Due to the resistance exhibited by the rails, a voltage drop occurs between the point where current is injected (take this as location type "A", usually the train locations) into the rail and the point where the current is sucked out (take this as location type "B", usually the substation locations, but also at locations where regeneratively braking trains suck curent from the running rails).
There is a distributed resistance between the running rails and the surrounding ground, due to imperfect insulation between the running rails and their support structures. The general body of the ground acts as a distributed conductor and a reference is found at a remote point, where potential is treated as 0.
With this reference point taken, rail potential is usually positive at location type "A" and negative at location type "B". There are of course exceptions to this.The amplitude of rail potential its polarity will have to be determined through computer simulation.
A touch voltage is defined as the potential difference between two points. For example, if a person happens to touch the running rail with one hand (say left hand) and a lineside structure with another (say right hand or two feet), he is subject to a touch voltage and a current will flow through his body. He/She will not feel anything if the current is small, but will feel a shock if it is high enough. IEC documents have figures and graphes showing how much a person can tolerate for how long.
According to Ohm's Law, the amplitude of this current is equal to the touch voltage divided by the total circuit resistance. The total circuit resistance consists in 3 parts:
1). The resistance of the body. There are empirical figures on this resistance.
2). The resistance of the conducting circuit (rail and ground). This part is usually small and can be ignored
3). The resistance of insulation between the person's body and the conducting circuit, for example, gloves or/and shoes, depending on how the person bridges the touch voltage.
In the worst case, if we ignore items 2) and 3) above, the current through this person's body is equal to the touch voltage divided by the body resistance. Consequently, the higher the touch voltage, the higher the current passing through the person's body.
In order that the railway system does not cause such hazard, the touch voltage has to be controlled to levels that are deemed safe. There is no universally accepted standard about this level, but it is generally in the order of 50 to 70 Volts.
To achieve this, the railway system needs to be simulated against specified design criteria with a host of parameters, including: track gemoetries, specified traffic level, configuration of the DC power supply system, earthing strategy, etc.
