The question "Why do stones curl" has always seemed to me to imply that there should be one answer, and only one. When I researched the subject as best I could some three years ago, I soon discovered that there simply cannot be one single answer. The summary of that research can be found here:
http://www.scottishcurlingicegroup.org/reports/WhyDoCurlingStonesCurl.pdfWhatever the real reasons are, they are quite useless if people cannot understand them, so I've always tried to find better ways of explaining the relatively simple scientific facts. These can be reduced to mass and momentum. The mass represents the energy of the stone, as imposed on the ice surface, and it is constant. The momentum is the product of the stone's mass and velocity, and is not constant. The velocity is both linear and angular, in direct relationship with the mass, which is why I prefer to talk of momentum.
People like Shegelski and Denny are very intelligent physicists and they try really hard to find scientific ways of explaining these things. When I first studied their reports (and many others!) I was quickly reminded just how ignorant I am of such things. Then I realised that they had not fully taken into account this stuff called water. In the latest Shegelski report that Bob pointed out there is now much focus on this and rightly so, because that is where -- in my humble view as someone who has studied curling ice -- the answer lies. The MSMM/F phenomenon, combined with the behaviour of amorphous ice, explains everything. The stuff on water can be found here:
http://www.scottishcurlingicegroup.org/reports/WaterInACurlingRink.pdfAlthough only a thin film of water, amorphous ice (call it frost, if you like) can be of deposition (where the vapour freezes without becoming a liquid and falls onto the ice) or condensation (where the vapour becomes liquid, as in mist, and then condenses onto the ice and freezes). The first will be like a fine dust, easily swept aside, while the second will stick like puppy stuff and has to be scrubbed aside. But both will behave much the same when under influence of the mass of the stone, say 20kg, with 1kg per pebble. When a stone passes over this stuff it will be able to melt at least some of it to use as lubrication, and the slower it travels the more it will melt, until it melts too much and the thin film of lubrication becomes like a wedge of resistance. We can't see this happening, but we know it does. So, momentum decides how long the stone will spend on the relative pebbles, while the mass does its work accordingly.
Now add to this the angular velocity from the turn of the handle, where the slower turning side of the stone (the inside) will spend more time on the pebble surface than the outer side. As the stone is released these are nearly equal in effect, but as it slows down the inner side melts more and more frost until friction overcomes lubrication and the stone draws. Cool the ice down too much and the stone will stay straighter, simply because it cannot melt the frost enough; warm the ice up too much and the stone will melt too much frost and will slam on anchors and also dive. We tried this once, and it took all of Iain Baxter's best cannonball weight to keep a stone straight enough to actually play a strike shot, which still curled over a foot.
It will be interesting to me if anyone ever succeeds in disproving this theory. There are complicating factors and differing circumstances, but this to me is why stones curl. Sweep the frost away and they stay straighter and travel further, just as they do when we sweep.
And then there are sanded stones, which I cannot comment on, because it is artificial and without any constant, and to replace the MSMM/F with plain friction is a different thing to curling.