Why Do You Use Less Tire Pressure for a Bigger Tire or Wider Wheel?

During the last several years, bicycle rim width at the brake track has been increasing.  Manufacturers who are producing the new wave of high-tech wheels are ignoring the old 19mm width standard, and commonly producing rims that are 23-25mm in width. This is done to improve both performance and aerodynamics.  

This increased rim width has manufacturers asking their customers to inflate their tires to a lower psi, and the obvious question is why. Why does a wider rim and/or tire require a lower psi? We get this question so frequently that we decided to write a blog article to explain the science behind it.


Tire Background
Before starting, let’s look at the basic parts of a clincher tire.  
Casing: The fabric that is used to shape the tire and support the air pressure in the tire.
Tread: The rubber coating put on the casing for grip on the road and to make it airtight.
Bead: This is the metal hoop that hooks into the clincher hook on the wheel.
Parts of a Tire
The casing is the important part for today’s discussion. The casing is made from a thread that is stitched together in a diagonal orientation to form a bias ply tire. This bias ply is what holds the tires structure when inflated with air. Without it, the tire would stretch like a ballon.   
Bias Ply Weave
Casing Tension and Hoop Stress
In order to understand why we use a lower pressure for a bigger tire or wider wheel, it’s important to understand hoop stress. To understand hoop stress, it helps to have a few visual examples. The picture below shows a large propane tank. It has a cylindrical body and cupped ends.
If we were to cut a section of the tank (Section A), we would get a circular shape like the one below.
There are three dimensions for the section. There is the outer diameter, the inner diameter, and the mean (average) diameter. For our calculations we are concerned with the mean diameter.
When the propane tank is full of propane, the pressure of the gas exerts a force on the wall of the tank as shown below.   
This force from the internal pressure creates a stress on the wall of the propane tank.  Wikipedia describes stress as follows:

“Stress is the force per unit area on a body that tends to cause it to change shape.”

In the case of a thin-walled vessel, (like the propane tank) the stress that the wall of the tank experiences is called hoop stress.  
So how does this relate to a clincher tire? If we were to section a clincher tire when it is mounted on the rim, you will see a shape that is very similar to the section from the propane tank. Yes, the rim and tire is not perfectly round but the principle is the same. As we inflate the inner tube, (increase the internal pressure by increasing the air pressure) the casing of the tire is stressed. When stressed, the fibers of the bias ply weave are placed under tension. This tension is referred to as casing tension.   

Calculating Casing Tension
To determine the casing tension, we need to define the equation for hoop stress.  
In the above equations we define the following as:

Wall thickness = the thickness of the tire casing

Mean diameter = the tire size

Pressure = the pressure the wheel is inflated to

We eliminate thickness since we can assume all of the tires in the calculations below have the same wall thickness.  
Setting the Base
As a starting point, we will use a 20mm tire at 120psi to calculate the casing tension.  
From the calculation above, you can see that the casing tension on the tire is 8,273.709Pa.  When calculating the appropriate psi for a new tire diameter, we will want to keep the casing tension at a constant 8,273.709Pa. To get the psi for each new tire size, we will want to rearrange the hoop stress equation used above to solve for pressure.  
Now that we have solved for pressure, let’s use a 23mm tire as an example and calculate the tire pressure needed to create the same casing tension we saw in the 20mm tire.  

As we can see, the tire pressure that creates the same casing tension for the larger 23mm tire is less then 120psi. Since bigger tires do not have thicker tire casings, we want to make sure we are not creating too much casing tension. This is why we keep the casing tension the same when we calculate the new tire pressure. It is also why you will see tire manufacturers lower their max tire pressure recommendations for wider tires.  Here is a list of tire pressures that relate to 120psi for a 20mm tire all the way up to a 30mm tire.  Remember, the tire casing tension is the same in each example.  
Lower Tire Pressures for Wider Wheels
As we widen the rim of a wheel, we by default widen the tire. It is not by a huge amount, but it does get wider.   The picture below shows what I mean.
The tire on the wider rim (left) is wider at the mid point then the tire on the narrow rim (right)
Since the tire gets wider with a wider rim, we increase the dimeter in our pressure equation above. This results in a lower tire pressure for a wider rim with the same size tire. The proper way to calculate it is to determine the percentage that it increases. Each wheel will be different and it will depend on what wheel you are comparing it to.
I hope this blog article was easy to follow and that you enjoyed it. I wanted to thank our good friend Tom Anhalt over at http://bikeblather.blogspot.com/ for helping me sort out my thoughts and teaching me a thing or two about casing tension. Please let me know if you have any questions or comments below.  
Take care,