I am curious to find the braking distance for a car on a road.
In attempting to find this out, I found that the braking distance for a car (on a flat road) is $$ d = \frac{v^2}{2\mu g} $$ where $\mu$ is the coefficient of friction between the road and tires (CRF), $g$ is gravity, and $d$ is the distance traveled. However, this book mentioned that $\mu$ increases as velocity increases. Right now, I'm having trouble finding said coefficient of friction.
This transportation engineering site gave several examples of CRFs at various speeds on a rainy road, but I'd like to understand if they needed to empirically measure it.
(EDIT: Of course $\mu$ increases as $v$ does; there wouldn't be a table if it didn't.)
In short, my question is this: Is there a general method of calculating $\mu$, given that the car is on a 0% grade, wet, asphalt-covered road? Or must $\mu$ be measured/calculated using empirical data?
(Note: not really a homework question; if it was, I'd just guesstimate the answer based on the data from the second link. I just want to understand the data better, if possible, as opposed to just having the value.)
Answer
I think there is not one general method to calculate this just because its too complex. If there was one F1 engineers would have an easier job.
Nevertheless you can guess $\mu$'s dependence from the data, as you pointed out, if you plot it. I just did it here
http://genflux.chartle.net/embed?index=47502
and seems an exponential decay which, makes sense. As you increase the velocity your tires will lack of adherence due to less contact. So my first guess is that you can write
$$\mu = e^{-b |\vec v|} + a \quad ; \quad a > 0, \quad b>0 $$
where $a$ and $b$ will depend on the data to be fit (your tires and conditions).
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