Why roller coaster loops aren't circular

Originally published at: https://boingboing.net/2024/07/12/why-roller-coaster-loops-arent-circular.html

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High g-forces can certainly be bad but your body can usually handle them for brief durations if the ride eases into them smoothly enough. It’s really the derivative of acceleration (a term technically known as “jerk”) that does the most harm, snapping your neck back and causing spinal injuries.

Fun fact: the 4th, 5th and 6th derivatives of position over time are named for the sounds your bones make when experiencing them.

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Of course if you want to have high g-force for a sustained time…

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Contributed by Popkin

Video for BBS:

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(I’m a retired professional seamstress, and…)

The term “Clothoid loop” caught my attention (introduced at 5:04 in the video). And now I know a little more about it…

A curve with so many names …

The clothoid equations were first defined by Leonhard Euler; this is why, in general Physics the curve is often called Euler spiral. The French physicists Augustin-Jean Fresnel and, later, Alfred Cornu, rediscovered the curve and defined its parametric equations – hence the curve is sometimes called Fresnel or Cornu spiral.

In 1890, Arthur N. Talbot, Professor of Municipal and Sanitary Engineering at the University of Illinois, defined for civil engineering the “railway transition curve” (Talbot – 1912), with similar equations as Euler did for elasticity and Fresnel and Cornu for optical applications.

The name clothoid was suggested by the Italian mathematician Ernesto Cesàro. The word clothoid comes from klothos, the Greek word for spin (wool) the shape of the curve thread that wraps around the spindle. The same root appears in the name of Clotho (The Spinner), one of the three Fates who holds the thread of human destiny.

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Brusio spiral viaduct and railway (Switzerland, built 1908), from above:

More or less every transition curve on the Autobahn is some sort of clothoid.

You only really notice them at the on- and off-ramps which have small radii (and are designed for ~40 km/h).
One of the reasons for using clothoids is that changes in direction are smooth, not sharp turns, which works beautifully with large radii.

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A similar concept makes an appearance in the 2022 novel How High We Go In The Dark by Sequoia Nagamatsu.

It’s kind of a dark story but basically a global pandemic creates an unprecedented number of terminally ill people—including many children—forcing humanity to find new ways to come to terms with death. One such innovation is an amusement park where parents can enjoy one last weekend of fun with their children culminating in a thrill ride to the Great Beyond.

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Snap, Crackle, Pop

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Sandbags and monkeys!

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Have you read Terry Pratchett?
If you did, you know why this opening line caught my attention.

Then, your post did. Thanks for that wonderful dive down the rabbit hole.

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Oh, I only know Terry Pratchett through occasional references that people here make. If I seem to have quoted him or something, it was unknowingly on my part.

I’m delighted to learn that you got some enjoyment from my post. Thanks for letting me know that

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The guild of seamstress in Ankh-Morpork was a bit of a euphemism.

https://wiki.lspace.org/Seamstresses'_Guild

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Well, I never!

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They did have an actual seamstress as well, for confused people who wanted their clothes repaired.

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You can always play it safe and just walk:

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In The Great (S2E7), someone pitches the idea of the Euthanasia Coaster to Catherine at the science fair. So good.

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