Which is better and why - over head or third rail electrification?

[apk55]

My understanding is that substations are supplied by lineside HV cables (33kV?) in separate troughing fed from a limited number of grid stations so no local issues and additional ones can go anywhere, halfway between is best for lower losses. There are/were restrictions on some lines due to heating of the rectifiers, more/longer peak trains and a basic off-peak service.

It is often the voltage drop between substations that limits the power available to trains. In addition the return voltage drop must be limited to a few volts for both safety and corrosion issues. The voltage drop represents a power loss or inefficiency and it also becomes difficult to detect faults. There are 3 possible ways of increasing the power available
1/ Increase the voltage to the maximum possible, already done in most cases unless they can get regulations changed and new trains that can handle higher voltage.
2/ Reduce the resistance of the conductors. This would mean even heavier conductor rail (or a parallel feeder with links) and a massive return feeder with links to the running rails.
3/ Reduce the substation distance. A typical substation is a sizable building at least the size of a large double garage. Finding land in the right area could be a problem and getting access to it another, as it would ideally located midway between two existing substations. This would effectively double the number of substations on a section of track. And they are not cheap, excluding land and access provision they probably cost several million pounds.

 

[broadgage]

That doesn't make sense. Even if the bodywork became live, people inside would be fine.

Agree, persons inside a metal vehicle CAN NOT get an electric shock as a result of the vehicle contacting live wires.
All parts of the vehicle are at the same voltage and no shock can be received. A person outside the vehicle and touching it would in theory be at risk, but in practice a railway vehicle is so well earthed that this removes the risk.

Being in contact with high voltages is not dangerous in itself, providing that no current can pass through the person and to earth.
Note for example that men suspended from helicopters can work on live overhead lines at hundreds of thousands of volts.
Birds can likewise perch on such lines.