B arry's T ire T ech

This is a series of articles on the technical aspects of tires, their care and usage.

My primary purpose in these articles is to help people understand tires and thereby reduce the risks we all face every day.

..........and since tires is just about the only thing I know about..........

Please drop me a note if you have a topic you want to see:

Barry@BarrysTireTech.com

Footprint (Contact Patch)

Complete Revision, including name. March, 2022. This used to be titled "Air or Tire".

What you should get from this page:

  • That the size of a tire's footprint CAN NOT be calculated from the inflation pressure and the load on the tire.
  • That it is the TIRE that holds up the vehicle, not the air or the air pressure - not even a little!.


First, it should be obvious that the size of the footprint (contact patch) is some how related to the inflation pressure and the load on the tire: Increase the inflation pressure and the footprint gets smaller. Increase the load and the footprint gets larger.

But the tire is NOT like a pressurized cylinder where the pressure in the cylinder is holding up the piston that is holding up the load. There is no piston and the air pressure immediately above the footprint is NOT holding up the tire. I go into that below.

Is there proof?

There is!!:

Archived Copy: Fact or Fiction?

Special Note: Long after I wrote the first version of this webpage, I attended a seminar where a student from Cranfield University (UK) presented a paper that addressed the issue on the relationship between the size of the contact patch and the inflation pressure and confirmed what I wrote above. Unfortunately, the paper wasn't published at the time of the presentation, but I am citing it here in the hope that it will be published in the future:

Evaluation of the Contact Pressure Distribution of a Rear Combine Tyre on a Hard Surface by P. A. Misiewisc, et al, presented at the 28th Tire Society Conference in Akron, OH, USA, Sep 15 and 16, 2009.

As of March, 2022, it is still unpublshed.

******************************************************************

Revised April, 2012

In the July, 2011 issue of Road and Track, they tested 3 high performance tires. They included some details about the tires - including the areas of the footprints at the same inflation pressure and load:

Road and Track - July 2011 - New Summer Rubber

Guess what?

The size of the footprints are different for each tire, even though they were measured at the same load an inflation pressure - and the average footprint pressure (load divided by the footpr

Road and Track - July 2011 - New Summer Rubber: Page 1

int area) does not equal the inflation pressure.

I'll leave it to the reader to do the calculations.

Revised July 2022

Unfortunately, the archived webpage doesn't including the images with the footprint sizes.

But luckily I saved a copy:

Road and Track - July 2011 - New Summer Rubber: Page 1

Road and Track - July 2011 - New Summer Rubber: Page 2

Road and Track - July 2011 - New Summer Rubber: Page 3

So here's the math:

-
Bridgestone Potenza S-04 Pole Position Cooper Zeon RS3-S Goodyear Eagle F1 Asymmetric 2
Pressure 32 psi 32 psi 32 psi
Load (lbs) 970 970 970
Tread Area (in2) 23.0 23.8 23.7
Void Area (in2) 11.5 9.2 12.3
Total Footprint Area (in2) 34.5 33.0 36.0
Load/Total Area (Footprint pressure) 28.1 psi 29.4 psi 26.9 psi

The inflation pressure does not equal the footprint pressure. Another confirmation.

Revised March 2022:

To the right is a graph from a paper that I found in the process of doing the revision.

Truck Tyres and Road Contact Pressures by P. Yap, 1989


Notice that the 2 types of tires have different lines. If the theory is correct, they should be the same.

Also notice that the pressures don't line up.While the radial tire is 100 psi contact pressure at 100 psi inflation pressure, the contact pressure is 88 psi at 80 psi inflation pressure.

And notice that the bias ply tire contact pressure is 75 psi at 80 psi inflation pressure, and if the line were extended to 100 psi inflation pressure, the contact pressure would be 88 psi.

This is another confirmation that the theory is incorrect.

Revised July 2022:

I found another one.

To the left is a table from:

Archived webpage from ARB: The Low Down Off Road Tire Pressures by Mark Allen 2011

Unfortunately, he did his calculations in metric units, except for the inflation pressure.

Allow me to translate that into English units:

Inflation pressure (psi) 40 35 30 25 20 15
Pressure tread places on ground (psi) 17.8 16.1 14.7 13.6 11.7 10.3

Revised Sep, 2022:

And one more:

Texas Transportation Institute:Measurement of Tire Footprint Pressures

There are several tables where the inflation pressure is compared to the average footprint pressure. None show the inflation pressure equals the average footprint pressure.

There's even a statement that says: "It is well-known, to tire engineers, that the average footprint pressure produced by a tire can be above or below the inflation pressure, depending on tire load." Page 22.

I'll leave to the reader to look this paper up and read it.

Now onto an analysis of the situation: The tire is attached to the rim and the rim is attached to the hub and it is the only thing between the tire and the vehicle. The tire is the only thing between the rim and ground (except for the air inside the tire).

Looking at the rim, you can consider the rim to be a hoop of material (it's usually a metal of some sort - typically aluminum or steel) with a flange on both edges of the hoop so that the air pressure doesn't force the tire off the rim.

I've indicated the 2 forces that are acting on the area in question - an upward vertical force acting on the tire (the ground support) and a downward vertical force acting at the hub (the weight of the vehicle). For the purposes of this analysis, we'll neglect the weight of the rim and the tire. The weight of these components is small compared to the weight of the vehicle and doesn't affect the outcome.

Now let's look at the rim (wheel) and the tire.

The rim is attached to the hub and it is the only thing between the tire and the vehicle. The tire is the only thing between the rim and ground (except for the air inside the tire).

Looking at the rim, you can consider the rim to be a hoop of material (it's usually a metal of some sort - typically aluminum or steel) with a flange on both edges of the hoop so that the air pressure doesn't force the tire off the rim.

Let's ignore the tire for the moment - We'll come back to it later.

The hoop shaped rim has a width, but if we look at the rim edgewise, it is a circle with a connection to the hub. This connection is sometimes called the "spider" - and the "spider" and the rim together make up the wheel.

The rim is completely surrounded by air and the air is under pressure. That pressure is pushing inwards on the rim, as illustrated to the right

The pressure that is being exerted on the rim is the same completely around the rim. There is no pressure differential from left to right or from top to bottom. In other words, there is no sideways force being generated on the rim and there is no vertical force being generated on the rim (up and down). No net force at all - just a pressure towards the center.

But we know the rim is carrying the load of the vehicle, so there must be something that is resisting the weight of the vehicle (and the upward force of ground) - and there is only one thing it could be.

The tire.

The tire is carrying 100% of the weight of the vehicle (and, of course, the rim). The weight of the vehicle is distributed around the structure of the tire, so that adds very little to the weight that is already being carried.

If this is so, what are the implications?

We all know that the tire deforms in the area of the footprint - you can see the sidewalls bulging out.

But if the tire is supporting 100% of the load, then the axle might also be pulling down from the top.

To the left is a schematic of this, where the solid lines are the unloaded tire and the dotted lines are the tire supporting the load.

If the tire is doing all the support, then the entire tire is being distorted. The sidewalls near the footprint (contact patch) bulge out because the tread is being compressed towards the rim, but also, 180° from the contact patch (the "top" of the tire), the rim is pulling down from the tread. This should cause the section height to increase (which is dimensions A and B), as well as the sidewalls to be sucked in a little (which is dimension C and D).

Revised March 2022: What followed this paragrah in the original page was an outline of an intended test where I predicted various measuremnts (including dimensions A, B, C, and D above) and follow that up with ACTUAL measurements.

With the tools I had, I couldn't do that with any precision, so I abandoned the project.




Barry's Tire Tech - Main Page