# I did a center of mass analysis of a Fosbury Flopping high jump by Yuliya Levchenko! [OC]

I’m a collegiate high jump coach in the NCAA, and I really appreciate this. It’s very interesting to see a visual representation of this concept! Awesome work. Thanks!

I like how you went the extra-mile, and also included the centre-of-mass projection for her little victory-hops

What kind of monster would I be to neglect those hops!

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

The beautifully of the 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 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

METHODS

Step 2 - Forget about it for 3 months

Step 3 - See another cool high jumping gif on reddit and then post to /sub/imagestabilization requesting a PanoGif (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 and manually track the jumper's joints through each frame. Then I port that data into Matlab, where I calculate the COM using the . 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

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

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 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?

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 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. It's an old video, as he's been focusing on other things recently. But still, good stuff.

Clearly you are the person to ask this then. I know nothing about high jumping, so why does her center of mass drive backwards right as she's starting her high jump?

She slows down her forward inertia so she passes over the bar more slowly and allows her legs to kick up over the bar. Otherwise she would risk hitting the bar with her legs or other body part.

As soon as she started celebrating my first thought was: "please let that stick figure celebrate too". OP Truly delivered on this glorious internet-day.

Yeah, you have to remember it's not the entirety of her mass that is shooting backwards, it's her hips shooting up and out away from the pole to giver her more time to get her legs up and over the bar.

Great work! you can see the genius of the fosbury flop, the center of mass passes under the bar.

I'll just leave this here : Yuliya Andriyivna Levchenko ( personal best 1.97 metres Monaco 2017 ) attempts the crushing 2 meter jump.

I actually turned the vectors off for the victory hops, because they make it look really cluttered (due to her jumping around in the same spot, rather than travelling as she is in the other parts of the gif)

And have hot girls try to avoid you... Isn't that already the case?

Data IS beautiful...but so are those abs, amitrite?

Ah yes, the depleted uranium pelvis. A well known olympic doping technique.

How can you calculate COM from an image? She could have Carbon fiber limbs and a depleted uranium pelvis which would totally make your analysis wrong!

Amazing work as always! I love being able to go through each frame and see the COM acceleration change -- really provides insight into those crucial milliseconds for the jumper just before the jump.

I wish this was something we could see on ESPN or in post-game analysis at the olympics in general.

Is it a reasonable conclusion to draw from this COM analysis that the COM does not necessarily go above the bar? This has got to be the advantage of the Fosbury Flop.

Ideally your trying to keep your center of mass straight and pointed backwards/up at point of impact. Try bouncing a yardstick over a bar in a similar fashion as the jumper. Now imagine hinges near the middle of the stick. The more bend in the hinges, the less the impact is directed back up through the body. Pointing the hips up/out is implemented after takeoff to work in congruence with the upward force from impact and the momentum of the approach.

MAKE THE MASS MORE SEEABLE

It truly is a win for us all.

I didn't plot the segment centers of mass here, but I did in this older handstand gif

Basically - the caluclations for the full body COM are based on the weighted average of the COMs of the individual body segments. I got those values from that provide estimates the relative weights of body parts (i.e. a person's leg is usually about 16% of their total body mass).

Obviously, these average values are only approximations (everyone's body is a little different), but they do a pretty decent job!

I did high jump in high school. My coach told me to jump straight up and my momentum would carry me over the bar. I mistakenly took it too literal and jumped backwards to counter my momentum and actually jump straight up...I landed the way she landed, but on the ground in front of the padding.

Yup! The COM is no longer on the body and is just below the back!

This is so cool, the high jump always looks nuts but seeing it with this much detail has made me realise how fucking close they get to the bar. Would love to see this sort of thing with pole vaulting or something similar

I got voted into oblivion because my joke about a stick figure being naked went over everyone's head but thanks for getting it.

It actually doesn't and that's the beauty of this technique, check the image in /u/majoen98 comment

I love how excited she gets!

Great work, man!

To see it go from individual frames of the original video to a PanoGif, then to this is... pretty special. The little catch up you did is a nice touch as well. Love it.

It only negates the jump if you knock it off in the course of the jump. Someone on the original post speculated that she must have already seen the ref put the flag up, signaling that the jump was officially over.

I wish I was that bar...

Great work, very interesting!

Would that approach be applicable to snowboarders doing corkscrews and precessions? An analysis of a triple cork would be impressive for sure!