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I have 57-559 (57 mm width, 559 mm diameter) / 26"x2.125" tires. I weigh about 95 kg / 210 lbs. The tire's sidewall shows a single pressure value of 300 kPa / 43 psi.
However, this calculator shows that given a fixed tire size, different rider + bike weights would have different optimal tire pressures.
Is there a way to calculate such an optimal pressure?
You can have an "optimum" tire pressure - unfortunately, when riding on road you want higher pressure, when riding on low grip surfaces you want lower pressure (more tire in contact with the ground), when riding on very uneven terrain you want again higher pressure to prevent flats, when jumping you want higher pressures, and so on and so on.
The desired tire pressure depends on where do you want to ride, and to a reasonable extent on what you "feel" - which might be different than what a different person of your same size/weight feels.
What you can do is find a "recommended" tire pressure and work from there. In time tire pressure drops, at some time you will find the pressure too low - measure it and remember it as your "minimal" tire pressure. Try with higher pressure than recommended and "feel the ride" - MTB tires with an extreme thread pattern at high pressure rumble very much on asphalt, a lower pressure "mellows" the ride (vibration into the hands).
I looked into it and found this PDF: 2004, Berto: "All About Tire Inflation", where the optimal tire pressures were found experimentally from a Tire Drop test, where
Tire Drop is the distance that the tire sags under the weight of the rider and the bike. For a given tire size and load, the optimum inflation pressure for comfort and rolling resistance produces a Tire Drop of about 15% of W (the Section Width) or about 20% of H (the height from the ground to the rim).
For my case, that document shows the minimum tire pressure somewhere around 25 psi / 172 kPa for a 26"x2.125" tire.
There is no such thing as optimal tyre pressure.
Tyre pressure is always a compromise between comfort, rolling resistance, grip and likelihood of puncturing. This depends not only on tyre dimensions and rider/bike weight but also on the terrain you're riding on and the weather.
Most tires are labeled by the manufacturer with maximum load - inflation numbers. These depend on the design, materials and construction of the tire as much or more so than its dimensions. While a manufacturer may be able to provide optimum inflation info I don't see any way to develop a calculator that would do more than give you a wild guess.
Even if by "optimal" we mean something specific and measurable like "least rolling resistance", there is no such pressure. Minimum rolling resistance depends on the surface. On a smooth surface, like a varnished wooden velodrome track, high pressure is best: the higher the better, with diminishing returns. On a bumpy surface, there is an optimal pressure with negative returns if it is changed either way. (And note, by the way, that an off-road tire with "knobs" constitutes a bumpy surface, even if ridden on a smooth surface.) The pressure depends on how big the bumps are, and the load on the wheel as well as suspension details. Practically speaking, it can only be experimentally determined; and for that to be valid, we actually need a way to measure the rolling resistance of that specific equipment on that specific surface.
