As a general rule a skier's upper body, including his head, should face down the hill.
The reason for this is not as obvious as you may have been led to believe. No doubt your teachers have made you face down the hill before, and you might have thought that this was solely to prevent you from facing up the hill to stop you from doing all those interesting things like backwards snow ploughs and skis crossing at the back etc. You would be right to assume this, but it is only the half of the reason.
Here is an example to show why your body should face down the slope. For now treat it as a purely theoretical experiment. By all means try it if you don't believe me (I've used it on numerous occasions as a demonstration), but for now just imagine you are doing it.
Find a good friend and ask him to hang as relaxed as he can be from a tree branch by his arms, so that his skis are perhaps six inches off the ground. Now get the tips of both skis and move them round so that they are at right angles to your friend's line of sight (or until he screams). His head and most of his upper body should still be facing forwards.
If you let go of his skis (make sure you get out of the way quickly), the skis will swing back of their own accord to their original position. In this weightless state they swing back quite simply because of the torsional qualities in the muscles and ligaments of your friend.
The thigh and stomach muscles, and the ligaments holding him together are wound up like a rubber band, and so long as the skier's body is facing down the hill, a turned ski will tend to swing back in the same direction when unweighted. Simple isn't it?
I said earlier that as a general rule the upper body should always face downhill, but there are a few occasions when it doesn't matter, and one or two occasions when it is even beneficial to face uphill. These exceptions will be discussed elsewhere under the title of 'Contre Virage', which roughly translates forn the French as 'counter turn'.
For example, it is quite in order for your upper body to be facing your ski tips when moving along on a fast traverse across the slope. You can also break the rule when running straight down the fall line and you want to look for goats, or chamois, or elk, high up above you as you tool along, but you must be aware that, depending on your speed, the slightest twist of your upper body, and even your hands and your head, can affect the direction of your skis.
Simon Dewhurst has taught downhill skiing in North America, Scandinavia and the European Alps for 35 years. He currently runs a ski chalet agency in the French Alps. His book "Secrets of Better Skiing" can be found at http://www.ski-jungle.com. If you have any comments about the above article, he will be happy to answer them.
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