Question

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.

Answer 1

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.