The studs contact the road for maybe 5% of the tire’s total rotation time. In that time, they react to the road temperature, and 95% of the time they manage not to react to the air temperature?
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I’ll definitely be passing on those new tires. You can get two or three sets from a cheaper category for the same price, and they’ve served me just fine so far. Then, with the money saved, I’ve been able to buy Nokian Tyres shares. 
This strategy, of course, requires that others don’t think the same way.
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From what I’ve read, tires react to the road temperature. The rubber compound beneath the stud hardens and softens according to the road temperature. The stud is never completely out of use. It’s hard to see how this wouldn’t have been tested extensively and thoroughly in all weather conditions.
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The world’s first winter tyre with retractable studs / Nokian Tyres
That’s a previous version of the same idea from the same company from 12 years ago. In these, the driver presses a button in the cabin and the studs come out.
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There have been others like this; here is a similar one from the past (image below). This product likely failed because asphalt bitumen clogged the sleeves, meaning the studs didn’t move (in/out) as designed. Perhaps this version from Nokian Tyres already works as intended; let’s hope so at least 
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“The studs touch the road for maybe 5% of the total tire rotation time. During that time, they react to the road temperature, and 95% of the time they manage not to react to the air temperature?”
Air transfers heat very slowly / with low “power” (air is a very good insulator for exactly that reason), so no, the tire’s operation couldn’t even be based on that.
You can test it for yourself outdoors: you can easily be without gloves, but try pressing your palm against ice on the ground.
Or in a sauna: you don’t burn even at 100 degrees, but if you touch, say, 100-degree water, you’ll burn immediately.
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Annual report is out for those interested.
Try blowing on your hand in a sauna and it’ll really start to burn. Airflow does the same to a tire, and since it spends 10-20x more time in the air than in contact with the road, it’s impossible to think that air temperature wouldn’t have an effect.
But regardless, as a shareholder I naturally hope there’s demand for these, even if I am skeptical about their functionality. With a good story, you can sell at least one set to those willing to try; if a second round doesn’t follow, then production will cease.
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The situation is not quite comparable because it’s specifically about heat transfer efficiency rather than just airflow/wind chill / temperature.
In a sauna, there is very high humidity which makes heat transfer efficient, whereas freezing air is very dry, meaning it transfers heat poorly even if there is a temperature difference between the elements. This difference is also smaller than in a sauna (38C vs 100C) and under humid conditions.
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