|Originally posted by Wear the fox hat ?:
Don't get me started. ...This could be as small as the ski's sidecut, or a pivot of more than 40 degrees". ... So, surely if the skiing angle is the sidecut of the ski, then you are carrying out a perfect carve? Am I right, or am I stupid?
a) LOL - Couldn't resist a good chance at a tweak!
b) Nope, you most certainly aren't stupid. What's going on is that there are various closely related definitions of steering angle, and LeMaster doesn't bother (as far as I remember) to carefully distinguish between them:
1) Because it is extremely clear, the definition I favor is the "local steering angle". Imagine you had a little video camera mounted above the edge of the ski looking directly downwards at the snow streaming by the ski at various points along its length. In a pure carve, the part of the edge near the tip goes over exactly the same bit of snow as the part of the edge near the tail. This means that the local steering angle all along the length of the ski is exactly zero.
Unfortunately, using this definition is a bit complicated because there is not just one "steering angle" for the whole ski, but an infinity of them for each point along the edge as you go from front to back on the ski. This definition, while precise, confuses some people because in a straight, flat ski schuss, because of the flair of the tip and tail, there is always positive steering angles in the forebody of the ski and negative steering angles in the aft section of the ski along one edge, and the opposite along the other edge of the flat ski. The maximum of any of these angles is small, just a few degrees, and the average along both edges and over the length of the ski is exactly zero, but it takes a bit of mental work to get to the conclusion that most people would say is obvious, namely, in a flat ski schuss, *THE* steering angle better be zero. Most people think of only one "steering angle", and it is better be zero in this case - no muss, no fuss, don't make a big deal about an infinity of steering angles.
2) In the quote you supplied from his book, LeMaster is being quite free and easy with the terminology. He seems to be implying that the minimum steering angle is always equal to the sidecut angle of your skis (ie, relative to the ski centerline). Well, this certainly isn't the case, because in a carve, the local sidecut angle at all points along the edge will be exactly zero. On the other hand, should one define the steering angle as relative to the centerline of the ski, in a carve, the steering angle will always be exactly equal to the angle the edge diverges from the centerline of the ski, so you will have a positive steering angle near the tip and a negative angle near the tail with an average value again equal to zero.
So, there you have it, one can define it locally or as an average along the length, with respect to each point on the edge, or with respect to the centerline of the ski, but one has to be clear and consistent about which definition you've picked.
The bottom line is that IMHO, you basically were caught up in a minor inconsistency in his text.
Obviously, to some extent, this is splitting hairs because for most recreational skidded turns, the steering angle (whatever definition you pick) is always considerably larger than the much smaller angles which define the shape of the sidecut.
Hope this helps (& you didn't mind the bit of earlier ribbing).
Tom / PM[ August 18, 2002, 09:51 AM: Message edited by: PhysicsMan ]