Hello John
Thanks for your comments.
1. The reason that the antenna current decreases linearly to zero at the end
of the antenna, is because sin(x) = x approx for small values of x, and for
most amateur antennas the lengths involved are only a fraction of a
wavelength.
Similarly the reason the voltage is practically constant over any continuous
segment of wire making up the antenna is because cos(x) =1 approx.
You are right about that, but I tried to explain it in a more practical
way. I think that my approach is technical correct.
2. There are several useful programs from G4FGQ for determining probable
environmental loss for a given site.
I intend to extend the page to related subjects (as enviromental losses,
measuring ERP etc..) at a later stage.
3. The values of Q for loading coils, that you have used in examples are
very conservative, it is not particularly difficult to obtain higher values
of Q especially for small elevated coils.
From my experience with loadingcoils (built about 10 of them and measred
them all here at the university) a Q = 300 is a 'average' value for coils
in the mH range using 1mm Cu wire. No doubt heiger Q's can be reached using
thicker wire, more spacing etc...
One remark : most 'simulating' software gives a far to high Q. I remind
that a 3mH coil with a calculated Q of 550 turned out to have a Q of less
than 250. So be carefull with calculation and prefer measurement.
4. From your explanation of how to calculate ERP, it follows that in order
not to exceed 1 watt ERP, we must not exceed approx. 0.55 watt radiated
power.
Due to its directivity, a short vertical monopole has a gain of 2.6dB over
a dipole (4.77dBi versus 2.15dBi for a dipole).
5. I thought at first that you had lost a factor of 4 (two squared) in
formula 5a, but later realised that the ratio is calculated with respect to
the average current in a monopole, which is 50%. It might be useful to make
this clear, assuming that it isn't just me who trips over this one.
I deliberately shipped all the math (this just scares most hams). But on a
later stage I intend to add the math on a seperate page.
6. The results of calculations agree well with those obtained from G4FGQ's
program TANT136.
We probably use the same theorectical background .... ..
7. The paragraph just above the graph in section 2.2, states that the gain
that can be achieved &is 6dB. The reason for this is that one can at most
double the average current in the vertical, which occurs when the current is
constant over the vertical segment.
That is the way I see it
8. Concerning Umbrella antennas, i.e. capacitive top loading with down
sloping top loading wires, you suggest a maximum vertical descent of 50%
should not be exceeded. In a comment regarding the Galveston NDB, someone
(sorry I have forgotten who) said that the textbooks on VLF recommend not
more than 30%. I decided to try to determine the optimum value and came up
with the following formula:
The Optimum length of a down sloper from the top is h(sqrt(1+sec(alpha))
1), where h is the height of the main mast and alpha is the angle of the
sloper from the vertical. Which this length the Radiation Resistance
compared with a monopole of the same height is increased by a factor of
4 * (1 + cos(alpa))^2 * (1  sqrt(cos(alpha)/(1+cos(alpha)))^2. This
increases monotonically with alpha. At 89 degrees, L is approx. 6.6 * h and
the Radiation Resistance is approx. 3 * that of Monopole.
For an angle of 45 degrees, the sloper should descend 39% of the height and
the multiplication factor for Rr is only 1.48.
Looks interesting, maybe I will put the umbrella antennas in a seperate
chapter (with more detailled information) later.
9. You give some useful results and graphs for inductive loading. I would
only like to comment that the elevated coil need not be the full value to
resonate the top part of the antenna. A combination of top capacitive and
inductive loading can be beneficial, e.g a 60 metre horizontal top and a 3
mHenry coil will practically achieve the full 6 dB increase.
That is correct, the antenna I use has a +/ 300pF tophat at 13m, a
elevated coil of +/ 1.8mH at 12m and a coil at the base of +/ 2mH.
BTW : the effect of an elevated coil was much more than expected, this is
explained in a additional page (see combined inductive / capacitive
toploading).
10. Section 2.7 Antennas with multiple vertical elements. This looks like a
good idea, which needs to be investigated further.
11. Section 2.10 Helical antenna. You point out that if capacitive top
loading is added the advantage of a helical antenna will be less. This is of
course relatively speaking. This is really a case of "less is more".
What I mean is : if you replace a 'straight' vertical without toploading by
a helical antenna you will win 2.5dB. But if you already have sufficient
capacitive toploading gain will be minimal (0.5dB or even less) and will
not be worth the effort.
Congratulations on a fine piece of work. I for one feel that at last I am
beginning to understand LF antennas.
Thanks, that was the meaning of this pages. But I do not have the 'wisdom'
all for myself so all comments are welcome and I will be happy to correct
any errors.
But one of the problems is that English is not my native language (you UK
and US guys are really spoiled on internet), so sometimes things are
understood differently from what I meant. Although I speak English very
often here at the university (thanks to  mainly  US guys who refuse to
learn Dutch even after living here for several years) my writing is far
from perfect. So if you find any errors in spelling and/or gramatics please
report them.
73, Rik ON7YD
