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Carve turn
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A carve turn is a skiing term, used to refer to a turning technique. A carve turn happens when the ski shifts to one side or the other on its edges. In this case, the ski turns itself and is driven by the sidecut geometry while losing no speed, unlike a normal parallel turn.
When attempting a carve turn, a skier is skiing in dynamic equilibrium, so, to balance the centrifugal force, the skier must bring their center of mass to the inside of the turn radius.

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Encyclopedia
A carve turn is a skiing term, used to refer to a turning technique. A carve turn happens when the ski shifts to one side or the other on its edges. In this case, the ski turns itself and is driven by the sidecut geometry while losing no speed, unlike a normal parallel turn.
When attempting a carve turn, a skier is skiing in dynamic equilibrium, so, to balance the centrifugal force, the skier must bring their center of mass to the inside of the turn radius. Beginners to the sport are often hesitant to angulate into these turns, as they feel that such an action will cause them to fall. Ski instructors are therefore tasked with teaching new skiers to overcome this hesitation.
Carving typically involves the skier making a series of "Cs", or half circles, down the hill. Some instructors teach their students to think of these half circles as a clock. For example, the most extreme left portion of a turn would be at 9 o'clock and the extreme right is 3 o'clock. The turns are accomplished by utilizing a "rolling" of both skis from edge to edge.
Shaped skis, also called parabolic skis, make carve turns possible at low speeds and with short turn radius. They were first developed in 1989, and were almost unheard of prior to the early 1990s, but have since become the most common, and in many areas, only recreational ski available. The idea of shaped skis was formed by approaching the occurrence of skidding from a different perspective. Two basic assumptions were applied: that the ski would bend when edged (edging is the angling of the ski running base with the snow surface) only to the point where the ski's center came in contact with snow surface. The ski would not skid only when all the points of the edge of the ski traveled through the same point on the snow surface. If radius of a turn is chosen together with edge angle, calculation of sidecut (intersection of snow and ski surface) was relatively easy. The final result was radical parabolic sidecut.
Recreational skiing is usually done at speeds in range between 5 m/s and 15 m/s with average turn radius of less than 15 m. Accordingly, sidecuts of modern recreational skis are calculated for turn radius of approximately 7 to 15 m.
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