# maximal acceleration of a wheel-driven vehicle

I was thinking about the maximal acceleration of a bicycle, I found a similar question.

What remains unclear is that I found two coefficients of friction, one for rolling and one for static friction.

So far I believed that I calculate the friction force like

$$F = \nu m g$$

where $$\nu$$ is the rolling resistance, but if I use the formula from the linked question I get the

$$a = \nu g = 0.004 \cdot 10\,\text{m/s}^2 = 0.04\,\text{m/s}^2$$

where $$\nu$$ is the rolling resistance between a tire and asphalt road.

Now that number seems to be rather low. This video states I have to use static resistance (0.4-0.6 can't be rolling resistance for tires). If I use the static resistance, the numbers don't match with the tire power consumption tests I found. What do I miss, how should I calculate the maximal acceleration? How do I calculate the power loss from friction? ($$P =F_\text{friction} \cdot v$$, but force of rolling or static friction?)

• thank you for the edit – H. Csaba Mar 11 '19 at 11:38

If you want to calculate the maximum acceleration, you need to use the static friction coefficient. If you apply a force greater than $$F=mg\nu_\text{static}$$, the wheels will start to slip. So this is the largest force the tyres can transmit to the ground.