A 4 dimentional "Klein coaster"...?

[DiogoJ42]

OK, so this has spawned out of a rather metaphysical Skype conversation. Please bear with me.

I assume we are all aware of the concept of a "Möbius" coaster, such as Grand National...

This takes it's name from the "Möbius Strip": a surface with only one side (when embedded in three-dimensional Euclidean space) and only one boundary.

But what if we knocked it up a notch? The three dimensional equivalent to a Möbius Strip is the so-called "Klein Bottle": a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined. Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary (for comparison, a sphere is an orientable surface with no boundary).
And it "looks like" this:

SO: if it is possible to have a "Möbius" coaster, then logically, it must be possible to build a "Klien" coaster.

.... The question is, what in the name of Wardley would this involve? Three racing tracks that count as one? Or would it transcend our known universe and start involving the so-called "fourth dimension" of time?

Discuss!

 

[Robert.W]

That is an... interesting.. concept for a coaster to say the least.. ouch!!

This does not look at all very comfortable.

 

[John]

Presumably it would be a similar to a mobius coaster but instead of parallel track it would use double sided track throughout, like the loop on Full Throttle at SFMM.

 

[rob666]

Discus!
Flat round weighted sports apparatus for throwing.
Do I win a prize?

 

[DiogoJ42]

Presumably it would be a similar to a mobius coaster but instead of parallel track it would use double sided track throughout, like the loop on Full Throttle at SFMM.

I think you might be on to something there matey. Presumably it would require some kind of 4D train that stays the right way up?

 

[Robert.W]

The Möbius strip exists in 3D, and that's why it's possible in reality, to create a roller coaster based off of the concept..
A "true" Klein Bottle can only exist in 4D, right? So I'd imagine a "Klein Coaster" would be much the same.

But the Klein Bottle can still be represented as an acutal physical model, in 3D. So it must be possible to construct an actual representation of what a Klein Coaster would visually look like in the 3D world, yeah? Maybe, I honestly don't know, but it does seem logical.

Getting the coaster to actually work would be another story all together. That is where the problem of the 4th Dimenstion really comes into play...

 

[Sauron97]

But the Klein Bottle can still be represented as an acutal physical model, in 3D. So it must be possible to construct an actual representation of what a Klein Coaster would visually look like in the 3D world, yeah? Maybe, I honestly don't know, but it does seem logical.

I thought that particular model was a case of one of those 'perfect circle' problems. You can get close to it but never actually have a true model, as it is an impossibility in our universe.
As for trying to make a coaster based off this model and what it would look like, god knows as the only input I can give Diogo

 

[DiogoJ42]

Does anyone fancy a challenge in No Limits...?