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I hope this question is on-topic for this site.

The city I live in (Chennai, in India) got a rapid transit metro rail a few years ago that uses overhead electrification of 25kV, 50Hz AC voltage to power the trains. I also know several other rapid transits over the world sometimes use a different method of powering trains called a "third rail", where a solid rail close the ground, which carries 700-1000V DC voltage to power the trains.

Doing some research, I read that the overhead voltages can carry high voltages since they are located high above the ground and thus, wont arc to the ground due to the capacitance, and the sheer magnitude of the AC voltage. This seems to be the reason why third rails use such thick rails, to carry high current with such lower voltages to output the same power an overhead rail would.

Now, the rapid transit in my city has some sections elevated and some underground. The elevated sections have a catenary wire like arrangement for the overhead electrification, while the underground portions have a solid metal rod attached to the top of a circular tunnel. A picture of this rapid transit's tunnel at a crossover is here:

enter image description here

Now, since the tunnel is underground, the earth surrounds the tunnel from all directions, including up. Wouldnt the same problem of the third rail, i.e, arcing to the ground also occur here. What is preventing the 25kV AC from arcing to the ceiling (which is infact the earth, so it's more or less similar to grounding).

Can someone please help me understand what I'm missing here?

Edit: another relevant picture of the tunnel itself for viewer enter image description here

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    \$\begingroup\$ Are you sure that those are 25kV overhead lines and not just the same electrical system as the 3rd rail or some intermediate one? If they are higher voltage, notice how the spacing is much greater than the 3rd rail, consider how it won't be as easily submerged, have garbage on it, rats running under it, or track workers walking near it. You probably want to ask someone with local knowledge of the system, many transit systems have a community of enthusiasts with a lot of collected knowledge. \$\endgroup\$ Jul 13, 2019 at 17:14
  • \$\begingroup\$ @ChrisStratton I am 100% sure that they are indeed 25kV 50Hz lines, I have read the "danger" signboards on the catenary poles (in the elevated sections), also the Wikipedia article confirms this. Furthermore, rats and garbage are seldom found, since the underground sections of this particular rapid transit have full height glass doors on the platform, so its impossible for anyone to access the tracks. \$\endgroup\$ Jul 13, 2019 at 17:19
  • \$\begingroup\$ ... Track workers, seems to be a possiblity though. \$\endgroup\$ Jul 13, 2019 at 17:19
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    \$\begingroup\$ @DKNguyen A third rail is an extra rail in a railway that carries power for electric locomotives. It's located between the two ordinary rails. \$\endgroup\$
    – Hearth
    Jul 13, 2019 at 17:44
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    \$\begingroup\$ @DKNguyen the regular rail is used for the earth side. But unlike with a model railroad where it's reasonable to insulate the rails from each other and the wheels from the axles, they don't use the rails to provide both sides of the circuit. The third rail doesn't really carry any mechanical load apart from its own weight and the contact pressure of the over- or under- running shoe. \$\endgroup\$ Jul 13, 2019 at 19:38

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According to answers to this question:

The breakdown voltage of air varies significantly due to changes in humidity, pressure, and temperature. However, a rough guide is that it takes 1 kV per millimeter.

Therefore your 25 kV overhead rods will be adequately spaced from the ceiling at a minimum of 25 mm / 1 inch; it looks like they have several times that.

The main reason for using lower voltages on 3rd rail systems is probably the size of the insulators to support the rail mechanically. Insulators aren't free air clearance; as the answer explains:

The breakdown gradient for creepage is lower than for clearance since dirt can accumulate on surfaces. Some dirt is partially conductive on its own, but many things can provide leakage paths after soaking up some humidity.

Your second photo of the tunnel appears to show the clearance from the ceiling is rather less than the creepage distance along the horizontal insulators. It would be impossible to mount a third rail on insulators of that size.

The safety of line personnel on 3rd rail is a factor for the lower voltage, but not the only one: direct contact with a 3rd rail at less than 1 kV is likely to be fatal to a human.

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    \$\begingroup\$ At high voltage, safety can be an issue of proximity and field gradient, not just direct contact. I've actually seen track workers contact the cover of energized 3rd rail systems with their trouser legs, and a drunk trespasser survived sitting on the cover board a while back. \$\endgroup\$ Jul 13, 2019 at 17:46
  • \$\begingroup\$ Thank you for your answer, I just checked out the linked question and answer. One thing that I'm not clear of: the linked question considers these voltages as DC. In an AC situation, wouldn't capacitive effects need to be accounted for? \$\endgroup\$ Jul 13, 2019 at 18:07
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    \$\begingroup\$ At a detailed level, yes, but the general principle remains the same. Creepage and clearance are different for the same voltage, and insulator size and mechanical strength is a problem for third rail but less so for overhead wire. \$\endgroup\$
    – Owain
    Jul 14, 2019 at 12:50

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