There are several purposes of using a weighted release.
One, it develops another type of one footed balance that is necessary for well rounded parallel skiing. You can't get off the big toe until you can balance on the little toe.
Second, it depends on, and helps develop a commitment to the new turn. By "commitment," I mean
allowing the CM to travel across the skis into the new turn before a change of direction in the skis happens.
Third, it effectively blocks any possibility of wedging because the transfer of weight is delayed until the fall line is reached.
Lots of people will use more general, menuever level concepts when describing how to do the weighted release (e.g. commit to the turn, get the CM into the turn, etc.). I think it's important to bring the description back to more specific, PMTS movement level instructions that begin low in the kinetic chain.
The movements that generally, create a release and engagement when on one foot during the weighted release are the same that do so when doing a transfer/release/engage pattern (turns done on the outside foot).
The movements of the release are flexing the old stance leg and flattening the skis to the snow. Fex and flatten.
The main movement for engagement is an active tipping of the inside foot/ankle to the little toe edge.
The difference in the weighted release is the sequencing of the transfer of weight from one foot to the other.
Just to emphasize, neither the release, the enganement, nor the transfer or weight is done by pushing off the old inside foot. In fact, starting completely on one foot with a 2-3 count traverse is good for blocking any tendency to do this.
The sequence is something like the following.
At the end of the turn, the force of the turn passively transfers much of the skiers weight onto the stance ski. This can be enhanced by further flexing of the free leg. It is the actions of flexing one leg or extending the other that transfers weight from one foot to the other. Some clarification may be needed here. If I flex one leg the weight transfers to the other. If I extend one leg weight is transfered to the leg that is extending.
At the end of the turn, when the free foot is completely light. Raise the free foot to the boot top. This completely transfers the weight to the old stance leg (new inside leg). Flex the stance leg and flatten the stance ski to the slope. Consistent, with concentating on free foot tipping, I have found that flattening/tipping the foot in the air to the slope works to flatten/tip the foot on the snow. This action will release the old turn and begin the new turn. I can't overemphasize the usefulness of concentrating on inverting/everting the foot that is in the air to make the correct movements happen in the foot on the snow.
At the release, don't try to twist the ski or your body. This is a big mistake that many people make. They attempt to "juice" the change of direction by turning/twisting the body into the turn.
Instead, concentrate on just balancing. Continue to flex and tip the ski on the ground to it's LTE. Be patient and concentrate on balancing on the LTE. As you begin to face the fall line.
Leave the leg that is in the air the same length. However, progressively flex the leg on the ground until the outside foot touches the snow at the fall line. Continuing to flex the inside leg through the bottom half of the turn will slowly transfer weight completely to the outside leg. Now, the process can begin again.
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Some comments on learning the turn. It is most difficult to correctly release from a dirrect traverse. So work your way into the tun by using a fan -- reverse fan progression.
Start by doing a few shallow banana turns on the LTE. Start from a steeper and steeper position to the falline until you can do a one footed LTE turn from directly down the fall line.
Now use a reverse fan progression to ease your way into a more and more difficult release on one foot. If you don't know what a fan -- reverse fan is, check out the carver excersise page on my website:
http://web.pdx.edu/~petersj/HoodCamp/CarverExercises/CarverExerciseIndex.htm#LearningProgression
I hope this helps someone. The main point is to use the same primary movements that are always used. Remember, that it is these movements that cause the CM movement not the other way around. To emphasize this I think it's good to do some turns with a definite pause on one leg (maybe a count of 3) before releasing. This interrupts/pauses the CM and makes you start everything fresh in the feet. It pays off by keeping the movements of your feet ahead of the movement of your body when you do turns allowing the CM to flow from one turn to the next.