(Inside Science) -- It may be obvious that heavy semitrucks stress and damage roads more than the average commuter sedan does. But by how much?

Since the 1960s, the Generalized Fourth Power Law has been used as a rule of thumb when considering the relative damage done to the pavement depending on a vehicle’s weight. The big picture is more complex, but the simplified, and perhaps elegant, equation, serves as a good starting point for this discussion.

**A “power”-ful function**

The AASHO Road Test was a multiyear experiment conducted by the American Association of State Highway Officials (AASHO) during the 1950s and is still perhaps the most comprehensive test on trucks and pavement damage. During the tests, trucks with different weights and configurations were driven around a loop until the road was damaged to a certain point. The tests ultimately resulted in 141 crashes and two fatalities.

The report produced an extensive list of equations for describing the data collected from the tests, and from those equations was born the Generalized Fourth Power Law. It’s a rule of thumb for comparing the amount of pavement damage caused by vehicles with different weights, in terms of axle loads:

In the equation, *W _{1}* is the weight of an axle on vehicle 1, which we would compare to

*W*, the weight of an axle on vehicle 2.

_{2}Let’s look at some numbers for comparison.

Consider a standard sedan with two axles and a total weight of 4 tons. Assuming an even distribution, each of its axles would bear the weight of 2 tons. Now consider a semitruck with eight axles and a weight of 40 tons -- each of its axles would weigh 5 tons. The relative damage done by each axle of the truck can be calculated with the following equation, and comes out to 40 times the damage done by each axel of the sedan.

Considering that the truck has eight axles and the sedan has two, the relative damage caused by the entire semitruck would be *40 x (8/2) *-- 160 times that of the sedan.

“The damage due to cars, for practical purposes, when we are designing pavements, is basically zero. It’s not actually zero, but it’s so much smaller -- orders of magnitude smaller -- that we don’t even bother with them,” said Karim Chatti, a civil engineer from Michigan State University in East Lansing.

**The limitation of the equation**

In theory, you can add axles to the truck to lighten the load of each axle. For example, if the same 40-ton truck had 10 axles instead of eight, each of the axles would now weigh 4 tons instead of 5, and the relative damage would become:

Even when considering the extra axles, the relative damage would still be lower, i.e., *16 x (10/2), *or 80 times the damage from the sedan, or half of that from the eight-axle truck.

In reality, the relationship is more complicated. For instance, adding extra axles increases the total weight of the vehicle, making it more damaging, especially to bridges, where the total weight instead of axle weight is the main concern.

Other factors in play are the vehicle speed, the number of wheels on each axle, the design and composition of the pavement itself, etc.

“It depends on a lot of things,” said Chatti, about the generalized law. “There’s a range. The [exponent] is not always four, it could range anywhere from three to six.”

However, as a generalized rule, the equation has been seen as adequate for serving as a guideline for regulations and policies.

**Converting the equation to tax dollars**

According to a report published by the Urban Institute, the annual expenditure on highways and roads in the U.S. was $181 billion in 2017, with roughly three-quarters of the budget coming from state and local governments, and a quarter coming from federal funding. When divvied up by the population, the amount was about $560 per capita.

While engineers seek to make pavements cheaper and more durable, interest groups such as the trucking industry and the railway industry, and even advocacy groups for bicycling, have been debating the question of who should pay what to use the road.

“Congress has done studies over the years, allocating which groups should pay more in terms of road user taxes,” said Joe Mahoney, a civil engineer from the University of Washington in Seattle. “Trucks do pay more in terms of road user taxes. They pay a fuel tax, particularly for diesel, and they also have other weight-related taxes that most other vehicles don't have.”

“I'm not going to say that they're fairly allocated. That's kind of like saying that income taxes for individuals are fairly allocated in the United States. I think you could probably debate that with some vigor, and you could do the same here,” he said.

While the debate about specific tax policies goes beyond the scope of this article, the rapid growth in lightweight cargo from online shopping has opened up a different conversation. This time, it is not about the weight of the trucks, but their sizes.

“There was always pressure for longer trucks without adding weight, which has gotten louder since we all seem to buy small light things delivered in big boxes full of padding in this century,” wrote Steven Karamihas, a mechanical engineer from the University of Michigan in Ann Arbor, in an email to *Inside Science*.

Regulations about the maximum length of vehicles are often specific to state and local jurisdictions and depend on the vehicle type and trailer configuration. In general, most states limit truck length to two standard 28-feet trailers, with a handful allowing three trailers.

In 2015, Congress struck down two pieces of proposed legislation to allow heavier and longer trucks, but the idea still is actively being lobbied for and against by opposing interest groups, such as Americans for Modern Transportation, and Coalition Against Bigger Trucks.

“If the cargoes are getting lighter, [trucking companies] will want to be able to carry more volume, obviously,” said Chatti. “But the concern here isn’t the deterioration of the pavement, it’s about safety and regulations.”