Frank,

You don't mention frequency. I assume it is still 8.07 MHz.

There's something seriously wrong!

The only change you have made (or I think you have changed) is to
increase the number of radials from 36 to 99.

Yet, for a length of 10 metres, the resistance of the radials ground
connection has INCREASED from a few ohms (for 36 radials) to 20.7 ohms
(for 99 radials).

This is impossible! It should either decrease to an even lower value
or at least remain the same.

Although I am not particularly interested in radiation resistance,
there is also something seriously wrong with Rrad. Rrad for a
1/4-wave vertical ought to be in the region of 34 ohms - not as low
as 13 ohms.

I think you use Rrad to calculate radials input resistance in which I
AM very interested.

I think you subtract the antenna input impedance, from the total
impedance of antenna + radials, to obtain the radials input
resistance.

Rrad + conductor resistance is the feedpoint resistance of the
antenna. You make it about 34 - 13 = 21 ohms too low.

If you subtract 21 ohms from YOUR radials input resistance values,
then the EXPECTED very low input resistance values for 99 radials are
obtained. But, of course, the radials input resistance should never
become negative.

If you are unable to find where the error arises then use my value of
Antenna Feedpoint Resistance = 33.8 ohms (which I have just
calculated.)

Could you please investigate your results and apply corrections? If
you are unable to determine the resonant input resistance of the
9-metre vertical antenna ( jX = 0) then use my value of 33.8 ohms
which, as likely as not, will not be exactly correct.

.................................................. .....................
.................................

Then change antenna height to exactly 3 metres and change frequency to
about 25 MHz. The exact frequency being that at which the antenna is
1/4-wave resonant with the feedpoint reactance being zero. Repeat
measurements for 99 radials.

Such measurements will be far more accurate than if they were made in
the field.

I have some nice graphs of input impedance, R + jX, versus radial
length for work you have already done. They tell me quite a lot.
----
Reg.

=======================================
Reg:

Here is the results of my analysis of a 99 radial monople:
Height 9 m, radial length from 0.5 to 10m, all conductors
#14 AWG copper, ground Er = 16, resistivity 150 ohm - m.
Radials 25 mm below ground. Antenna efficiency includes
the surface wave.

Radial Radial Radiation Ant
Length Z Resistance Efficiency
(m) (ohms) (ohms) (%)

0.5 63.0 - j 33.6 13.2 17.6
1.0 47.7 - j 18.2 13.2 21.7
1.5 41.8 - j 13.7 13.2 24.1
2.0 38.3 - j 12.5 13.2 25.7
2.5 35.7 - j 11.2 13.2 27.1
3.0 33.4 - j 10.8 13.2 28.3
3.5 31.6 - j 10.5 13.1 29.4
4.0 29.8 - j 10.1 13.1 30.6
4.5 28.2 - j 9.5 13.1 31.7
5.0 26.8 - j 8.9 13.1 32.8
5.5 25.7 - j 8.2 13.1 33.8
6.0 24.7 - j 8.0 13.2 34.7
6.5 23.9 - j 6.9 13.2 35.6
7.0 23.2 - j 6.2 13.3 36.4
7.5 22.6 - j 5.5 13.4 37.7
8.0 22.1 - j 4.8 13.5 38.0
8.5 21.6 - j 4.2 13.7 38.8
9.0 21.2 - j 3.5 13.8 39.5
9.5 20.9 - j 2.9 14.0 40.2
10.0 20.7 - j 2.2 14.2 40.9

Note that the radiation resistance is computed
from the total radiated power (including surface
wave) divided by the RMS base current squared.

The radial input impedance is derived from
the difference between the antenna input
impedance and the radiation resistance. A
fraction of an ohm can be attributed to the
copper losses in the monopole. Also
some of the imaginary part of the radial impedance
must be due, in part, to the input impedance
of the vertical section.

With 0.5 m radials the surface wave accounts for
2% of the total radiated power. With 10 m radials
the surface wave accounts for 5% of the TRP.


Frank
CM Reg's 99 radial Vertical

CM (WG)

CE

GW 2 1 0 0 0 0 0.0968 -0.025 0.00082

GW 35 4 0 0.0968 -0.025 0.026 0.5 -0.025 0.00082

GW 70 4 0 0.0968 -0.025 0 0.5 -0.025 0.00082

GW 105 4 0 0.0968 -0.025 -0.026 0.5 -0.025 0.00082

GR 1 33

GE -1 2

GN 2 0 0 0 16 0.0067

FR 0 1 0 0 8.07 0.01

LD 5 0 0 0 5.8001E7

WG

EN



CM Reg's 99 radial

CM (GF)

CE

GF

GW 1 90 0 0 9 0 0 0 0.00082

GE -1

EX 0 1 90 00 83.83328192 0

LD 5 0 0 0 5.8001E7

RP 1 101 1 0000 200 0 -2 1 200

RP 0 91 1 1000 0 0 1 1

RP 0 19 73 1002 -90 0 5.00000 5.00000

NE 1 1 46 1 200 45 90 1.0 1.0 1

NH 1 1 1 1 200 89 90 1.0 1.0 1

EN

Reg,

The frequency is still 8.07 MHz. I was also puzzled by the radiation
resistance, but I arrived at the value differently than in previous models.

Anyway, I think I have discovered the error. In computing the surface
wave at 200 m I assumed the loss would be insignificant. This does not
appear to be true. For example; at a 26 degree elevation angle
normalization of the E-field to one meter produces essentially the same
result from either: 200 meters, or 400 meters. At zero degree elevation
angle, where the surface wave dominates; normalization from 200 m
or 400 m produces significantly different results -- as shown below:

Elevation Distance E- field
Angle (m) normalized
(deg.) to 1 meter
(V)

26 200 83.0
26 400 83.3
0 200 67.5
0 400 45.5

I had this at the back of my mind when making the calculations.
To be honest it is pretty much a no brainer, since
it is well known that the surface wave diminishes rapidly at
the higher frequencies.

All your comments are noted. For the moment I would like to perform an
integration of the Poynting Vector in the near field. Hopefully it will
provide a more realistic radiation resistance. Now to figure out
how to do this in Excel.

Frank





"Reg Edwards" wrote in message
...
Frank,

You don't mention frequency. I assume it is still 8.07 MHz.

There's something seriously wrong!

The only change you have made (or I think you have changed) is to
increase the number of radials from 36 to 99.

Yet, for a length of 10 metres, the resistance of the radials ground
connection has INCREASED from a few ohms (for 36 radials) to 20.7 ohms
(for 99 radials).

This is impossible! It should either decrease to an even lower value
or at least remain the same.

Although I am not particularly interested in radiation resistance,
there is also something seriously wrong with Rrad. Rrad for a
1/4-wave vertical ought to be in the region of 34 ohms - not as low
as 13 ohms.

I think you use Rrad to calculate radials input resistance in which I
AM very interested.

I think you subtract the antenna input impedance, from the total
impedance of antenna + radials, to obtain the radials input
resistance.

Rrad + conductor resistance is the feedpoint resistance of the
antenna. You make it about 34 - 13 = 21 ohms too low.

If you subtract 21 ohms from YOUR radials input resistance values,
then the EXPECTED very low input resistance values for 99 radials are
obtained. But, of course, the radials input resistance should never
become negative.

If you are unable to find where the error arises then use my value of
Antenna Feedpoint Resistance = 33.8 ohms (which I have just
calculated.)

Could you please investigate your results and apply corrections? If
you are unable to determine the resonant input resistance of the
9-metre vertical antenna ( jX = 0) then use my value of 33.8 ohms
which, as likely as not, will not be exactly correct.

.................................................. ....................
................................

Then change antenna height to exactly 3 metres and change frequency to
about 25 MHz. The exact frequency being that at which the antenna is
1/4-wave resonant with the feedpoint reactance being zero. Repeat
measurements for 99 radials.

Such measurements will be far more accurate than if they were made in
the field.

I have some nice graphs of input impedance, R + jX, versus radial
length for work you have already done. They tell me quite a lot.
----
Reg.

=======================================
Reg:

Here is the results of my analysis of a 99 radial monople:
Height 9 m, radial length from 0.5 to 10m, all conductors
#14 AWG copper, ground Er = 16, resistivity 150 ohm - m.
Radials 25 mm below ground. Antenna efficiency includes
the surface wave.

Radial Radial Radiation Ant
Length Z Resistance Efficiency
(m) (ohms) (ohms) (%)

0.5 63.0 - j 33.6 13.2 17.6
1.0 47.7 - j 18.2 13.2 21.7
1.5 41.8 - j 13.7 13.2 24.1
2.0 38.3 - j 12.5 13.2 25.7
2.5 35.7 - j 11.2 13.2 27.1
3.0 33.4 - j 10.8 13.2 28.3
3.5 31.6 - j 10.5 13.1 29.4
4.0 29.8 - j 10.1 13.1 30.6
4.5 28.2 - j 9.5 13.1 31.7
5.0 26.8 - j 8.9 13.1 32.8
5.5 25.7 - j 8.2 13.1 33.8
6.0 24.7 - j 8.0 13.2 34.7
6.5 23.9 - j 6.9 13.2 35.6
7.0 23.2 - j 6.2 13.3 36.4
7.5 22.6 - j 5.5 13.4 37.7
8.0 22.1 - j 4.8 13.5 38.0
8.5 21.6 - j 4.2 13.7 38.8
9.0 21.2 - j 3.5 13.8 39.5
9.5 20.9 - j 2.9 14.0 40.2
10.0 20.7 - j 2.2 14.2 40.9

Note that the radiation resistance is computed
from the total radiated power (including surface
wave) divided by the RMS base current squared.

The radial input impedance is derived from
the difference between the antenna input
impedance and the radiation resistance. A
fraction of an ohm can be attributed to the
copper losses in the monopole. Also
some of the imaginary part of the radial impedance
must be due, in part, to the input impedance
of the vertical section.

With 0.5 m radials the surface wave accounts for
2% of the total radiated power. With 10 m radials
the surface wave accounts for 5% of the TRP.


Frank
CM Reg's 99 radial Vertical

CM (WG)

CE

GW 2 1 0 0 0 0 0.0968 -0.025 0.00082

GW 35 4 0 0.0968 -0.025 0.026 0.5 -0.025 0.00082

GW 70 4 0 0.0968 -0.025 0 0.5 -0.025 0.00082

GW 105 4 0 0.0968 -0.025 -0.026 0.5 -0.025 0.00082

GR 1 33

GE -1 2

GN 2 0 0 0 16 0.0067

FR 0 1 0 0 8.07 0.01

LD 5 0 0 0 5.8001E7

WG

EN



CM Reg's 99 radial

CM (GF)

CE

GF

GW 1 90 0 0 9 0 0 0 0.00082

GE -1

EX 0 1 90 00 83.83328192 0

LD 5 0 0 0 5.8001E7

RP 1 101 1 0000 200 0 -2 1 200

RP 0 91 1 1000 0 0 1 1

RP 0 19 73 1002 -90 0 5.00000 5.00000

NE 1 1 46 1 200 45 90 1.0 1.0 1

NH 1 1 1 1 200 89 90 1.0 1.0 1

EN