RD2.0, thanks for the link, but in case we don't have the ARRL 22nd edition, what is the Caption noted at the beginning of the section where you read your reference?
If it is not a new article, we may be able to find the reference in an older ARRL edition.
I might be able to help some here as I have way to many versions of said book (all but three in fact
)...
22'nd edition, page 3-17 (or Chapter 3 page 17) figure 3.33 caption.
I don't have a 21'st edition, but I do have a 20'th edition. The figure and its caption does not exist in the 20'th edition. Further, there is far less information in this subtopic on radials in the 20'th edition. Therefore, this info seems to be a more recent addition to the book series.
Here is a picture of said figure and its caption. I can quote the section of the book as well, but I am not sure how much of it I am able to post here before infringing on the copyright so I will limit myself to a paragraph...
The section which starts on the previous page, and continues to the next page, talks about elevated radials in general, and includes a part of different size radials including this paragraph on the same topic...
But feed point impedance is not the only problem created by asymmetric radial lengths. Figure 3.33 compares modeled radiation patterns between symmetric and asymmetric systems at 7.25 MHz. The amount of pattern distortion varies across the band from a fraction of a dB at 7.0 MHz to 3 dB at 7.25 MHz. Besides the distortion, the gain in all directions is smaller for the asymmetric case. Computing the average gains for the symmetric and asymmetric cases in Figure 3.33, there is about a 1.6 dB difference. What this tells us is that asymmetric radials can lead to significantly higher ground losses!
Before this it talks about how asymmetric radials will affect impedance. After this it talks about the variation of current on the radials and the vertical element, it continues on and talks about how more radials has less sensitivity to a radial system's asymmetry as well as other nearby objects. It also states this in italics.
Whenever possible an elevated ground system should use 10 or more radials.
Which flies in the face of the so called 'common knowledge' used in the CB world that for an elevated ground system four radials is enough... Sorry, it was just a snippet that I just had to include. Back to the topic at hand...
Finally it goes on to talk about using shortened radials on large (low frequency, aka 80/160 meter) antennas where you might not have enough room for a full radial system.
Having different length or unevenly spaced radials will affect the azimuthal pattern (such as the one in the chart shown above) such things, however, won't affect the "take off angle". Angling the radials down might affect the "take off angle" on a 5/8 wavelength antenna, but not because angling the radials affects the angle of radiation. In that case what is happening is you are adding more signal with a vertical polarization that is out of phase with the upper radiation portion of the antenna causing the dominant lobe to be a higher angle lobe. The low angle lobe still exists, it is just no longer dominant. If you are working with 1/4 wavelength antennas as they are in that section of the book, you can angle the radials from horizontal to straight down and the radiation angle will not change, unless you have another problem that needs to be dealt with...
I want to point out that this section in general is assuming 1/4 wavelength antennas. I wouldn't assume that use of radials on a 5/8 wavelength antenna will have completely equal effects. For example, a 5/8 wavelength antenna has a matching system that can account for any impedance difference simply because a 5/8 wavelength antenna will need such a device anyway. Further, the current distribution will be different on such an antenna as well, the current peaks on the radials will not be as high to begin with, and as such the radiation pattern difference between radials on a 5/8 wavelength antenna should be less than if the same radials are on a 1/4 wavelength antenna.
The DB