How do you calculate the rolling resistance of flat and inflated car tires?

Answer

Trains and trams are referred to as “rolling stock” in the industry. This does not include cars and trucks. Don’t cars roll on the road? The answer is: less. Trains and trams have rolling wheels. Cars have “less rolling” wheels, and we call that driving rather than rolling. These linguistic names illustrate that car tires and train wheels are different enough to give their working process different names from an industrial perspective.

Pneumatic tires have a relatively high rolling resistance, compared to, for example, solid train wheels. This is due to the following phenomenon: while spinning, the tire is repeatedly pressed in a new part of the circumference. Each point of the tape is thus continuously pressed and released, again and again. Pressing the tire takes force, and you can already suspect that work will be done here. We get some of that work back when the belt continues to roll, and that part of the belt can return to its original shape (like a spring). We will not get another part of the work back, and will be converted into heat (like a damper). Train wheels also do the above, but much less.

Note: By work I mean the physical concept: force X displacement in the direction of that force, which you have already learned in school.

A tire is optimized for a certain tire pressure. If your tire is too flat, rolling resistance generally increases. Because the tire is flatter, it is compressed further, and the sidewall of the tire moves more, resulting in more internal friction, heat production, and higher rolling resistance. With the car you don’t feel the influence of the tire pressure directly, you can just give more gas to compensate. On a bicycle, on the other hand, it’s a different story: the difference between flat tires and well-inflated tires is very tangible.

Calculating rolling resistance is a very complex process. In engineering sciences, this is generally handled with numerical calculations. An obvious technique is “Finite Element Method” (FEM). The tire is modeled as a system with many springs and dampers. These springs and dampers are then given characteristics in function of all kinds of parameters. The resulting mass-spring-damper system can then be solved numerically with the FEM method. This explanation is, of course, extremely brief. In this paragraph you have some keywords with which, if desired, you will be able to find a lot of reading on this subject.

Is this complex approach necessary? Maybe, maybe not. It is possible that a kind of formula can be derived to link the consumption of your car to your tire pressure. But what if you buy other tires with different characteristics? Do you have to have a new formula? I have not come across such a formula yet. I think it can be set up, but that it would only be applicable within a very limited area.

In conclusion, I would mainly make sure that the tire pressure is as the manufacturer prescribes. With a heavily loaded car (eg when traveling), you can slightly increase the tire pressure.

Academic reading on the Internet:
https://www.google.be/search?q=tire+FEM