Out of interest, just how inefficient is 3rd rail compared to OHLE when considering energy lost? Obviously I get that it has other serious limitations aside from efficiency like how much power can be drawn (considering it is a 750V system) and safety, but is it really as bad as people make out?
The "inefficiency" characteristic is essentially a more accurate statement of the same aspect as is represented in looser descriptions such as "how much power can be drawn (considering it is a 750V system)". The fundamental point is that the power loss per unit length of
the same conductor, for a load of the same
power, goes as the square of the current - or as the inverse of the square of the voltage, which is essentially the same thing for the same power load. So this source of power loss is (25000/750)^2 = 1111 times more significant for the lower voltage system. Eek!
Of course, the two systems are
not using the same conductors. The standard contact wire for OHLE is I believe 16x16mm copper (alloy), which taking the resistivity as the same as copper at 16.8nΩ.m gives a resistance per kilometre of 1000*16.8e-9/(16e-3^2) = 65.625mΩ/km. The support wire is in parallel with this, but I don't know its size or material; assuming it's about the same we probably end up with a total of about 33mΩ/km.
Conductor rails are of steel, and the popular sizes appear to be 100 and 150 lb/yd (aargh) - so call it 50 or 75 kg/m. Using a density of 7850kg/m^3 we get cross-sectional areas of 0.0064 or 0.0096 m^2, which looks realistic; using a resistivity value of 100nΩ.m gives a resistance per kilometre of 1000*100e-9/(0.0064 or 0.0096) = 16 or 10 mΩ/km. This brings the comparison factor for losses per km down to 274 or 171. It's no surprise that at some locations a third rail system can see the voltage at the train drop by 30% or so when it starts off.
The steel-faced aluminium conductor rail they use on the Underground apparently has a resistivity of 7mΩ/km. So if this was used universally on the Southern network the resistive losses per km would now only be 120 times worse...
However, one of the much-touted advantages of 25kV is that "the feeder stations can be spaced much further apart". So although the losses per km between the feeder and the train are much lower, the number of km over which they are incurred is about 10 times as great. This means the hypothetical "Southern with LU Al rail" is only 12 times worse, and things are beginning to look a little brighter.
One obvious thing that suggests itself at this point is to have third rail with more feeder stations closer together, say every 500m or so. This is not quite as daft as it immediately sounds. You have to step the voltage down to somewhere roughly in the region of 750V at some point before it gets to the traction motors, so it's basically a question of whether you do this on the train or at the trackside, and there are quite a few advantages to doing it at the trackside. Most obviously, the train doesn't have to lug the weight of the transformer about, nor deal with keeping 25kV away from the passengers. A concrete slab in a hut at the lineside is a much more benign environment for electronics than the extremes of vibration, temperature, filth etc it has to put up with on a train, and not having to design it to suit severe weight and size constraints as well is a great help with thermal management and reliability; also with maintenance. Factors like the possibility of load sharing in busy areas or the extreme intermittency of load in more rural parts of the line can be taken advantage of to reduce the size of the individual units compared to the necessary worst-case continuous-load rating of ones on board trains themselves, and to further increase overall reliability. If you have feeder stations at a tenth of the current conventional spacing then you only have a tenth of the distance of high-loss path to send the current through.
Another obvious thing is to take the concept of separating the wear-resisting and current-carrying functions further than the steel-faced aluminium rails idea does already, and use steel rails with connections every few tens of metres to a heavy aluminium bus bar close to, but not actually part of, the track. The bus bar can then be made with a much larger cross-sectional area than if it has to pretend to be a rail, and the different thermal expansion coefficients of steel and aluminium aren't a problem any more, ditto their different electrochemical potentials. Ten times the area gives one-tenth of the losses.
The current return also needs to be taken out of the running rails and given a similarly low-resistance path ("Warning to staff: do not step on
any rail"; the voltage developed on the running rail by the return current can be quite significant); in other words, a four-rail system rather than three. As well as the usual things such as keeping stray currents out of the signalling system and buried metal objects, this gives you the very great advantage of being able to double the voltage by stealth, as it were: one rail at +750V and the other at -750V gives you a 1500V supply to the train, but the exposed voltages on the track are still no more than 750V to ground; and of course double the voltage means one-quarter of the losses.
And of course you could increase the voltage to ground in any case; the reason for using 750V originally is that voltages around that range are most convenient for the technology of traction motors, and more particularly of traction motor control systems, that was available at the time, whereas now that we have power semiconductors coming out of our ears the limits of practicality are much wider. Safety wasn't without some influence, but the major factor was practicality, and the association with safety basically developed out of the observation that they got away with it. It's actually a rather bad voltage for safety, especially DC - "enough to make you grab on but not enough to throw you off". We'd be just as happy with 1kV or more now if they'd been using it all along.
The safety thing is overblown, in any case, because for some reason a few years ago third rails had the misfortune to be selected by the random spotlight of fashion as a new trendy cause to shriek about, and now everyone quotes the resulting report which used totally bent statistics to paint a lurid picture of people within 100m of railways dying like flies from third rails leaping up and jumping at them. I prefer to believe the report I found a couple of years before that which was written by people who did not have any particular axe to grind, which said that the number of railway staff falling victim to third rail and to overhead was about the same. (Which makes sense: overhead may be much more out of the way, but it's much easier to forget it's there, and it jumps gaps, and if you do get zapped by it you very much tend to stay zapped.)
Having said that, the idea of having many more feeders at closer spacing makes it possible to clobber a great deal of the safety objection in any case. At one feeder per section, or more, you simply have them only switch on when a train is in the section. Most of the time the live rail isn't.
It is often said that third rail precludes regenerative braking. This is no longer the case. It was a constraint imposed by nearly all practical rectification methods being passively commutated unidirectional devices. Now that actively commutated bidirectional devices are readily available, the ability of a feeder station to transfer power in either direction is something you more or less get for free.
(It is also often said that third rail precludes speeds over 90-100mph. This is because nobody has properly tried. It was true of pantographs before they properly tried, too - starting with the APT crew - the Shinkansen before that tried improperly, and took it out in maintenance. Still, in this country, for practical purposes as opposed to numbers-chasing, 100mph is mostly enough in any case - the important thing is to keep it up, and avoid having to slow down for speed restrictions and signal checks - and if efficiency is the concern, then with energy use going as the square of the speed (and power as the cube), increasing speed is really bad for you.)
Third rail is very lossy
in the way it is done at the moment - ie. either stuff 100 years old doing what was practical then, or newer stuff imitating the bits that still are 100 years old to keep it all the same. It doesn't
have to be done like that; with some assembly of elements such as those I have outlined into a coherent whole, its efficiency could be made comparable with what is currently accepted for overhead systems - but with vastly less disruption to install, no rebuilding all the overbridges and freaking out over tunnels, far less hassle finding clearance, all the work and all the maintenance conveniently at ground level, etc. etc.