How math and physics determine sports!
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- Опубліковано 14 тра 2024
- This video investigates the physics behind a curved trajectory of a football. Roberto Carlos' impossible free-kick goal is taken as an example and reproduced using pure mathematics. The main focus is the Magnus effect which is responsible for the force generated on a rotating object that travels through a fluid. An analytical model was first developed and solved numerically in MATLAB. A Monte Carlo simulation was utilized to investigate the effects of varying parameters on the trajectory of the ball.
Music: www.bensound.com/ - Наука та технологія
This guy is a very hard-working man. No other word! I would like to see these types of channels on UA-cam.
Salute to your work... Never thought what I am learning is school can be this much Fun and cool
Really great video! Love your content! Looking forward for the new one 😊
More to come!
Hello, Would you plz share the MATLAB code with us. thanks in advance
Hey man, I really loved the work you put into making this simulation and video! It also got me thinking about the magnus effect on soccer balls and what "knuckleballs" really are. Please don't read my comments as criticism of your work, it's more that I am hoping to start a nice discussion.
When I see footage of sharply curved shots it often strikes me that the ball seems to be spinning a lot less quickly than I would think is needed. Also Carlos' shot seems to not spin very fast, which makes me think that the magnus effect is only one component of the lift on the ball. The other component I guess would be deformation of the ball, departure from its initially approximately spherical shape while it wobbles due to the impact of the kick.
I feel this idea is supported by the fact that hitting a proper knuckleball (as I understand it) entails hitting it very straight through the center so that hardly any spin is given and the trajectory becomes unpredictable due to the ball's elastic wobbling after the impact.
I couldn't tell from your video how you determined the imparted spin due to the off-centre touch, which would already have had some assumptions in there (shear fiction of the contact with the shoe for example), so the one thing we cannot compare with the Roberto Carlos footage is the amount of spin.
I suspect your simulation needs more spin than Roberto Carlos did to achieve that curve , and I wonder if adding the ball's deformation and subsequent aerodynamic changes would improve the result.
Probably a LOT of work and a LOT of assumptions to be added...
Cheers!
Hi Qluq77, thanks for your comment, you are raising interesting points. This simulation used dynamics of rigid bodies to calculate the trajectory of the ball and determine the rotation about its own axis. In reality, of course, the ball deforms into an ellipsoid as it travels so assuming a perfect sphere introduces some error into the calculations. It's hard to say how significant this error is. Introducing material non-linearities into this model would make it incredibly complex to model/solve and honestly, I wouldn't know how to relate the deformation of the ball with the travel velocity (or shot power) since the amount of deformation would be dependent on the internal pressure of the ball. My intuition (no scientific backing just my opinion) tells me that the more inflated the ball is the less this error would be significant since obviously a softer (deflated ball) deforms much more.
Bias incoming: maybe assuming a perfect sphere is not an awful assumption since I am sure FIFA would ensure the ball is fully inflated for such a match.
When it comes to the knuckleball effect, I can't come up with a decent explanation nor an objection to yours so I'm sure there is some of that going on. I would have to read up a bit more and watch some shots to see the behavior of the ball and if there is some other effect that might be missing. Good discussion.
Amazing!
Great work
Glad you think so!
Legit work done here. Very pleased to see a new vidio from you. Loving it, waiting for the next one
amazing superb and many more!!!!
can you please share the Matlab code?
Too cool
Mind blowing 🤯
Exactly how we felt when we discovered the results!
hey man, I am working on my extended essay for the ib. I am doing something very similar to your work. My research question is: "With a numeric simulation, how can I derive how a football must be shot on a free kick to score a goal?" I have already programmed a Python simulation allowing me to give 6 starting conditions: spin speed and 2 angles for the axes and shot speed + 2 angles for direction. I have also made a simple visualisation of the shots. The final step I want to take is the same thing you have done: I want to find out how much of the force is translated into spin and ball speed. Do you have some material on that, for example, a formula or something? I am not sure if I formulated this well enough for you to understand, I sometimes struggle with expressing myself with these scientific questions, as I am not a native speaker... Thanks in advance for your help!!
Hey buddy, I would recommend the book: Vector Mechanics for Engineers (10th ed) by Beer. More specifically Section 18 and Sample Problem 18.1. This will guide you through a 3D example. For modelling rotating bodies (balls) the magnus force plays a huge role. You would need to introduce this force separately which is a function of the spin of the body.
@@TheEngineeringHub thanks so much!!
Hi, thank you so much for the video, could you just explain on how you got the equation and what step size you used when using Euler's Method?
Hi, the underlying physics can be found in a generic dynamics textbook. I followed Chapter 18 of Vector Mechanics for Engineers by Beer, 10th ed. Sample Problem 18.1 should be a good starting point. In regards to the step-size, it had to be fairly small because the Euler's method is very poor, I don't exactly remember the size now but the model was prone to numerical instabilities unless the step-size was very fine. If I were to re-do the model now, I would convert the equations to a state-space representation and use 4th Order Runge-Kutta solver which is much more accurate and doesn't require as small of a time-step. Cheer!
Hi. I really liked the model. Can you explain the randomization method and how you modeled and used the figure 2 and 3. Thanks
Hi Ali, thank you for your feedback! The randomized method is basically a trial and error procedure that randomly samples values for the input parameters. The fancy word for this class of algorithms is "Monte Carlo Simulation" (MCS). MCS is mostly used for risk quantification but I applied it here as a means for solving the differential equations. These algorithms rely on repeated random sampling to obtain numerical results. Since the solution to the set of differential equations that govern the ball is highly sensitive to the kick location and angle at which the ball is hit, this method is an effective way to figure out a range of input values that produce a solution. Alternatively, it is also possible to manually change the input parameters for every simulation until you find parameters that produce a solution. Another reason for using such approach is the fact that the equations are too complex and an analytical solution does not exist, so I resorted to a sort of "brute force approach". I hope that clarifies things a bit.
@@TheEngineeringHub Thanks for getting back.
Yeah, that does give me a basic idea. It's interesting, I will look into it a little more. Any references that you would suggest?
Also, are you planning to do any more sports simulation?
Very nice.
Thank you! Cheers!
hello can anybody share the MATLAB code used in this amazing study
Hello man. really good video! I'm at my last year at danish gymnasium (High school), and i am writing my large assignment in mathematics and physics. I really find your method interesting, and is it possible in any way, that you can share the code u wrote in math lab with me, so i can use it in my assignment?
Sincerely,
Jacob
Hi Jacob, if you provide us your email, we can arrange something. Cheers
Are you a phd or masters? Quite impressive. I don’t remember learning about Magnus force in undergrad Engineering
I am a phd, but the Magnus effect I studied on my own, it's not usually taught in regular curriculum
@@TheEngineeringHub ok good, i am also from Canada and we took Dynamics but I was worried I wasn't paying attention in class :)
Interesting. Good work in Matlab, but the musik background is awful ...
Thank you for your feedback Stefan, we appreciate it.
Wow! That was mindblowing! This was a great video.
I m also surprised you needed tons of calculations to find out you re not Roberto Carlos 😅
Just joking.
Hahaha I had a feeling I am not but had to make sure 😅🤣
Man!!! I hope your salary is adequate!!!
Haha so far this video generated about $1.59 in ads 😅 but there is something more than money when reading comments of satisfied viewers. Hopefully you found it interesting and as mind blowing as we did!
@@TheEngineeringHub man!! After your video I want to start over my education!
@@constantined9015 education in the STEM fields would give you skills to calculate really cool things. But probably would not make you a millionaire :D ... unfortunately