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Another way to possibly get better accuracy is to pump the tyres to several different pressures, and for each pressure, re-measure the tyre contact surface.

From there, you could then simply average out the results - or better still, the data would help you reason about the pressure<->area relationship. Just going by the P=F/A formula, pressure should be inversely proportional to area, but people have pointed out things like the tyre sidewall stiffness will affect this. Taking several pressure<->area measurements would help you reason about this - perhaps the sidewall means P = F/A + x, and with multiple datapoints, 'x' can be calculated.

I was thinking the same but I imagine you'd have to buy a tyre pump as well in order to re-inflate the tyres. Not sure how much they would cost...

A 12v pump which plugs in to a cigarette lighter socket costs about $15 / 12 GBP. They're not the fastest things in the world but they work and there's no labour other than screwing them on and off.

It’s possible (but laborious) to use a bicycle pump to fill a car tire: they use the same kind of valve and bicycles use a higher pressure than cars do, there’s just a lot more air to move.

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