Surely, somewhere, there must be a formula for estimating this sort of tyre wear?

Doubt it. There are an awful lot of variables and many of them will be difficult to estimate. If you really wanted to find out, experiments would probably be required.

""Or if there isn't, possibly forum members could suggest a likely solution?

OK, here goes.....

DONT DO IT.

Sorted, I think you'll agree

Surely, somewhere, there must be a formula for estimating this sort of tyre wear?

Or if there isn't, possibly forum members could suggest a likely solution?

Tread depth gauge?

Seriously though, the wear won't have been much if anything, starting up a steep hill in a heavily loaded car with the wrong wheel drive is always likely to end up in wheelspin.

However you should congratulate yourself, i mean that sincerely, far better to engage the clutch quickly and let the tyres slip if anything, maybe you used .5mm of rubber, that's a lot cheaper and easier to replace than .5mm of clutch lining plus heat damage to the pressure plate (especially if you have a DMF) slipping the clutch would have caused had you slipped it instead, a steep hill start is always hard going on any vehicle not designed specifically for such events with ultra low gears available and grip in the right places ie not the front wheels only.

Had you been the fortunate :-) yeah right, owner of an automated manual Fiat 500, and some other cars with these unfit transmissions are just as bad, then you would not have been able to start on the hill anyway and if as steep as you suggest quite likely the car would not have ascended the hill at all with 4 people on board unless you had a clear run at it...we had a special method of loading these contraptions on the top deck of car transporters, even with a slight run up all they could manage was to get onto the very back of the deck then they would peg out...then a colleague would raise the deck level with you sitting in the seat so the car could then be driven to its correct deck spot.

Tip for getting up that hill in snowy weather, reverse the Kia up, then it become correct wheel drive.

Don't worry about a bit of tyre smoke, seen regularly from the rear wheels of our old Merc when it was younger and in the hands of my very own hooligan SWMBO.

Edited by gordonbennet on 10/10/2019 at 19:22