Sounds interesting, please explain.
Well a third rail DC system, unlike an AC system (25kV), has to be kept as a closed circuit as ground leakage problems will cause corrosion of metallic objects in the return path, for example rails will corrode as they leak current into the earth.
THis is the reason we cannot have steel sleepers in third rail areas.
This means the resistance of the running rails becomes a major factor, in the cae of a system where both of the running rails are available for current return standards assume a typical value of ~19mOhm per kilometre of track.
While that is, by normal standards, rather small and in the case of an AC system would be smaller than that of the overhead wiring conductor, a high conductivity aluminium/steel third rail has a resistance of only 7mOhm/km.
That means that the majority of the resistance in the circuit is actually on the 'ground' side of the load.
Let's say we have a second conductor rail equivalent conductor (so 7mOhm/km) which we can connect in parallel with either the conductor rail or the return rail, which should we do?
If we connect it in parallel with the conductor rail the resistance of the conductor side of the circuit drops to 3.5mOhm/km, but the running rail side resistance doesn't change - so the loop resistance is 22.5mOhm/km.
If, however, we connect it in parallel with the running rail the conductor rail resistance stays at 7mOhm/km but the running rail side resistance drops to just
5.1mOhm/km. So the loop resistance is only 12.1mOhm/km.
Which means the substations can be
85% further apart.
There is also another factor - while we normally, simplistically, assume that the ground conductor remains at 0V and the entire 'voltage drop' appears as a literal drop in the voltage of the 'hot' conductor. However this is not the case, some of it will appear in as a 'voltage rise' in the voltage of the ground conductor.
This is a serious problem since the running rail in a third rail system will have a voltage relative to the 'true ground', this can become a safety issue if this voltage becomes larger than about 60V as it can deliver dangerous shocks to people who happen to come into contact with the running rail for whatever reason.
The ratio of the split between voltage drop in the hot conductor and voltage rise in the ground conductor is determined by the relative resistances of the two.
If no extra conductor is employed the actually permissible voltage drop for the system is only
82V. This drops in the scenario where the extra conductor is on the 'hot side' to only
71V, whereas if the extra conductor is on the 'ground side' the voltage drop climbs to
142V - combined with the reduced loop resistance that would permit 3.25x the substation spacing than the base case with no extra conductors.
This means that it is probably required that any available conductors be added to the ground side of the system to hold down the running rail voltage rise even if that is not the optimal placement in terms of minimising the overall loop resistance.
This finding also opens the door to the idea of employing recent advances in switched mode power supplies to have devices analogous to AC 'booster' transformers to draw the current from the running rails and hold down their voltage. I will run some calculations on that after my exams I think before I post the aforementioned tract on third rail in the 21st century.