By the same logic, all gas cars should be taxed on a sliding scale, where the more fuel-efficient cars are taxed at a higher rate. It's important to society that we incentivise people to drive the most polluting and climate-destroying vehicles.
Of course fuel-efficient cars will still have similar impacts on road congestion and parking. So the real question is: what percentage of the fuel tax goes to paying for road damage, and what fraction goes to compensation for other externalized costs: urban congestion, parking, smog, noise, collision risk, pedestrian stress levels, etc?
There's also radar reflection, "Observe that the received power drops with the fourth power of the range, so radar systems must cope with very large dynamic ranges in the receive signal processing." - https://www.eetimes.com/radar-basics-part-1/
I would also call it a classic as I learned it from this scene in Robert Heinlein's book "Rolling Stones": "The result was eight shiny right-angled corners facing among them in all possible directions —a radar reflector. ... The final result was to step up the effectiveness of radar from an inverse fourth-power law to an inverse square law — in theory, at least. In practice it would be somewhat less than perfectly efficient ...", https://archive.org/details/rollingstones0000robe_q7v9/page/...
A quick search on Google Scholar finds there's a fourth-power law for shock waves:
"A fourth-power law relating the stress jump through a steady structured shock wave and the maximum strain rate within the shock wave has received recognition as a unifying relation over a sensibly wide range of materials and shock compression amplitudes." - https://pubs.aip.org/aip/jap/article-abstract/107/1/013506/2...
"Observations on the fourth-power scaling of high-pressure shock waves in solids" at https://pubs.aip.org/aip/jap/article-abstract/130/24/245901/...
and one with irradiance, though at the forth-power of the cosine:
"The cosine-fourth-power law states that the irradiance at any point in the image formed by a photographic lens, in the absence of vignetting, is equal to E_0 cos^4 β" - https://nvlpubs.nist.gov/nistpubs/jres/39/jresv39n3p213_A1b....
I also found the following at https://pubs.aip.org/aip/jap/article-abstract/75/6/3075/4001... :
"The third‐order nonlinear optical susceptibility χ(3) of this glass was found to be proportional to the fourth power of the radius of the colloid particles or the fourth power of the absorption coefficient at the peak of a plasmon band when the total volume of the colloid particles was constant."
https://sino-inst.com/pipe-flow-vs-pressure-relationship-cal...
This came to my attention when I was teaching Physics 102 at Cornell which was an auto tutorial course for pre-meds that had an unusual focus on fluid mechanics for an intro physics course.
(That would be the theory at least. How well such a proposal would survive the lobbying onslaught from pro-combustion groups is another question...)
could you try compassion for your fellow humans instead?
EVs are charged at home, so it is hard to tax per refill. Certainly within EVs there ought to be differences based on weight and wear on the roads. However, they are bypassing paying for their shared good of common roadways. With the migration away from fossil fuels, we will have to find a new way to pay for road repairs
Electric cars still use roads, which still need to be maintained. There's no "extrapolation of logic" required, because the tax on the most fuel efficient cars already dwarfs that which would be paid by electric cars.
But now that EVs are a viable alternative the gas tax should still exist to offset the externalities involved.