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