I wonder if you could do even better by putting paint or ink on the outside of the tire, driving over a piece of paper, and seeing what fraction of the paper touched your tire (and thus what fraction of the rectangle boundary actually touches the ground).
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.
>I wonder if you could do even better by putting paint or ink on the outside of the tire, driving over a piece of paper, and seeing what fraction of the paper touched your tire.
Yes you can. It's called "chalking" tires and is commonly used to figure out what pressure achieves optimal contact patch.
You'd basically just be measuring the maximum width of the contact patch, not its area. The best solution would be to lift up each tire, put a piece of paper under it, let the car down, then remove it, measuring the darkened area.
