"In our earlier discussions of the carved turn, we assumed for the sake of simplicity that the ski carved uniformly throughout the turn. Field observations of even the most accomplished skiers indicate that this cannot be true. Even the most purely carved turn must involve some skidding." The Physics of Skiing, pg. 37.
They go on to break down the turn into three sections, "the skid stage", "the early carve stage", and "the advanced carve stage". The amount of skidding is greatest at the beginning of a turn which matches the concept of the critical edge angle. Also, I believe the necessary amount of skidding will be more on a hard surface.
The implications of this are kind of astounding. The perfect carve turn is not something that is accomplished merely by the physics of tipping a ski. Tipping the ski to get a perfect arc is an oversimplification of a very complex physical problem. But, this false conclusion has led to the impossible combination of defining expert skiing as creating a perfect arc with no rotary input. Come on, tipping the ski and balancing on the arc is easy. For some reasons those simple and effective movement patterns elude intermediate skiers, but it's not hard to do. What's hard to do is ride the arc on a hard surface and not skid. This is because skidding during the turn is part of the natural physics of how the skis work.
I can only conclude that it's become like the Emperor's new clothes. Whoever recognizes skidding in their own skiing must have low skill similar to whoever sees the Emperor as naked must be incompetent. Therefore, people who have the proprioception to recognize the truth are often silent. On the flip side, I've often seen how people are unable to recognize skidding and/or rotary input in their own skiing or in videos. Creating a perfect track is probably so hard, because there must be movements involved that people are failing to analyze, describe, and teach. Skiers go out trying to tip and ride, letting the ski do all the work refusing to steer since that's "inferior skiing", but instead of the perfect arc, they get what the ski's natural design allows. I can imagine after trial and error, some stumble onto the exact combination of tipping and steering that gives a nice track in some circumstances without even being aware of what they are actually doing.
I understand the need to justify rotary inputs - most skiers use them - and trying to quote a paragraph that seems to imply it (btw what revision of the book you have? that's on page 139, not 37).
The reality is that they never said any kind of rotary input was applied. They only study the skidding, i.e. the output.
Also, on the next page, they explain what they actually mean: that given the snow deformation, some parts of the edge will skid (i.e. have a lateral displacement) based on some factors:
At no point do they imply that someone needs to apply any kind of rotary input. In fact, the 3 phase carve model is a copy&paste from another study, of a 1987 ski racer making a GS turn, which had to skid the specific turn they measured:
Now - if you study a skidded turn and conclude that the ski skids is one thing, but to extrapolate and use this as the basis to conclude that all skiers skid all turns, is... uhh... not mathematically correct. It's a fallacy.
Here is a modern ski racer, making a GS turn in a course, on equipment and using a technique that evolved for some 30 years since that study - I've slowed it down a lot, so you show us that magical rotary input! As far as I can tell, the ski's edge is never displaced off its trajectory during the entire transition and initiation (admitedly, not the cleanest possible, but easy to find and paste here)...
Now - if I was a physicist trying to generalize the model of a ski turn, I would consider a model that allowed for skidding and for all sorts of inputs, like pivoting, edging, pressure and then I would say that they occur more or less in every turn and that would give me a nice mathematical model, fully aware that either of those can be zero at any point of the turn. The problem with that approach is that some then would assume that the zero doesn't have to be zero, forget the DIRT of the BERP and proclaim that all turns must involve pivoting because it was observed in at least one instance and it's part of the model...
That's why I'm not a physicist...
p.s. I do not categorize expert skiing as creating a turn without rotary inputs, although that is certainly a good skill to own and expert skiers do tend to own that particular skill and working to own that skill will improve anyone's skiing - but I try to be mathematically correct in generalizations. I'm not a fan of the word, because it bundles together good inputs with bad inputs and no inputs... and so does "edging" btw...
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