"Do you think it is possible to have a formula to calculate correct tyre pressures for a given day?"
yes.
but the same as with "jetting software" (driven off air density) it will only be as good as the inputs / modelling you perform.
the amount of grip you get from a tyre depends on the operating temp and structure.
you can predict the operating temp of the tyre if you know the heat capacity, the work done in the tyre as it flexes, friction between track and tyre, the cooling of the air flow and the heat transfer from/to the track.
a lot of the parameters become near constants so id concentrate on:
air temp track temp (have a factor for if it is wet as conduction will have increased)
id use a varying factor for each track as this should account for grip and tightness/number of corners
tyre wear needs to be accounted for
you also need to think about how pressures affect handling and also how tyre temps will vary depening on front/rear wheels positions, toe in/out, caster/camber.
driving style will become a factor at some point
its an interesting subject and would be a good academic exercise but....
i think the practicalities come down to just measuring the temps across all 4 tyres at the end of a session. whether you need to increase/decrease the contact area or increase/decrease the tyre flexing is the big question :)
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