Fourth rail current paths under fault conditions

That is probably the best way of describing potential difference I've ever seen. Thank you.

Depends how big the hole is...

Not if the bottom of the hole next to the smaller building is the same height above sea level as the ground next to the taller building................

Indeed there would. (disregarding the fact that material you have removed from the hole would even more microscopically move the centre of gravity of the planet).

But unless there is a very large electrostatically charged object hovering nearby, none of these variations in potential would apply in the voltage scenario to which this was supposed to be an analogue!

Of course if the hole was deep enough we would be in RIPAS territory, with a new tube line to the antipodes.

However, we are being discourteous to the OP, who would I expect would still like to know how the +420/-210 voltage difference is actually maintained - I'm imagining a battery of 105 6V cells connected in series, with the positive and negative rails connected to the respective ends of the row, and an earth connection between the 35th and 36th cells, (counting from the negative end)! (or perhaps more realistically, three 210V dc dynamos connected in series, with an earth connection between no 1 and no 2).

And is there any provision for the failover situation he describes?

This old thread might help.

Traction Current

Excellent post by RailTechnician, there. A pity he left the site.

As I suspected, the resistors are not involved in the actual voltage reduction, but their use is rather clever, providing a more fault tolerant system than the one I envisaged above.

The generator creates a 630V potential difference which, as the item in the other thread states, is not directly referenced to earth. The big resistors he describes act as a potential divider to put earth two thirds of the way from positive to negative.

Under the fault condition described, the resistance between earth and one of the rails falls to zero - a short circuit in parallel with a big resistor (remember that the effective resistance of two resistors in parallel is given by 1/R = 1/r1 + 1/r2. However enormous r1 is, if r2 is zero then 1/r2 is infinite, so 1/R is infinite, and R is zero)

Effectively what the short circuit is doing - changing the ratio of the two resistances and thus the voltages) either side of the earthed point from 2:1 to 0:1 (or 2:0),

However, the generator is still forcing a potential difference of 630V between the two rails. If one rail is earthed, the other will therefore be at the full 630V above (or below) earth.

Using my height analogy again, think of the generator as a rigid vertical rod 630cm long connecting the two rails together. The positive rail must be 630cm above the negative rail. If you hold the rod one third of the way up, then the upper rail will be 410cm above your hand (the level of which we shall define as "Earth"), and the lower rail will be 210cm below it.

Now hold one end of the rod. That puts one of the rails at the level of your hand, and the other is 630cm above (or below) it.

Remember that it is mere convention that defines "earth" as zero. (Just as we have chosen arbitrary values for zero in temperature scales - such as the freezing point of a particular chemical under certain atmospheric conditions found at a particular altitude on only one known planet)
Planet Earth itself actually carries a small net electrostatic charge, and local surface variations occur e.g because of thunderstorms. Electrical equipment earthed to two bodies that are electrically isolated from each other - for example two spacecraft, or an aircraft and the ground - may actually be at different potentials. If they get too close, a current will flow to equalise the potentials. That is, according to one theory, what happened to the Hindenberg.

I often wondered how the earth fault relays on rolling stock worked. My son, Who Knows About These Things as he is fleet engineer for the Southern Railway, explained it a while ago. Whilst this applies to his trains, presumably modern tube stock has earth full detection.

I always assumed that all the electrics on Southern stock was earthed through the bodywork; indeed on older stock such a sQ and Standard stock it probably was as everything worked on line volts. but, with the advent of stock with low-voltage lighting and control, everything is separately earthed, isolated from the train body, so any fault between line volts (in his case the running rails) and the low voltage from battery or MG source) needs to be addressed. So they have an earth fault relay or MCB. It works bit like the RCD (or whatever the new name is for it) that you find in your house which detects either + or - to earth and trips out before you electrocute yourself.

I guess the large (value not physical size) resistors mentioned in Rail technician's thread do the same job, so as soon as one of the supply rails ups the voltage, this is detected by a relay and trips out the substation, preventing 650 volts going through to earth by whatever means. Which is also why there's lengthy neutral sections between LT and NR power supply systems at Putney, Gunnersbury and Queens Park.