There has been much discussion over the years of the necessity of matching tire tread depth when replacing fewer than four tires on full-time four wheel drive automobiles. I was faced with this problem recently and considered both of the recommended approaches: purchase a used tire having the correct tread depth, or purchase a new tire and have it shaved down to match the tread depth of the existing tires.
I decided instead to purchase two new tires and to perform rolling tests to determine whether it was actually practical to compensate for tire size differences by adjusting tire pressure. While working on that project, I gradually realized that there was a more important story to be told.
FIRST, I came across a directly relevant paper published by the SAE in 2020, written by authors from Michelin North America. This paper can be read for free on the SAE website, or if you sign up for a free account, you can download it. The citation is:
Kan, Y., Hoffman, S., and Carter, T., Tire Rolling Radius Evolution with Tread Depth and the Implications for Tire Replacement on All-Wheel Drive Vehicles, SAE Technical Paper 2020-01-5070, 2020, doi:10.4271/2020-01-5070.
Kan, et. al., measure the actual rolling radii of a number of different tires (all 255/55R17) and how those radii vary with tread depth. The measurements were made on a vehicle traveling at a nominally constant speed over a long linear track. They used rotational speed encoders mounted on the wheels being tested and a GPS system to measure the linear speed of the vehicle. The linear speed divided by the rotational speed gives a direct measure of the tire rolling radius. They tested pairs of tires, one of each pair being as supplied by the manufacturer, and the other having been "buffed" to 3/32 in. tread depth to represent a worn tire.
They point out that it is well known in the automotive engineering community that the free radius of a tire is larger than the rolling radius. The free radius (times 2 pi) is what we measure when we measure the circumference of a tire. The rolling radius is what matters to the center slip mechanism of full time 4wd vehicles.
Everyone, including Kan, et. al., has always assumed that the free radius of an individual tire will vary directly 1:1 with tread depth. However, their on-car results show that the rolling radius varies only 1/3 as fast; for example, a 3/32 change in tread depth results in only 1/32 inch of change in rolling radius. (This was averaged over 6 different tires from several manufacturers, but it was essentially the same for all of them.)
On the other hand, they show that the rolling radius varies a LOT between manufacturers and models for the same size tires. That is not necessarily a surprise, but it is good to see actual data on this.
What the authors do not address, and what is of most interest to us who need to purchase tires, is the variation in rolling radius between different tires of the same manufacturer and model. It has been assumed that tires having different tread depths will have different free radii (1:1 variation, as mentioned above), and thus, most likely, different rolling radii.
My car is a 2017 Outback 2.5 Premium with the CVT. My tires are Bridgestone Alenza AS Ultra, in 225/65R17 size. I bought 4 new tires to replace the OEM tires on 1/11/2023 at mileage 19618. I hit a road hazard and blew out one tire in early September, 2024. At the recommendation of Discount Tire, two tires were replaced on 9/11/2024 at mileage 24,307. The tires are apparently identical except for their date codes and, of course, their histories. At installation of the new tires, the older tires had 8/32 of tread depth, whereas the new ones had 10/32.
SECOND, when I started my rolling tests, I had no thought or intention to measure the circumference of my tires. However, trying to understand my test results impelled me to do just that. Imagine my surprise when I found that all four of my tires were within the 1/4 inch circumference tolerance quoted by Subaru! This means that tire tread depth is not a reliable indicator of tire size; at least for this specific tire model!
Because this result was so surprising, I measured the tires 3 times (all at 36 psi). The first time I was expecting to see large differences, so I used a surveyor's fiberglass tape that had 1/8 inch graduations, and I estimated the measurements to the nearest 0.05 inches. After getting that initial result, doing additional work on the rolling tests, and thinking about it further, I decided to obtain a precision steel tape and redo the measurement two additional times. For the second measurement, I used the millimeter scale on the tape, and I estimated the measurement to the nearest 0.2 mm. For the final measurement, I turned the tape upside down, reversed it, and used the inch scale. That time I estimated to the nearest 0.02 inches.
My results, tire circumference in inches (millimeters converted) in order from first to third:
Tire A, tread depth 8/32: 89.40 89.35 89.38
Tire B, tread depth 8/32: 89.55 89.47 89.46
Tire C, tread depth 10/32: 89.60 89.52 89.50
Tire D, tread depth 10/32: 89.50 89.48 89.48
This is good news for me, but THIS APPEARS TO BE BAD NEWS IN GENERAL. It only stands to reason that if tires of the same manufacturer and model can have the same size with different tread depths, they could also have different sizes with the same tread depths. This implies that there is no guarantee that buying even 4 new tires will result in having 4 tires of the same size.
THIRD, it is bad news - unless:
As part of my initial testing efforts, I measured the pressure dependence of the loaded radius of my tires. The loaded radius is the distance between the road and the center of the axle, and Kan, et. al., point out that it is always smaller than the rolling radius. What I found during those tests was that there was a dramatic difference in the pressure dependence of the old and new tires, with the older tires being more responsive to pressure differences. It is not practical to describe these measurements here, but I have written a short report that I will gladly send to anyone who requests it. Just send me a private message; I won't spam you.
Given that, maybe it should not be a surprise that my new and old tires have matching sizes. There appear to be solid reasons why tires might tend to have constant circumferences as they wear! Sure, it is possible that I just got lucky -- but then you have to also admit that when you buy 4 new tires you are gambling that they are all the same size. Millions and millions of new car purchases, manufacturers development and testing, etc., tend to argue against the likelihood of that.
Kan, et. al. did not test old tires that had small tread depths; they tested new tires that had been buffed. If all old tires are more responsive to pressure, then it is not hard to believe that their rolling radius results would have shown even less dependence on tread depth than they report if they had used old tires. In this regard, it is also useful to consider that when they tested tires on a road wheel, they found an even smaller dependence (7%) of rolling radius on tread depth, and they say that there is theory that claims that it should be about 10%. They do not attempt to explain the differences between these results.
In view of all this, I say that there is a real possibility that matching tire tread depth when replacing a single tire is not only not necessary, but could actually be harmful in the case of new tires that have been shaved or buffed.
Clearly I can't answer this question by myself. What needs to happen is for a large number of people interested in this problem to actually measure their tires and to report their results.
These measurements are not that hard to do. It took me less that 3 hours, using my car's jack, to remove each wheel individually, measure the tire, and replace the wheel. And I am an old guy who moves slowly!
Actually making a circumference measurement accurately requires attention to detail. A flat tape needs to be placed around the circumference at the center of the tire and needs to be in close contact with it at all points. If there are two people available, one can hold the ends of the tape while the other goes around the tire adjusting its position. It is not necessary to pull the tape extremely taut.
To make the measurement by oneself requires that you loosely position the tape around the tire and then, starting at the back of the tire, use pieces of duct tape to attach the measurement tape to the tire at several positions around the tire until you end up at the front, where you can grasp the two ends of the tape and bring them side-by-side to make the measurement. I recommend 3M No Residue duct tape, as it sticks adequately well and removes cleanly from your fiberglass or steel measurement tape without damaging it.
I decided instead to purchase two new tires and to perform rolling tests to determine whether it was actually practical to compensate for tire size differences by adjusting tire pressure. While working on that project, I gradually realized that there was a more important story to be told.
FIRST, I came across a directly relevant paper published by the SAE in 2020, written by authors from Michelin North America. This paper can be read for free on the SAE website, or if you sign up for a free account, you can download it. The citation is:
Kan, Y., Hoffman, S., and Carter, T., Tire Rolling Radius Evolution with Tread Depth and the Implications for Tire Replacement on All-Wheel Drive Vehicles, SAE Technical Paper 2020-01-5070, 2020, doi:10.4271/2020-01-5070.
Kan, et. al., measure the actual rolling radii of a number of different tires (all 255/55R17) and how those radii vary with tread depth. The measurements were made on a vehicle traveling at a nominally constant speed over a long linear track. They used rotational speed encoders mounted on the wheels being tested and a GPS system to measure the linear speed of the vehicle. The linear speed divided by the rotational speed gives a direct measure of the tire rolling radius. They tested pairs of tires, one of each pair being as supplied by the manufacturer, and the other having been "buffed" to 3/32 in. tread depth to represent a worn tire.
They point out that it is well known in the automotive engineering community that the free radius of a tire is larger than the rolling radius. The free radius (times 2 pi) is what we measure when we measure the circumference of a tire. The rolling radius is what matters to the center slip mechanism of full time 4wd vehicles.
Everyone, including Kan, et. al., has always assumed that the free radius of an individual tire will vary directly 1:1 with tread depth. However, their on-car results show that the rolling radius varies only 1/3 as fast; for example, a 3/32 change in tread depth results in only 1/32 inch of change in rolling radius. (This was averaged over 6 different tires from several manufacturers, but it was essentially the same for all of them.)
On the other hand, they show that the rolling radius varies a LOT between manufacturers and models for the same size tires. That is not necessarily a surprise, but it is good to see actual data on this.
What the authors do not address, and what is of most interest to us who need to purchase tires, is the variation in rolling radius between different tires of the same manufacturer and model. It has been assumed that tires having different tread depths will have different free radii (1:1 variation, as mentioned above), and thus, most likely, different rolling radii.
My car is a 2017 Outback 2.5 Premium with the CVT. My tires are Bridgestone Alenza AS Ultra, in 225/65R17 size. I bought 4 new tires to replace the OEM tires on 1/11/2023 at mileage 19618. I hit a road hazard and blew out one tire in early September, 2024. At the recommendation of Discount Tire, two tires were replaced on 9/11/2024 at mileage 24,307. The tires are apparently identical except for their date codes and, of course, their histories. At installation of the new tires, the older tires had 8/32 of tread depth, whereas the new ones had 10/32.
SECOND, when I started my rolling tests, I had no thought or intention to measure the circumference of my tires. However, trying to understand my test results impelled me to do just that. Imagine my surprise when I found that all four of my tires were within the 1/4 inch circumference tolerance quoted by Subaru! This means that tire tread depth is not a reliable indicator of tire size; at least for this specific tire model!
Because this result was so surprising, I measured the tires 3 times (all at 36 psi). The first time I was expecting to see large differences, so I used a surveyor's fiberglass tape that had 1/8 inch graduations, and I estimated the measurements to the nearest 0.05 inches. After getting that initial result, doing additional work on the rolling tests, and thinking about it further, I decided to obtain a precision steel tape and redo the measurement two additional times. For the second measurement, I used the millimeter scale on the tape, and I estimated the measurement to the nearest 0.2 mm. For the final measurement, I turned the tape upside down, reversed it, and used the inch scale. That time I estimated to the nearest 0.02 inches.
My results, tire circumference in inches (millimeters converted) in order from first to third:
Tire A, tread depth 8/32: 89.40 89.35 89.38
Tire B, tread depth 8/32: 89.55 89.47 89.46
Tire C, tread depth 10/32: 89.60 89.52 89.50
Tire D, tread depth 10/32: 89.50 89.48 89.48
This is good news for me, but THIS APPEARS TO BE BAD NEWS IN GENERAL. It only stands to reason that if tires of the same manufacturer and model can have the same size with different tread depths, they could also have different sizes with the same tread depths. This implies that there is no guarantee that buying even 4 new tires will result in having 4 tires of the same size.
THIRD, it is bad news - unless:
As part of my initial testing efforts, I measured the pressure dependence of the loaded radius of my tires. The loaded radius is the distance between the road and the center of the axle, and Kan, et. al., point out that it is always smaller than the rolling radius. What I found during those tests was that there was a dramatic difference in the pressure dependence of the old and new tires, with the older tires being more responsive to pressure differences. It is not practical to describe these measurements here, but I have written a short report that I will gladly send to anyone who requests it. Just send me a private message; I won't spam you.
Given that, maybe it should not be a surprise that my new and old tires have matching sizes. There appear to be solid reasons why tires might tend to have constant circumferences as they wear! Sure, it is possible that I just got lucky -- but then you have to also admit that when you buy 4 new tires you are gambling that they are all the same size. Millions and millions of new car purchases, manufacturers development and testing, etc., tend to argue against the likelihood of that.
Kan, et. al. did not test old tires that had small tread depths; they tested new tires that had been buffed. If all old tires are more responsive to pressure, then it is not hard to believe that their rolling radius results would have shown even less dependence on tread depth than they report if they had used old tires. In this regard, it is also useful to consider that when they tested tires on a road wheel, they found an even smaller dependence (7%) of rolling radius on tread depth, and they say that there is theory that claims that it should be about 10%. They do not attempt to explain the differences between these results.
In view of all this, I say that there is a real possibility that matching tire tread depth when replacing a single tire is not only not necessary, but could actually be harmful in the case of new tires that have been shaved or buffed.
Clearly I can't answer this question by myself. What needs to happen is for a large number of people interested in this problem to actually measure their tires and to report their results.
These measurements are not that hard to do. It took me less that 3 hours, using my car's jack, to remove each wheel individually, measure the tire, and replace the wheel. And I am an old guy who moves slowly!
Actually making a circumference measurement accurately requires attention to detail. A flat tape needs to be placed around the circumference at the center of the tire and needs to be in close contact with it at all points. If there are two people available, one can hold the ends of the tape while the other goes around the tire adjusting its position. It is not necessary to pull the tape extremely taut.
To make the measurement by oneself requires that you loosely position the tape around the tire and then, starting at the back of the tire, use pieces of duct tape to attach the measurement tape to the tire at several positions around the tire until you end up at the front, where you can grasp the two ends of the tape and bring them side-by-side to make the measurement. I recommend 3M No Residue duct tape, as it sticks adequately well and removes cleanly from your fiberglass or steel measurement tape without damaging it.
