Earlier quoted context omitted.
> Road wear scales with the fourth power of weight over an axle. Cars are not getting more axles, even SUVs, so this is a constant multiplicative factor. I would be happy with a tax that scales as the fourth power of the mass, no problem. That would be actually quite dissuasive very quickly. Though even a linear scaling would be an improvement over the current situation. > Most fuel consumption is about overcoming dr…
What do you mean by constant multiplicative factor’. Are you saying that cars are perfectly balanced between front and back axels (surely a reasonable thing to want for tyre wearing if nothing else). The point about the scaling is that it is not linear: if you double the weight over an axle, you get 16 times the wear but perhaps 1.5-2x the fuel consumption. For this reason I dispute that fuel duty effectively taxes t…
Right. An implicit assumption was that the weight repartition does not change much, i.e. that if 2/3 of the weight is supported by the front axle, that ratio would be similar for a hatchback and a SUV. This does not seem completely unrealistic when comparing ICEs with other ICEs or EVs with other EVs (though EVs will have a very different weight repartition compared to ICEs due to the way batteries and motors are integrated).
With this in mind, the front axle bears 2/3 * m_1 for a sedan of mass m_1 and 2/3 * m_2 for a SUV of mass m_2. So the effective weight (as seen considering only one axle) is just a linear function of the actual weight. It changes the magnitude, but it does not change the scaling.