How do stun guns not kill people?

Question

Now, I've seen a lot of answers to this sort of question, but most of them provide answers that don't actually make sense from a physics perspective.

As an example of such an answer, I've commonly seen it mentioned that stun guns avoid killing people because they use transformers to step up the voltage and reduce the current. Of course, because transformers reflect impedance, the current flowing between the electrodes when the human body completes the circuit will just obey Ohm's law with the stepped up voltage.

Now, even with the more modest stun gun claims of, say, $150\: \mathrm{kV}$ and a generous estimate of the resistance of the human body ($100\: \mathrm{k \Omega}$), that would mean a current of $1.5\: \mathrm{A}$, more than enough to kill or cause serious damage.

As, I see it, there are only a few possible explanations:

1. Manufacturers are lying, and the voltages generated by stun guns between the electrodes are much lower than reported.
2. The pulses are just too short in duration to cause serious damage.
3. The placement of the electrodes (no more than an 2-3 inches apart) means that the path taken by the current never goes much below the skin, and definitely doesn't wind through vital organs.

Based solely on my intuition, I would think 3 is the most likely explanation (with a healthy dose of 1 as well, since some of the claimed voltages are obviously far too high), but I'm not too sure that's the case.

Any insight on which, if any of these is the correct explanation?

EDIT: The responses got me wondering what would be the limiting factor if the typical designs did not use a capacitor, which led me to another fundamental limiting factor, which I think is what was behind the point that drawing such power from a small device could not be sustained.

To step up the voltage from a $9\:\mathrm{V}$ battery (the typical sort used in stun guns) to $150\: \mathrm{kV}$ would require stepping voltage up by a factor of approximately 16,667 times. Since the current in the secondary would also have to be reduced by that factor, for the current to be $1.5\: \mathrm{A}$ in the secondary, it would have to be $25\: \mathrm{kA}$ in the primary.

Drawing that sort of current from a $9\:\mathrm{V}$ battery is just not possible, as the internal resistance of the battery is too high (not to mention that even if you could draw that sort of current from a $9\:\mathrm{V}$ battery the battery would probably be instantly depleted or components would melt or explode). Typical $9\:\mathrm{V}$ batteries have internal resistances around $1.5\: \mathrm{\Omega}$ (http://ww2.duracell.com/media/en-US/pdf/gtcl/Product_Data_Sheet/NA_DATASHEETS/MN1604_6LR61_US_CT.pdf, for example), so drawing a current that high is out of the question.

Incidentally, if my thinking on this point is correct, that also explains why most stun guns step up the voltage a bit, charge one capacitor of higher voltage than the battery, and use that discharge to charge an even higher voltage capacitor.

The batteries simply can't generate enough current to be stepped up that far without such a multi-tier approach.

Does my reasoning on this point seem correct?

Again, thanks for your patience and help!

Answer 1

Your assumption that Ohm's law is fully accurate for the stun gun + human circuit isn't correct. A stun gun uses a capacitor to store charge and the capacitor is constantly being recharged to deliver a series of high-voltage pulses.

A capacitor has a finite amount of charge. Once it's charged, that's it, it can never deliver more charge than that until it is recharged. The measure of the stun gun voltage is when it's an open circuit. Basically the voltage is telling you how strong the electric field is but it isn't telling you something that's very useful for Ohm's law.

The graph of a charging and then discharging capacitor looks something like this:

The only thing the resistance of your body can affect is how quickly the discharge occurs. It's not possible to deliver more charge than is stored in the capacitor and it is the capacitance that is the primary safety mechanism.

So the voltage of the open circuit at the peak is not really a meaningful measure of the total amount of current that will flow per pulse.

Regarding your option 1: it isn't a lie but yes, you're somewhat right anyways (voltage drops on discharge).

Regarding your option 2: the pulses duration is closely related to the capacitance of the capacitor so yes, this is somewhat right too.

Regarding your option 3: I'm sure there is some amount of "skin effect" but I'm not sure how much.

I should also mention that sometimes stun guns DO kill.

Answer 2

Numbers 2 and 3 are correct. That 150 kV rating is for open circuit. Once you put a load on it the voltage is going to drop fast because it can not deliver the kind of power your are suggesting by assuming both voltage (150 kV) and current (1.5 A) will be constant. The body will also start to conduct and the impedance will drop as well as different layers of our skin are more conductive. The rapid charge/discharge pulsing also insures that very little energy is actually delivered to the target.

For example compare two tasers the M26 and X26 to other medical devices.

Based on studies done to current flow through the different layers of skin some basic conclusions have been made about the safety of tasers.

Current decreases rapidly with distance from electrode. The fat and skeletal muscle layers have an electric shell effect on currents that reach into deeper tissue layers (such as the heart): -The fat layer attenuates the electric field by at least 25 times, even under worst-case minimal thickness assumptions -Skeletal muscle preferred longitudinal (with the grain) electrical conduction diverts about 88% of the current away from deeper tissue layers

In the muscle layer: -the transverse current density is less than 15 mA/cm -the equivalent field strength is in the 15-30 V/cm range: greater than 2.25 V/cm – threshold to capture motor neurons but much low lower than levels required for irreversible electroporation (1600 V/cm – Gehl et al. 1999

The fat and skeletal muscle layers significantly reduces the current that reaches deeper into the body. The skin-heart minimal distance for typical in-custody suspects is at least two times greater than the maximum distance estimated by theoretical models as being necessary to induce VF [ventricular fibrillation]

TASER currents are much lower than levels required to trigger ventricular fibrillation (by at least 33 times margin for X26, higher margin for M26) (read more)

Repeated shocks have killed people. And there have been well over 100 "possible taser related" deaths.

Between June 2001 and June 2007, there were at least 245 cases of deaths of subjects after having been shocked using Tasers.[87] Of these cases:

--In 7 cases, medical examiners said Tasers were a cause or a contributing factor or could not be ruled out as a cause of death.

--In 16 cases coroners and other officials stated that a Taser was a secondary or contributory factor of death.

--In dozens of cases, coroners cited excited delirium as cause of death. Excited delirium has been questioned as a medical diagnosis.

--Several deaths occurred as a result of injuries sustained in struggles. In a few of these cases head injury due to falling after being shocked contributed to later death. Some police departments, like that of Clearwater, Florida, have tried to eliminate such incidents by prohibiting taser use when the suspect is in danger of falling.

A study published by the American Journal of Cardiology found that California police departments that introduced Tasers experienced significant increases in the numbers of in-custody sudden deaths and firearm deaths in the first full year following deployment. The rates declined to predeployment levels in subsequent years. No significant change in the number of officer injuries was found.