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There's also a heavy correlation between carcass design and performance characteristics. When I bought my Pirelli P Zero Nero M+S tires, I emailed their technical support to ask what was the difference between that and the 3-season P Zero Nero other than just tread material and available sizes. I was told the carcass was designed to create a smaller contact patch to increase pressure against the pavement.
I am not questioning that you are reporting accurately what they told you, but it makes no sense. The size of the contact patch is a function of the pressure to which the tire is inflated: a tire that is inflated to 32 psi will have a larger contact patch than than the same tire will when inflated to 35 psi, and at 41 psi the contact patch will be smaller still. IOW, to get a smaller contact patch, it is not necessary to alter the construction of the tire; all that is needed is to pump a few more pounds of air into it.
IIRC, the carcass of the P Zero Nero M & S is built around inexpensive polyester plies, while that of the P Zero Nero is built around more expensive rayon plies (rayon has a more linear characteristic over a wider range of temperatures than polyester does, justifying the extra cost for a tire where performance is important). So, even though the tread design of the P Zero Nero is identical to the tread design of the P Zero Nero M & S, they are different tires. And it is the tread compound of the M & S tire that allows it to stick to snow, simultaneously undercutting its wet braking ability compared to the P Zero Nero.
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I'll just bring up something many are familiar with - the common "deck shoe" like a Sperry Topsider. The rubber material is inherently hydrophilic, but they place hundreds of tiny little "wave" cuts in the sole which bite onto wet surfaces and "squeegee" water away from the surface. Or you could compare a solid rubber sole to a treaded sole like a hiking boot. The solid rubber is great on dry pavement but can get slippery even on merely damp pavement, while treaded soles create more pressure on a smaller area.
It is a little bit more complicated than that. On the route where I walk our dog is a quarter-mile stretch of wooden sidewalk. In the rainy winter months in Portland, that wooden surface can get quite slippery, and I often walk out in the street in the asphalt pavement to avoid slipping.
However, my footwear makes a very great difference. Most days, I am wearing New Balance M807 trail running shoes when I walk the dog. Those shoes (which currently are about halfway through their useful life) have a tread, but walking on the wooden sidewalk is like walking on slick ice when the sidewalk is wet.
Some days, however, I wear a pair of Doc Marten's (the old version, made in England). The soles of those, while not yet completely worn out, are getting fairly smooth. Counter to your theory, the Docs have
some grip -- not great, but
much more than the New Balances -- despite their near smooth surface.
Again, it is the tread compound, not the tread design, that appears to make all the difference.
