For fun, I'm trying to play with really simple simulation of a Tesla Model 3. Modeling its acceleration and such. But I've hit a roadblock early on despite validating my math several times.

What I want to do is given the motor's (current) torque, wheel radius, mass, and a timestep $dt$, figure out how much the speed of the car should change.

When I look up values for this car, here's what I get:

• Peak torque: $\tau = 639\ \text{N}\cdot\text{m}$
• Mass: $m = 1800\ \text{kg}$
• Wheel radius: $R = 0.2413\ \text{m}$

Here's how I'm calculating acceleration:

$$ F = \frac{\tau}{R} \\ a = F/m \\ a = \frac{\tau}{Rm} $$

So in code, here's how I'm updating the car's speed. dt equals the time, in seconds, since the last frame rendered, so it's usually around 0.016 (60 fps):

const force = torque / car.wheelRadius
speed += (force / car.weight) * dt

However, after a few seconds, the speed of my simulated car is only $\text{2-3 m/s}$. For the actual car, it would be closer to $\text{30 m/s}$. I thought that was odd, so I plugged some real-world approximations of how the car works into WolframAlpha to figure out how much torque it "should" have, only to see that it said $\text{3800 N} \cdot \text{m}$! That's way more than the car's specs say.

What am I doing wrong here? Why is my simulated car so slow, and why does the math tell me the Model 3 should have 5x more torque than it claims to have?

For fun, I'm trying to play with really simple simulation of a Tesla Model 3. Modeling its acceleration and such. But I've hit a roadblock early on despite validating my math several times.

What I want to do is find the car's velocity at a time $t$ given the motor's torque, wheel radius, and mass.

When I look up values for this car, here's what I get:

• Peak torque: $\tau = 639\ \text{N}\cdot\text{m}$
• Mass: $m = 1800\ \text{kg}$
• Wheel radius: $R = 0.2413\ \text{m}$

Here's how I'm calculating acceleration:

$$ F = \frac{\tau}{R} \\ a = F/m \\ a = \frac{\tau}{Rm} $$

Considering that I'm modeling torque as constant, acceleration will also be constant, which means:

$$ v(t) = at = \frac{\tau}{Rm}t $$

However, when I plug in $t = 3.2$ (the Model 3 accelerates from 0-60mph in 3.2 seconds), the velocity is only $\text{4.7 m/s}$. It should be closer to $\text{30 m/s}$. Where is this discrepancy coming from? Are the official numbers I found simply wrong?