Recently I bought a used copy of "Reference Data for Radio Engineers"
published by Howard Sams in 1975. On page 27-6 the following applies to
this topic:

QUOTE

The effective height of a grounded vertical antenna is equivalent to the
height of a vertical wire producing the same field along the horizontal as
the actual antenna, provided the vertical wire carries a current that is
constant along its entire length and of the same value as at the base of the
actual antenna. Effective height depends upon the geometry of the antenna
and varies slowly with wavelength. For types of antennas normally used at
low and medium frequencies, it is roughly 1/2 to 2/3 the actual height of
the antenna.

For certain antenna configurations, effective height can be calculated by
the following equations.

Straight Vertical Antenna: h = 1/4 lambda

Effective Height = [lambda/pi*sin(2*pi*h/lambda)]*sin^2(pi*h/lambda)
where h = actual height

clip

END QUOTE

This may be useful toward the earlier thread started here by Reg ("Back to
fundamentals"), that went off in several directions.

RF

"Richard Fry" wrote in message
...
Recently I bought a used copy of "Reference Data for Radio
Engineers"
published by Howard Sams in 1975. On page 27-6 the following
applies to
this topic:

QUOTE

The effective height of a grounded vertical antenna is equivalent to
the
height of a vertical wire producing the same field along the
horizontal as
the actual antenna, provided the vertical wire carries a current
that is
constant along its entire length and of the same value as at the
base of the
actual antenna. Effective height depends upon the geometry of the
antenna
and varies slowly with wavelength. For types of antennas normally
used at
low and medium frequencies, it is roughly 1/2 to 2/3 the actual
height of
the antenna.

For certain antenna configurations, effective height can be
calculated by
the following equations.

Straight Vertical Antenna: h = 1/4 lambda

Effective Height =
[lambda/pi*sin(2*pi*h/lambda)]*sin^2(pi*h/lambda)
where h = actual height

clip

END QUOTE

This may be useful toward the earlier thread started here by Reg
("Back to
fundamentals"), that went off in several directions.

RF
===========================================

Thanks Richard for digging up an ancient copy of RDFRE.

I do not have ready access to the 'bibles' these days.

I recall the RDFRE as being not altogether a reliable publication. It
was useful as a general purpose look-up paper which needed checking
particularly when using formula. Approximations were used without
saying so as I have found to my cost.

Your quote refers to "Types of antennas normally used" and "for
certain configurations". This indicates to me an uncertain range of
dimensions. Perhaps some antennas in the range considered were
top-capacitance loaded, others were not, some thick and fat, some very
slender, some guyed, some not, some with tall base insulators, some
not. Even Terman lumps together a range of dimensions and draws
conclusions common to the collection.

I recall seeing reference to "Effective Height" in the ancient tomes
from 1900 to 1940.

The theoretical effective height of a short receiving vertical above a
very good gound was stated to be EXACTLY HALF of actual height. As the
actual height approaches 1/4-wavelength the effective height increases
(I think) to about 0.64 of actual height which, reassuringly, equals
2/Pi. (I am always reassured when a number like 2/Pi appears in
guesswork.)

So the voltage measured between the bottom end of a 1-metre vertical
antenna and ground is exactly half of the field strength in volts per
metre. And my program has been corrected accordingly to give the
correct value for receiver power input.

The 'bibles' refer to "Induced voltage" but the learned authors forgot
to state beween which points on the antenna the voltage is referred.
This is an open invitation for readers to jump to the wrong
conclusions.

Incidentally, the field strength at a distance of 1 Km from a 1000
watt transmitter was always correctly calculated by my program to be
300 millivolts per metre. The calculation does not use the concept of
"Effective Height". It uses the concept of power gain relative to
isotropic.

Nowhere in the program is the concept of images in the ground,
reflections from the ground and half-hemispheres invoked. I was
pleased it didn't arise in the discussions. It would have been yet
another direction to get bogged down in.

Nice to have your interest.
----
Reg, G4FGQ.

"Reg Edwards" wrote
Your quote refers to "Types of antennas normally used" and "for
certain configurations". This indicates to me an uncertain range of
dimensions. Perhaps some antennas in the range considered were
top-capacitance loaded, others were not, some thick and fat, some very
slender, some guyed, some not, some with tall base insulators, some
not. Even Terman lumps together a range of dimensions and draws
conclusions common to the collection.
__________________

Radiators were not lumped together to be covered in common by the equation I
quoted. This section continues with individual equations for small loop,
and Adcock antennas -- which further I omitted as indicated by the snip
statement in my post.

Section 2-10 in Kraus' "Antennas," 3rd edition, has much more analysis of
effective height. I know you scorn learned authors and their bibles, but
perhaps a quick read of this would save you from repeating such
investigations to your personal satisfaction, and answer a few of the
questions you ask of others here. Maybe you can borrow a copy from your
local library.

RF