A brachistochrone subway is not a cost-effective idea - Comments

[rude man]

rude man submitted a new PF Insights post

A Brachistochrone Subway Is Not a Cost-effective Idea

Continue reading the Original PF Insights Post.

 

[mfb]

Where is the point in the circle arcs?
You know the fastest way to get from A to B in general - let the deepest point of the brachistrochrone be at a depth of h. What is the ideal shape if you want to take a longer distance, but with depth limited to h? Well, just add a straight section in between the brachistrochrone halves. It will run at the maximal possible speed, and you already know the first and last part cannot be faster.

For the 1600m distance, you need 22.6 s for the curved sections, and 12 seconds for 800m at 66m/s, for a total of 34.6 seconds.

 

[Delta31415]

Well this was worth reading i learned something interesting today so thanks for writing this.

 

[Greg Bernhardt]

Very unique entry!

 

[rude man]

Where is the point in the circle arcs?
You know the fastest way to get from A to B in general - let the deepest point of the brachistrochrone be at a depth of h. What is the ideal shape if you want to take a longer distance, but with depth limited to h? Well, just add a straight section in between the brachistrochrone halves. It will run at the maximal possible speed, and you already know the first and last part cannot be faster.

For the 1600m distance, you need 22.6 s for the curved sections, and 12 seconds for 800m at 66m/s, for a total of 34.6 seconds.

Good observation. Thanks.

 

[rude man]

Following mfb's observation, the title of my blog should be changed to "Modified Brachistochrone Subway!". mfb has come up with the ideal solution and it resurrects the viability of the Brachistochrone in subway engineering!

 

[256bits]

Interesting topic.