# The Fourth Power Rule

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.

1. I think the only reason why these taxes come up is to stick it to us. People that only drive think we are getting a free ticket and that makes them angry. Instead of joining in the fun, they want us to pay out more so that we can join their pity party.

2. Well, the only answer is that if a tax is imposed, I will have to start carrying a lot more weight on my bicycle so I can get my money’s worth!

3. BikeSC says:

Not to mention the fact that the vast majority of money for transportation comes from income tax and property tax, not registration or gas tax.

4. jd says:

Great article. I wish this sort of analysis was commonplace, especially by the major media sites, so that auto-centric fools would stop thinking so irrationally.

5. One counter argument I’ve heard is that regardless of use wear and tear, allocating street space to bicycles has a real estate cost attached to it. Although there is a point to this, it starts to seem ridiculous once we consider the vast swaths of land devoted to car-only freeways, and the fact that much more space is devoted to PARKED cars than MOVING bicycles, even in dense urban areas.

Another one I’ve encountered is that bicycle infrastructure (striping, curbs, etc) costs money. However, at least where I live, most bike lane striping coincides with when a street was getting repaved and restriped anyway, making the cost essentially free (beyond the engineering/design). Better, protected bike infrastructure is more expensive, but as an earlier commenter pointed out most street funding in CA does not come from car user fees (less than 35%), so people who drive less or not at all are most likely already paying more than their “fare share”.

6. cyclist for fee says:

I love this sort of analysis which helps highlight the absurdities of the “cyclists don’t pay their fair share arguments.” When using facts, we find that it is drivers that do not. In any case, as someone who primarily uses a bike to get around, I would be ok with the state adding \$5 to the cost of a bicycle sale, esp if it led to more bike facilities (cyclists get crumbs of nearly all transportation budgets in this country, so any additional funding is great).

The main reason I’d be ok with a charge like this though is to simply shut people up who use that “cyclists don’t pay their fair share” argument.

7. Cyclist says:

You did a good job of calculating the maintenance cost. But you did not consider the initial cost. Building bike lanes and infrastructure is not free, and if we are to ask for improvements there I don’t think it’s unfair to be asked to pay our share.

Having said that, if someone already drives a car and pays taxes for it, I don’t think it is fair to ask those to pay twice. You’re paying for a normal share, but if you commute by bike then you’re causing much less damage.

8. Cyclist, please refer to the previous comments for rebuttals of your points about construction costs. People who drive little or not at all already contribute a disproportionate amount of money toward roadway funding, which doesn’t even come close to being covered by user fees (gas taxes, registration fees, etc). See this link for a calculation of how little roadway funding is contributed by drivers (less than 35% here in CA): http://taxfoundation.org/blog/road-spending-state-funded-user-taxes-and-fees-including-federal-gas-tax-revenues

9. MikeOnBike says:

It costs money to build sidewalks, but I can’t recall anybody trying to tax pedestrians (or shoes) to pay for sidewalk construction.

Accommodations for all traffic (including cyclists and pedestrians) are built in to the cost of road construction. That’s part of the deal of having a “public way”.

And the costs of bike/ped accommodation go up as motor traffic speeds and volumes go up. (Quiet back streets don’t need fancy bikeways.) So the costs should largely fall on motorists. As it is, bike/ped accommodations are a rounding error in transportation budgets.

10. Does anyone think the total revenue collected from all bicycle-related sources will actually cover its cost of administration? Will there be any realistic projection of revenues exceeding expenses in the next decade? It is not very likely this avenue will ever produce a positive revenue stream. That being the probable outcome, what then, is a more realistic reason for new licensing requirements?

There must be something of value in this information – it isn’t rocket-science, it’s simple math: it is unlikely to produce the stated objectives.

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