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I did a little research and found out some interesting things.
First, you can measure the weight of your car based on the psi in each tire. You measure the "contact area" (in square inches), or the area of the tire that is in contact with the ground. You multiply this by psi to get pounds for each tire, then you add up all tires. This confirms a direct link between tire pressure and weight from the car.
But, I also read that the tire will pump up faster when not weighted, although the difference is negligible. The contact area compared to the total surface area of the tire is too small to make much difference.
It would be interesting to jack up the car and see what the difference in psi is.
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Charlie
1966 912 Polo Red
1950 VW Bug
1983 VW Westfalia; 1989 VW Syncro Tristar Doka
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