0.1.0 Equations
\(\ddot{x}=\frac{2\mathcal{T}}{d\cdot m\cdot i}-C_{rr}\cdot g-\frac{k_d \cdot\dot{x}^2}{m} \quad (1)\)
0.1.1 Simulation Model
0.2.0 Results
- We get around 40 m/s at 6.7s
0.3.0 Issues
- We failed to account for the driving slip which would have lowered the acceleration
- Gear box ratio could also hv degradation
0.4.0 Rework
Using the friction model of 1.0, we derived a new set of ODEs and formed the simulation as shown.
The results were much closer.
Sources
-
Audi, Sport Q4 45 e-tron Datasheet
-
Audi, Sport Q4 45 e-tron Website
-
EU, Annex 1, Part A. Category C1 tyres (passenger car) of Regulation (EU) 2020/740 of the European Parliament and of the Council of 25 May 2020 on the labelling of tyres with respect to fuel efficiency and other parameters
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Wikipedia * Needs to be vetted