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Thread: Measuring Skater Jump Height

  1. #1
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    Measuring Skater Jump Height

    This thread is about quantitatively measuring the jump height of different skaters. This post is about how to analyze videos of performances to do so, for anyone that might want to calculate a skater's jump height on their own. As you can imagine, it may be somewhat conceptually dense, though I think it's simply a matter of thinking through the various issues, and I try to lay out the reasoning in detail.

    The TL;DR version is this: Take a video of the skater's jump, usually 25 FPS or 30 FPS. If it's 30 FPS, watch on frame-by-frame and look for identical (repeated) frames. If it has any, it's likely really just 25 FPS (with frames inserted). If it doesn't, then it's 30 FPS. Take the difference between the first frame where the skater is in the air, and the first frame where the skater lands (touches the ice). Then plug that number of frames into the following:

    Height (in centimeters) = 981 * (frames/FPS/2)^2 / 2

    For example, if the skater's first frame in the air was frame 2526, and the skater's first frame on the ice was frame 2539, then the number of frames was 13. For a 25 FPS video, this becomes:

    Height = 981 * (13/25/2)^2 / 2 = 981 * (0.26)^2 / 2 = 33 cm

    The error in measurement varies from 5 cm for a 25 FPS video to 2 cm for a 60 FPS video.

    -----

    A skater's jump height is an important indicator of how many rotations they can achieve in the air. The greater the height, the more time they have to rotate and thus the more rotations they can do. Height is also one bullet point for a jump's GOE (Grade Of Execution) score.

    Making some basic assumptions about the skater, such as that air resistance is negligible and that the skater's legs are fully extended (or similarly extended) for takeoff and landing, the height can be calculated from the jump duration by the following:

    height = (gravity) * ((duration/2)^2) / 2

    This is based on the equation of motion for a body under uniform acceleration. The reason why the duration is divided in half is because the skater is moving upward for half of the jump's time, then vertically is stopped (regardless of the horizontal motion), then accelerates downwards for the latter half of the jump. The vertical distance traveled during the second half (which is the same as the distance during the first half) gives the height of the jump. Gravity is taken to be 9.81 m/s^2. So for example, if a skater is in the air for 0.6 seconds, then the height of the jump would be:

    height = (9.81 m/s^2) * ((0.6 s/2)^2) / 2
    = 9.81 * (0.3)^2 / 2
    = 0.44 m or 44 cm

    So although this is about measuring jump height, this is somewhat misleading. What is actually measured is the jump duration, and the jump height is then inferred from that.

    The only remaining question, then, is how to measure how long the skater was in the air during the jump.

    One way to measure the jump duration is by using a video of the skater's jump. Videos consist of image frames displayed one after another, usually with a set duration between each frame. A video's Frames Per Second (FPS) is the reciprocal of the duration. For example, a video that plays at 25 FPS has a duration of 0.04 seconds between each frame. The error of the measurement is related to the duration between each frame. Thus, a higher FPS means a lower error in measuring jump height. Assuming an error of +- 1 frame, the measurement error of a jump lasting about half a second, corresponding to a height of about 31 cm, for different FPS is below:

    FPS Error
    60 2 cm
    50 2.4 cm
    30 4 cm
    25 5 cm

    As you can see, the error is significant relative to the height at the lower FPS. 25 and 30 FPS are common. 50 FPS is rare, and is usually really just 25 FPS interlaced that has been de-interlaced. I will occasionally see 60 FPS but it's pretty rare, and usually means a very big video file.

    To count the number of frames, take the difference between the first frame when the skater first leaves the ice (i.e. skates no longer touching the ice) and the first frame when the skater first lands (i.e. first skate touches the ice). Keep in mind that the skater actually took off sometime in between the last frame when the skate was touching the ice and the first frame when no skate is touching the ice, and also landed sometime in between the last frame when no skate is touching the ice and the first frame where the skate is touching the ice.

    As a practical matter, determining this can sometimes be difficult, and I think this is where a lot of the arguments, err, internet discussion, can occur. For example, depending on the video resolution and brightness/contrast settings, it can be difficult to tell if the toe pick was still touching the ice or not in a given frame. Because of this, I tend to let one "inform" the other. For example, let's say a skater's toe pick was barely on the ice at frame 459 and clearly in the air at frame 460, and when I look at the landing, the skater was clearly in the air at frame 473 and clearly on the ice at frame 475, but I'm not sure if it was on the ice or not at frame 474. In this case, I'm more likely to use frame 475, because the skater (based on the takeoff) was in the air for longer than what the frame count would suggest. Thus, I try to match the conditions of the takeoff and jump: I try to match a "barely took off" with a "barely landed", and a "clearly took off" with a "clearly landed", when necessary.

    Some other considerations for the video are its resolution and its brightness/contrast. Higher resolution means more detail can be seen, which makes it easier to determine when the skate has left the ice. Brightness and contrast affect whether or not you can judge this; a video that's too bright, or has too high of a contrast, will make the ice completely white, making it difficult to gauge if the skate is in contact with the ice or not. Obviously, the video should show the skater's skates, and the more zoomed in on the skater, the easier it is to judge if the skate is in contact with the ice.

    Occasionally, the replays that are shown while waiting for the skater's scores can be used. But I find that in practice this is tricky; they can only be used if they are from the same camera, and are not simply the same footage with just repeated frames inserted. The math for using replays is similar (although it needs to take into account how much slower the replay is being run), except significantly more checks need to be done to make sure that the replay can be appropriately used. But occasionally they can provide very accurate determinations of a skater's jump height.

  2. #2
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    This post will be for measurement results for different skaters at events.

    I think in providing the results it's important to consider the circumstances surrounding the jump:
    * How late in the program the jump was performed. Early ones tend to be higher, since the skater has more energy left. Therefore, I list how long after the music started when the jump began. I may be a second or two off with this but I don't think it needs that level of precision.
    * Whether the jump was done in combination or not. I'm not a skating expert but I *believe* that a jump following another, such as a triple toe after a triple lutz, is somewhat lower but rotates faster than if the jump (such as triple toe) were done on its own. At any rate, I include this information.
    * Whether the jump was judged under-rotated or the skater fell on the jump. This indicates that there may have been something lacking in the execution of this particular jump attempt, and therefore it may not indicate the skater's usual jump height. I don't think wrong edges matter, but I'll include them simply because I basically copy from the judges' scorecard.

    For each analysis I will try to provide a link to the original video, as well as the FPS and the error. I only ran through these results once (i.e. I didn't go back and double-check them) so anyone is free to look at the videos for themselves and let me know if there are any errors.

    The format is: jump notes (combo order), time in program: duration (height)

    Tuktamysheva, Elizaveta
    2014 Grand Prix Final (Barcelona) Free Skate
    https://www.youtube.com/watch?v=hzh0Hha3KRQ (50 FPS via clipconverter.cc, error is +-0.02 s or +-2.4 cm)
    3Lz (1/3), 18 s: 0.64 s (50 cm)
    2T (2/3), 19 s: 0.44 s (24 cm)
    2Lo (3/3), 20 s: 0.42 s (22 cm)
    3Lz, 37 s: 0.62 s (47 cm)
    3F, 50 s: 0.54 s (36 cm)
    3T (1/2), 121 s: 0.56 s (38 cm)
    3T (2/2), 122 s: 0.52 s (33 cm)
    3Lo, 132 s: 0.52 s (33 cm)
    3S (1/2), 148 s: 0.50 s (31 cm)
    2A (2/2), 151 s: 0.50 s (31 cm)
    2A, 200 s: 0.52 s (33 cm)

    Radionova, Elena
    2014 Grand Prix Final (Barcelona) Free Skate
    https://www.youtube.com/watch?v=8ex3fEoGU1o (50 FPS via clipconverter.cc, error is +-0.02 s or +-2.4 cm)
    3Lz (1/2), 29 s: 0.56 s (38 cm)
    3T, 31 s: 0.46 s (26 cm)
    3F, 43 s: 0.52 s (33 cm)
    3Lz, 73 s: 0.56 s (38 cm)
    3Lo (1/3), 150 s: 0.52 s (33 cm)
    1Lo (2/3), 151 s: 0.12 s (2 cm)
    3S (3/3), 152 s: 0.44 s (24 cm)
    2A, 164 s: 0.46 s (26 cm)
    2A, 176 s: 0.46 s (26 cm)
    3Lo (1/2), 189 s: 0.52 s (33 cm)
    2T (2/2), 191 s: 0.36 s (16 cm)

    Wagner, Ashley
    2014 Grand Prix Final (Barcelona) Free Skate
    https://www.youtube.com/watch?v=GC4MkorU-4w (50 FPS via clipconverter.cc, error is +-0.02 s or +-2.4 cm)
    2A, 28 s: 0.48 s (28 cm)
    3F (1/2), 52 s: 0.52 s (33 cm)
    3T (2/2), 53 s: 0.46 s (26 cm)
    2A (1/2), 64 s: 0.46 s (26 cm)
    2T (2/2), 65 s: 0.34 s (14 cm)
    3Lo (1/3), 127 s: can't tell (camera was panned out)
    1Lo (2/3), 128 s: can't tell (camera was panned out)
    3S< (3/3), 129 s: can't tell (camera was panned out)
    3F, 146 s: 0.56 s (38 cm)
    3Lo, 159 s: 0.54 s (36 cm)
    3Lz, 213 s: 0.56 s (38 cm)

    Pogorilaya, Anna
    2014 Grand Prix Final (Barcelona) Free Skate
    https://www.youtube.com/watch?v=kZFJvmOhygY (50 FPS via clipconverter.cc, error is +-0.02 s or +-2.4 cm)
    3Lz (1/2), 26 s: 0.60 s (44 cm)
    3T (2/2), 28 s: 0.52 s (33 cm)
    3Lo (1/3), 46 s: 0.54 s (36 cm)
    1Lo < (2/3), 47 s: didn't measure
    3S (3/3) fall, 48 s: 0.44 s (24 cm)
    3F !, 130 s: 0.54 s (36 cm)
    3Lz (1/2), 142 s: 0.56 s (38 cm)
    2T (2/2), 144 s: 0.38 s (18 cm)
    2A, 155 s: 0.52 s (33 cm)
    2A, 168 s: 0.48 s (28 cm)
    3Lo, 181 s: 0.52 s (33 cm)

    Lipnitskaya, Julia
    2014 Grand Prix Final (Barcelona) Free Skate
    https://www.youtube.com/watch?v=9hx5Du8vTJg (50 FPS via clipconverter.cc, error is +-0.02 s or +-2.4 cm)
    3Lz (1/2), 30 s: 0.56 s (38 cm)
    3T (2/2), 31 s: 0.48 s (28 cm)
    2A < fall, 48 s: 0.44 s (24 cm)
    3Lo, 128 s: 0.54 s (36 cm)
    2A (1/3), 141 s: 0.44 s (24 cm)
    3T (2/3), 142 s: 0.52 s (33 cm)
    2T (3/3), 144 s: 0.36 s (16 cm)
    1F e, 158 s: 0.42 s (22 cm)
    2F ! fall, 176 s: 0.44 s (24 cm)
    2S, 192 s: 0.46 s (26 cm)

    Hanyu, Yuzuru
    2014 Grand Prix Final (Barcelona) Free Skate
    https://www.youtube.com/watch?v=LG31sjv5tS8 (50 FPS via clipconverter.cc, error is +-0.02 s or +-2.4 cm)
    4S, 21 s: 0.66 s (53 cm)
    4T, 41 s: 0.70 s (60 cm)
    3F, 55 s: 0.62 s (47 cm)
    3Lz (1/2), 142 s: 0.64 s (50 cm)
    2T (2/2), 144 s: 0.46 s (26 cm)
    3A (1/2), 161 s: 0.62 s (47 cm)
    3T (2/2), 162 s: 0.54 s (36 cm)
    3A (1/3), 182 s: 0.62 s (47 cm)
    1Lo (2/3), 183 s: 0.16 s (3 cm)
    3S (3/3), 184 s: 0.50 s (31 cm)
    3Lo, 195 s: 0.54 s (36 cm)
    3Lz < fall, 206 s: 0.60 s (44 cm)

    Fernandez, Javier
    2014 Grand Prix Final (Barcelona) Free Skate
    https://www.youtube.com/watch?v=E0tTPFPlV5Y (50 FPS via clipconverter.cc, error is +-0.02 s or +-2.4 cm)
    4T, 23 s: 0.70 s (60 cm)
    3S (1/2), 44 s: 0.60 s (44 cm)
    2T (2/2), 45 s: 0.58 s (41 cm)
    3A, 61 s: 0.60 s (44 cm)
    4S, 142 s: 0.66 s (53 cm)
    3F (1/3), 158 s: 0.56 s (38 cm)
    1Lo (2/3), 159 s: didn't measure
    3S (3/3), 160 s: 0.52 s (33 cm)
    3Lo, 172 s: 0.58 s (41 cm)
    1Lz (1/2), 191 s: 0.32 s (13 cm)
    2T (2/2), 192 s: 0.40 s (20 cm)
    3T, 202 s: 0.52 s (33 cm)

    Voronov, Sergei
    2014 Grand Prix Final (Barcelona) Free Skate
    https://www.youtube.com/watch?v=GCTMvpyxJ60 (50 FPS via clipconverter.cc, error is +-0.02 s or +-2.4 cm)
    4T, 19 s: 0.68 s (57 cm)
    3A (1/2), 41 s: 0.68 s (57 cm)
    2T (2/2), 42 s: 0.46 s (26 cm)
    3T (1/2), 60 s: 0.68 s (57 cm)
    3T (2/2), 62 s: 0.54 s (36 cm)
    3Lz, 82 s: 0.58 s (41 cm)
    3A, 179 s: 0.68 s (57 cm)
    3S, 191 s: 0.54 s (36 cm)
    3Lo (1/3), 201 s: 0.60 s (44 cm)
    2T (2/3), 203 s: 0.42 s (22 cm)
    2Lo (3/3), 204 s: 0.42 s (22 cm)
    2A, 209 s: 0.60 s (44 cm)

    These are some results from the Olympics Individual Ladies Short Program. The video was 25 FPS but was interlaced, so I used Avidemux to separate the interlaced frames and effectively convert the video to 50 FPS (albeit at half the resolution). Additionally, some replays, when usable, were played at 1/3, so those jumps were analyzed at the equivalent of 150 FPS (0.00667 s per frame).

    The format is the jump, special marks (such as under-rotations or falls), which jump in a combination or sequence if applicable, how late in the program the jump occurred, the jump duration and error, the height and error, and marking if it was based on a replay or not. The heights were based on the jump duration. The height duration error was calculated by taking the difference between if the duration were one frame shorter and one frame longer, and dividing in half.

    Sotnikova, Adelina
    2014 Olympics (Sochi) Short Program
    Torrent file (XXII Зимние ... программа.mpg) (25 FPS interlaced, analyzed as de-interlaced at 50 FPS)
    3T (1/2), 32 s: 0.64 +- 0.02 s (50 +- 3 cm)
    3T (2/2), 34 s: 0.52 +- 0.02 s (33 +- 3 cm)
    3F, 58 s: 0.6 +- 0.02 s (44 +- 3 cm)
    2A, 94 s: 0.54 +- 0.02 s (36 +- 3 cm)

    Kim, Yuna
    2014 Olympics (Sochi) Short Program
    Torrent file (XXII Зимние ... программа.mpg) (25 FPS interlaced, analyzed as de-interlaced at 50 FPS)
    3Lz (1/2), 24 s: 0.63 +- 0.007 s (48 +- 1 cm) (replay)
    3T (2/2), 26 s: 0.53 +- 0.007 s (35 +- 1 cm) (replay)
    3F, 53 s: 0.58 +- 0.02 s (41 +- 3 cm)
    2A, 85 s: 0.54 +- 0.02 s (36 +- 3 cm)

    Asada, Mao
    2014 Olympics (Sochi) Short Program
    Torrent file (XXII Зимние ... программа.mpg) (25 FPS interlaced, analyzed as de-interlaced at 50 FPS)
    3A < fall, 26 s: 0.66 +- 0.02 s (53 +- 3 cm)
    3F <, 51 s: 0.52 +- 0.02 s (33 +- 3 cm)
    2Lo, 105 s: 0.48 +- 0.02 s (28 +- 2 cm)

    Kostner, Carolina
    2014 Olympics (Sochi) Short Program
    Torrent file (XXII Зимние ... программа.mpg) (25 FPS interlaced, analyzed as de-interlaced at 50 FPS)
    3F (1/2), 29 s: 0.64 +- 0.007 s (50 +- 1 cm) (replay)
    3T (2/2), 31 s: 0.49 +- 0.007 s (30 +- 1 cm) (replay)
    3Lo, 49 s: 0.58 +- 0.02 s (41 +- 3 cm)
    2A, 106 s: 0.5 +- 0.02 s (31 +- 2 cm)

    Gold, Gracie
    2014 Olympics (Sochi) Short Program
    Torrent file (XXII Зимние ... программа.mpg) (25 FPS interlaced, analyzed as de-interlaced at 50 FPS)
    3Lz (1/2), 32 s: 0.6 +- 0.02 s (44 +- 3 cm)
    3T (2/2), 34 s: 0.46 +- 0.02 s (26 +- 2 cm)
    3Lo, 95 s: 0.52 +- 0.02 s (33 +- 3 cm)
    2A, 113 s: 0.5 +- 0.02 s (31 +- 2 cm)

    Lipnitskaya, Julia
    2014 Olympics (Sochi) Short Program
    Torrent file (XXII Зимние ... программа.mpg) (25 FPS interlaced, analyzed as de-interlaced at 50 FPS)
    3Lz (1/2), 29 s: 0.52 +- 0.02 s (33 +- 3 cm)
    3T (2/2), 31 s: 0.5 +- 0.02 s (31 +- 2 cm)
    2A, 44 s: 0.47 +- 0.007 s (27 +- 1 cm) (replay)
    3F << fall, 119 s: 0.46 +- 0.02 s (26 +- 2 cm)

    Wagner, Ashley
    2014 Olympics (Sochi) Short Program
    Torrent file (XXII Зимние ... программа.mpg) (25 FPS interlaced, analyzed as de-interlaced at 50 FPS)
    3F (1/2), 27 s: 0.56 +- 0.02 s (38 +- 3 cm)
    3T << (2/2), 28 s: 0.42 +- 0.02 s (22 +- 2 cm)
    3Lo, 90 s: 0.52 +- 0.02 s (33 +- 3 cm)
    2A, 108 s: 0.46 +- 0.02 s (26 +- 2 cm)

    Suzuki, Akiko
    2014 Olympics (Sochi) Short Program
    Torrent file (XXII Зимние ... программа.mpg) (25 FPS interlaced, analyzed as de-interlaced at 50 FPS)
    3T <<, 26 s: 0.53 +- 0.007 s (34 +- 1 cm) (replay)
    3Lz (1/2), 48 s: 0.5 +- 0.02 s (31 +- 2 cm)
    2T (2/2), 49 s: not measured (can't see skate)
    2A, 111 s: 0.5 +- 0.02 s (31 +- 2 cm)

    Edmunds, Polina
    2014 Olympics (Sochi) Short Program
    Torrent file (XXII Зимние ... программа.mpg) (25 FPS interlaced, analyzed as de-interlaced at 50 FPS)
    3Lz (1/2), 22 s: 0.6 +- 0.02 s (44 +- 3 cm)
    3T < (2/2), 23 s: 0.44 +- 0.02 s (24 +- 2 cm)
    3F, 43 s: 0.59 +- 0.007 s (42 +- 1 cm) (replay)
    2A, 139 s: 0.48 +- 0.02 s (28 +- 2 cm)

    These are some results from the Olympics Individual Ladies Free Skate. The video itself ran at 25 FPS, so the results are not very precise. Some of the measurements were based on replays, resulting in higher accuracy. There were generally two types of replays. The first ran at 3x slower than regular speed (checked by syncing up with the images when the program played at regular speed), so it basically showed video at the equivalent of 75 FPS. The second had some skipped frames and uneven timings, so its results were not used. Whether or not replay was used in the measurements was indicated in parentheses.

    The format is the jump, special marks (such as under-rotations or falls), which jump in a combination or sequence if applicable, how late in the program the jump occurred, the jump duration and error, the height and error, and marking if it was based on a replay or not. The heights were based on the jump duration. The height duration error was calculated by taking the difference between if the duration were one frame shorter and one frame longer, and dividing in half.

    I did this for the 12 highest scoring skaters in the free skate, let me know if I should do it for the other 12 skaters as well.

    Sotnikova, Adelina
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    3Lz (1/2), 31 s: 0.6 +- 0.04 s (44 +- 6 cm)
    3T (2/2), 33 s: 0.44 +- 0.04 s (24 +- 4 cm)
    3F, 60 s: 0.6 +- 0.013 s (44 +- 2 cm) (replay)
    3Lo, 73 s: 0.56 +- 0.04 s (38 +- 5 cm)
    2A (1/2), 134 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3T (2/2), 136 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3F (1/3), 152 s: 0.56 +- 0.04 s (38 +- 5 cm)
    2T (2/3), 153 s: 0.4 +- 0.04 s (20 +- 4 cm)
    2Lo (3/3), 154 s: 0.4 +- 0.04 s (20 +- 4 cm)
    3S, 167 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2A, 175 s: 0.48 +- 0.04 s (28 +- 5 cm)

    Kim, Yuna
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    3Lz (1/2), 21 s: 0.6 +- 0.04 s (44 +- 6 cm)
    3T (2/2), 22 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3F, 41 s: 0.56 +- 0.014 s (38 +- 2 cm) (replay)
    3S (1/2), 62 s: 0.48 +- 0.04 s (28 +- 5 cm)
    2T (2/2), 63 s: 0.44 +- 0.04 s (24 +- 4 cm)
    3Lz x, 149 s: 0.6 +- 0.04 s (44 +- 6 cm)
    2A (1/3), 162 s: 0.56 +- 0.04 s (38 +- 5 cm)
    2T (2/3), 164 s: 0.44 +- 0.04 s (24 +- 4 cm)
    2Lo (3/3), 165 s: 0.32 +- 0.04 s (13 +- 3 cm)
    3S, 180 s: 0.48 +- 0.04 s (28 +- 5 cm)
    2A, 225 s: 0.52 +- 0.04 s (33 +- 5 cm)

    Asada, Mao
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    3A, 26 s: 0.65 +- 0.013 s (52 +- 2 cm) (replay)
    3F (1/2), 47 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3Lo < (2/2), 48 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3Lz e, 67 s: 0.56 +- 0.013 s (38 +- 2 cm) (replay)
    2A (1/2), 140 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3T < (2/2), 142 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3S, 152 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3F (1/3), 168 s: 0.56 +- 0.04 s (38 +- 5 cm)
    2Lo (2/3), 169 s: 0.36 +- 0.04 s (16 +- 4 cm)
    2Lo (3/3), 170 s: 0.36 +- 0.04 s (16 +- 4 cm)
    3Lo, 180 s: 0.56 +- 0.04 s (38 +- 5 cm)

    Kostner, Carolina
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    3Lz, 27 s: 0.64 +- 0.04 s (50 +- 6 cm)
    2A (1/2), 47 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3T (2/2), 48 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3F, 64 s: 0.63 +- 0.013 s (48 +- 2 cm) (replay)
    3Lo, 125 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3T (1/2), 142 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2T (2/2), 144 s: 0.36 +- 0.04 s (16 +- 4 cm)
    3S, 155 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3S (1/3), 169 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2T (2/3), 171 s: 0.36 +- 0.04 s (16 +- 4 cm)
    2T (3/3), 172 s: 0.36 +- 0.04 s (16 +- 4 cm)

    Gold, Gracie
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    3Lz (1/2), 20 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3T (2/2), 22 s: 0.48 +- 0.04 s (28 +- 5 cm)
    2A (1/2), 39 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3T (2/2), 41 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3Lo, 51 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3F e fall, 135 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3Lz, 152 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3S (1/3), 166 s: 0.48 +- 0.04 s (28 +- 5 cm)
    2T (2/3), 168 s: 0.28 +- 0.04 s (10 +- 3 cm)
    2T (3/3), 169 s: 0.28 +- 0.04 s (10 +- 3 cm)
    2A, 217 s: 0.48 +- 0.04 s (28 +- 5 cm)

    Lipnitskaya, Julia
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    3Lz (1/2), 31 s: 0.53 +- 0.013 s (35 +- 2 cm) (replay)
    3T (2/2), 33 s: 0.49 +- 0.013 s (30 +- 2 cm) (replay)
    2A (1/3), 48 s: 0.44 +- 0.04 s (24 +- 4 cm)
    3T (2/3), 50 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2T (3/3), 51 s: 0.36 +- 0.04 s (16 +- 4 cm)
    3F, 126 s: 0.48 +- 0.04 s (28 +- 5 cm)
    2A, 139 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3Lo <, 155 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3S fall, 176 s: 0.51 +- 0.013 s (31 +- 2 cm) (replay)
    3Lz e (1/2), 190 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2T (2/2), 190 s: didn't measure (skates out of camera field of view)

    Wagner, Ashley
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    3F (1/2), 26 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3T < (2/2), 27 s: 0.44 +- 0.04 s (24 +- 4 cm)
    2A, 49 s: 0.44 +- 0.04 s (24 +- 4 cm)
    3S, 65 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3Lo (1/2), 123 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2A (2/2), 125 s: 0.44 +- 0.04 s (24 +- 4 cm)
    3Lz e, 138 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3Lo, 151 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3F (1/3), 206 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2T (2/3), 207 s: 0.32 +- 0.04 s (13 +- 3 cm)
    2T (3/3), 209 s: 0.32 +- 0.04 s (13 +- 3 cm)

    Suzuki, Akiko
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    3Lz (1/3), 27 s: 0.55 +- 0.013 s (37 +- 2 cm) (replay)
    2T (2/3), 28 s: 0.33 +- 0.013 s (14 +- 1 cm) (replay)
    2Lo (3/3), 29 s: 0.32 +- 0.013 s (13 +- 1 cm) (replay)
    2A (1/2), 45 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2T (2/2), 46 s: 0.4 +- 0.04 s (20 +- 4 cm)
    3Lz, 64 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3F e fall, 150 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3Lo, 167 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3S (1/2), 179 s: 0.48 +- 0.04 s (28 +- 5 cm)
    2T (2/2), 181 s: 0.28 +- 0.04 s (10 +- 3 cm)
    3S, 211 s: 0.48 +- 0.04 s (28 +- 5 cm)

    Edmunds, Polina
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    3Lz (1/2), 20 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3T (2/2), 22 s: 0.44 +- 0.04 s (24 +- 4 cm)
    3F (1/3), 46 s: 0.59 +- 0.013 s (42 +- 2 cm) (replay)
    1Lo (2/3), 48 s: 0.16 +- 0.013 s (3 +- 1 cm) (replay)
    3S (3/3), 49 s: 0.49 +- 0.013 s (30 +- 2 cm) (replay)
    2A, 85 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3F < fall, 151 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3Lz, 163 s: 0.6 +- 0.04 s (44 +- 6 cm)
    3Lo (1/2), 204 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2T (2/2), 205 s: 0.32 +- 0.04 s (13 +- 3 cm)
    2A, 220 s: 0.48 +- 0.04 s (28 +- 5 cm)

    Marchei, Valentina
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    2A (1/2), 33 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3T (2/2), 34 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3Lz, 54 s: 0.64 +- 0.04 s (50 +- 6 cm)
    3F e, 76 s: 0.6 +- 0.04 s (44 +- 6 cm)
    2A, 86 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3S, 174 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3Lz (1/2), 193 s: 0.64 +- 0.04 s (50 +- 6 cm)
    2T (2/2), 195 s: 0.32 +- 0.04 s (13 +- 3 cm)
    2S (1/3), 228 s: 0.44 +- 0.04 s (24 +- 4 cm)
    1T (2/3), 229 s: 0.28 +- 0.04 s (10 +- 3 cm)
    2T (3/3), 230 s: 0.36 +- 0.04 s (16 +- 4 cm)

    Meite, Mae Berenice
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    2A, 12 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3S (1/2), 25 s: 0.52 +- 0.013 s (33 +- 2 cm) (replay)
    3T (2/2), 27 s: 0.56 +- 0.013 s (38 +- 2 cm) (replay)
    3Lz, 45 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3F, 65 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3Lo fall, 86 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3Lo (1/3), 169 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2T (2/3), 171 s: 0.44 +- 0.04 s (24 +- 4 cm)
    2T (3/3), 172 s: 0.44 +- 0.04 s (24 +- 4 cm)
    2A (1/2), 188 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3T (2/2), 189 s: 0.56 +- 0.04 s (38 +- 5 cm)

    Murakami, Kanako
    2014 Olympics (Sochi) Free Skate
    Torrent file (Sochi 2014 ... ARD HD) (25 FPS, error is +-0.04 s or about +-5 cm)
    3T (1/2), 22 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3T (2/2), 23 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3Lz e, 42 s: 0.57 +- 0.013 s (40 +- 2 cm) (replay)
    2Lo, 59 s: 0.48 +- 0.04 s (28 +- 5 cm)
    3F (1/2), 135 s: 0.56 +- 0.04 s (38 +- 5 cm)
    2T (2/2), 137 s: 0.36 +- 0.04 s (16 +- 4 cm)
    3F, 154 s: 0.56 +- 0.04 s (38 +- 5 cm)
    2A, 163 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3S (1/2), 180 s: 0.56 +- 0.04 s (38 +- 5 cm)
    2Lo (2/2), 182 s: 0.36 +- 0.04 s (16 +- 4 cm)

    Analysis of Midori Ito's jumps:

    Ito, Midori
    1989 World? Free Skate
    https://www.youtube.com/watch?v=0FiPOgClYWw (30 FPS)
    3Lz, 23 s: 0.57 +- 0.033 s (39 +- 5 cm)
    3A, 54 s: 0.7 +- 0.033 s (60 +- 6 cm)
    3F, 68 s: 0.6 +- 0.033 s (44 +- 5 cm)
    2T, 79 s: 0.43 +- 0.033 s (23 +- 4 cm)
    3Lo, 118 s: 0.53 +- 0.033 s (35 +- 4 cm)
    3T (1/2), 186 s: 0.53 +- 0.033 s (35 +- 4 cm)
    3T (2/2), 188 s: 0.53 +- 0.033 s (35 +- 4 cm)
    3S, 223 s: 0.5 +- 0.033 s (31 +- 4 cm)
    2A, 232 s: 0.6 +- 0.033 s (44 +- 5 cm)

    Ito, Midori
    1990 Worlds Free Skate
    https://www.youtube.com/watch?v=yvgWI8QDrzQ (25 FPS)
    3Lz, 17 s: 0.64 +- 0.04 s (50 +- 6 cm)
    3A, 54 s: 0.72 +- 0.04 s (64 +- 7 cm)
    3F, 99 s: 0.56 +- 0.04 s (38 +- 5 cm)
    2S, 146 s: 0.44 +- 0.04 s (24 +- 4 cm)
    3L, 171 s: 0.56 +- 0.04 s (38 +- 5 cm)
    3T (1/2), 206 s: 0.52 +- 0.04 s (33 +- 5 cm)
    3T (2/2), 208 s: 0.52 +- 0.04 s (33 +- 5 cm)
    2A, 240 s: 0.56 +- 0.04 s (38 +- 5 cm)

    If there are any discrepancies (if you count a different number of frames or if I didn't list a fall etc.), let me know.
    Last edited by Vanshilar; 01-02-2015 at 06:23 PM.

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    This post will be for analysis and comparison of different skaters and their jumps.

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    Say no to horrendous costumes Meoima's Avatar
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    you are amazing

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    My goodness! Which skaters are you planning to do this for?

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    Yuzu and Javi have identical heights on their quad sal and toe
    Last edited by HanDomi; 12-24-2014 at 08:00 PM.

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    ◟ʕ´•ᴥ•`ʔ ノ shiroKJ's Avatar
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    Wow! Thank you so much for this. Its interesting to see the differences...Maybe in the future, once we have more data we could see how much the time and height differs between single jumps and ones done in combination as well

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    Wow.... amazing...

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    Thank you so much for your amazing effort, this is certainly interesting.

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    Say no to horrendous costumes Meoima's Avatar
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    Quote Originally Posted by HanDomi View Post

    Yuzu and Javi have identical heights on their quad sal and toe
    same coach you know

    PS: Vanshilar, can you help us with the short program? I think jumps in short programs might be different to jumps in the long. Thank you.
    Last edited by Meoima; 12-25-2014 at 02:10 AM.

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    Size 7 Knife Boots Sam-Skwantch's Avatar
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    Liza's lutz is huge!!!! 50cm

  12. #12
    Say no to horrendous costumes Meoima's Avatar
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    Quote Originally Posted by Sam-Skwantch View Post
    Liza's lutz is huge!!!! 50cm
    yes, the same height as Yuzuru's luzt
    And I've thought Yuzuru's luzt is iffy.

    Maybe Liza can do a quad one day. 3A is possible for her I know.
    Last edited by Meoima; 12-25-2014 at 02:26 AM.

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    btw, how does horizontal distance factor into all of this? I'm not too familiar on the physics of trajectory. (sorry if I missed it in your original post about how the math was applied)
    Last edited by AprilS; 12-25-2014 at 02:30 AM.

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    Quote Originally Posted by AprilS View Post
    btw, how does horizontal distance factor into all of this? I'm not too familiar on the physics of trajectory. (sorry if I missed it in your original post about how the math was applied)
    Horizontal distance is independent of vertical. It's determined by the horizontal speed as the skater takes off. Measuring horizontal distance from video is much, much more difficult (maybe not impossible but any measurement has huge uncertainties) than jump height which we can calculate from air time (easily calculated with relatively small uncertainty) and gravitational acceleration (which varies a bit from pole to equator but can be approximated as constant). The varying camera angles, camera panning during the jumps, zooming in/out, everything adds to the difficulty of calculating horizontal distance from video (makes it pretty much impossible). You'd have to be there live and take a tape measure to the ice marks.

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    I've updated the measurements with some from Olympics FS. Take those measurements with a grain of salt because they're somewhat preliminary right now, I need to double-check them (they're an older set from before I starting using my current method) and they're from a 25 FPS video so the measurement errors are fairly large. But they should be in the right ballpark.

    Quote Originally Posted by AprilS View Post
    My goodness! Which skaters are you planning to do this for?
    Really, just whichever skaters people seem to be most interested in. Since my time is limited, I have to prioritize them.

    Quote Originally Posted by Meoima View Post
    PS: Vanshilar, can you help us with the short program? I think jumps in short programs might be different to jumps in the long. Thank you.
    Yeah, I'll try to get through most of the GPF SP ones, since the Youtube user that I'm getting these videos from (GutsuFan) has the SP videos in 50 FPS as well. (I've skipped Rika Hongo but if people think I should include her for completeness or interest um let me know.)

    Quote Originally Posted by CarneAsada View Post
    Horizontal distance is independent of vertical. It's determined by the horizontal speed as the skater takes off. Measuring horizontal distance from video is much, much more difficult (maybe not impossible but any measurement has huge uncertainties) than jump height which we can calculate from air time (easily calculated with relatively small uncertainty) and gravitational acceleration (which varies a bit from pole to equator but can be approximated as constant). The varying camera angles, camera panning during the jumps, zooming in/out, everything adds to the difficulty of calculating horizontal distance from video (makes it pretty much impossible). You'd have to be there live and take a tape measure to the ice marks.
    Actually...when I get around to writing about measuring jump rotation (such as how under-rotated a jump was) I'll talk about measuring horizontal distance from video. It's just from a fancam of the entire rink though (not from a zoomed-in network camera). Basically, in order to measure the jump rotation, I need to establish the skater's x-y coordinates in the rink at both takeoff and landing, and also the video camera's x-y coordinates, in order to determine the camera's angle offset. In doing so, it's easy to calculate the horizontal distance traveled by the jump. (I will also calculate the skater's speed going into the jump, simply by looking at the several frames preceding the jump, as well as the horizontal speed of the jump itself.) But yeah, it's not from the network cameras (which would be difficult), it's based on fancam video that shows the entire rink so I can establish rink coordinates.

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