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# Number Theory/Modeling a Single Train running on three tracks.

Question
QUESTION: Dear Prof Scott

Will there be advantages in modeling a train running on three tracks instead of two tracks ?.

I Feel the advantage would be carrying more people capacity for a compromise of Train manufacturing design and additional cost incurred for the same.

Thanks & Regards,
Prashant S Akerkar

ANSWER: I don't believe so.  The reason it seems they have two tracks is in case they get two trains going opposite directions.  At such a place, one train can pull off and let the other train go by.  In most places right now, there is only one track.

www.wmata.com/rail/maps/map.cfm?  As can be seen here, where railways come together, the passengers have to get off one and on another at transfer stations, for they don't mix tracks very often.  One of the lines is reserved for rush hour traffic and the other line is for trains that move slower than that.  As can be seen on this map, trains that carry passengers have frequent stops along the way.

Here in this map of Great Britain, they have some secondary lines, but it appears that they never have three lines   www.raileurope.com/europe-travel-guide/england/map.html

I was thinking that in major railroad depots they would allow changing of the tracks and have more than two lines, but I haven't found this.  Could you find this anywhere?

---------- FOLLOW-UP ----------

Train running on two r
QUESTION: Dear Prof Scott

Thank you.

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

Will there be advantages in modeling a train running on three rails instead of two rails ?.

I Feel the advantage would be carrying more people capacity for a compromise of Train manufacturing cost incurred.

All Trains run on two rails. Now the same train will be running on three rails.

Merits : Length and Height of the train remains the same, adding a new rail 3 for the single train will result in increase of train width. Now the Load (People, Luggage) carrying capacity will increase. i.e. More People can commute / travel in the train.

Demerits : Manufacturing cost = Raw Materials cost + Labour cost. Manufacturing cost for the New Train construction to run on three rails will increase.

Thanks & Regards,
Prashant S Akerkar

From the articles I have seen most of the time there are two, four, or six tracks.
Occasionally in double tracks, both are used for the same direction, but this is not common.
From this, it does not seem like three rails would be useful since the same number of trains must go in either direction.

As was stated, double tracks are fairly common and a reference to them is
en.wikipedia.org/wiki/Double_track

Now that I think about it, I have seen places where there are up to four rails.
In en.wikipedia.org/wiki/Quadruple_track , it is said that they have two lines running in either direction.  One is for trains that are fast and one is for trains that are slow.  As can be seen in this article, there are a few places with 3 tracks in either direction.

An article on the necessity of dual tracks is on where they have very extreme slope. It is
en.wikipedia.org/wiki/Funicular .  As of lately, these trains have been counterbalanced by add weight to the car the wish to be descending the hill while draining the tank of the one ascending the hill.

It then lists a fairly equal number of advantages and disadvantages for each.

Later on it says they are found in America, Europe, and Asia.

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Prof Scott Thank you. Thanks & Regards, Prashant S Akerkar

Number Theory

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