MISC | Underground-to-Ground Station question

[1772]

I guess this is a question for the mathematicly gifted readers on this forum.

On this blueprint of a station, you see the platforms are at street level, but when exiting the station, the trains go into an underground tunnel.

Now, the question is, how long does the climb between platform and tunnel need to be, to make it comfortable/unnoticeable.



Symbols:

S = Station
E = Entrance
P = Platform (about 400 meters long so you get the scale of things).
T = Tunnel

[KingNick]

Well I'd say everything under a 25 ‰ is comfortable. So considering the average height of catenaries (5,5 m), plus some earth between the tunnel and the buildings over the tunnel 15 meter altitude difference should be the minimum.

Considering all these assumptions the tunnel has to be 600,19 Meters long.

[1772]

Originally Posted by KingNick

Well I'd say everything under a 25 ‰ is comfortable. So considering the average height of catenaries (5,5 m), plus some earth between the tunnel and the buildings over the tunnel 15 meter altitude difference should be the minimum.

Considering all these assumptions the tunnel has to be 600,19 Meters long.

You mean, the railway between the platform and the tunnel needs to be 600 meters?

[KingNick]

The climb as such has to be 600,19 meters long.

[Silver Swordsman]

It fully depends on the power/weight ratio of the trainset used on the line. Freight trains can take a 1% grade at maximum, while HSR and light rail can take 3-4%. If we're looking at a 4% grade, and a 19m height difference, 4/100=19/x; 1/25=19/x; x=19*25; x= 475

Since 4% is very steep for a train, it is safe to assume that 500m-600m is probable.

[1772]

600 semes to be the consensus. Thanks!

[chornedsnorkack]

A consensus pulled out of ass.

Height: depends on what is built over the tunnel.

The tunnel itself needs to be anywhere 5 and 7 m, depending on the loading gauge of the railway. US piggybacking and double stacked containers mean 6 m height of trains themselves, plus a metre for catenary and clearance to ceiling. Many passenger railways elsewhere, however, are limited to about 4 metre height.

Then there is whatever is above. If it is streets restored after railway building by cut and cover, or new buildings designed over the tunnel - less than a metre ceiling thickness. If it is existing buildings... then you have basements, pile foundations, space for works to support basements during excavation, or bedrock roof... a lot.
The ruling gradients of railways vary widely. Many passenger and freight railways demand low ruling gradients to haul long trains by weak locomotives. Whereas many high-speed railways have powerful engines with distributed traction, and therefore also tolerate high gradients.

Finally, on such short slopes, much of the distance will be taken up by transition curves and vertical curvature limits.

[Tom 958]

Originally Posted by chornedsnorkack

Finally, on such short slopes, much of the distance will be taken up by transition curves and vertical curvature limits.

Indeed. If the maximum grade is 4% and a 15m difference in elevation is required, the vertical curves will push the total length of the grade well beyond 600m. This:



isn't a very accurate depiction. Probably the ends of the vertical curves would be about where the P and T are, equidistant from the midpoint of the grade as drawn.

That said, it might be that agencies sometimes tolerate grades that are nominally in excess of the maximum, since in a situation like this, there'd be only a single, theoretical point at which the maximum grade is reached before the grade flattens out again. Whether that's done or not, I don't know. But it's likely that it is. And it's fun to ponder.