My question is about how dangerous a momentary amount of current is vs the duration. Like is there a reasonably consistent relationship between current duration through the body and relative danger? I.e. 1 amp for 1 second vs 0.01 amps for 100 seconds. I imagine that's a bit complex to determine, but otherwise is there a duration for which a normally deadly amperage would shock someone but not cause a heart attack? I read an article about research into a possible electric weapon that would shock someone on the scale of nanoseconds to stun them without risking killing them.
Details on unidirectional short pulses (<10 ms).
Of less interest if considering typical waveforms of supply distribution and equipment, but covering waveforms purposely generated, capacitor discharge, arc phenomena.
Ref. IEC 60479-2 (2007)
For short pulses the standard indicates the energy as the main factor to determine if fibrillation may occur. So for pulses of various shapes (rectangular, half sinusoidal cycle, decaying exponential) the key parameters are dc peak value (rect pulse), rms and peak value (sinus pulse), rms calculated over 3*tau and peak value (expon pulse).
The energy is always the square of dc or rms value multiplied by duration (for the exponential pulse duration is 3*tau).
The threshold of pain for current flowing between extremities is in the order of 0.0001 A2s (Ampere squared second).
Ventricular fibrillation has been determined to occur following the curves below.
Above C1 up to C2: low risk of fibrillation (up to 5% of probability);
Above C2 up to C3: average risk of fibrillation (up to 50% of probability);
Above C3: high risk of fibrillation (more than 50% probability).
Of course and it is disciplined by different standards in different countries. I am used to IEC standards, so IEC 60479-1 is the reference for current-duration limits, distinguishing between perceivable intensity, peripheral muscular effects, more serious effects, e.g. on heart, injury, death. See IEC 60479-1 Figure 20 and 22 below for ac and dc systems, respectively, and Table 11 and 13, again for ac and dc, for interpretation. ...
Except special cases with such a specific application that needs starting back from the fundamentals (i.e. current intensity mentioned above), electrical safety is usually assured by limits of touch voltage and step voltage, in steady and transient conditions. This means that you estimate touch voltage for a conductive part (enclosure, cable shield, pipe, etc.) with a recognized method (in the standards or known electrotechnics), and then you compare it to limits (in the standards).
- calculation of induction (magnetic field coupling from a power line) onto a conductive part (e.g. pipe, cable, fence, handrail);
- estimation of maximum voltage occurring in various configurations of leakage and failure inside equipment: it's a sort of safety case, but you almost always end up with the largest supply voltage; internal step-up transformers, HV converters, etc, shall be treated separately, considering energy, maximum delivered current, etc to assess if they may be dangerous
- calculation of voltage drop along earthing conductors (such as reinforcement rebars, a concrete floor, etc.) to estimate step voltage, that is the voltage difference between the feet of a person that is walking, working, etc. In this case a good standard is IEEE Std. 80, focusing on power stations/substations.
Calculation methods are more or less all in agreement, but standards may indicate different scenarios, different assumptions. This is what distinguishes applications: for residential applications the IEC 60364-4-41 may be more restrictive than EN 50122-1 for railways; for equipment, depending on use and the desired safety level you might have IEC 61010-1, IEC 60950, etc, instructing differently on the type of safety case and analysis they deem appropriate. An example of differences between parameters used for calculations is the assumed resistance for the victim: depending on hand touch voltage, step voltage between feet, likely wet environment, worker with good protecting equipment, skilled and in good health, etc.
To simplify, if limits only are considered, we may have different voltage-time curves, where lower voltages are tolerated for longer times. EN 50122-1 tables for ac and dc systems follow.
IEC 60364-4-41 assumes typical LV voltage levels and 50/60 Hz, thus giving a smaller range of tripping times (Table 41.1). They also specify on which current level a circuit breaker for leakage to ground (RCD, residual current protective device) shall trip: as said, 50 mA may kill you, thus 30 mA or less are normally adopted.