|Originally posted by GF:
...However, you make an assumption that the ski-tips lay on the same radius at all points in the turn, and that's where you make an error...the inside ski-tip goes ahead of the outer ski-tip at some point in the turn (usually during the entire second half of the turn), and so it is at a point further along the circle...
Hi GF - Thanks for the thought provoking reply. I don't think I have ever seen anyone suggest that particular mechanism before. You are absolutely correct that I did make an implicit assumption that the effect of tip lead on divergence was negligible compared to other reasons for divergence or convergence of the skis. However, I still think this is true, and I will outline my reasoning below.
First, in modern, higher-level skiing, tip-lead has been greatly reduced, so I wouldn't base an argument on assuming that it is present.
Second, even if tip lead is present, perhaps, as you suggested, in a skier with older technique, its effect on ski parallelism is negliglble.
Lets assume conditions most favorable to your argument - a huge amount of tip lead even for an old school skier (say, 1 foot), and a skier making a tight carved turn (say, of radius 5 meters - around half of the sidecut radius of the most deeply sidecut skis currently available for sale).
If you do the geometry, the divergence due to the mechanism that you suggested is only 3.488 degrees. In reality, maximum tip leads even for old-school skiers are usually more like 6 inches (not 1 ft), leading to divergences (due to the mechanism you postulated) in the 1.5 degree range.
This is the reason that in my previous post I said that the small divergence angle due to tip lead is negligible compared to the much larger angles between the skis that skiers intentionally or unintentionally introduce because of their technique. For example, in a modest stem (or diverging step) position on a pair of 170 cm boards, if the tips are separated by 2 inches and the tails by 1 foot (or visa versa), the skis will be off parallel by 8.5 degrees, about 5x larger than what arises from the tip lead mechanism you suggested.
Tom / PM
PS - Sorry for the mini-hijack, folks.