Tire Rolling Circumference: Real-World Measurements

Hello,

When calculating the torque curve from the logged acceleration data and engine speed, all data related to the overall gear ratio (RPM to km/h) is particularly sensitive because any variation in this data essentially affects the result quadratically.
The gear data can be quite accurately researched, but the rolling circumference already allows for a tolerance of -2.5%...+0.5% of the standard value (which, due to the sinking of the loaded tires, is about 3% below the calculated value of an unloaded tire).
The entire permissible tolerance range of 4% for the rolling circumference results in an uncertainty of approximately 14 horsepower in my calculations for a vehicle in the 160 horsepower class, and I would like to reduce this potential error margin based on real-world data.

During my measurements of the rolling circumference of new tires in the garage (measured as the distance traveled by a sliding device for exactly one revolution of the rear wheels), I consistently obtained values that were quite close to the middle of the tolerance range for three different tire types and sizes, specifically around 0.5% below the nominal value, or 3.5% below the calculated unloaded circumference. This leads me to the tentative assumption that most new tires have a loaded rolling circumference that is in the middle of the tolerance range, meaning approximately 0.5% below the nominal value.

This allows for a tolerance of 2% downwards, for example, if the tires wear down.
This uncertainty (due to the lack of individual measurement of the rolling radius) still affects the calculated maximum power (Pmax) in the 160 horsepower range by approximately 7 horsepower.
Therefore, I would like to establish a rule of thumb for the rolling circumference of tires over their lifespan, so that the rolling circumference does not have to be re-calculated for every reliable measurement of the torque curve.

It is important to determine whether the specified tolerance range of -2.5% . . . ,5% of the nominal value applies only to new tires, or whether even worn tires with a remaining tread depth still within the -2.5% limit must comply.
Who knows anything about this?

Hi Ulf, isn't that just as detached from reality?

That would mean that all the tires would have the same tread pattern for 'use' and would also wear out at the same rate.

I assume that this standard applies to new tires. After all, the manufacturer produces new tires, not worn-out ones.

To get a more accurate result in real-world scenarios (this applies to speed, power, etc., all calculations that use the indirect distance through the transmission), one should determine the actual rolling circumference as you have done, and then subtract it from the assumed standard circumference. This will allow for a more accurate calculation.

A more comprehensive approach would be to incorporate a regular adjustment that takes into account the tire's circumference speed and air pressure. This is because the circumference increases at higher speeds. Furthermore, it's worth considering how a higher air pressure might offset this effect at lower speeds.
I think this could be a good topic for a doctoral thesis, or at least keep an R&D department busy for a while.

But since you're probably looking for a time-consuming project to occupy yourself with - go for it .

Devilseye503 wrote:

hello ulf, isn't that just as detached from reality?

If he assumes that all tires from all tire manufacturers have absolutely identical rolling circumference changes in every sidewall cross-section, then no.

Since that is completely detached from reality, the project is likely to fail from the very beginning.
Just driving the tire with the wrong air pressure can cause this to happen automatically.
I'm not referring to the tire pressure listed in the vehicle's owner's manual. In 90% of cases, that information is incorrect. The tire manufacturer provides a recommended tire pressure based on the (actual) load on the wheel. This recommendation almost never matches what the vehicle manufacturer specifies for their car. Therefore, the actual rolling circumference also varies.

I suppose, theoretically, one could start with a standard model of a tire. As a guest listener in an electrical engineering lecture, I was amazed by the lecturer's shortcuts. He repeatedly skipped steps during his example calculations, when rearranging formulas, when omitting intermediate results, and even when the numbers became too complicated. I started to doubt whether it was even possible to arrive at a reasonably correct answer through calculation.

Therefore, when it comes to a rough calculation or simply comparing different vehicles, it should be possible to use a standard tire size for the calculations.

Besides that, when measuring the circumference of various new tires that were supposedly the same size, I observed discrepancies of several centimeters. Furthermore, the tread depths vary by millimeters depending on the tire model and tread design, even in new tires from the same manufacturer and model. Therefore, your calculation based on precise dimensions of the actual tires used could lead to completely different results with the next vehicle if it uses different tires.

Yesterday, I tested the Pirelli Zero Nero tires on a 6L Cupra TDI and, indeed, I measured a circumference that was 0.7% above the calculated average .