Below is a revised and updated version (2022) of an article originally published in 2007 by Trevor Laak on his SkateCoach/wordpress.com blog which details jump height estimates based on jump air times. That article can be found at this link.

The idea is simple: Ignoring negligible air friction and aerodynamic effects, once a skater leaves the ice the trajectory of their center-of-mass is governed by the physics equations of simple projectile motion. We can therefore calculate a fairly accurate estimate of their jump height based on air time measurements. As noted in this article about minimum jump air times, it is very easy today to measure air times and all coaches should be using this information to help their skaters. However, air time is very abstract to most skaters. It is usually easier for skaters to understand they need to jump 2 inches higher as opposed to stay in the air an extra few hundredths of a second. This understanding can dramatically affect skater motivation.

This article has been updated from the original to include estimates of jump height for air times greater than 0.66 seconds (since elite skaters are jumping higher). It has also been revised in terms of current phone camera technology as opposed to the more common stand-alone video camera technology of 2007. The difference between interlaced and de-interlaced video capture is now essentially a thing of the past. But capture rates in multiples of 30 frames per second (30 fps, 60 fps, 120 fps, etc), which is based on the old NTSC 29.97 frames per second standard, continue to be used.

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Figure Skating Jumps – Are Figure Skaters Projectiles?
By Trevor Laak

Revised December 2022

The title above is eye-catching on a number of levels.  Have you ever been on one of those high sessions with 25 skaters? Sometimes the speed and intensity of those sessions feels like a battle zone…

The work of figure skating video analysis experts has demonstrated that there is a minimum flight time requirement for each of the major jumps.  For example, a double lutz needs to be in the air for 0.350 seconds or longer while a double axel needs to be in the air for 0.45 seconds or longer.  These values have been determined by analyzing hundreds or thousands of jumps with various video analysis programs and apps.

Using commonly available video analysis apps on their smartphones, coaches can directly measure the time a skater remains in the air. Alternatively, a coach may single-step through a video and count the number of frames a skater is in the air. You do this by advancing the jump entry and take-off frame-by-frame until the skate blade just leaves the ice.  You mark that as your starting point (setting the time measurement to zero, or using that frame as frame zero) and advance the jump frame-by-frame through the flight until the skate blade just touches the ice.  Most apps will simply give you the time difference, but the number of frames from the start to the end point also gives the flight time, as video cameras shoot frames at fixed time intervals.

In North America, the traditional NTSC video standard is 29.97 frames per second, and most modern smartphone cameras have retained this basic rate by using 30 frames per second and multiples of 30 frames per second to capture video. 60 frames per second is very common in 2022 and most newer phones now have slow motion capture rate capabilities of 120 frames/second and even 240 frames/second.  Traditionally, figure skating video analysis experts have used 60 frames per second as the standard capture rate, due to how legacy video analysis programs such as Dartfish or Pro-Trainer handled the 29.97 fps video from legacy consumer video cameras.

The actual capture rate is now kind of irrelevant since the video analysis apps directly calculate the time for you. But the chart below and minimum jump air times are still usually provided in 1/60 second increments.

So here’s an example.  Minimum air time for a double axel is 27 frames at 60 frames per second.

27/60 = 0.450 seconds

Naturally we don’t have to count the frames anymore, as our smartphone apps simply tells us the time as 0.45 seconds.

[Warning:  We’re going to geek out on math and physics for a few paragraphs, but you can skip ahead to see the height and flight time tables below.]

Now to calculate an estimate of how high the jump was, we apply the laws of physics.  In basic physics courses, there is almost always a part of the course devoted to “projectile motion” and the associated equations.  We’re going to consider our in-flight skaters as projectiles!  For our situation, the equation of interest is the simplified time-acceleration-distance equation.

This equation states that the distance an object travels under constant acceleration from rest is one half the acceleration rate times the square of the time.  The equation looks like:  Distance = 1/2 x Acceleration x Time x Time.  For our skating jump analysis, we need to use half the total flight time since the total flight time represents the time to go to the peak of the jump and return to the ice. We only want the time for the one-way trip from the top of the jump to the ice.

The acceleration of a projectile is simply the pull of gravity.  And gravity has a constant acceleration of 386.088 inches/sec2.  Using the double axel minimum flight time of 0.450 seconds,  the descent-only time is 0.450/2 = 0.225 seconds.  Plugging all of this into the equation yields:

Distance = 0.5 x 386.088 x 0.225 x 0.225 = 9.78 inches

Thus, I usually tell my skaters a double axel requires a minimum of 10 inches of jump height. It’s very easy to imagine and it seems reasonable to them.

Just for theoretical completeness, the actual jump height is slightly lower than measured/calculated.  The reason is that a skater always points his or her toe at take-off but usually flexes the toe in the air and upon landing.  This makes calculating height based on air time a tiny bit inaccurate.  But the result is close to the theoretical and it’s certainly close enough for day-to-day coaching.

(Some skaters land with their landing leg slightly bent.  Their jumps are actually slightly smaller than that indicated by the table below.)

Here’s the whole table (based on frames at 60 frames per second) including the individual jump minimum air times from this post.

 

Frames in Air	Flight Time in Seconds	Height in Inches	Height in Centimeters	Jump (minimum)
10	0.1667	1.3	3.3
11	0.1833	1.6	4.1
12	0.2000	1.9	4.8
13	0.2167	2.3	5.8
14	0.2333	2.6	6.1
15	0.2500	3.0	7.6
16	0.2667	3.4	8.6
17	0.2833	3.9	9.9
18	0.3000	4.3	10.9	1A, 2S, 2T
19	0.3167	4.8	12.2
20	0.3333	5.4	13.7	2Lo
21	0.3500	5.9	15.0	2F, 2Lz
22	0.3667	6.5	16.5
23	0.3833	7.1	18.0
24	0.4000	7.7	19.6
25	0.4167	8.4	21.3
26	0.4333	9.1	23.1
27	0.4500	9.8	24.9	2A
28	0.4667	10.5	26.7	3S
29	0.4833	11.3	28.7	3T
30	0.5000	12.1	30.7	3Lo
31	0.5167	12.9	32.8
32	0.5333	13.7	34.8	3F, 3Lz
33	0.5500	14.6	37.1
34	0.5667	15.5	39.4
35	0.5833	16.4	41.7
36	0.6000	17.4	44.2	3A
37	0.6167	18.4	46.7
38	0.6333	19.4	49.3	4S, 4T
39	0.6500	20.4	51.8
40	0.6667	21.4	54.4
41	0.6833	22.5	57.2
42	0.7000	23.7	60.1
43	0.7167	24.8	63.0
44	0.7333	26.0	65.9
45	0.7500	27.2	69.0
46	0.7667	28.4	72.1	4A
47	0.7833	29.6	75.2
48	0.8000	30.9	78.5

 

It’s pretty fascinating to understand the ramifications of this table.  For example

• A double lutz needs to be have a minimum flight time of about 0.35 seconds, so it will be 5.9 inches high.
• If a triple lutz needs to have a minimum flight time of 0.53 seconds, it will be 13.7 inches high.

OK… let that sink in!  The triple lutz needs to be 2.30 times the height of the double!!  WOW!  This really helps explain by so few skaters actually get all those triples.

I hope this was interesting and useful.

 

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