In the main, DX signals will arrive at your station between 5 degrees and up to about 15 degrees. The absolute average is around 5 degrees. That's not to say SOME signals won't be arriving as low as 1 degree (eg long-haul DX on 40m) and up to 20 degrees for some 80m signals. Links to these papers follows:
https://www.arrl.org/files/file/antpl... - published by ARRL
http://on5au.be/Cebik-2/ThePseudo-bre... - Cebik's Brewster Angle discussed
https://en.wikipedia.org/wiki/Curtain... - Interesting observation about curtain arrays noting low angles
https://www.arrl.org/files/file/QEX_N... - Read the very last paragraph - page 20

The main arguments I debate and dispell are as follows:

1) the 5 degree “myth” has been around for 5-6 years and has been produced by newcomers who use modelling
2) the software “they” use is free so is unlikely to be accurate enough
3) the 5 degree angle, and I quote “does not appear to exist”
4) the reference angle should not be less than 10 degrees
5) the optimum angle from a QW is 26 degrees
6) buy the ARRL Antenna Handbook (agreed!)

After this video was filmed, an academic sent me a message (edited):

This 5 degree thing is actually a very technical issue. The papers on it are very interesting and complex. Firstly there is definitely the thing that [redacted] goes on about - the pseudo Brewster angle. Unfortunately for [redacted] it’s irrelevant in vertical 1/4 waves. In fact the very paper [redacted] quoted in his video states this fact. Secondly, there is no doubt that true DX does arrive at very low angles. This has been known for years. The fight to achieve low angles is well known. What he cannot deny is that 1) DX comes in at low angles. 2) comparing values of gain at any angle is just that - a comparison (a bit like dB). You can compare any number of things using the benchmark of your choice. In summary, do Brewster angles have any relevance to ground mounted verticals? NO. Does DX on long hops come in at low angles? YES. Regardless of where you chose to measure, it’s just a comparison.

An engineer had this opinion (edited):

Concerning modelling software, YES in the early days the free programs were a bit hit'n'miss and the commercial units were very expensive. The commercial units were also difficult to use and you needed a PhD to be able to run the darn things, so in the hands of an inexperienced operator you could torture the data to confess to anything....

However, technology has moved on and the likes of EZNEC and MMANA stared to become very competitive with some of the very expensive commercial gear and started producing results which were very favourable indeed. This all at a fraction of the price for full flung commercial stuff and just about any reasonably competent Tech could use them. The latest iterations of MMANA now are fully spec'd and DO take into consideration such things as wire diameters, end effects, brewster angles if applicable, etc.

In the main all these variables are configurable if you dig deep enough but normally assumed for general use. So, in the case of modelling a 1/4w ground mounted vertical for instance MMANA etc will know to ignore any brewster effect because it is not applicable. However, start changing the diameter of your wire antennas and the software kicks in a compensates.

A Broadcast Engineer sent me this:

The angle of radiation is definitely well known for DX and more so as we go lower in frequency. From a commercial point of view we design our AM towers to give a low angle of radiation so we get the widest audience possible. If we get this low angle then we are assured of the fill-in anyway. We are concerned about the ground conductivity and will build on a peat swamp if at all possible. But it is not the Brewster effect that worries us but the HUGE return currents we have to deal with.

Another opinion from an engineer (edited):

.. about the pseudo-Brewster angle showing an ELEVATED vertical with elevated radials - [redacted] falsely assumes that a ground mounted 1/4w vertical will act the same way. YES, there is a Brewster effect with an ELEVATED vertical but little to NONE with a 1/4w GROUND MOUNTED vertical.

Final note from me. I am not an expert at mathematics and can hardly understand this Brewster Angle anyway. I am only interested in ground-conductivity because I know that an excellent ground will give better results for a vertical. And for best effect, this ground needs to be for hundreds of wavelengths (eg sea water). But it'll still work regardless.

That's all on this subject. It's a huge topic and if I find some more decent quality information, maybe we can revisit this topic another day.

Thanks for watching. .See you on the next one! Callum.