Well I posted this on slashdot. It seemed like I should put it somewhere more linkable, as I'm actually quite proud of it [edit] hmm.. [/edit].
Having heard that road wear is proportional to the fifth power of axle weight, I thought I would see what wear proportion that works out as for HGVs, given that there are presumably more cars than trucks, and the differing mileages of these types of vehicle. As I write this, I have not done the final calculation. I will use a couple of papers and some government statistics.
Looking at a couple of papers (The economic and environmental benefits of increasing maximum truck weight: the British experience, Alan C. McKinnon, 2005. The cost of relying on the wrong power—road wear and the importance of the fourth power rule (TP446), Richard Johnsson, 2004, Impacts of Increased Goods Vehicle Weight Limits - A European Case Study, Proceedings of Fourth International Symposium on Heavy Vehicle Weights and Dimensions, 1995, the exact proportion of axle weight to road wear varies depending on factors including road surface type, anywhere from 3rd or 4th power of axle weight, all the way up to the 9th power. I chose 4 as a lowish-average.
Taking a Heavy Goods Vehicle (HGV) weight of 15 tons and an average of 4 axles (HGV maximum weights: a brief guide gives a maximum for HGVs of 44 tons over 6 axles, and I don't have a good source, but the minimum to count as a HGV is 7.5 tons, presumably with 2 axles), this gives 3.75 tons/axle. For cars I assumed 1.5 tons and two axles; 0.75 tons per axle. The ratio of these figures is 5. 5^4 = 625 times as much road wear per axle.
Traffic statistics are in vehicle-kilometres, so to use these we need to multiply this back up by the number of axles per vehicle. 4 for trucks and 2 for cars gives 625*(4/2) = 1250 times as much road wear per vehicle per kilometre.
Keeping with the euro theme, I got transport statistics from the UK department for transport. 240 billion miles driven in the UK in 2011 by cars/taxis, heavy goods vehicles 16.4 billion. 240/16.4 = 14.63 times as many miles driven by cars, compared to heavy goods vehicles (I have deliberately left out 'vans', or other vehicles that carry smaller loads than the HGVs that my axle weights are for). So now we have 1250 times as much road wear per vehicle for HGVs, divided by 14.63 as the ratio of cars-HGVs, gives 85.4 times as much road wear by HGVs. Take the reciprocal and subtract from 1 to get that as a proportion, 0.988, or 98.9%.
My estimate for axle weight for HGVs I think is low if anything; I could easily have gone for 20 tons over 4 axles, which would have given 99.6%. I have also assumed that HGV weight is evenly spread over the axles; it strikes me that the rear axles will carry more weight, and so since the road wear varies with the 4th power of this, the real figure is probably higher.
