Are Figure Skaters Projectiles?

The title above is eye-catching on a number of levels.  Have you ever been on those high sessions with 25 skaters?

Actually, this post is a follow-up to my discussion of slo-motion versus computer analysis.  In that post I made the bold claim that the minimum height for a double axel is 60% higher than the minimum height for a double lutz.  In this post, I’ll show how I got those numbers.

Warning:  This post is extremely technical so if you just want the final answer, see the height and flight time tables below.

The work of figure skating video analysis experts has demonstrated that there is a minimum flight time requirement for each of the jumps.  For example, a double lutz needs to be in the air for 0.367 seconds or longer while a double axel needs to be in the air for 0.467 seconds or longer.  These values have been determined by analyzing hundreds of jumps with various video analysis programs such as Dartfish or Pro-Trainer.

Using the video analysis software, a coach can 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 and advance the jump frame-by-frame through the flight until the skate blade just touches the ice.  The number of frames from the start to the end point give the flight time, as video cameras shoot frames at fixed time intervals.

In North America, the video standard is 29.97 frames per second but the magic of modern video analysis software such as Dartfish and Pro-Trainer allows those programs to double the number of pictures for certain consumer video cameras.  (In a future post I’ll discuss the technical details of interlace vs. progressive scan.)  That means we can resolve the jump flight time to 1/60th of a second (actually 1/59.94 of a second).

So here’s an example.  I’ve never analyzed a double axel with less than 28 frames of flight time at 60 frames per second.

28/60 = 0.467 seconds.  Dartfish and Pro-Trainer have timers so you don’t actually have to count the frames.

Now to calculate an estimate of how high the jump was, I 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 as the Time in the equation as the skater at the peak of the jump has no vertical speed (“from rest” at the top of the jump to full speed at landing… to use the simplified equation).

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 0.467,  the decent-only time is 0.467/2 = .2335 seconds.  Plugging all of this into the equation yields:

Distance = 0.5 x 386.088 x .2335 x .2335 = 10.53 inches

Just for theoretical completeness, the actual jump height is slightly lower.  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 the number of frames method a tiny bit inaccurate.  But the result is close to the theoretical.  A double axel must be 10.5 inches high or you can forget it.

(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:

Frames in Air	Flight Time in Seconds	Height in Inches
10	0.1667	1.3
11	0.1833	1.6
12	0.2000	1.9
13	0.2167	2.3
14	0.2333	2.6
15	0.2500	3.0
16	0.2667	3.4
17	0.2833	3.9
18	0.3000	4.3
19	0.3167	4.8
20	0.3333	5.4
21	0.3500	5.9
22	0.3667	6.5
23	0.3833	7.1
24	0.4000	7.7
25	0.4167	8.4
26	0.4333	9.1
27	0.4500	9.8
28	0.4667	10.5
29	0.4833	11.3
30	0.5000	12.1
31	0.5167	12.9
32	0.5333	13.7
33	0.5500	14.6
34	0.5667	15.5
35	0.5833	16.4
36	0.6000	17.4
37	0.6167	18.4
38	0.6333	19.4
39	0.6500	20.4
40	0.6667	21.4

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

• A double lutz needs to be have a miminum flight time of about 0.36 seconds, so it will be 6.5 inches high. 
• If a triple lutz needs to have a minimum flight time of 0.58 seconds (estimated), it will be 16.4 inches high.

OK…has that sunk in yet???  The triple lutz needs to be 250% higher than the double!!  WOW!  Do you see why so few skaters actually get all those triples?

I hope this was interesting and useful.  If you are enjoying this blog, please pass the URL along to your friends that may be interested.  Also, please leave a comment as I would love to hear from you.

Trevor

Why Computer Analysis And Not Just Slo-Motion?

One 0f the main uses of video analysis software with figure skaters is determining flight times.  Why?  Because flight time or jump height largely determines jump success.  For example, based on all the video that I have analyzed, I have never seen a double axel that had less than 0.467 seconds of flight time.  And other video analysis experts have confirmed this value.

Dartfish experts Chris Conte and Audrey Weisiger use a value of 0.500 seconds for double axel.  But I have personally measured a handful of double axels at 0.467 and in fact, one of the skaters I work with regularly in Madison lands it consistently with that flight time.  But she is very slender and has an awesome rotation rate.  So most skaters that are not as slender will probably have to meet Chris and Audrey’s 0.500 second minimum.

If a skater is ready to work on double axel but cannot perform a single axel with at least 0.467 seconds of flight time, she should spend nearly 100% of her effort making her jump bigger.  The chances are simply not good that she will be the first skater ever to land a double axel with less than 0.467 seconds of flight time.

This feature of video analysis software truly sets computer jump analysis apart from basic slow-motion video analysis.  Of course, basic slo-motion has been used by coaches for years and is very common in figure skating.  But computer analysis provides flight time and takes coaching to another level.  Knowing the flight time of the jump is critical for understanding what is possible.

All the time, I see skaters that are attempting double axels and triples that simply do not have the height necessary to land those jumps.  And unfortunately, they continue to practice them over and over, teaching themselves to fall or teaching themselves to land cheated jumps.  Since their coaches don’t realize they will never land it without more height, they keep doing it, and ingraining an incorrect movement that can be nearly impossible to change.

And that largely explains why double axel separates the really good skaters from the rest.  At the recent Frank Carroll  workshop in Milwaukee, Mr. Carroll described skaters having jumps and jump combinations through double lutz as being very good… but skaters with a double axel are in another class.

And that’s also evident in some surveys I’ve done.  Many coaches rarely get the chance to work on double axel.  And when they do, they are almost never successful.  The percentage of ladies that actually learn to do it consistently is very small indeed.  And no wonder… just getting any female athlete to jump 10.5 inches off one leg is quite a feat! (10.5 inches represents 0.467 seconds of flight time based on projectile motion calculations… more about that in a future post!)

And here’s some more astonishing but useful numbers.  Minimum flight time for double lutz is about 0.366 seconds.  That makes the difference in flight time between double axel and double lutz just 0.1 seconds.  But guess what?  Those 0.1 seconds represents a whole 4 inches!!!  So you can do a double lutz with just 6.5 inches of height but you have to jump over 60% higher to land a double axel!  No wonder so many skaters never get one…

If you have skaters working on double axel, do yourself and them a favor by getting a computer analysis done.  Find someone to help you if you don’t have the tools yourself.  The bottom line is – computer video analysis is truly a major leap forward in figure skating coaching for advanced skaters. 

Trevor

Great Dartfish Substitute for Figure Skating Video Analysis

I have a couple of video analyses ready to put online but I’ll need a day or so to convert them to streaming format.  So check back soon for an analysis of a double flip and a double toe loop.

People always ask me if I use Dartfish for my video analysis work.  Dartfish has become the standard software package for analyzing figure skating.  You even see Dartfish Stro-Motion images being used on television broadcasts of major skating events.  And rumor has it that the PSA has been talking to Dartfish about becoming “strategic partners.”

But I don’t use Dartfish.  Dartfish is very expensive and the extensive feature set is not required for day-to-day analysis work.  Instead I use another program called Pro-Trainer.  Pro-Trainer can be purchased from Sports Motion.  This software sells for $169 at the time of this post.  Considering that the least expensive Dartfish version is nearly $1000, Pro-Trainer is a great substitute.

Pro-Trainer has been used extensively in minor league baseball and is relatively stable.  I have found a number of bugs but the program does a nice job considering the price.  It does provide 60 frame per second capture if you have a mini-DV camera.  (If you’re looking to buy a video camera for video analysis work, go with a mini-DV camera instead of a hard disk or DVD version.  It’s all about video compression and I’ll explain in a later post.)

Pro-Trainer is a bit more difficult to operate than Dartfish but what do you expect for $169!  Once you get used to the series of actions required, it’s very simple.  And Pro-Trainer also has a recording capability…the video analyses that I post on this blog were all created with it.

When you install Pro-Trainer for the first time, it defaults to golf analysis.  But you can customize it for figure skating.  I’ll create a screen capture of how to do this in the near future.

Want to get into computer video analysis but can’t afford Dartfish?  Check out Pro-Trainer…it works for me.

Trevor