Tom Gellie breaks down why carving on one ski is hard: you're probably not doing inside-hip adduction. The fix is one-ski drills and mirror work to nail the hip position on both sides.
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If you can't carve on one ski, it's probably because you can't make this move with your inside hip. It's called adduction, and it means you don't have to tip your whole body inside like this. De Melzer does a great job of demonstrating the right hip position of the inside leg. Watch Skellie again to get this hip adduction movement in your mind. I won't lie to you, this movement is really hard to train. However, if you can incorporate this inside leg movement by doing some one-ski ski training, it will really help your overall skiing and both legs being symmetrical throughout the ski turn. The best advice: get in front of a mirror and see if you can emulate that inside hip position, then get out and practice on both sides like Demelza does here, and you'll find your skiing improves drastically.