A carve turn is a skiing

Skiing

Skiing is a recreational activity using skis as equipment for traveling over snow. Skis are used in conjunction with boots that connect to the ski with use of a binding....

 term, used to refer to a turning technique in which 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

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

 while losing no speed, unlike a normal parallel turn

Parallel turn

The parallel turn in alpine skiing is a method for turning. It is based on the idea of rolling the ski onto one edge, allowing it to bend into an arc. The ski then follows the arc shape and turns, without sliding. This is in contrast to earlier techniques like the stem Christie, which accomplishes...

.

History

Shaped skis, also called parabolic skis, make carve turns possible at low speeds and with short turn radius. They were first developed in 1988 by Jurij Franko in Slovenia

Slovenia

Slovenia , officially the Republic of Slovenia , is a country in Central and Southeastern Europe touching the Alps and bordering the Mediterranean. Slovenia borders Italy to the west, Croatia to the south and east, Hungary to the northeast, and Austria to the north, and also has a small portion of...

n ski producing company Elan

Elan (company)

Elan is a Slovenian company, located in Begunje, specializing in the production of sporting goods. It is best known for its skis and snowboards. Other products include sailboats from 30 to 50 ft length, motor yachts, apparel , equipment for sports facilities...

 who calculated a suitable flex pattern for new kind of skis with his colleague Pavel Skofic. They organized a project dubbed SideCut Extreme – SCX – and set out to build prototypes.

Shaped skis were almost unheard of until the early 1990s, when skiers began noticing certain advantages to the deeper sidecuts of snowboards, especially alpine snowboards, and the carving ability that this shape offered over the traditionally-shaped ski. Skis of this new shape 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

Skid

Skid may refer to:* Skid, a pallet, a metal, wood or plastic platform for holding machinery or equipment* Skid , an outward side-slip in an aircraft turn* Skid steering, a method of steering in which wheels or tracks are skidded sideways...

 only when all the points of the edge of the ski traveled through the same point on the snow surface. If radius

Radius

In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...

 of a turn is chosen together with edge angle

Angle

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

, calculation of sidecut (intersection of snow and ski surface) was relatively easy. The final result was radical parabolic sidecut.

Dynamics

When attempting a carve turn, a skier is skiing in dynamic equilibrium

Mechanical equilibrium

A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

, so, to balance the centripetal force

Centripetal force

Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...

, the skier must bring their center of mass

Center of mass

In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...

 to the inside of the turn radius

Radius

In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...

. This is very much like a cyclist leaning to the inside of a turn to avoid being thrown off of his bicycle (incidentally, the typical movement speeds of biking and skiing are quite similar). 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 therefore teach new skiers to overcome this hesitation.

The ski is made with a side-cut radius. This is the radius of a circle that would fit into the shape of the edge of the ski if viewed in plan-view.
This is approximately the maximum radius of turn that can be cleanly carved.
Expertly used skis are capable of carving clean circular arc segments whose approximate minimum radius is proportional to the cosine of the angle of tilt multiplied by the side-cut radius.

Path

Carving typically involves the skier making a series of "Cs", or half circles, down the hill (with two consecutive "C"s forming an "S"). Skidding turns on the other hand would rather follow a "Z"-shaped path.

Some instructors teach their students to think of these half circles as a clock

Clock

A clock is an instrument used to indicate, keep, and co-ordinate time. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell". A silent instrument missing such a mechanism has traditionally been known as a timepiece...

. 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.

Speed

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.

Unlike a skidding turn, which primarily uses the skidding effect to reduce speed (hence the "Z"-path), a (perfect) carving turn does not lose any speed because there is no braking action in the turns. It is rather the reduction of the average path slope angle that results of the carving skier's S-shaped path down the slope (as opposed to a path that goes straight down) that reduces the skier's speed. If the carve skier wishes to go slower, the only thing he has to do is wait a littler longer before initiating the next C-turn (making the "C" longer). This will lead him to ski more and more parallel to the slope (in extremes uphill), reducing the average path slope angle.

Snowboarding

A carve turn is distinguishable by its subsequent "pencil line" mark left in the snow

Snow

Snow is a form of precipitation within the Earth's atmosphere in the form of crystalline water ice, consisting of a multitude of snowflakes that fall from clouds. Since snow is composed of small ice particles, it is a granular material. It has an open and therefore soft structure, unless packed by...

. This indicates that only the edge of the board is making contact with the snow, and no slippage is taking place. The rider is using the camber and side-cut radius to achieve the arc

Arc

Arc may refer to:-Mathematics:*Arc , a segment of a differentiable curve*Arc , a particular type of set of points of a projective plane*Arcminute, a measure used for angles, equal to 1/60th of a degree...

 in the snow. This arc transfers the maximum possible amount of energy

Energy

In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 and speed

Speed

In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...

into the next turn, as opposed to losing that energy through transfer to the snow. It's a balancing act that involves the riders variable of speed, snow compactness, rider weight, rider height, board length, board chamber, side-cut radius and more. A skilled rider does not have to think about all these things, but rather all of this is accomplished by muscle memory in just fractions of a second.