Reg wrote:
"What is the value of the constant C?"

395

It is found on page 137 of Kraus` 1950 edition of "Antennas".

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
Reg wrote:
"What is the value of the constant C?"
395
It is found on page 137 of Kraus` 1950 edition of "Antennas".
Best regards, Richard Harrison, KB5WZI

Richard,

You didn't read something correctly.

Reg asked for "C" for a small vertical with uniform current over a
perfect groundplane.

You are off by nearly a factor of 4 times.

For a monopole with uniform current, C=1580
For a monopole with triangular current C= 395

Radiation resistance is four times greater when the antenna has uniform
current.

73 Tom

wrote:
For a monopole with uniform current, C=1580
For a monopole with triangular current C= 395

Radiation resistance is four times greater when the antenna has uniform
current.

Reg didn't say "uniform current". He said "uniformly distributed
current". A triangular current wave is uniformly distributed,
i.e. it has a linear taper. Seem to me we need to find out
what Reg meant by "uniformly distributed current". I thought
he meant uniformly triangularly distributed. I think Richard
thought the same thing.
--
73, Cecil http://www.qsl.net/w5dxp

Tom, W8JI wrote:
"You didn`t read something correctly."

OK, here is the arithmetic.

Radiation Resistance of a Short Electric Dipole:

RR = 80 pi squared (L/lambda)squared

Constant = 80 (8.97) = 790

But a short monopole has 1/2 the resistance of a short dipole.

790 / 2 = 395

All Reg asked for was the constant.

Best regards, Richard Harrison, KB5WZI

Richard,

Your calculation is OK as far as it goes. However, you overlooked the
fact that "L" is different for the dipole and the monopole. The monopole
has 1/2 the length of the dipole or 1/4 the length squared.

The coefficient Reg asked for is therefore 4 times the number you quoted.

73,
Gene
W4SZ

Richard Harrison wrote:
Tom, W8JI wrote:
"You didn`t read something correctly."

OK, here is the arithmetic.

Radiation Resistance of a Short Electric Dipole:

RR = 80 pi squared (L/lambda)squared

Constant = 80 (8.97) = 790

But a short monopole has 1/2 the resistance of a short dipole.

790 / 2 = 395

All Reg asked for was the constant.

Best regards, Richard Harrison, KB5WZI

Gene Fuller wrote:
Richard,

Your calculation is OK as far as it goes. However, you overlooked the
fact that "L" is different for the dipole and the monopole. The monopole
has 1/2 the length of the dipole or 1/4 the length squared.

The coefficient Reg asked for is therefore 4 times the number you quoted.

1.) He could have gotten length correct and assumed current was
triangular. That would reduce radiation resistance by a factor of four.

2.) He could have assumed uniform current and gotten length wrong by a
factor of two, and that would reduce radiation resistance by a factor
of four.

Gene Fuller wrote:
"However, you overlooked the fact that "L" is gifferent for the dipole
and monopole."

L is not a constant. L is a variable in another part of the formula. The
difference in radiation resistance between a dipole and a monopole is a
constant. It equals 2, not 4, not 8, or not 16.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
Gene Fuller wrote:
"However, you overlooked the fact that "L" is gifferent for the dipole
and monopole."

L is not a constant. L is a variable in another part of the formula. The
difference in radiation resistance between a dipole and a monopole is a
constant. It equals 2, not 4, not 8, or not 16.

Best regards, Richard Harrison, KB5WZI

Richard,

I guess this must be the week for basic math explanations.

Let's try it with numbers.

The equation shown in Kraus "Antennas", 2nd edition, page 216, for the
radiation resistance of a short dipole with constant current is:

Rr = 80 pi^2 (L/lambda)^2

80 pi^2 is about 790, so the equation is rewritten as:

Rr = 790 (L/lambda)^2

In the convention used by Kraus, "L" is the total length of the dipole.

I presume the equivalent discussion is contained in the 1950 edition of
"Antennas".

As a test case, let's suppose that L is 8 meters, and lambda is 80
meters. We immediately see that Rr is 7.9 ohms.

OK, now take the monopole over perfect ground that Reg mentioned. The
monopole length that corresponds to one half of the test case dipole is
4 meters. The radiation resistance of the monopole is 3.95 ohms.

So, the question becomes determining the correct coefficient for the Rr
equation. (L/lambda) is now 0.05, not 0.10.

Therefore,

Rr = 3.95 ohms = X (0.05)^2

I believe you will discover that "X" must be 1580.

This is set up using the definitions for L as stated in Kraus (dipole)
and as stated by Reg in his monopole query. Of course you can set up
your own rules, but that would be addressing a different problem.

73,
Gene
W4SZ

Richard Harrison wrote:
Tom, W8JI wrote:
"You didn`t read something correctly."

OK, here is the arithmetic.

Radiation Resistance of a Short Electric Dipole:

RR = 80 pi squared (L/lambda)squared

Constant = 80 (8.97) = 790

But a short monopole has 1/2 the resistance of a short dipole.

790 / 2 = 395

All Reg asked for was the constant.


If you'll read more in the chapter of Kraus you're quoting, you'll
notice that L is the length of the dipole, not the length of a monopole.
Do the proper substitution and you'll get the correct answer.

Roy Lewallen, W7EL

Roy, W7EL wrote:
"Do the proper substitutionn and you`ll get the correct answer."

Yes. The warning also appears on page 137:
"In developing the field expressions for the short dipole, which were
used in obtaining (5-56), (5-56) is the value of radiation resistance,
the restriction was made that lambda is much larger than the length of
the dipole L." No problem there, Reg specified a short monopole.

Kraus does a sample calculation for a short dipole. I used Kraus` data
and got the same answer when duplicating his calculation.

But Reg was not asking for an answer to a specific problem. Reg was
asking for the value of the constant in a formula of the same form.
Kraus gives it as 80 pi squared for a dipole.. This is 790.

We know that a monopole has half the resistance of a dipole. Example: 73
ohms and 36.5 ohms. 790 / 2 = 395. That`s not a resistance, it is only
the value of a constant which must be multiplied by (L/lambda) squared
to give the radiation resistance of a very short monopole.

Best regards, Richard Harrison, KB5WZI