Why are roller coaster loops not circular? | Hacker News Reader

Why are roller coaster loops not circular?

datagenetics.com

194 pointssqueakynick47 comments

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://web.archive.org/web/20070827183113/http://fy.chalmers...

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

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

http://www.jbonneau.com/publications.html

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.

I think my edit snuck in at about the same time as your reply, sorry about that.

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).

Some great blog posts there - lots to read later. I'll work out a way to give you some feedback if I have any ... :)

I’m really not sure I see your point. This is about math and physics, so I would assume anyone who writes about it writes about the same things and has similar diagrams.

Also, this is not a scientific paper. As long as words, diagrams or very specific and very novel ideas (nothing of that kind seems to be happening here) are not lifted directly I really fail to see the problem.

My math and physics textbooks in school didn’t contain any citations either.

I obviously can't prove anything, but it's seems pretty likely the danish blog about clothoids 'inspired' that section of the article. It would be polite to say so.

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.

I think his mind started from the common example of a weight sitting on a table. There is a force of gravity one direction and an opposing force of the table pressing up against the weight keeping it where it is. For a coaster that isn't inverted you can say the same, gravity pulls one way then the track is pushing the other way. He just forgot it is reversed once the coaster is upside down.

I would mention the great Roller Coaster Tycoon pc game series (1999-2004): 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.

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

His name is Chris Sawyer, the creator of Transport Tycoon and Roller Coaster Tycoon 1+2: 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

The track is providing a downward force - the inertia of the rollercoaster car pushes it up against the track. The track returns the same amount of force in return.

Careful with phrases like "inertia .. pushes"... does it really?

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.

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.

Jerk is also the guy talking loudly on his cellphone while a subway moves between stations. There is a clear limit to how much jerk average standing(or sitting) passengers can survive before they fall down on the guy and knock his teeth out. :)

I always wondered if there were a sociological commentary in the fact that yank is defined as jerk * mass.

aaaah so the bigger the jerk the harder you have to yank him to bring him down?

Actually no I thought the term might have been coined by British physicists after spending too much time around us Americans...

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.

Might not be in most but it certainly is for some. The subway in the Atlanta Hartsfield Jackson airport accelerates and decelerates that way. It makes it feel like you're probably going way faster than you are. I've seen just a few people almost fall over if they aren't holding on properly.

>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.

The acceleration curve you describe would have infinite jerk at the start, stop and halfway points. A |jerk| minimizing curve for a fixed travel time would gradually (linearly) increase to maximum acceleration during the first 1/4 of the trip, gradually decrease back to no acceleration over the next 1/4, gradually increase to full deceleration over the next 1/4, and finally gradually decrease to no deceleration over the last 1/4.

DC-powered rail systems such as the Chicago "L" can be jerky because the motor controllers are stepped not continuous. It's basically late 19th/early 20th century technology. The AC-powered systems in their newer rolling stock offer smoother operation.

I think the stops would have to be very close together for this to be a factor. If a train trip is jerk limited, then the train would not reach maximum acceleration between stops. It is more likely that a train trip is acceleration limited where the train does not reach full velocity between the stops.

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?

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

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

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.

There is a whole lot of interesting material about clothoid curves in Raph Levien’s PhD thesis 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.

Anyone else think of this while reading the article?

http://en.wikipedia.org/wiki/Euthanasia_Coaster

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).

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

> 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?

http://www.coaster101.com/ is somewhat of a coaster news site. Also has some interesting information regarding roller coaster construction

There's the American Coaster Enthusiasts - http://www.aceonline.org/joinace/

There's http://www.coasterforce.com/, and many large theme parks (or chains of theme parks) have forums created around them as well.

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.)

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

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

This needs an ELI5/TLDR version....

Read it later when you have more time, I enjoyed the garden-path walk to get to the answer. Hopefully you will too.

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.

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

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).

Love the animation.

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