Brachistochrone curve. Fastest route for a ball.

Brachistochrone curve. Fastest route for a ball.

A Brachistochrone curve is the fastest path for a ball to roll between two points that are at different heights. A ball can roll along the curve faster than a straight line between the points.

The curve will always be the quickest route regardless of how strong gravity is or how heavy the object is. However, it might not be the quickest if there is friction.

The curve can be found using calculus of variations and optimal control.

Source:
@donttrythis (Twitter)

@engineeringandarchitecture
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[nexusmas]

Lesson learned : when running, make sure your body is curved so you reach slower but faster at the same time

[livedandletdie]

The straight line has constant acceleration.
The regular curve had a lot of acceleration but too much distance, and the brachistochrone is the perfect balance of acceleration and distance.

[willfr]

And that kids is why spiderman gets to the crime scene faster than the cops

[phatoni]

The goal here is to transform gravitational force into forward momentum as efficient as possible. One factor that has an influence on efficiency is friction. Another factor is that earlier acceleration leads to a higher velocity at the end. You have to optimize for friction (yielding in negative acceleration) vs. maximum initial acceleration.

[caseyquinnmusic]

“Sometimes taking a straight path in life isn’t always the best and fastest to get to where you want to be.”
-Just Some Guy

[ryankane]

I like how the bottom diagram is completely different than the actual thing

[Pxragon]

“If you need to go somewhere in life, just take a brachistochrone curve towards it.”

[yearleftforneet]

Moral of the story = the shortest way is not always the fastest way

[k_gold]

Brachistochrone is such a good way of showing how complex stuff still rely on basic laws of nature, at the highest point, the acceleration is maximum, and as the curve flattens in such a way everywhere it provides the maximum amount of acceleration possible at that point. That way we aren't losing any time

[Gsestav]

I did my math thesis about this got a 9/10 very interesting subject

[ThePhysicsMathsWizard]

I think the middle curve gives the ball more time for acceleration, and it is steeper than the straight diagonal line, the last curve is even steeper at the start but the ball accelerates for a short time and comes to a nearly flat path.

[EIGHT]

Most motivating video I’ve seen. Though your life goes down hill, the rebound will make you out ahead.
Keep your head held high!

[Mindless_view]

This explains very well why the person who lives closest comes latest.

[leventebrinton]

This is how spiderman swings, its explained by Peter Parker and Doctor octavius in spiderman 2. Spiderman way of swinging is the fastest way to go.

[nathanbates]

90 degree angle or short turn - sudden change in direction kills the momentum.

Diagonal - doesn't allow the ball very much acceleration from the force of gravity

Curve - A lot of acceleration upfront allows the ball to speed up and the softer curve doesn't kill too much momentum.

[alexeipino]

The theory about a straight line being the fastest doesnt seem to cover gravity and the y axis

[中山ガバ]

I hear a Japanese ancient temple, Horyuji, adopted this curve in building to help rain flow fast and smoothly to keep dry, which means ancient carpenters realized the law from their experience.

[AkashIssar]

This is cool . And now makes sense why Fred Flintstone reached his car so fast sliding that Brach... dinosaur

[him.]

The perfect example is How Spiderman use his web for travelling as shown in this video

[croc_moat]

The best crossover ever, two legends finally met, when I saw it for the first time I almost shit myself from happiness