To stay on topic. I am talking about why they would recommend lengths of coax that are half wave multiples. Not about some mistake in a patent.
To start with, with all due respect, in the context of your post, that was on topic...
But to answer the rest...
When an RF signal travels up a feed line, unless a certain condition is met, impedance and reactance (typically shortened to the variables R and X) change as well. At distances of electrical half wavelength multiples, impedance and reactance comes back to what they were at the feed point of the antenna, effectively reproducing what is seen at the antenna.
So lets throw SWR into the equation. Impedance and reactance are directly related to SWR, in fact, you can directly calculate SWR from these two variables. Because of this, many people (including some that are very intelligent) think SWR changes along the length of the coax with the changes in impedance and reactance. This, however, is a mistake.
What actually happens is, as you travel up the coax, impedance and reactance change in such a way that SWR does not change. While oversimplified, think of it like several different math problems that all have the same result at each part of the feed line. At one point you will have, say, 5+5, while another point it will have something like 4+6, or 3+7. While the real math equation is much more difficult than this, this should serve a basic example as to what is happening.
So, when it comes down to it, you would only need such a length when using something more than SWR when tuning an antenna, such as an antenna analyzer. The thing is when they wrote that manual such devices were rare at best, as well as rather expensive relatively speaking, especially in the hobby space. Although in todays world, such devices are much cheaper and more common, not to mention much more capable. Many of the newer ones today can, in fact, get around this need for a specific coax length if you follow certain steps.
There are also other limits to half wavelength multiple lengths of coax that they overlooked. For example, something else Avanti didn't take into account, is that half wavelength multiples are good for one frequency only, not an entire CB band as their directions imply.
The DB