Discussion about fees and taxes for bicycles so that we cyclists “pay our fair share” often turn to mentions of the “Fourth Power Rule.” What is this mysterious Fourth Power Rule?

Back in the 1950s and 1960s, highway engineers researched damage done to road beds and road surfaces for the purposes of allocating who should pay how much into the various road maintenance funds. The American Association of State Highway Ofﬁcials (AASHO; they added Transportation to their organization name during the 1973 OPEC oil embargo) collated this research and published their findings as a “Special Report” for a highway engineering conference in 1962.

What these researchers found is that damage to the roadbed is proportional to the 4th power of the axle load of the vehicle, and they called this “the Generalized Fourth Power Law.” This means that if you double the weight on an axle, your vehicle does sixteen times the damage to the road. The result is those signs you see on the backs of truck trailers that say “This truck paid $4,182 in highway taxes last year.”

Let’s take an example. A Toyota Prius weighs about 3,000 lbs, which is 1,500 lbs per axle. A Lincoln Navigator weighs in with a curb weight of 6,000 lbs, or 3,000 lbs per axle.

(3000 / 1500)4 = 24 = 16



Because of this extra highway wear and tear, the extra real estate required by these larger vehicles (the trend to larger vehicles during the 90s and 2000s contributed all by themselves to 20% more highway congestion over this time period), and the higher law enforcement and emergency services expenses incurred by these vehicles, the owners of large, heavy SUVs pay sixteen times what the owners of economy cars do in registration fees and gas taxes.

Oh wait, no they don’t, because we live in Bizarro Land. Owners of large vehicles can often take advantage of tax incentives not available to the owners of smaller vehicles. But I digress. Let’s look at another example.

We’ll start once again with our 3000 lb Prius and compare that against a tractor trailer with a gross weight of 70,000 lbs. The Prius, as before, has 3000 lbs over two axles, so that’s 1500 lbs per axle. The tractor trailer has 70,000 lbs spread over five axles; the weight distribution isn’t even across those five axles, but for the purposes of this exercise we can pretend that we have 14,000 lbs per axle.

(14,000 / 1,500)4 = 94 = 6561



You saw that, right? A tractor trailer causes roughly 6500 times more road damage than a Prius.

It’s a Rule of Thumb

Let’s break now to remind our listeners that the Fourth Power Rule is a rule of thumb. It’s meant to give rough guidance for policy makers if they want to figure out what the “fair share” of the cost is for road maintenance. Research on this topic since the 1960s has shown that the actual road damage from light vs heavy vehicles can vary significantly depending on existing road conditions, the road construction methods, and even factors like tire pressure and suspension systems.

In other words, since we’re talking about transportation and tax policy, the Fourth Power Rule is good enough for government work.

There’s also a speed component to the Fourth Power Rule. It’s usually not talked about because vehicles all mostly travel at the same speed, but when we compare a 15 MPH bicycle against a 60 MPH Prius, that 4X speed difference means a 4X difference in road damage.

Unlike axle loading, the damage due to speed is mostly linear. In other words, twice the speed equals twice the damage. To keep things simple, I’ll ignore this factor, but when you see the bicycle numbers below feel free to multiple by two times to four times.

Bicycles bicycle bicycles bicycle bicycles

Let’s come full circle to the topic at hand, which is the perennially proposed bicycle tax. We’ll start once again with our hypothetical Prius, and this time compare it against a fully laden bike commuter with loaded panniers who might weigh 220 lbs with bike. That’s 1,500 lbs per axle for the Prius, and 110 lbs per axle for the bike and rider.

( 1,500 / 110)4 = 144 = 38416



We see the Prius does 38,000 times more road damage than a bicycle.

California Senator Mark Deaulnier’s proposed bicycle tax doesn’t have an amount – that will be left to local jurisdictions who may wish to impose such a tax – but let’s use Colorado Springs’ modest $4 bicycle sales tax as an example. If cyclists pay our “fair share,” the sales tax on a small automobile such as the Prius should come in at a cool $154,000. The Lincoln Navigator and other vehicles with twice the weight of the Prius have a sales tax sixteen times higher, which comes to $2.5 million.

So how about we propose an amendment to Senator Desaulnier’s bill? Any bicycle tax imposed will also have a “fair share” clause, such that the new car sales tax be equal to the fourth power of the axle loading difference between a bicycle and the motor vehicle.

A little more seriously: a $150 thousand sales tax for vehicles is more than a little ludicrous. A $4 bike tax might seem reasonable, but in my view it’s equivalent to charging hundreds of thousands of dollars for vehicles.

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