The Figure Skating Jump

CR 402
The Physics of Figure Skating Jumps
Briana D. Lackenby (figskate@bu.edu)

Anyone who has watched figure skating live has notice the amazing speed and distance that world class skaters achieve during their jumps. Its not hard to notice that as the skater performs more and more rotations his or her air position becomes tighter. As the number of rotations in the air increases, the skater will obtain a greater angular velocity and a smaller moment of inertia by decreasing the distance(radius) of their arms and free leg from their body. When a skater performs a single jump both their free leg and arms are farther away from their body causing an open air position and a larger moment of inertia. When the skater pulls in they obtain a tight air position which decreases their moment of inertia. The first skater to ever complete a quadruple jump was Kurt Browning of Canada at the 1988 World ChampionshipsNowadays men are consistently completing quadruple jumps and continuing to push the limits of figure skating farther.


There are many important aspects to the figure skating jump, however the most important are rotation, speed, and amount of knee bend obtained going into the jump. There are two areas where the speed can be investigated, going into the jump and how fast you rotate in the air. Once a skater enters the air there are no forces that can change his or her angular momentum. We can calculate the skaters angular momentum by multiplying their moment of inertia by their angular speed. It makes sense that if a skater is to perform more revolutions in the air, their rotational speed must increase with each increasing rotation. However before the skater can perform the rotations they must get into the air. Its important to obtain the necessary knee bend to vault themeselves in the air.

What I investigated with my experiments was whether or not the angle between the skaters front leg and their picking leg increased or decreased with increasing rotation. The jump that I used to investigate this was the single and double lutz jump. The lutz jump is performed by skating backwards towards one of the corners of the rink, then the skater reaches back with their picking foot and vaults themeselves into the air for the desired number of rotations. To investigate this I had one of my students perform both single and double lutz jumps many times. While she was performing these jumps I watched her front knee bend. Then we simulated the jump entries on the ice however this time the skater did not jump but rather stopped when the toe pick entered the ice. It was at this point that I was able to measure two things:

  • The distance from her front knee to the floor
  • The distance from her front foot to her toe pick mark

    This procedure was used for both the single lutz jump and the double lutz jump, the numbers I obtained were as follows:

    SINGLE LUTZ JUMP

    DISTANCE FROM FRONT KNEE TO ICE and DISTANCE FROM FRONT FOOT TO TOE PICK MARK


  • 36.83cm, 52.07cm
  • 36.58cm, 53.85cm
  • 36.83cm, 51.31cm
  • 37.08cm, 50.55cm
  • 36.83cm, 52.58cm

    • DOUBLE LUTZ JUMP

    36.07cm, 64.52cm

    36.58cm, 63.50cm
    36.32cm, 63.25cm
    36.07cm, 65.02cm
    36.58cm, 64.26cm

    Next I took the two measurements and used the:

    PYTHAGOREAN THEOREM (a2+b2=c2)

    to find the length of the hypotenuse, which would be from the skater's front knee to their toe pick mark. The numbers I obtained from these calculations were as followed:

    SINGLE LUTZ JUMP

    63.78cm

    65.10cm
    63.16cm
    62.69cm
    64.20cm

    DOUBLE LUTZ JUMP

    73.92cm

    73.28cm
    72.94cm
    74.35cm
    73.94cm

    After I made these calculations I also found the angle between the skater's front leg and their picking leg, I did this by using THE INVERSE TANGENT The angles (in degrees) I obtained from this calculation were as follows:

    SINGLE LUTZ JUMP

    35.27

    34.19
    35.67
    36.26
    35.01

    DOUBLE LUTZ JUMP

    29.21

    29.94
    29.87
    29.02
    29.65

    From all of these calculations I concluded that as the number of revolutions the skater is performing in the air increases so does the distance between the front foot and the toe pick. Also as the number of revolutions in the air increases the angle between the skater's front leg and picking foot decreases. This happens because by decreasing the angle the skater is able to obtain more knee bend and thus vault themeselves higher in the air. when the skater had more knee bend and a smaller angle between the front leg and the toe pick, the jump appeared to acheive more height. Though I did not do any tests for speed and acceleration, from observing the skater jump I noticed that the skater seemed to skate faster into the double lutz jump and slower into the single lutz jump. Other observations that I made were that the skater definately had a much tighter, closed position during the double lutz jump, and a much more open position during the single jump. However neither jump seemed to take longer to complete in the air, this supports the idea that speed of each rotation increases as the number or rotations being performed increases.

    REFERENCES:

  • Book:Figure Skating by Carlo Fassi, published by Charles Scribner's Sons New York, 1980
  • Magazine:Skating, published by the United States Figure Skating Association
  • Book:Physics by Cutnell and Johnson, published by John Wiley and Sons New York, 1998



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