Hoop Stress and Why Tire Pressure Should Decrease with Increased Tire Size
By Lennard Zinn
This report filed June 24, 2024
We recently delivered a gravel touring bike to a customer. When he picked it up, we gave him a rundown on his bike, including maintaining his waxed chain and the pressure to pump his tires up to depending on conditions and how much weight he has in his front and rear panniers.
His new bike has 700 X 45C Challenge Getaway Tubeless Ready tires. I explained that, on gravel roads with his 185 pounds and no extra weight on the bike, he would want to run those tires at around 30psi. He was shocked and said, “That seems counterintuitive to me.” He wanted to pump those tires as high as or higher than he pumps his 700 X 25C tires (100psi)! He went on to explain that he would have figured that the bigger the tire, the higher the pressure, not the other way around. I realized that others may have this same misconception.
So why run them at lower pressure?
The short answer:
Bigger tires will roll faster, grip better, and be more comfortable to ride if you run them at lower pressure. One can measure those first two items, as I did numerous times over the decades for my articles for VeloNews, and you can feel the latter.
In tire tests I organized at Wheel Energy Oy in Finland as well as ones I did with multiple riders on gravel roads using electric-eye timing, the data always produced a U-shaped curve of rolling resistance as a function of tire pressure. In other words, “Crr” (the coefficient of rolling resistance) is at a maximum at zero psi tire pressure, and it steadily decreases with increasing tire pressure until it reaches a pressure where Crr is at a minimum. The amount of pressure that minimizes rolling resistance with a given tire is dependent on the rolling surface; the rougher the surface, the lower the pressure that minimizes Crr. And each increase in tire pressure after that inflection point of minimum Crr results in a corresponding increase in rolling resistance.
The same goes for tire grip. At very low tire pressures, the tire will fold over when cornering; if you’ve ever tried to ride home on a flat tire, you’re familiar with this. This caused Tadej Pogacar to crash late in this year’s Giro d’Italia when his team car instructed him to go around the next corner before stopping to change his flat tire. And at overly high tire pressure, the tire’s contact patch on the road will be reduced to the point that it will lose traction and slide under cornering forces that wouldn’t break it free at lower tire pressure.
The increased comfort you feel at lower tire pressure is because the bike doesn’t bounce up as high at every bump in the road as it does when the pressure is high. This is the same thing that reduces rolling resistance and increases grip: the bump is absorbed into the tire rather than causing the tire, bike and rider to deflect, costing energy as well as traction.
The longer answer:
The stress on the tire would become too high if you were to continue running the same or higher pressure with increasing tire width. There is a safety reason that the max tire pressure imprinted on the sidewall of the tire is lower on wider tires than it is on narrower tires. That max tire pressure is a percentage of the burst pressure of the tire—the pressure at which it blows off the rim. It takes less pressure to blow a fatter tire off a rim than it does to blow a skinny tire off.
The max tire pressure imprinted on the tire is not the full measured burst pressure; it is a percentage of that pressure to allow not only for variations in production of the tires, but especially for increases in internal pressure with temperature. That safety margin is to prevent the tire that you pump to the max rated pressure on a cool morning from exploding when it’s hotter later, especially when descending switchbacks with rim brakes and carbon rims. It also might save a mess someday when you leave your bike inside a car parked in the sun.
I think that people largely assume that the recommendation for running bigger tires at lower pressures than smaller tires is a choice based entirely on considerations like the likelihood of pinch flats, comfort, perhaps rolling resistance (all of which are valid) and don’t consider it a necessity in terms of safety (i.e., not over-stressing the tire).
If you do not lower the pressure with a wider tire (or the same tire on a wider rim, making the tire wider), you must lower the pressure simply to get to the same level of stress on the tire casing and rim walls as you had before with the narrower tire and/or rim.
Why is the stress on a wider tire greater than on a narrower tire if they are at the same pressure?
We can’t have this discussion without talking about stress (σ), which has the same units as pressure and is defined as “the force per unit area on a body that tends to cause it to change shape.” I will show why you must lower the pressure as the tire gets wider in order not to increase the stress on the rim and tire walls.
With a cylindrical thing like a tire/rim combination, we are talking about hoop stress — check out the illustration of the cylinder section in the link. Hoop stress is what is trying to tear your tire casing apart, fold overheated carbon rim walls outward like a limp taco shell, and yank your tire beads out of the rim, so pay attention.
The hoop stress on the wall of the cylinder is:
σ = force per unit area = f/a
The area (a) of the cylinder being stressed in this case is the length (l) of the cylinder times its thickness (t), or:
a = l*t
The force (f) being applied by the air inside the tire and rim is equal to the air pressure (p) multiplied by the length (l) of the tire/rim cylinder multiplied by the radius (r) of the tire/rim cylinder’s cross section (i.e., the tire width). But the radius (r) is equal to half of the diameter (d), so:
f = p*l*d/2
and:
σ = f/a = (p*l*d)/(2*l*t) = (p*d)/(2*t)
(since the cylinder lengths on the top and bottom of the equation cancel each other out)
To keep the stress on the tire casing and on the rim walls the same with a bigger tire and/or rim, the stress on the wider tire must equal the stress on the narrower tire, so the ratio of their stresses must equal 1. Using the subscript “n” to refer to the narrower tire and the subscript “w” to refer to the wider tire, we have:
σw = σn
σw/σn = 1
since σ = (p*d)/(2*t),
σw/σn = ((pw*dw)/(2*tw))/((pn*dn)/(2*tn)) = 1
We will assume these are the same tire model in different width, meaning their wall thickness is the same, so tn = tw, and those terms cancel each other out top and bottom in the equation, leaving:
σw/σn = pw*dw/pn*dn = 1
so:
pw*dw = pn*dn
Let’s assume his 700 X 25C tire has a cross-sectional diameter (dn) of 25mm when it is on your rim and that his 700 X 45C tire has a cross-sectional diameter (dw) of 45mm when on the same rim. Since c = π *d, the circumference of the 25mm tire’s cross section is:
cn = π *dn = π * 25mm = 78.5mm.
Similarly, the circumference of the 45mm tire’s cross section is:
cw = π *dw = π * 45mm = 141mm.
Maintaining the same stress (σ) on the rim and tire walls with his 45C tires as 100psi in his 25C tires requires that:
pw*dw = pn*dn,
Then:
pw = pn*dn/dw = (100 * 25)/45 = 56 psi
Thus, just to maintain the same stress on the tire and rim walls with the wider tire, he must decrease his tire pressure by 44psi! (And, of course, to get a softer ride on gravel than a tire pumped up so hard would cause, I recommended around 30psi. As he was protected from pinch flats with tubeless tires, and they would roll faster on that rough surface, there is no reason not to.)
Since I have shown that pressure to maintain the same hoop stress (same hardness when inflated) is proportional to tire width (i.e., the cross-sectional diameter d), then a 33mm cyclocross tire at 70psi or a 5-inch (127mm) fat-bike tire at 18psi feels as hard as a 23mm tire at 100psi. They feel as hard because they are as hard — the tension on the casing is the same in each case (assuming the tire casing is the same thickness, that is). And with clincher tires, the outward force on their rim walls is the same as well.
― Lennard
As a frame builder, Lennard Zinn has been designing and building custom bicycles for over 42 years; he founded Zinn Cycles in 1982. He was a technical writer for VeloNews for over 35 years, from 1987 through 2022 and now has a Tech Q&A column on Substack. He is a former U.S. National Cycling Team member and author of many bicycle books including Zinn and the Art of Mountain Bike Maintenance, Zinn and the Art of Road Bike Maintenance, and The Haywire Heart. He holds a bachelor’s degree in physics from Colorado College. Readers can send brief technical questions to: [email protected].
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