Here's a topic for some fun discussion.
You can close and open your ankles. This movement tilts the lower leg forward or upright, thus moving the knee fore-aft.
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What do you do with your ankles as you ski?
Instructors, do you teach your clients to do anything with their ankles?
Start with just this one.
Some things come naturally--or should, if intimidation doesn't get in the way. Other things, no. So, walking around on skis on the flats should come naturally. If students don't let themselves get freaked out by the fact that snow is slippery, and they might skid a bit (oh, the horror), it's a lot like walking around in street shoes. Pick up one foot, then the other. Move the body over the foot that you've moved and set down. Balance on one foot at a time. All good skills to have available when skiing.
But...in important ways skiing is very different from walking, or from just about any other movement that people do in their daily lives or are naturally adapted to do. And these differences largely come down to how we use our feet and ankles. While it's true that we want to be balanced dominantly on one ski, most of the time, we ordinarily accomplish this while keeping our feet (through the medium of our skis) both planted on the snow at the same time, all the time. We keep our feet close to one another, fore-aft. This changes only modestly through the turn cycle. We don't want a lot of random, unproductive movements of the feet. Beginners want to shuffle their feet. It can take some work to cure them of this.
Walking consists of pushing ourselves off with one foot, and then catching ourselves from falling with the other foot, repeatedly. For each foot, it's plantar flexion to push off, followed by a momentary release of all tension while the foot is in the air, followed by progressive dorsiflexion with the muscles in eccentric tension, as we cushion the impact and slow our body mass from being pulled into the ground. A rapid cycle involving repeated flexion and extension, and repeated application and release of tension. In skiing, we want to slow all of this down, and simultaneously adopt a posture that is far more flexed in the ankle (and in the other joints) than our usual standing, resting posture. This is a challenge for new skiers. Their instinct is to stand tall--inappropriate. Their instinct, when they feel resistance from the fronts of the skis, is to react with muscular plantar flexion, as they would when walking or running to keep themselves from falling forward--unnecessary in skiing. Their instinct, in moments at which they feel little resistance from the skis in any direction, is to let their feet and ankles go rather limp--which can lead to the stance deteriorating, and leaves them ill prepared to react quickly to the forces that the mountain will soon be rapidly throwing at them.
The functions of strong plantar flexion in skiing are rather limited. I would say that they are principally (1) for reacting to variations in terrain, for the purpose of restoring balance, and (2) for jumping. Those who use extension in transition are using plantar flexion for that purpose--but I'm in the school that would ordinarily like to use flexion in transition.
So, I would teach students:
(1) Maintain functional tension in the feet and ankles at all times. I like the Squaw Valley coach Ron Kipp's video on this subject. Not to say we should overdo it. We don't want to be stiff, or wear ourselves out. We just want to be ready to act, and want to avoid going limp and letting outside forces realign our joints.
(2) Dorsiflexion, and more dorsiflexion. Pretty much all the time. Our instincts are to use plantar flexion inappropriately, so we have to focus on counteracting that. It's going to be rare for a student to dorsiflect too much. You'll never collapse due to too much dorsiflexion. The cuffs of your boots will stop you.
(3) Others have noted that the muscles that create dorsiflexion are relatively weak. But we don't have to rely entirely on muscular action to create dorsiflexion. The first step in dorsiflecting is--to stop plantar flexing. Dorsiflexion can happen if we just stop blocking it.