But what if the skier is moving mostly forward (in the direction their skis are pointing) and then progressively tips that old outside-ski onto its LTE ? I think this will simply cause that ski to initiate a new turn. The skier need not be "carving" for this to work - it also works for Open Parallel. The factor determining outcome is the forward progress of that ski vs. the sideways movement of that ski. If it's moving forward fast enough, LTE engagement will simply promote turning. This is tightly coupled with the idea of a "Steering Angle".
This reminds me of a drill I was given to learn one footed edge change/skiing. Skiing balanced on both skis more or less in a straight line on green terrain, what happens when I alternate between the LTE and BTE on my right ski? I also notice that I cannot engage the LTE unless my foot is under my hip laterally. michael why do you say this is tightly coupled with the idea of a Steering Angle?
Oops, sorry - I missed the question in your last sentence until I re-read things just now.
When skiing on one foot, you're right - the LTE will not properly engage unless that foot is (laterally) under that hip. Further, it will not properly initiate a turn unless it is also under that hip in the Fore/Aft sense. People find it difficult to initiate a turn on the outside-edge of the single ski (when one-ski skiing) primarily because that foot generally sneaks ahead just a bit since most skiers are used to creating an early inside-half lead. Creating this 'lead' of the inside-half inadvertently moves our CM *back* in relation to the foot we're continuing to stand on - and the other foot isn't there to take over as our new primary support foot. We end up on the tail of the ski, which tries to take us across the hill instead of into a new turn.
On the issue of Steering Angle, consider an Open Parallel turn where the skier is still skidding/drifting near the end of the turn. At that moment they have a 'positive' Steering Angle where the ski is still deflecting the skier's momentum (they're still turning) and all is good. Now... what happens if our skier (while still skidding largely sideways) tips the skis onto the new (downhill) edges?
This is why Steering Angle matters so much for Intermediate skiers. If a moderate or large Steering Angle exists then the skis need to be tipped onto the edges away from their direction of general travel (to permit the skis to slide over the snow without 'catching' the leading edge). Once the skier gets to a small enough Steering Angle, the problem of tripping over the leading edges is greatly reduced.
Advanced skiers tend move across their skis and tip them onto the new edges while the Steering Angle is still quite large. They can do this because they're moving their body with more accurate timing and making well planned directional movements. Instead of tripping over that "early edge", the Advanced skier permits the ski to continue moving forward (the direction the ski was already going) while their upper body continues along a more direct path down the slope - knowing the ski will engage and arc around to realign with the path the upper body is traveling in time to avoid a face plant. This requires advanced timing, sufficient pressure on the ski tips and the ability (and willingness) to rapidly tip the skis while 'falling' into the new turn.