Liz Westcott
Math In Figure Skating
Liz Westcott
Massena Junior High
Grade 8
Liz Westcott
37 Elm St
Massena, N.Y. 13662
315-769-6574
Math is something we use everyday, from measuring in cooking, to the ratio of shampoo to hair in the shower. But math is also a vital part of the sport of Figure Skating, in different, and in more ways than you would think.
Olympic skaters fly through the air, making jumps with two or three rotations look effortless, while keeping their takeoffs and landings smooth. But the truth behind the matter remains, skating ability comes from years of effort and practice; math only provides the building blocks to construct the tower of success.
Skaters are judged with a marking system that ranges from 0 to 6 in increments of one tenth. Beginning skaters will receive marks beginning with 0.1 and senior level skaters will receive marks in the 4’s and 5’s depending on their ability. The marks by the judges are then arranges based on the ordinal position that and individual judge gives to a skater. It is these ordinals that are posted for the skaters to view. Some test can be judges by only one judge and this is called “single paneling”. Most events or tests are judged by 3 to 5 judges. A referee is responsible for timing an event or test if there is a time limit.
Many geometric principals find their way into figure skating, but in very subtle ways. Algebra and trigonometry make an appearance also. An average skating rink is 200’ by 85’ with rounded corners area to skate various moves. The long axis (vertical) and the short axis (horizontal) of the rink must always be kept in mind.
Many moves are skated parallel to the long axis and a few are skated parallel to the short axis. One move is called a spiral and the idea is to extend the free leg at a 900 or greater angle compared to the skating leg. The glide must extend a length of ½ the long axis of the rink so it is necessary to be able to bisect the length. The diagram shows basic consecutive edges. This move is skated parallel to the short axis. A skater must fit in 4-6 of these moves. This is where a little bit of algebra comes in to approximate how much space can be devoted to each edge. The pattern on the ice resembles a sine or cosine graph, as do many of the moves in skating. The amplitude and period of the curve varies with the various moves.
Brackets are another move that requires the ability to bisect the long axis of the rink. They have a turn that must be locate at the top of the bracket or ½ the way through the curve, which also requires the ability to bisect or divide in two. Changing of feet occurs along a line parallel to the long axis of the rink. A new sequence is started ½ through the long axis of the rink.
Parallel lines are not the only straight line in skating; a few of the moves are skated along a diagonal. A Choctaw Sequence is one of these. This move is done across a diagonal and looks like a line with a negative slope on an X and Y-axis. The return of this move looks like a line with a positive slope. Skaters are scored on their ability to perform a Choctaw Sequence that covers the diagonal length of the rink.
Looking at these diagrams make it look like skating is simply the position of the blade on the ice which is not correct. Skating is truly a 3-3-D sport with the X, Y, and Z planes. Skating involves not only the layout of moves on the ice, which is 2-D, but also height. Most single jumps are 1 revolution or 360 degrees of rotation, but an axel is 1 ½ revolutions or 540 degrees of revolution. A half jump is 180 degrees of rotation. Jumps require the knowledge of take offs and landings as well as height to achieve the rotation necessary. The jump to achieve the height is not straight up but is at an angle. The path a skater takes from take off to landing is a parabola. The diagram of the flip jumps shows only the 2-D movement but the skater must gain adequate height on the jump to rotate in the air and land smoothly on the left blade’s outer edge.
Timing comes into play as one of the very basic math concepts in skating. As more time in the air is managed due to greater height, more rotations can be done and there you have the makings of double and triple jumps. Also tied into timing is the knowledge of clockwise and counterclockwise. Skaters are expected to be able to perform many moves in both a clockwise and counterclockwise direction. Usually one direction is easier for the individual skater but they must be able to perform both. This symmetry is found in many of the moves but not the jumps.
Skaters actually are balancing on the edges of their blades most of the time. The more acute the angle the edge of the blade makes with the ice, the deeper the edge. Skaters strive for the deepest edge their can without toppling over. The picture shows the position of the blade on the ice during a right outside edge.
Circles make an appearance in skating moves. Spins involve rotations and centrifugal force. The spin needs to be centered over a point on the ice and the required number of rotations accomplished. The number of rotations of a spin is greater than those of a jump. Centering the spin one point on the ice so the skater does not travel on the spin is key to accomplishing the maximum number of rotations. Shoulders should be kept parallel to the ice surface during the spin.
Power circles involve a set of concentric circles with increasing diameter from the center to the outside, They are skated with increasing speed as well as increasing diameter. The skater must control the use of the power created by the crossovers used as there is a maximum of 15 crossovers allowed to complete the circles.
Skating uses many mathematical concepts. These concepts are very subtle and do not require the use of a graphing calculator but to the skater; however, knowledge of these concepts will allow a skater to more skillfully and gracefully execute the moves. These moves are performed on the ice without music and are the more technical part of skating. Once mastered, they can then be combined, as the skater desires to create a free skate program to selected music. It is this free skate portion of skating that most of us are familiar with, but behind every great free skate program are the moves, and behind all great moves, there lies the math that makes them possible.
Resources:
- The Official USFSA Rulebook Published August 2003 by the United Skates Figure Skating Association, Colorado Springs, CO
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