Highweighs

via Wikipedia

This week I thought I'd look into something I've often wondered: Where does the different speed limit for trucks on highways come from?

My assumption has always been that it was a safety issue. Trucks have more mass, and therefore more kinetic energy,

and more momentum,

both of which are factors in collisions. However, each is directly proportional to mass. Typical car masses are around 2,000 kg, and trucks have a maximum total mass of 36,000 kg. That would suggest the speed ratio should be around 1:4.24 for energy, or 1:18 for momentum, while the actual ratio is 1:1.18.

Another thought that occurred to me was stopping distance – Intuitively, I'd expect a truck to take a longer distance to stop, but the more I thought about it, the more I questioned that expectation. The basic model of friction physicists learn is that the force is given by the coefficient of friction between the two surfaces, μ, multiplied by the forces pushing the surfaces together. For a vehicle on a flat road, that's just the force of gravity, mg. We can get the acceleration with Newton's 2nd Law:

According to this, the masses cancel, and the acceleration is μg no matter what you drive.

The answer is that the simple friction model isn't good enough: Tire friction does not increase linearly, but tapers off according to an exponential factor:

We can plug in some numbers to see how well this matches the speed difference. After a bit of algebra, the ratio of stopping distances is

Using ⍺ = 0.7 gives a ratio around 0.6, and ⍺ = 0.9 gives 1.05, putting the stopping distance nearly equal!

The real answer though, is actually neither of those – When finding the image at the top of the post, I noticed the title was "TN environmental speed limit". The actual reason is that trucks (and cars) get better mileage at lower speeds, and since diesel exhaust includes worse pollutants that normal gas, limiting fuel use in trucks is a priority.