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# Rollercoaster loops

#### cf69

##### New Member
Now dont let the title fool you. I was wondering if it was possible to take a run of the mill vertical loop but have it completely flipped upside down. I have provided pictures so u can get a better understanding of what I'm talking about. Im also interested in the science of why it can or can not be done. Thanks in advance.  #### Attachments

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#### lachlan

##### Member
I think a pretzel loop is similar to what you're talking about. An upside-down vertical loop would look more squashed, as the bottom would need to curve less tightly than the top to keep forced on riders in check.

I'm sure someone else can explain it better. Done right, I imagine it would be really fun #### JoshC.

##### Active Member
The closest thing I can think of to what you describe is a Norwegian loop (which is like a pretzel loop for non-flying coasters): https://coasterpedia.net/wiki/Norwegian_loop

For a bit of science, the three key equations to think about would be:

F=ma (force on the train/riders - force equals mass times acceleration)
a=v^2/r (acceleration on a circle - velocity squared times radius of the circle)
v=2*pi*r/T (velocity on a circle - 2*pi*radius divided by time taken to go through the circle)

So the force taken going through a loop is:
F=(4*m*(pi)^2*r)/(T^2)

Of course, with almost all modern vertical loops, they're not perfect circles - they're squished a bit. So to get a more accurate equation, you'd need to calculate the radius at any given time (I guess you can model it as some function of time, but this is going to make things a bit too complicated..).

Anyways. Imagine you've got two vertical loops - a standard one and a downward mirror image one (like in your photos). The standard one will take more time to go through the loop - the train has to fight gravity to get up the loop, loses speed, then goes down the loop slower. The mirror image one will take less time to go through the loop - the train goes down very quickly, and has more initial speed to go up the loop when fighting against gravity.

As mentioned above, you would certainly need to flatten out the crest of the loop in the mirrored version. That is where the radius is at it's largest, so would be exerting the most force. But to flatten it out, you need to lose the clothoid-like shape of the loop, and that's where you eventually get something like a Norwegian loop.

So tl;dr - if it were to be done, it would have to be done very slowly, and even then would still be uncomfortable. So probably not worth it.

• shaunthatkid

#### cf69

##### New Member
yes i did just mirror it cause id figure it was the easier way to visualize it. Ah got it so the norwegian loop is the closest to achieve what im envisioning. Thanks. I'm sure given enough time and advancements it could be possible.