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And to measure how much of the grooves are in contact with the ground, you could add a known weight to the car (like 100kg of people), measure it with and without that weight and see what proportion of the grooves you need to account for to get 100kg difference.

You'd get better accuracy from a bigger added weight, but the bigger the added weight the more you risk changing what you're measuring by forcing more tire rubber into contact with the ground.

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