Backflips and MoCap - a friendly introduction to data driven movement analysis
This is the first work of writing in what I plan to be a collection of posts that will relate to cool movements and how to analyse them — to find weak-points in execution and optimal paths for improvement. I’ll draw upon my knowledge of physics to explain the mechanics of the movements under analysis and use Motion Capture (MoCap) data to elaborate on and visualise my explanations.
While going through this process I wish to show people why I am so exited about what technology can offer when applied to movement analysis. There are many ways how data like this can help guide the process of designing workout programs for individuals. By giving deeper insights into their current state, that might otherwise be hidden to the naked eye or swept from memory a long time ago.
Who am I to talk about this?
For one I have been an athlete almost all of my life. Starting off with Judo practices at the age of 5 and switching to Cheerleading at the age of 20, where I am currently an active member of the Swedish National team.
The curiosity of doing flips probably stemmed from an internal desire to show-off. As soon as I kind of landed a front-flip I showed it to my friends on the grass. I remember it vividly, proudly announcing to the friendly faces gathered around me: “Check this out”, taking a few quick steps, punching my legs into the ground to initiate the front flip, “gracefully” landing on my buttocks, followed by cringe and laughter of those who gathered.
Nevertheless, that was not the last time I did it. The journey of front- and backflips started in judo practices, bouncing off a tractor wheel tube, with my coach spotting me. As time progressed I eventually started practising without the bouncy wheel on foam mats as well as other flips on the trampoline.
And by the time I was 13 I was showing off my amazing backflip skills in school, which was of course super safe since I had backpacks as cushions. Not too long after that I took away the elevation and did some flips on a level floor and today I’m even better at it.
Alongside my interest and history with sports and flips, I was keen on sciences in school. This interest in science, maths and physics led to an undergraduate in Engineering Physics, in the interest of utilising the knowledge in matters related to the human body led me to acquire a graduate degree in Biomedical Engineering.
And as of this writing this post I am working for Qualisys, producing Motion Capture Systems, which enables me to apply my technical expertise in matters relating to but not limited to human bio-mechanics.
Because of my tight involvement in sports as an athlete and my engineering background, my brain is always on a lookout for fun ways to utilise technology in sports — to use technology to help with skills development and understanding.
Before diving into the backlfip breakdown, I’ll briefly describe what is this MoCap data I’ve been talking about.
Motion Capture
Humans have captured motions in some shape of form for more than a century with techniques like chronophotography and rotoscopy. Which have helped pave the way the field of Motion Capture (MoCap), which has many applications. One of the most popular fields is entertainment, where MoCap is used to create computer animated characters. Another popular area is human bio-mechanics and currently one of the most popular ways to capture human motion is using Marker-Based Optical systems, the same kind of system I used to capture data for this post. I will describe the process of getting a 3D representation of the human skeleton with the commercial system from Qualisys and it goes as follows.
The systems utilises spherical markers and calibrated cameras, by this I mean we know their location and orientation in space, as well as a mathematical model of camera lens distortions. The cameras work in the near infrared range and illuminate light in the same spectrum into the measurement volume.
The markers are retro-reflective, which means that light is reflected back in the same direction were it comes from. This makes it easy to detect the markers in 2D on each camera view. The 2D information together with camera location information is used to perform tracking and 3D reconstruction to obtain the 3D position of each marker.
After this step we get unlabelled trajectories of 3D points, seen as red dots in the image below. These points then need to be identified, because we need to know which marker is placed on the knee, which is placed on the ankle etc. After identification we can fit a skeleton model to the markers (orange cones in the image).
At this stage we have a fully digital representation of the subjects skeleton joint locations as well as orientations, in this case 300 data points in each second for each skeleton segment. By differentiating the data we can also obtain the velocities and accelerations for each segment. If we add up the number for a 10 s measurement we get this number:
300 Hz ×10 s × 22 segments × 6 DOF × 3 (pos, vel, acc) = 1 188 000,
which all together seems like a whole lot, but worry not, I’ll explain what’s so great about the data. So without further ado, let’s dive into the backflip breakdown.
Backflip — The breakdown, as the way I see it
For this analysis lets break down The Backflip into three phases (P) that span over a time period and are separated by two events (E), distinct points in time.
When doing an in depth analysis one often looks at a movement from many different aspects, but for now lets keep it simple.
Phase 1— Set
In this phase one of the main goals it to generate a lot of vertical velocity, that will be one of the main contributing factors to the height of the backflip. As seen below, this phase involves the subject squatting down, while swinging the arms back and exploding back up while swinging the arms upwards.
By doing this the subject generates power from the legs to propel the body up at a highs speed, while the arm swing helps generate initial rotation velocity that will help with the actual flipping motion.
Event — Takeoff
A simple definition for the takeoff (TO) would be the moment both feet leave the ground. The three images below show the video frame of the takeoff.
Now let’s look at some MoCap data, below is a plot of the foot position on the vertical axis (Z). One whole backflip is in that plot and it is quite clear just by looking at it, where the feet leave the ground and when they return to the ground. But to pinpoint the exact time, we need a little different definition, since all we see are numbers on a graph.
Luckily we do have some more information than just number on the graph. We know that the graph represents the position of the feet in vertical (Z) axis. One way would be to say that TO happens when both left and right foot value of Z reaches above a threshold, like this:
Left Foot Z >Threshold AND Right Foot Z > Threshold
After we set the threshold value, we have a concept of a simple TO event detector that we can write into a computer program. The easiest way to set a threshold is to do it manually, from this example a threshold of 200 mm would give us the approximate position, but there are very limited cases where the same threshold will work. I’ll leave intricate discussion about event detection algorithms to another post.
One thing to note here is that the video was captured at 50 Hz, but the MoCap data was captured at 300 Hz. So for example, both video frame 1 and video frame 2 have a corresponding MoCap frame, but we also have 5 more MoCap frames in between.
So having a higher frame rate helps us pinpoint the exact location of the event in time more precisely. But of course we could also capture video at a very high frame rate, but to extract the event from a video using a computer program, we would need a lot of extra work and more complicated algorithms.
Phase 2— Flight
This is the phase where all the visual magic happens. The body rapidly turns around 360 degrees with the crowds going wild in amazement. But how does this happen.
As physics tells us, given a fixed amount of energy to a rotating object, the object will spin faster when there is less weight far away from the centre of mass. The rotational velocity in relation the mass is described by angular momentum. A great way to test this out is on an office chair, start the rotating with arms out to the side and pull them in tight. For more extreme effect, pull the arms in faster and have weights in your arms.
The same physics apply when rotating around other axis of reference. When one starts off with the body in a stretched out position as described earlier and pulls in the legs towards the upper body and grabs as tight as one can, the initial rotation speed will increase dramatically.
Lets look at the physics that describes this more closely. The angular momentum can be written as:
L = I × ω .
Therefore, L depends on the inertia (I) and the rotational velocity (ω) . We know from the chair experiment that ω increased when the subject pulled in the arms. Without taking into account any external forces, like the wind resistance. we can consider L to be constant. Then we know that when ω increases, I has to decrease for the equation to hold true.
In its simplest form the equation describes the angular momentum of a point mass, which has no shape, but can also be generalised to objects. Lets look at the formula again, but this time by expressing inertia as r² × m, it depends on the mass of the rotating object m and its distance from the rotation axis r.
In case of an athlete doing a backflip, the total inertia depends on the location of all the limbs in relation to the rotation axis. By taking these observations into account we get a formula looking something like this:
L = ∑ ᵢ rᵢ² × mᵢ × ωᵢ ,
where the index i denotes each limb. We can safely assume that during our subjects jump the mass does not change. Therefore we now know that when ω increases, the distance r has to decrease to satisfy the constraint that L is constant. This distance r in our case is the distance of each joint segment from the centre of mass, which is the point the body rotates around.
All this matches well with the reasoning that tightening up into a small ball increases the rotation speed in a backflip. Now lets look at the angular velocity of our measured backflip. Below is a graph of the angular velocity of the hips over time.
On the graph, the flight phase is highlighted in green. We see that at in the beginning of the phase, the angular velocity is relatively small. However, it increases rapidly as the phase progresses, because the athlete assumes a tucked position. It decreases again when the athlete opens up the tuck, but does not reach zero right away at landing.
To see some crazy rotation speed and jump height action, check out Aaron Cook, the person to land the worlds first standing double backflip.
Event — The touchdown
The event that ends the flight. A definition that we can use to manually detect this from video, would be the moment both feet touch the ground. Again as for the takeoff, I have illustrated this with the video frames. At this moment the subject has (hopefully) rotated enough to have the centre of mass above the feet.
Thinking back to the graph of feet positions, it was quite clear as well, approximately where the feet touch the ground. But this time let’s have a look at slightly different graphs.
First let’s use the position values to calculate the velocity. A simplified formula to get the velocity goes as follows:
ν = ∇X / ∇t ,
where ν is the velocity and ∇ t is the time it took to travel over distance ∇X. This formula gives us the average velocity over the give time. The ∇ sign means that we calculate a difference of values. In the case of this velocity formula ∇t = t₂-t₁, is the difference in time and ∇X = X₂-X₁ is the difference of position within the same time-span.
When the time difference is rather small, then we get an approximation of the derivative over time — in other words, we have numerically approximated the derivative function. This has yielded us the velocity, change in position over time.
With our 300 Hz MoCap data this is rather sufficient and by applying this strategy to the vertical position of the feet we get the following result.
This graph is still rather intuitive. The first hump where the velocity is positive, that is where the feet rise higher. The big downward hump is where the feet get closer and closer to the ground. Just before the velocity hits zero again, that is where the feet land.
If we repeat the numerical differentiation process on the velocity we get the acceleration, change in velocity over time.
α = ∇ν / ∇t
Plotting the acceleration looks like this.
A plot of acceleration (α) is a little bit less intuitive, but whenever the acceleration is positive, the speed is increasing. So the first bigger hump is where the feet lift and their ν increases. Just after that the α turns negative, which means the ν decreases, which is evident in the first big hump on the ν graph, where there are two little peaks.
Before, we defined the touchdown event as the moment both feet touch the ground. But this exact moment is a bit difficult to find without force plates. However, when talking about when the feet hit the ground. It is not the moment the toes lightly touche the ground, but rather the moment all movement of the foot suddenly stops — then we can turn our attention to the α plot. At the last peak, there where the α value is the highest overall, that is the moment the feet have hit the ground.
Moving on, we can now calculate our first parameter — flight time, defined as the time the feet hit the ground, the touchdown event (TD) subtracted by the time the feet leave the ground, the takeoff event (TO).
Flight Time = TD-TO
In this example the flight time was ~0.65 seconds. This parameter highly correlates with the maximal vertical position of the centre of mass. The higher one jumps the larger the flight time. The more time we have in the air, the easier it is to make it all the way round. One can rotate slower with more time and still make it around.
Phase — The landing
After the first contact with the ground there is still work to be done before the backflip is finished. Assuming everything else was done good enough, the athlete now has to engage the legs to stop the momentum that has built up on the way down, stay in a calm and controlled position and of course smile.
While one do it just like in the above gif, it is not recommended to begin with. Instead absorbing the momentum by bending the legs and squatting down, something like this.
Further Analysis with MoCap Data
Now we have gone through all the events and phases. We’ve looked into how we can use the base data, position over time, to calculate velocities and accelerations. How to approach finding the events from data. As well as, defined a temporal parameter, flight time.
But what else can the elaborate MoCap data give us. For one, consider this. Right now I only showed one reference video view, the backflip from the front, like this.
But perhaps we want to view the flip from the side instead, with 3D data we can choose any view we want.
3D MoCap gives us much greater power to visualise data and do that automatically, without user intervention. One can use such visualisations to better convey an idea or feedback to an athlete. In the 3D visualisation above, I have also chosen to show the trajectory of the toes over time. When pausing the playback during landing, we can see that the athlete landed slightly in front of the original position.
And since we have the underlying data, we can also calculate the horizontal displacement in cm. In the above case this value results to 10 cm. This value can then be plotted in a simplified format, as seen on the right side above — to show quickly what is expected instead.
Another parameter we can look at is the takeoff angle. In the image below I defined this as the angle between the vertical direction and the line between the middle of the toes and head, which is not the very best way to define it, but will do just fine for visualisation purposes. It would be more optimal to tie the angle to the direction of the ground reaction force or direction of acceleration of the centre of mass, but I’ll leave that to another post.
Takeoff angle in this case is 14 degrees as compared to the vertical direction. This angle can then be compared to optimal ranges. In the given example the body is rather straight, but the head is still tilted slightly back, so it is not yet perfect.
Note that is also possible to land in approximately the same spot with a sub-optimal jump, from the perspective of just one simple observation. That is why looking at a collection of parameters of interest is beneficial.
These two parameters, takeoff angle and horizontal displacement, can be used to assess if the jump height an athlete is achieving could be further improved by adjusting technique during the set. One common mistake that also contributes to loss in jump height, is when an athletes throws the head back and jump backwards. When an athlete does this there will be a higher negative displacement, as well as a high takeoff angle.
Final Thoughts
Backflips are what they are, some think they’re cool ,some think they’re corny. When I throw backflips in the park, some say I’m a show-off, who knows, perhaps that is even true. But most of the time I’m just putting in the hours to get better, to perform better than I did before.
The theory on how a backflip is executed can be all fine and dandy. But when you are interested in actually doing one yourself or teaching someone else, all kinds of factors come into play. For example, the following:
- Having the raw strength in your muscles to produce enough force that will give enough height to the jump.
- Having the coordination to time muscle activation all around the body to produce the sequence of internal forces required to actually rotate fast enough.
- Having the mental courage to hold through the whole movement without suddenly changing the movement patter to disrupt the flow.
What MoCap allows us to do, is measure sports specific metrics that in turn allows us to take science into sports. It opens doors for movement assessment, which is data driven and automated.
One can go even further by combining the movement information with other data. For example, historical data of an athletes strength training program, their emotional status, their nutrition or other potentially contributing factors.
With all this data, we can apply complex analysis that can help design skill training, strength training, nutrition or mental training programs in order to find the most optimal path to success
If you liked what you read, then let me know, since that will increase my motivation to write some more. And even of you didn’t then let me know, since that will give me the opportunity to better myself as a writer.
