Please help me out with the math. What is the length of a 5/8s wavelength 2
meter antenna? I've got something that might be able to be cut to the freq.

Moody-

Did you realize what a stimulating topic this was going to be? Perhaps I can
help by announcing that there are two slightly different legitimate answers.

First, radio waves travel very close to 300 million meters per second. The two
meter band is roughly at a frequency of 150 million Hertz, so one wavelength
would be 300 million divided by 150 million. I think you get the idea, and can
use your exact frequency to get the exact wavelength. In the case of a 5/8th
wavelength antenna, simply multiply the calculated wavelength by 5/8 (or
0.625). (One inch equals 0.0254 meters.)

To use such an antenna, you must find a way to connect your transmission line
to the antenna and a ground plane, so that it matches. In other words, you
want to transfer the maximum amount of power to the antenna so it can be
radiated, and reflect the minimum amount of power back to the transmitter.

The beauty of a 5/8th wavelength (ground plane) antenna, is that it is
extremely easy to match. Its input impedance is 50 Ohms resistive in series
with a small amount of capacitance. Therefore you need a small amount of
series inductance to match it. Some higher-frequency examples use the
stainless element itself, wound in a small coil near its base.

The other "legitimate" answer is that a given 5/8th wavelength antenna you buy,
may actually be 0.58 wavelength, NOT 0.625. Such antennas are usually called
5/8th because of the confusion between 0.58 and 5/8.

The beauty of a 0.58 wavelength (groundplane) antenna, is that it concentrates
the maximum amount of power towards the horizon, compared to other similarly
constructed antennas (according to my Antennas Professor, 35 years ago). While
it is true that there is a small lobe towards the sky above, the main lobe is
sharper than the lobe of a quarter wave ground plane, and is aimed almost
directly at the horizon. If the vertical element were any longer (say, 0.625
wavelength), the lobe pointed up would increase and sap some of the power from
the lobe towards the horizon. If it were shorter, the main lobe would be
fatter and power would be spread over a larger, slightly higher angle.

A drawback of the 0.58 wavelength antenna is that it is not as easily matched.
Such antennas are often matched with a tapped coil. The bottom of the coil is
connected to ground, the top to the antenna element, and the co-axial
transmission line center conductor is connected to a tap on the coil.

73, Fred, K4DII