It is well known that the high voltage output of Tesla coils will usually not produce a noticeable electric shock. It is widely explained that this is due to the "Skin Effect", which causes radio frequency current to stay near the surface of a conductor and avoid the nerves and organs of the human body.
I tried putting some numbers into this and did some experiments and believe that the non-shocking nature of frequencies in the hundreds of kilohertz is not only due to the skin effect, but also to human nerves not responding to these frequencies.
One factor is the resistivity of human flesh. In the Great Hamburger Experiment of 1996, I made a mixture of approx. 89 percent ground beef, 10.89 percent water, and .11 percent salt and warmed it up to a bit above body temperature in a microwave oven. Several trials at measuring the resistivity of this mess gave me an average of 70 ohm-cm. In one instance I had a cross section area of 16 cm^2, a distance between electrodes of 4 cm, and got an amp of 60 Hz AC to flow with a voltage of 18 volts.
Someone else tells me that human flesh has a resistivity more like 40 ohm-cm.
Now, for the Skin Effect Formula in the "CRC Handbook" (Handbook of Chemistry and Physics, Chemical Rubber Publishing Co.): ("High Frequency Resistance", within "Radio Formulae", pages 3323-3325 in the 43rd Edition 1961-1962, probably different pages in different editions)
The book says to first calculate "x", which is:
x=pi*d*sqr(2*u*f/rho)*sqr(1/1000)
d is the conductor diameter in cm. Depending on where and how you measure,
my wrists are about 5 cm. in diameter.
u is the permeability of the conductor, which is usually close enough to 1.
f is, let's say, 175,000 Hz. (Approx. freq. of my latest Tesla coil)
rho is the resistivity of the conductor in ohm-cm, let's say 40.
I plug all this in my calculator and get an x of 46.5. The next formula tells me that the ratio of resistance to DC resistance is, within 1 percent if x is more than 7:
x/2.828 + .25
which is about 16.7.
To get this, current would (roughly) be confined to the outermost .075
centimeter of skin, not including the less-conductive outer layer of the
epidermis. If I got all the numbers right, it sure seems like the current
stays far away from the heart. But it would still cause quite a shock if
nerves responded to it.
In fact, if you hold a metal object and conduct as much as 60 mA of 175
KHz through it and your hand, you will feel little or no shock - not even
where the current enters and exits your skin. (DISCLAIMER - I don't
guarantee safety of trying this yourself!) It does appear to me
that human nerves do not respond to this frequency.
Now, for the Great Insane Shocking Signal Generator Experiment of 1997:
Results:
Low audio frequencies 80 Hz and less seem most shocking.
As frequency was increased above about 80-100 Hz, the burning/pain
sensation decreased but the "tingly" shocking sensation did not lose much
of its intensity until the frequency reached 500 Hz. Roughly at that
point, the shock began to be less intense in all ways as the frequency was
increased further. It was noticeably less intense at 1 KHz than at 500 Hz,
and a fraction as intense at 5 KHz as at 500 Hz. At 20 KHz, there was
almost no sensation of shock at voltages where lower frequencies are
painful.
Now for skin effect for a 2 centimeter diameter thumb at 20 KHz, assuming that 40 ohm-cm in any way represents reality:
My calculator tells me that x is 6.28. The chart in the CRC Handbook says that resistance of my thumb should be about 2.49 times the DC resistance. Even if the current is confined to the skin, you would feel it there unless the nerves weren't responding.
1a. Blood in blood vessels is very conductive and could make more current reach your heart than you think. Resistivity of outer regions of the body may be higher, forcing more current to the interior. Resistivity may be higher than I think - this issue can make current flow less confined to the skin than predicted. The nerve system in the heart may not have the frequency response I described above.
2. Some Tesla coil shocks have some low frequency component - such as if there was a voltage peak and associated charge on the secondary when current starts flowing to you and there is no charge or opposite charge when current stops flowing through you. This can be worse should the oscillation be unreliable for any reason. Although such a shock here may be not much, it could jolt you into bumping something and causing damage or causing you to contact a more lethal current somewhere else.
3. Non-shocking high frequency AC can cause burns. Should the burn penetrate through the dermis, it can take many months or years to heal and the burned tissue might never be the same again. Do note that if any muscle cells are totalled, they are generally not replaced - same as nerve cells. Nerve cell damage is often (not always) non-total, although non-totally damaged nerve cells can take an awfully long time to regenerate a long dendrite or a long axon.
4. Spark-gap Tesla coils usually have lethal primary circuits. There is a
bit of popular misconception that neon sign transformers and oil burner
transformers can't kill - they can! The range of currents most likely to
cause heart fibrillation (fatal!) from an arm-to-arm shock with 50-60 Hz
AC is 100 to 1,000 mA. Neon sign and oil burner transformers (usually
20-30 mA) are below this most-deadly range, but are still dangerous and
can sometimes kill!
With the capacitors used in spark-gap Tesla coils, the RMS current
available to a load in series with a spark gap can greatly exceed what the
transformer can normally deliver - I have lit incandescent lamps to an
extent indicating an RMS current of 1 amp when the average current was
under 10 mA. Even considering that much of the frequency content here is
less-hazardous higher frequencies, the low-frequency content can have RMS
current well above average and the danger is *increased* by having
capacitors.
5. This is not complete. I have more Tesla coil safety/hazard stuff HERE which I recommend reading. However, I do NOT guarantee that to be either accurate or complete so DO NOT sue me if you die!
Please read my Copyright and authorship info.
Please read my Disclaimer.