(Do a "Google" for engineering calculations for inclined railway tracks. (I found this if it's of interest) There is only one unique speed for a given angle of track banking where the force of the weight of the locomotive goes at right angles down into the tracks.
Our skis make grooves like railtracks. But we can vary the angle of inclination of the track - unlike the loco driver who must regulate speed exactly for every curve.)
You achieve this choice of speed and angle by feel. If it isn't right you make subtle adjustments to the inclination, the speed, the radius of turn. You change speed by choice of line. You don't need to throw them sideways.
Well done Davey. Just want to highlight the problem with tipping too much isn't sliding down the track (or icy on-ramp) like the train engineer's problem. You can make that groove at any angle higher than the critical angle because sliding down the groove doesn't derail you; it just helps put more pressure on the bottom of the groove (and your knees). However if you try and turn too tight for your given speed, your critical angle will become higher than your current tipping angle given your current speed. If you try and make a 2g turn at 50 mph, you will need to tip your skis to resist the forces while balancing on the skis (preferably the inside edge of the outside ski), and the ski will try and dial up a turn according to the (cosine (tipping angle) X side cut radius) formula. It will not succeed; it will skid along at some wider radius. If you hit a bump and the ski momentarily digs in, you're toast.
How can a ski hold LESS well when tipped to a higher edge angle?
Because edge angle on the snow plays such a significant role in the carving radius of a turn, too much edge angle can actually cause a ski to hold less well than "just enough" edge angle. Especially at high edge angles of 45 degrees and up, a slight change in edge angle can have a tremendous influence on the ski's carving radius. For example, an edge angle (on the snow) of 60 degrees (cosine = .5) creates a theoretical carving radius of one half the ski's sidecut radius. Increasing the edge angle just 15 degrees further from 60 degrees to 75 degrees (cosine = .26) nearly cuts the theoretical carving radius in half again--about one quarter of the ski's sidecut radius! When the ski bends into a tighter radius arc than the turn the skier is trying to make, it will not carve--or hold--nearly as well as when tipped to the optimal angle. Conversely, if you let the ski tighten the turn to whatever radius it bends into, it will cause a dramatic increase in the g-forces (centrifugal force) caused by the turn. That can cause the snow itself to break away under the load, and can also increase the stress on the body, making it more difficult to sustain the intense force--either way resulting in the ski skidding because of too-high edge angles.
Edited by Ghost - 11/8/15 at 6:16am