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

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• rude man
In summary, a rude man submitted a new PF Insights post about a Brachistochrone subway not being a cost-effective idea. The post discusses the ideal shape for a longer distance with a limited depth and suggests adding a straight section between the brachistochrone halves. This would result in a total time of 34.6 seconds for a 1600m distance. The post also mentions a reader's observation that could potentially make the Brachistochrone subway a viable option in subway engineering.
rude man
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rude man submitted a new PF Insights post

A Brachistochrone Subway Is Not a Cost-effective Idea

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vanhees71
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.

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

Very unique entry!

mfb said:
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.

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!

Interesting topic.

What is a brachistochrone subway?

A brachistochrone subway is a hypothetical transportation system where the train follows the path of a brachistochrone curve, which is the fastest possible descent between two points. This concept was first proposed by mathematician Johann Bernoulli in 1696.

Why is a brachistochrone subway not cost-effective?

A brachistochrone subway is not cost-effective because it would require extensive construction to create the curved tracks and the necessary infrastructure. It would also require specialized trains and technology, making it expensive to build and maintain.

Has a brachistochrone subway ever been built?

No, a brachistochrone subway has never been built in real life. While it has been theorized and studied by mathematicians and scientists, the practicality and cost-effectiveness of such a transportation system have prevented it from being implemented.

Are there any other drawbacks to a brachistochrone subway?

Aside from the high cost, a brachistochrone subway would also have limitations in terms of the distance it could cover. As the curve is optimized for the shortest distance, it may not be suitable for longer journeys, making it less versatile compared to other forms of transportation.

Could a brachistochrone subway be feasible in the future?

While it is unlikely that a brachistochrone subway will be built in the near future, advancements in technology and construction methods could potentially make it a more feasible option. However, it would still require significant investments and research to overcome the current limitations and make it a viable transportation solution.

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