If you have ever seen the Physics experiment where two metal balls are started in the same place at the same time, one follows the curved line, the other follows the diagonal straight line . The curved line, ball always wins because the initial vertical drop is steeper in the curved line. Once into the fall the curved line offers momentum to gain and maintain speed and the curved line ball is always faster. The straight line is shorter. This done in the falline and in a laboratory situation. But if you apply it to skiing. A carve is always faster then a skid. The more angled the ski the faster the same arc as a the skidded turn.
In the equation : V squared Velocity, over R, the radius of the arc, equals A acceleration or centripetal force.
http://www.harbskisystems.com/hhsite/eq ... 20copy.tif
The thing they don?t tell you in physics class is that the equation is dependent on the value R, which is in skiing, how you can tip and in what part of the arc you tip. Velocity is speed, so the faster you are traveling, the better your chances of staying upright in a turn, (with the same angles) again if you can tip the skis to at least an angle that works for that higher speed. . If you ski slower, it is more important to tip correctly, if you want to get big angles without falling over. So, if you should try to achieve a low R value (because in the formula it is divided into V), which means a smaller arc radius , you have to ski faster to stay upright with less edge angle.
As far as skiing with the skis flat, trying to complete arcs on green slopes, it is very slow. I have to really skid for Green Camp skiers, so my students can follow me in a series of turns, as I speed up quickly when I put the ski on edge, and they slow with less edge angle.
I often find myself in a bad situation on crowded slopes, as I?m arcing very round completed curves and I see someone out of the corner of my eye, beside me, skiing almost straight downhill, barely pushing the tails to the side staying with me, the whole run.