Website for Nathan Moore, Physics, Winona State University
A letter to the editor in the local papers (Jan 2019) claimed that bicyclists were freeloaders because they don’t pay the gas tax, which pays for the roads bicyclists use.
One reader recently wrote to this paper, claiming that bicyclists and other “freeloaders” should pay their fair share of the costs of road maintenance. In Civil Engineering there is a well-known “Fourth Power Rule” which describes the damage caused to a road by a vehicle. Basically, damage is proportional to the fourth power of the vehicle mass.
So, let’s do some 8th grade math. A football lineman on a Trek might weigh 300lbs. A Honda Civic weighs about 3,000lbs. The damage the bicycle does to the road is proportional to 300 the the fourth power, and the Civic’s damage scales as 3000 to the fourth. How much more damage does the Civic do? That would be (3,000/300)^4, or 10,000 times more damage. Please note, the Civic is 10 times heavier than the bicyclist, but the Civic does far more than ten times the damage! So, if you want to charge a bicyclist $1 for the damage they do to the road each year, you should also (in fairness) charge the Honda Civic driver $10,000.
The math doesn’t get better as the weight of the vehicle increases. By the same argument, if commuting by bicycle causes $1 of damage per year, a 5800lb Chevy Suburban should be assessed $139k each year.
Should I carry the argument further? If a bicycle does $1 of damage each year, an 80,000lbs semi-truck hauling sand down Hwy 14 the same distance will do (80,000/300)^4 = 5 billion dollars worth of damage.
I agree that the gas tax is stupid. A semi-truck getting 7mpg pays (per mile) 5 times more gas tax than a Honda Civic driver getting 35mpg. By contrast, the semi-truck does 500,000 times more damage to the road than the Civic. A fairer road tax system would take this comparative impact into account.