he claims that on 2m mobile antenna a 1/4 wave antenna out put is more shaped like a donut and a 5/8 wave antenna's output is flat like a pancake.
Well, it would be somewhat if you used a small ground plane on the 1/4 wave
antenna and an infinite one on the 5/8 wave. As antenna misrepresentations
go, it's not too bad, and is probably what many of the textbooks say.
Take a balloon and blow a bit of air into it (but not enough to inflate it all the
way.) The flatter you squish it top-to-bottom, the further it bulges out on
the sides. The same thing with your omnidirectional antenna pattern: the
more you squish it into the horizontal plane, the high the signal at the
horizon.
Now if you look at the theoretical diagrams of 1/4 and 5/8 wave radiators
over infinite perfect ground, you'll see that that (except for a couple of
high angle lobes) the pattern of the 5/8 wave whip is, indeed, flatter than
the 1/4 wave whip, and gives more gain at low angles. This is the
theoretical 3dB gain. HOWEVER, if you put the two antennas in free space,
giving each the same horizontal 1/4 wave radius ground plane to work
against, the actual difference is much less - perhaps 1/2 dB or so.
Why is that? The gain of the 5/8 wave whip over perfect, infinite ground
is due to the height of the radiating portion over that ground, not anything
intrinsic about the antenna itself. If you put ground radials on a 1/4 wave
vertical and elevate the top of it to be at the same height as the top of
the 5/8 wave whip, they'd work about the same.
In the case of a mobile antenna on 2m, the roof of even a large van is
not big enough for a 5/8 wave whip to develop the rated gain that
it would have over an infinite ground plane - you'd need something that
extend out to 50 or 100 wavelengths, which isn't practical to drive down
the highway.
So the 5/8 wave has a somewhat flatter pattern, and a little more gain
than a 1/4 wave whip in the real world, but, from my experience switching
between the two, I'd say about 1dB difference on the top of my van.
He also mentions a ringo ranger vertical antenna being a stacked vertical diople
As is just about every other 2m antenna with a radiator about 8' long. It's a
very popular design because it gives you useful gain in a reasonable length.
The ASA IsoPole is similar, though it has a second bottom cone to provide
additional feedline decoupling. (The Ringo Ranger added a decoupling stub
and radials below the feedpoint after AEA advertising pointed out how
common mode currents on the feedline distorted the radiation pattern.)
You can call it colinear dipoles, or an "Extended Double Zepp" (EDZ), or
whatever you want. There are two half wavelengths providing the
radiation and the ends are spaced about 1/4 wave apart, which is about
the optimum spacing if you are using a simple phasing stub. You can
build your own antenna to do the same thing using several possible
designs. If you look inside some of the fiberglass-encased antennas of
similar length you'll probably find about the same arrangement.