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Fat tires are associated with good bump absorption. Is this due to their fatness, or is it due to the low pressure with which they can be used?
If I pump a fatbike tire to 120 psi (yes, that would be absurd), will it still absorb bumps better than a 23mm tire at the same pressure?
To make it stupidly simple, assume that the tire has a roughly rectangular cross-section. So a 1-inch tire is 1 inch across has a width of 1 inch in contact with the pavement, while a 4-inch tire is 4 inches across and has a width of 4 inches in contact with the pavement.
Also, for the sake of simplicity, assume that the tire is perfectly flexible -- that the stiffness of the tire carcass and tread is not a factor.
And assume that we have a 200 pound bike+rider, and that the weight is evenly distributed between front and rear, meaning there is 100 pounds of weight on each tire.
At 50 PSI the 1-inch tire will need to have two square inches == two linear inches in contact with the pavement, while the 4-inch tire will need to have 2 square inches == one-half linear inch in contact.
On a 24 inch wheel, the 1-inch wide tire will deflect about 0.04 inches, while the 4-inch tire will deflect about 0.0026 inches.
If you hit a bump which momentarily doubles the force on the wheel (and the size of the contact patch), the 1-inch tire will deflect about 0.168 inches, while the 4-inch tire will deflect about 0.01 inches. (Using this online calculator.)
So the narrower tire is "softer" by a factor of (0.168-0.04) / (0.01-0.0026) = 0.124 / 0.074 = 1.7.
After reading the answers here and becoming more curious, I found this article, which agrees with @Daniel.
to briefly summarize it, they found that at the same tire pressure the narrower tires deflected more and had a lower stiffness (force over displacement)
A curious finding is that a difference of 1 bar (14psi) makes more of a difference that a 5mm tire change. I suppose the problem becomes that with a 23mm tire there is only so much room for compliance. Additionally, they found that tire width had very little effect on small bumps (8mm in this test) and that the main factor was tire pressure:
at this point it seems that for bumps smaller than the tire diameter, the shape and size of the bump is driving the stiffness more than the effective width of the tire itself.
That article also links to another article which discusses the sensation of tire stiffness as an expression of hoop stress, which they call casing tension. To me, this seems like a much more logical explanation as to why a wider tire will feel stiffer at a given pressure (again agreeing with @Daniel). I would suggest reading the article, but I did my best to briefly explain the end result. Essentially, the equation for hoop stress is based upon wall thickness, diameter, and pressure.
Wall thickness = the thickness of the tire casing
Mean diameter = the tire size [cross sectional area of tire]
Pressure = the pressure the wheel is inflated to
Maintaining a constant casing tension and wall thickness we can solve for pressure and see that the pressure is inversely proportional to the diameter.
The real benefit of wider tyres is that you can run them at lower pressure, and if they have nice flexible sidewalls the ride is much softer because the tyre deforms over bumps rather than making the rider rise over them.
You won't feel it, but at the same pressure the fat tyre will feel softer because it will deflect more for the same change in applied force.
That happens because as the tyre compresses over a bump the pressure inside the larger tyre rises less than in the smaller tyre, and the tyre itself flexes less. But we are talking zero to quite a number of decimal places (question is about rider weight, but if you use "2G" instead of "twice the mass" it works just the same)
My experience is with 406 tyres, where it's easy to get high pressure tyres up to about 55mm wide. So I have had tyres down to about 32mm wide on the back of my commuter and up to 55mm wide, all happy to run at 6 bar. My mental habit is to pump them to 6 bar, and I can't tell the difference in ride quality between them. The wider tyres have more rolling resistance, but on flat roads that is a fairly small effect. I suspect it's from the wider contact patch meaning I hit more small bumps on Australia's rough roads. As soon as I hit a soft surface the wider tyres have much more rolling resistance, unless it's just the right softness for the skinny tyre to sink in while the fat one floats.
The flexing effect is because the wider tyre presents a flatter bottom surface, so there is a tiny difference in how much flexing happens around the edges of the contact patch. Again, I'm am not sure that you'd be able to measure it, but it's quite possibly there.
