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There are plenty of references to this claim on the internet that tying knots in power cables will prevent a piece of equipment e.g. television or computer from a power surge.

How can this be debunked (or proven) using mathematics?

I stumbled across this which seems reasonable to me, but is there some way this can be proved?

The surge impedance of any line is the square root of its inductance divided by its capacitance, and electromagnetic waves travel most readily down a line where that surge impedance doesn't change. A point of changing impedance is a discontinuity that causes a partial reflection of the wave back towards its source. As an example, the end of the line is a surge impedance jump to infinity and the whole wave is reflected back (which means the wave voltage at the open end doubles!) This is also the reason why you want to use terminators on the ends of coaxial cables. Open-ended cables will reflect back the signal causing poorer picture quality and ghosting (and similar things happen for poorly made connections that have higher impedances than the surge impedance of the coax).

Knotting the line gives that part of it a higher inductance (think of the knot as a coil with a couple of turns). That means two surge impedance discontinuities (from line to knot, and from knot back to line). It seems to me (too lazy to resort to doing the math) that this is bound to reduce the magnitude (voltage and current) of a surge passing through the knot because some will be reflected back. However, I'd guess that the reduction would be small.

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    $\begingroup$ Similar recent question on Skeptic.SE: Does tying a knot in a power cord provide any protection against lightning?. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Aug 26, 2011 at 4:12
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    $\begingroup$ Damned if you do, damned if you don't. Quote: "One just need to coil up the cable a sufficient number of times, or use too much insulation around the cable, or both. Laboratory tests have shown that ignition ... may easily occur in such cases. At one such incident it was sufficient to coil up the cable three times and cover the coil in clothing." Fire or lightning? Take your pick. $\endgroup$
    – Willie Wong
    Commented Aug 26, 2011 at 14:14
  • $\begingroup$ @Willie - Thanks for that link. It would have been good if they linked to the 'laboratory tests' they mention. $\endgroup$
    – going
    Commented Aug 27, 2011 at 10:06

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You can calculate the inductance of such a coil and estimate the capacitance of the wire and try to work it out like a transmission line problem.

This might not be necessary here. According to Wikipedia the duration of a typical lightning event is in the range of 1-100 ms. If we compare this with the line frequency of 50 Hz (20 ms) and can assume that the coil in the wire does not prevent your TV or computer from working how should it protect from lightning? The effects of a 100 ms current pulse of electricity is for most purposes not to different from a DC voltage (disregarding the rise and fall of the pulse) because the frequency dependence of electrical circuits is small if you don't add big capacitors or similar items.

What really helps though are varistors or zener diodes that are used in surge protectors. They have switching times in the microsecond range and can "cut off" the current/voltage pulse long before it reaches it's maximum.

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  • $\begingroup$ The inductance of a power cable is nearly independent from "coiling" status! It's just a symmetrical line rolled op. Think of the fact, that it is a bifilar winding, one thread goes in one duirection, the other goes "back". So the inductance is the inductance of a Lecher line. $\endgroup$
    – Georg
    Commented Nov 4, 2011 at 19:42
  • $\begingroup$ @Georg: Did I state that it is not a Lecher line? The question was whether coiling it up makes a difference. I said no because it does not make a difference at low frequencies. You wrote "nearly independent", so why is my answer incorrect? $\endgroup$
    – Alexander
    Commented Nov 4, 2011 at 19:56
  • $\begingroup$ For low frequencies of about 1 MHz (wich is a typical frequency of a flash) coiling up does not make a difference. Things may differ fore wavelengths about the distance of wires in the cabel or between cable windings. $\endgroup$
    – Georg
    Commented Nov 4, 2011 at 20:56
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A coiled mains cable behaives like a 'common-mode' inductor, Ligtning behaives a little like an impulse - if you could take the FFT of a lightning strike, it would have quite a large bandwidth. A coil in the line may have some impact against the common mode, high-frequency component of the lightning and there may be some benifit in the form of reduced energy avaliable, but knoting the cables won't save your equipment.

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The knot (I prefer three loops about 12" diameter) is definitely an inductor, inductance of which responds to a surge CAUSED by lightning. NOTE: It's ONLY a surge of existing voltage with the fundamental source frequency remaining ≈ 60 cycles and any residual frequencies being harmonics of 60 logarithmically higher to infinity in frequency and logarithmically lower in amplitude. Any change in either capacitive reactance OR inductive reactance in an AC circuit mitigates the "resonance" of the impedance - A GOOD thing as far as the surge is concerned. The fabricated loops in an AC conductor, whether it's mains or branches, is not CODE-conducive but is realistic and it DOES lessen the amplitude of a surge, SIGNIFICANTLY. CODE is mostly good because SAFETY is primary. However, some codes are politically fabricated for reasons too numerous to mention. The KNOT, or preferably "LOOPS" concept is well-founded not only in commercial AC applications but antenna and cable TV coax —as well as long runs of CAT5E, CAT6 and on up, ethernet, even though these electrical charactoristics do not involve 60 cycles. It's a practical principal that DOES work using the "LOOPS" arrangement I described. The only reason that LOOPS is not a guaranteed cure-all for surges is because of the infinite electromagnetic amplitude that surges can comprise. Cheers! 36 years in telecom & RF Network Operations —IEEE / FCC w radar commercially-licensed.

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    $\begingroup$ Welcome to Physics.SE. Note that it's very difficult to read a post with so many capitalized words like that. Instead, you can enclose words with a single asterisk, like *example* for italics and via double asterisks -- **example** for bold $\endgroup$
    – Amit
    Commented Nov 14 at 19:43
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    $\begingroup$ The caps lock is indeed terrible and would merit a downvote on its own (I'm not the one who downvoted though since I don't know much about the subject), for more information on how this is perceived see theoatmeal.com/pl/minor_differences/capslock $\endgroup$
    – Yukterez
    Commented Nov 14 at 19:55

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