Usain Bolt’s Split Times and the Power of Calculus | Hacker News Reader

Usain Bolt’s Split Times and the Power of Calculus

quantamagazine.org

115 pointsfurcyd18 comments

Haven't read this article yet - but I studied the picture at the top of the link carefully.

Not only was Bolt a mile ahead of his competitors and not only did he turn to face the crowd as he was crossing the finish line... Usain Bolt's shoelace was untied...

Haha, the article calls it out as well

"Even with his celebration (and an untied shoelace) he set a new world record of 9.69 seconds."

The wiggles are interesting. But they also open up a can of worms - how precise is the measuring instrument, and which part of Bolt is it measuring? His feet, knees, torso, forehead? In engineering parlance, what’s the metrology design? Think of UB as a noodle with each part having different instantaneous velocities.

Numberphile created an entertaining video regarding Bolt's speed, the speed of light, and the distance he actually covered while sprinting.

https://www.youtube.com/watch?v=tflf05x-WVI

Seems to be promoting a new book that was released yesterday:

https://www.amazon.com/Infinite-Powers-Calculus-Reveals-Univ...

The subheading does say this:

This adapted book excerpt from Infinite Powers ...

So it might not be correct to say the article is promoting the book, rather, the article is adapted from parts of the book.

If I'm not mistaken, interpolation methods existed before the invention of calculus. Interpolation was used to reduce astronomical data before calculus, afaik.

Would it be possible to find the speed on any given moment without calculus? Is it just easier with calculus?

This article brings to my mind the joke about the physicist and spherical chickens in a vacuum.

"Assume a perfectly spherical cow of uniform density"...

The 100m dash have three phases, acceleration, top speed, and speed endurance. Almost all sprinters deaccelerate at the last 20m. Bolt had very good speed endurance, probably because his 200m training.

Source? And why would they decelerate? Extrapolating from your last sentence – fatigue? Would be interesting to compare acceleration at 80m in a 100m sprint vs. a 200m sprint.

> Extrapolating from your last sentence – fatigue?

Yes. They train to exert the maximum amount of effort in order to optimise their time. If they're at maximum speed at the finish line it does them no good, they likely could have expended more energy to be quicker in the middle of the run to cut their time.

The energy system that is used for explosive power can only last a few seconds, after that muscles have to use another energy source

https://en.wikipedia.org/wiki/Bioenergetic_systems#ATP-CP:_T...

Probably just the topics of the article, but I think this is the first of the recent glut of fluff pieces that I enjoyed almost every bit of.

I was rather disappointed in this article, since it was making the connection to calculus. Where is the curve of acceleration? Where is the curve for jerk? Where is the calculation for maximum force on his body from that acceleration?

https://en.wikipedia.org/wiki/Jerk_(physics)

You are disappointed at the article for not being a different article? Velocity is the derivative of position

Yes, I am disappointed that an article with "power of calculus" in the title left most of the power of calculus out of the article.

>Velocity is the derivative of position

Thanks, hadn't noticed that.

The main thesis of the article was that high resolution measurements can sometimes obscure the pattern, and that scientific insight requires knowing what details to idealize away. The high resolution data showed the acceleration and deceleration of each stride. On the other hand, the graph based on the the coarser split times hides these bumps and allows for easier analysis using calculus.

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