I did a center of mass analysis of a Fosbury Flopping high jump by Yuliya Levchenko!

Idid a center of mass analysis of a Fosbury Flopping high jump by Yuliya Levchenko!

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1. dorky2 says:

Thank you for this! I am a high jump coach and I explain this COM concept to my athletes, and this gif is going to help us out next spring!

2. sandusky_hohoho says:

Hello!

So, I did another center of mass (COM) analysis thing, this time of a expertly executed high jump by Yuliya Levchenko! [You can see previous posts of mine here](https://www.reddit.com/r/dataisbeautiful/search?q=author%3Asandusky_hohoho+title%3A%5BOC%5D&sort=new&restrict_sr=on)

The beautifully of the [Fosbury Flop](https://en.wikipedia.org/wiki/Fosbury_Flop) style of high jumping (turning around and jumping back-first over the bar) is that it allows the COM of the jumper to travel *under* the bar while the body moves *over* it. When you jump, the amount of energy you put into your body defines the ballistic trajectory of your COM. Once her feet left contact with the ground the trajectory of Yuliya’s COM was determined by the same classical Newtonian mechanics that define the trajectory of a cannonball in flight.

However, although your COM is a *description* of your body, it is not a *part* of your body. It is entirely possible to move your body into a shape where your COM is not in your body at all (you can see this in the later parts of this old [handstand gif](https://np.reddit.com/r/dataisbeautiful/comments/4rup10/i_did_a_simple_mechanical_analysis_of_that/) I posted some time back). Dick Fosbury’s great insight was to realize that by bending the body around the bar during a jump the jumper could get their body over a bar that was too high to clear with their COM.

Just one of the myriad ways that we manipulate the inexorable physics of our bodies to push the boundaries of human performance. Although this high jump is an extreme example, these same mechanics are inherent in the way that your central nervous system allows you to control the movement of your body through your everyday life

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METHODS

Step 1 – [See cool high jumping gif on Reddit](https://np.reddit.com/r/sports/comments/6onr3j/yuliya_levchenko_high_jump_for_196_pb_at_european/)

Step 2 – Forget about it for 3 months

Step 3 – [See another cool high jumping gif on reddit](https://np.reddit.com/r/sports/comments/73zhvp/dick_fosbury_changes_the_high_jump_forever_with/) and then post to /r/ImageStabilization [requesting a PanoGif](https://np.reddit.com/r/ImageStabilization/comments/740u9f/request_could_someone_please_stabilize_this_high/) (shout out to u/ibru for the incredible stabilized gif!!)

Step 4 – Do all the same stuff I normally do to make these gifs:

First, I pull the video into [Tracker](https://physlets.org/tracker/) and manually track the jumper’s joints through each frame. Then I port that data into Matlab, where I calculate the COM using the [Winter anthropometry tables](https://i.pinimg.com/originals/a1/3f/e2/a13fe228065014805ff3186e0bb7fbb6.jpg). COM acceleration is calculated by taking the double (numerical) derivative of COM position – That is, you find COM velocity by finding the difference in COM position on each frame, and then find acceleration by finding the difference in COM velocity (diff(diff(comXY)) in Matlab). FYI, this is also known as “calculus.” Then I just sex up the visualizations and throw it on the Internet!

[Raw videos, data, and Matlab code available here](https://www.dropbox.com/sh/nol5zx20w7r2zr0/AAAfJF6od7ykOs2PI8QgsX4Ia?dl=0)

_________________________
What I assume will be Frequently Asked Questions –

*1- Can I use this gif for a class/presentation/project/etc?*

Absolutely!! One of the coolest things about making these gifs is the number of teachers, trainers, and students who have told me that they use my animations for classes, etc. I can’t always respond in detail to folks’ questions (sorry!), but I always appreciate it. Anything I post online can be used for any purpose. If you are presenting in a professional academic or scientific setting, please attribute it to my [real-person identity](https://utexas.academia.edu/JonMatthis)

*2a – Why aren’t the COM acceleration vectors uniform during ballistic flight?*

They should be, and the fact that they aren’t is indicative of error somewhere in this analysis. I can think of a few possibilities – 1) This is a 2D image, but there is a lot of motion out of the image plane, 2) the stabilization is not perfect, which causes spatial warping that would break conservation of energy assumptions, 3) Error in my selection of the marker locations, and the noise in the tracking, 4) Error in the Winter anthropometry tables.

*2b – Couldn’t you make an optimization algorithm to adjust the weights and positions of the different segment COM based on the assumptions that they should be uniform during ballistic flight?*

Probably! I tried doing that for the [Triple Jump gif](https://np.reddit.com/r/dataisbeautiful/comments/5lsm1u/i_did_a_center_of_mass_analysis_of_a_stabilized/) I posted a while back, but never got it working. The code is all still up there, so maybe you could do it? I believe in you!

*3 – Why didn’t you run your COM biz on the original Fosbury high jump gif that u/ibru so [lovingly stabilized](https://streamable.com/7mk1h)?*

Honestly, I just got lazy. As much as I wanted to analyze the Fosbury jump for the history of it, Yuliya had much better form that captures the interesting mechanics of the jump. Also, the Fosbury video was recorded at a high framerate, which means it had double the frames of the Yuliya vid. As such, it would have been a lot of effort to do the joint tracking for that video, and I didn’t feel like going through it. Someday, I will get some [automatic joint tracking software](https://github.com/CMU-Perceptual-Computing-Lab/openpose) working on my computer, which will *massively* speed up my work flow. When I do, I may go back to the Fosbury gif.

[Obligatory Brother Plug](https://www.youtube.com/watch?v=-G1lh_6ohq8). It’s an old video, as he’s been focusing on other things recently. But still, good stuff.

3. Daxl says:

Righteous !