JASP, I just read this thread and I like your posts.
FoM, you seem to imply that an even distriubution of pressure, and in particular in the transition is a good thing, and Oisin you seem to imply that a forceful extension early in the turn is the go to move for racers. I strongly disagree with both of these statements, and I'll explain why I think so.
I apologize in advance for the length of this explanation but I know it has been an epihany for at least some people.
When an edge is engaged in the snow you can divide the force that the edge affects the snow with in two major components.
1. The force component that is tangent to the snow surface. This force is given by the instantaneous turn radius of the CoM. If you are going straight (or free-fall "straight") this component does not exist. If you are doing tight SL turns at WC speeds this force is huge. It is proportional to the square of the speed and inversely proportional to the turn radius of the CoM. This can also be called the centripetal force.
2. The force component perpendicular to the slope. The time average of this component is given by the steepness of the slope and the weight of the skier. If the slope is flat the average is equal to the weight (multiplied with g to be strict).
Now you may have noticed that I used the term "average". The interesting thing about the second component is how it is distributed in time throughout a turn. In a static "park and ride" turn the size of this force is quite constant and proportional to your weight x cosine(slope angle).
On the other side of the spectrum we have a highly dynamic turn, like a WC SL racer that flies through the transition with very little pressure on the skis and has a short by very intense engagement of the edges. Say for example and simplicity that he has no noticable pressure for 2/3 of the turn and that he has a high but constant pressure during 1/3 of the turn. This means that the second force component will be proportional to 3 x weight x cosine(slope angle) during this 1/3 of the turn.
In other words you cannot change the average magnitude of this force, only where it is distributed.
Now if we consider the following facts:
-The steeper it becomes the less is the average of the second force component (due to the cosine(slope angle), if you don't know your trigonometrics you just have to trust me on this one)
-The steeper it becomes the faster we go if we carve
-The faster we go the higher the first force component will be due to higher speed and tighter radius
-The resultant force of the combination of the two force components compared to the edge angle is what determines if the edges hold or not. Ron refers to this as the platform angle.
Now this means that to hold an edge in the steeps you either have to increase the edge angle OR increase the second force component (off course the best is to do both).
Up to moderate speeds and steeps and on grippy surfaces it works pretty good to just increase the edge angles, but pretty soon you will reach a limit, for example:
-in soft snow the resultant force is too much along the snow surface and the ski will break loose because of "shaving"
-On ice the ski can very easily break out and skid.
-If you are going very fast the edge angle is larger than what you can handle (read hip to the snow angles)
Now if it easy to realize that if the second force is larger the edge hold will be better. If we take the example above it is like making the force pushing the skis down into the snow three times larger.
So, the core of this is simply that if you want your edges to hold under tricky circumstances you need to have more dynamics in your skiing, i.e. a short but intense edge engagement followed by a longer "float" with very little pressure. One way of viewing this is that if you have this force component significant when the edges are not engaged you are wasting it.
How you get the dynamics is a whole new subject, but some examples are:
-Old school push edge set where you push down on you edges short and abruptly with muscular effort to get a float into the next turn.
-Modern SL turns where you float through transition, delay the edge set by angulation instead of pushing, set the edges by "landing" with already extended leg. Still above the fall line. Continue increased edge angles and counter until the vaulting effect (Or toppling as it is called in this thread) starts to throw you upwards and into the next turn. Retract at exactly the right moment to get a new float into the next turn.
-A longer GS turn where the float is longer so that the body is almost upright in the middle of the transition, but there is still a float similarly to the SL turn.
The tell tale sign that this is going on in a montage is that the CoM is going up and down. You can see this in most WC footage.
In the context of this thread you can view this kind of float as a kind of falling from one turn to the other, where the state of the fall is given by linear and angular momentums as well as the external forces (gravity and friction) as JASP explained. As said, "semantics".
Oisin, the problem with an early forceful extension is that you disrupt how the second force component is distributed throughout the turn. This means you are compromising both higher edge angles and edge grip later in the turn.
FoM, same goes for having too much snow contact in transition, it will make high level dynamic skiing impossible.