
Why are roller coaster loops not circular? - squeakynick
http://www.datagenetics.com/blog/march42014/index.html
======
maxerickson
As seems to be a pattern with this blog, the article is a little too similar
to existing materials to not have any citations. Here the tree starts at
Wikipedia, bounces through Archive.org and ends up at a Danish blog with some
interesting images:

[http://en.wikipedia.org/wiki/Vertical_loop](http://en.wikipedia.org/wiki/Vertical_loop)

[http://web.archive.org/web/20070827183113/http://fy.chalmers...](http://web.archive.org/web/20070827183113/http://fy.chalmers.se/LISEBERG/eng/loop_pe.html)

[http://www.matematiksider.dk/vejgeometri.html](http://www.matematiksider.dk/vejgeometri.html)

Nothing is taken directly from the source material though.

Edit: Just to expand a bit on calling it a pattern, this blog:

[http://www.datagenetics.com/blog/september32012/index.html](http://www.datagenetics.com/blog/september32012/index.html)

uses a figure (and analysis) very reminiscent of _A birthday present every
eleven wallets?_ from here:

[http://www.jbonneau.com/publications.html](http://www.jbonneau.com/publications.html)

~~~
squeakynick
Ouch! tough crowd :)

Sorry, I don't mean to cause offence to anyone. I blog things I find
interesting. I use my own words, create my own animations, derive my own
formulas (and the spelling and grammar mistakes are all mine!)

When I use the photos/images from others, I give credit and link back to
sources as much as I can from available data.

I've have on the order of 100 blog articles now. I'm sure over the course of
these I've trodden on a few feet (sorry), just as much as I've blazed new
trails.

We can all become better by listening to feedback, and I'll try to do better
at providing additional sources of information and inspiration.

~~~
unwind
I thought it was great! One nitpick: the word "Acceleration" is mis-spelled in
the first section
([http://www.datagenetics.com/blog/march42014/eq0.png](http://www.datagenetics.com/blog/march42014/eq0.png)).

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jameshart
Initial explanation of "why the roller coaster doesn't fall off" is poor. In
fact, the explanation doesn't even mention gravity, which is odd, because if
the coaster were to fall off gravity would presumably be the force
responsible. The author explains that the track is applying a downward force
on the inverted coaster: but that force would surely combine with gravity to
accelerate the coaster downwards, which is the opposite of the apparently
observed phenomenon we're trying to explain here. Of course that -is- what
happens, but only because the coaster is going fast enough that gravitational
acceleration downward would curve the cars down less than the track does.

The trick is to realize that an unguided rollercoaster, not on a track, wants
to travel along a parabola (not in a straight line, as indicated in the text).
If the coaster is going fast enough, then the radius of curvature of the
parabola at that location in the coaster's trajectory is greater than that of
the track, in which case the track gets to apply additional centripetal force
and turn the coaster -more- than it 'wants' to. If the coaster is going slow,
then the radius of curvature of the parabola will be less than the radius of
the track, and the natural path of the coaster will tend to pull it down away
from the track.

Of course, at that point, you find out what -really- stops the coaster from
falling off, which is that it's riding on a tubular steel track with wheels
clamped both above and below the rail...

All of which is mentioned - later in the article, but as an introductory
section, messing up the basics so badly really undermines the article.

~~~
frik
I would mention the great Roller Coaster Tycoon pc game series (1999-2004):
[http://en.wikipedia.org/wiki/RollerCoaster_Tycoon_(series)](http://en.wikipedia.org/wiki/RollerCoaster_Tycoon_\(series\))

You can design your own roller coaster and measure the G-forces. High g-forces
will scare them off and low forces won't attract many guest to take a ride.

~~~
logicchains
Note that the original Roller Coaster Tycoon was written almost entirely in
x86 assembly, and by a single person.

~~~
frik
His name is Chris Sawyer, the creator of Transport Tycoon and Roller Coaster
Tycoon 1+2:
[http://en.wikipedia.org/wiki/Chris_Sawyer](http://en.wikipedia.org/wiki/Chris_Sawyer)

He has kept low profile for at least 10 years :(

Another similar single person developer is Geoff Crammond of the Grand Prix
formula 1 series games (also low profile since 10 years):
[http://en.wikipedia.org/wiki/Geoff_Crammond](http://en.wikipedia.org/wiki/Geoff_Crammond)

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symmetricsaurus
Roller coaster design is one of the areas where you can actually use the 3rd
time derivate of position, the jerk, to good effect. So the jerk is the change
in acceleration over time. A typical motion with high jerk is when you are
riding in a car and the driver turns the wheel quickly, not a very comfortable
experience.

The same is true for roller coasters; high jerk motions are uncomfortable. So
you have to not only take the limits of comfortable acceleration into
consideration but also try to minimize the jerk.

~~~
lesterbuck
Jerk is also a limit in how fast a subway can move between stations. There is
a clear limit to how much jerk average standing passengers can survive before
they fall down.

~~~
hueving
I don't think this is the limiting factor in most subway systems though. I've
never been on one that accelerated during the entire first half of the segment
and decelerated during the second half at the same rate, which would be the
case if they were being limited by jerk.

~~~
pessimizer
>I've never been on one that accelerated during the entire first half of the
segment and decelerated during the second half at the same rate, which would
be the case if they were being limited by jerk.

No, that would be the case if the _only_ limit was jerk. When stations are
close to each other, it feels like this is exactly what happens.

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crazygringo
I'd love to read this page but it's using 88% CPU on Chrome on OSX. I can
barely even scroll the page. :( There's no Flash, must be some crazy
processor-intensive JavaScript animation?

~~~
squeakynick
Yeah, the Processing animation on the page is a little intense. I rushed it
out last night. I'll work on that later today.

~~~
squeakynick
I converted it to an animated GIF. Hopefully this gives better performance for
you.

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nraynaud
this kind of shape is also used in high speed machining, when there is no need
for a precise path (pocket roughing for example), it's better to avoid the
shock (infinite jerk) of a circular arc.

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robinhouston
There is a whole lot of interesting material about clothoid curves in Raph
Levien’s PhD thesis
[http://www.levien.com/phd/phd.html](http://www.levien.com/phd/phd.html)

Don’t be put off by the fact it’s a PhD thesis, a genre not generally noted
for good clear writing. The tone is scholarly, but unusually readable, and
there’s a surprising amount of well-researched historical material (chapters 5
and 6).

He used a design tool based on these curves to design the popular open source
monospaced font Inconsolata.

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josefresco
Anyone else think of this while reading the article?

[http://en.wikipedia.org/wiki/Euthanasia_Coaster](http://en.wikipedia.org/wiki/Euthanasia_Coaster)

------
ce4
The article claims that you're exposed to constant G-force in such an unround
"circle". This is only partially true (if you're riding in the exact middle of
the train), because the vehicle is so long.

Riding in a rollercoaster is really a very different experience if you're a)
sitting in the very front, b) in the middle or c) in the last compartment. I
like to sit in the last seat :-)

Imagine the very first part of the ride, a horizontal track with a sharp edge
downwards:

Especially the last compartment is really fun because you get the most forward
acceleration in the beginning (when 90% of the train is "falling" downwards
and the last compartment is still in a "horizontal" position. This leads to
almost 1G forward acceleration while the first compartment is facing downward
without accelerating too much because the biggest part of the coaster is still
in a horizontal position).

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winslow
Ahh so this same explanation could be used for why you can't swing yourself up
and over a swing set bar? Unless you go mythbusters style and use rockets?

[1] - [http://youtu.be/torrlSW6VnA](http://youtu.be/torrlSW6VnA)

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yread
> Roller coaster enthusiasts exploit these differences and compare notes as to
> the better places to sit on each ride to maximize the hang times, g-forces
> and ride experiences.

Hmm that sounds interesting, is there a "Roller coaster news" somewhere?

~~~
goatforce5
It's a very easy effect to feel.

> At this point, the last car still has not been passed the point of tightest
> radius. When it does pass, it will be travelling quicker and thus experience
> a higher acceleration.

Find a coaster without a long line and ride it twice in quick succession, once
from the very front and once from the very back.

On almost any coaster from the back row you should be able to feel the
sensation of being pulled over the crest of a hill as the front carriages pick
up momentum. I think the back is often a better ride on most coasters.

(The front is good on suspended coasters though. No one in front of you
blocking your view, and loops will often have the track disappear entirely out
of your view which is quite an odd experience.)

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jxf
I loved the position-acceleration-velocity animation. I'd love to know how was
that created (i.e. with what tools).

~~~
squeakynick
I quickly wrote/tested in VB, then converted it to Processing (which is very
cool for things like this).

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dallasgutauckis
This needs an ELI5/TLDR version....

~~~
vlasev
Here you go. If you have a straight track and then you have a circular loop
you'll feel no extra force until the circular loop's start and then all of a
sudden you'll feel a lot of force because you are suddenly turning around the
arc. This is really uncomfortable so in roller coaster design they make the
turns ease-in gradually. The track is mostly straight at first and rises quite
a bit while the turning radius decreases. At the top the turning radius is the
smallest for the tightest part of the curve. Then the track eases out to get
you back to the initial lack of extra force. If you draw something like this
you get a teardrop shape.

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rafekett
guess without reading the article: uses less material per unit length of track

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NextUserName
Two reason that I can guess (before reading any comments or the article).

1\. More energy is lost the wider the loop is. This is because on a truly
round loop, the cars would be pushing hard against the widest part of the
circle as the cars change from going from right to left (or vise-verse). By
not going out as far, you don't have to come as far back to get to the top of
the loop.

2\. The geometry of the loop is tuned partially based on the number of cars.
Most roller coasters have between 6 and 10 cars. You want the first one to be
starting on the way down way before the last one all the way to the apex. This
uses gravity to help with overall velocity. The easiest way to achieve this is
by distributing the sharpest part of the angular transition at the top of the
loop.

Perhaps I should not post a comment before reading, but I am curious to know
what others think (off the cuff).

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stansmith
Love the animation.

