Effect of "extra" edge angle
Bob Peters hit the nail on the head: "If you go all the way and use an edge angle even greater than what's required to simply carve the ski, you'll bend the ski even more, resulting in an even smaller turn radius..."
To see this, make yourself a little plastic or cardboard cutout of the sidecut of a ski that looks sorta' like this:
Note that my little sketch only depicts the forebody of the ski. Duplicate and flip it, and you will have the aft section as well. Join the two sections together, laminate them, & you will be set to demo "how modern skis help you turn " to anyone who asks (and many who don't
Now, get your small, model ski up on edge, and slide it along some not too slick surface as if it were carving on packed snow (i.e., tip, tail and underfoot area ALL touching the snow). Give it even more edge. The ski decambers even more but this stops when the underfoot area touches the snow. Once again, push it along (in this condition) as if it were carving. The more edge angle, the more decamber you get on hard surfaces, and hence, the tighter the turn. For most skis on hardpack, it only takes only a negligible downward force (5 - 15 lbs) to bottom out the center of the ski at any reasonable angle, so the force required is usually never an issue.
As it turns out, there is a very simple formula relating the theoretical carving radius to the physical sidecut radius of the ski:Theoretical (pure) carving radius = Cosine (edge angle) * Sidecut radius.
Of course there are limits as to how much one should "over" edge. For example, over-edging in racing will slow you down (for a variety of reasons).
================================================== ======Critical edge angle
(Sorry, but I'm going to be lazy and cut and past from an old 2001 message of mine.)
From my message posted September 10, 2001 02:54 AM in the thread, http://www.epicski.com/cgi-bin/ultimatebb.cgi?ubb=get_topic;f=4;t=000505;p=2#0000 28
"...If this traversing skier is in balance and fairly upright (i.e., not in an angulated or banana-shaped position (as viewed from the rear)), the bottom of his skis will be close to parallel with the surface of the earth. As he goes across the hill, the compression of the snow under his skis will generate a little shelf in the snow for him to stand on. In this case, the little snow shelf will also be close to parallel to the surface of the earth. This will happen no matter how steep the hill he is on (within reason).
On the other hand, if the skier is again in balance (i.e., his CM is directly above his edge), but has assumed an angulated position, the little snow shelf that he is actually standing on will no longer be parallel to the surface of the earth – the part of it furthest into the hill will actually be slightly lower than the part just under the surface of the snow. Under the weight of the skier, this sideways ramp angle makes the ski want to cut into the hill even more, and ensures that the ski won’t sideslip.
For the in-balance, but upright skier, should it happen that the little snow shelf that he is standing on tilts slightly outward instead of inward, then, the weight of the skier will tend to drive the ski off of this shelf, and ensure that the ski begins to sideslip.
This is THE fundamental phenomena that makes angulation important.
In technical terms, first draw a line between the center of mass of this hypothetical one-legged skier and the ski edge in contact with the snow. Next, draw a line perpendicular to the ski passing through its edge. The angle between these two lines is the “critical edge angle”. If it’s one way (positive), your skis get driven into the shelf, and don’t sideslip. If it’s the other way (negative), they slide off the shelf and you slip.
It is important to realize that this angle is NOT the normal edge angle that people generally talk about in skiing. The normal edge angle is simply the angle between the base of the ski and the snow. In contrast to the critical edge angle, the normal edge angle depends on the angle of the hill you are on, and might only vary by a few degrees out of many between a skidding and non-skidding situation..."
Tom / PM[ November 14, 2003, 10:46 PM: Message edited by: PhysicsMan ]