You need to record your pressure or temperature at the end of the run as well.
The maths is that the pressure divided by temperature K at the beginning of the run = the pressure/temperature K at the end of the run.
(k=kelvin, add 273 to your figures)
The aim is to bring the tyres 'on' to the same temperature and pressure regardless of what you start off from.
Each make of tyre has a different ideal temperature and pressure range. In F1 racing they say that a pressure difference of 0.02 bar can make the difference between poor and excellent performance. F1 tyres run around 1 to 1.2 bar and around 100C and we believe kart tyres run around the same pressures but only up to 60C
But lets assume you could put the same temperature into the tyre each time, raising the cold temperature from ambient to 60c
In the first practice your theoretical end pressure was: 280K= 273 +7, 333K= 273 + 60 10 psi/ 280 K temperature = X/333 K temperature therefore X=10*333/280 = 11.9 psi
In the second practice X = 8*333/288 = 9.25 psi so 2.65 psi difference once the tyre was hot.
What you could have done was calculate the pressure of the cold tyre to produce the right pressure when hot
At a quick guess, since the increase in air temperature was 280K to 288K, a rise of 288/280 or 0.03 (0.0277), you should have reduced your tyre pressures by 1/30th which conveniently is one third of a psi in 10Psi =9.7
If you came in with your tyres at 60C the pressure would have been 11.2,(if you can measure.277, your pressure would be 11.5)
If you came in with the pressure at 11.89 then your tyre temperature would be 80C
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