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I married a physicist

Okay, I did it. It was 31 years ago and now the word “nontrivial” is part of my vocabulary. And “epsilon.”
The other day, my husband said, “You know, I think I’m getting better gas mileage lately.” So, I asked, “Did you get a tuneup or something?” He replied, “No, but my tires are wearing down.”
So, can your tires wearing down cause a noticeable increase in apparent gas mileage? Would you do the math for me?

In theory…yes. New tires often decrease fuel economy due to the extra grip of the tread. When the tread wears down there is less resistance which could explain an increase in fuel economy.

Yes and no…there is less rolling resistance with bald tires but ask him if “it makes up for the change in final drive ratio caused by the decrease in diameter from the wear of the tires which has a negative affect on mpg’s ?”

See what his response is…

No one can do the math because it’s so variable from one tire to another, one car, one temperature, one road surface, one…etc.

And, tell him “if the tires were not rotated or the car had poor alignment, the uneven increase in tread wear could increase rolling resistance… You have too much free time. Take out the trash.”

Throw this at him. The useful tread depth is about 1/4" so a new tire is about a 1/2 larger in diameter than a worn out tire. Most tires run around 26 to 27" in diameter so a 1/2" amounts to almost 2%. That means as the tires wear down, the odometer is showing up to 2% more miles between fill ups and that will look like a 2% increase in gas mileage, when the actual gas mileage did not change.

To put that in terms a physicist would understand, the apparent mileage increases but the real mileage does not.

Worn Out Tires Increase Traction And Cause Greater MPG Efficiency . . .

(That’s why drag racers use “slick” tires with no tread, not for better MPG, but for more efficient use of power. They apply more rubber to the road and make better use of engine power by creating more traction.)

. . . However, that only works on dry roads. On wet surfaces traction suffers tremendously. That’s why regular car tires have tread and aren’t slick. They’re a compromise between good traction on dry roads and good traction on wet roads.

Next time it’s wet for several days, or he’s driving a long distance on wet roads, ask your husband to carefully check his mileage.


+1 for asecular!

After reading the above posts you will conclude that fuel mileage is very minimally affected by how much tread is left on the tires, and much more affected by:

  1. The amount of air in the tires; higher pressure will give bettter mileage.

  2. Driving style and pattern; this can affect mileage by up to 30 %!!! This is the most impartant variable.

3 State of tune of the car. All spark plugs have to be firing perfectly.

  1. Condition of the fuel system, dripping or plugged injectors can affect engine power.

I have been measuring gas mileage on and off our cars for a few years now. A week’s driving in the city may give 35 mpg, while a weekend on the road and in the mountains will get us 42 mpg.

At the risk of being boring, tell your husband that he must:

  1. Tank at the same station, same pump every time. Stop at the first click. Don’t let an attendant fill the tank.
  2. Come back when you need gas, same station, same pump. Average 3 fillings at least.

If the driving pattern is the same, and the weather is as well, your husband MIGHT observe a tiny fraction of an mpg difference. Tell your husband the driving environment is not a laboratory, and his margin of error is many times larger than any improvement he might have noticed.

If he still insists he gets better mileage on worn tires, he must have been driving with insufficient air in them in the past. Or he has a very rich imagination!

A couple of thoughts:

First, Docnick is right. There are factorsd that have a much larger affect on fuel economy than tires - or even worse, differences in tires.

  • BUT -

The rolling resistance of a tire is NOT the result of the friction with the road surface (OK, partially), but the biggest contributor is internal friction of the materials themselves - techincal term: Hysteresis.

And the amount of RR is also affected by the volume of material being deflected as it moves through the tire’s footprint. That means that as tires wear, the RR goes down. You can measure this in the lab where the difference in rolling diameter has no affect.

  • and rolling diameter doesn’t change proportionally to the difference in tread depth. Unlike solid objects, tires roll at about 97% of the measured free-standing diameter - and the difference in tread dpeth has less of an affect on rolling diameter than the simple calculation suggests.

So the Physicist might be right, but there is a good chance it is also his imagination.

"and the difference in tread depth has less of an affect on rolling diameter than the simple calculation suggests."

Its pretty darn close to the simple calculation, close enough to use the simple calculation. Now a lot people think that because air pressure affects the height of the tire, that it also affects rolling circumference and that is not the case.

I will agree that there a re a lot of factors that would affect gas mileage and my explanation was overly simple, but physicist seem to like the real to apparent comparisons like real power vs apparent power so I though this was the best thing she could throw at him. I wouldn’t be surprised if that isn’t what he was thinking anyway.

“…Now a lot people think that because air pressure affects the height of the tire, that it also affects rolling circumference and that is not the case…”

Sorry, but inflation pressure DOES affect rolling cirecumference - it’s just not as much as people think.

Here’s a video that shows it - even though that wasn’t exactly what they were trying to demonstrate. The difference is very small, but it is detectable.

Opps, let’s try this again.

"Sorry, but inflation pressure DOES affect rolling cirecumference - it's just not as much as people think."

Actually that is what I meant, it didn’t come out quite right.

This is what I had guessed, but I didn’t have great faith in my theory. So what exactly is happening in the tire to change the circumference, is that known? Is it as simple as less deformation at the road surface?

It’s mostly the stretching of the tire as it is pressurized.

Obviously a change in as much as .5 inches, which is very significant in tread wear makes very little difference in the actual circumference…but it does make a difference. On the order of less then 2 inches arithmetically which is hardly recognizable in your tests as the circumference of the actual tire tries not to change like a dozer track. But, over a mile with an arithmetic difference of 130 plus linear feet and with a tire circumference that tries to remain constant, there will be squirming as the tire circumference cannot complete it’s actual circumference under the force of this arithmetic difference. The rim will not allow it. So, there will be some slight but significant loss of circumference IMO.

We discussed this before and though I agree that the difference is much less then most would even be concerned about in your utube presentation there is a difference as evenTire Rack and every car tire manufacturer and maker of every awd car will stipulate. How much depends upon the tire and a multitude of other factors. But the fact remains…all awd system manufacturers recognize the stress it adds to the system over time with wear differences. There is some change and traveling at 60 mph vs a demo at much lower speeds would elicit this change enough to cause greater problems which affect drive train components AND milage more then your near static test.

So , call it squirm if you will, but just calling it tire stretching with no affect is incorrect. The tire will not stretch 130 feet over a mile. And my point is "not as much as what people think " does mean it’s insignificant as the dynamics of high speed travel amplify this small difference. It happens similarly with balancing a tire when very little weight means nothing at low speeds but can shake everyone silly and cause big problems with everything at higher speeds.

So for me, it is very small, but it IS VERY significant !

This is what I had guessed, but I didn’t have great faith in my theory. So what exactly is happening in the tire to change the circumference, is that known? Is it as simple as less deformation at the road surface?

If you mean why is the circumference not pi times the diameter - The best guess I have is that the belt is acting like a tank track. A tank track has the same “circumference” regardless of how it is distorted - and it doesn’t matter how much tread the track has, the length of the track is the length - even when moving.

EXCEPT, that a tire’s belt isn’t completely inextensible like a tank track is. It can change. The phenomenon is called pantographing - where the steel belts act like parallelograms and change length and width. It doesn’t change much, but you can measure the difference.

That’s why differences in inflation pressure make a very slight difference in rolling circumference.

If lower pressure did not affect rolling circumference, my wheel-speed-sensor-based Tire Pressure Monitoring System would not work. And it DOES work. I can testify to that just as surely as I can testify to the fact that sheetrock screws can cause slow leaks.

And, to quote Red Green, “going faster on a flat tire will NOT produce enough centrifugal force to make it round again…”

Re: the physicist’s comment to his missus; yes, worn out tires can improve gas mileage because they can have lower rolling resistance. But they do so at the expense of safety…they also have less traction on wet surfaces and can be more subject to road damage.