There are a lot of formulas about these calculations. On the General test, it asks the approximate lengths for some antennas. They ask for approximate because of the variables for the exact length of any given antenna.

Anyway, I just try to remember a few numbers – because I am terrible at memorizing a bunch of them.

First, the speed of light = 299.8 million meters per second. 300 is close enough.

Second, wave length = speed of light / frequency in MHz.  The wave length of 14.000MHz = 300 /14.0 = 21.43m

Third, ½ half wavelength is the wavelength / 2 ( I know, too simple) = 21.43m / 2 = 10.7m

Fourth,  to roughly convert m to ft, multiply by 3.3 (easier for me to remember than 3.28), 10.7 x 3.3 = 35.31’.

So a completed ½ wave dipole at 14.0MHz total length is 35.31’ in free space. Each side of the dipole is ½ this length – 17.7’.

Now, we don’t normally put our antennas in free space because the towers would cost too much. 😉 The actual antennas are going to be shorter. How much shorter depends a lot of variables.

Generally, the actual length is about 5% or so shorter. So you can easily see that 10% is 3.5’ so 5% is about 1.75’. The actual difference depends on your particular installation and may even shorter. When you build your antenna, you can just use the free space number and then adjust the length when you test your antenna. Notice that 14.0MHz is the bottom of the 20m band (14.000MHz to 14.350MHz). Higher frequencies have shorter antennas. The length for 14.350MHz is ((300/14.350)/2) x 3.3 = 34.5’. So if you start with the free space number, you can shorten the antenna to any area in the band you want.

When you shorten the antenna, just fold the extra length back on the wire and wrap it back on the wire. This means you can adjust it later if you want to make it longer for a lower frequency.

There is a formula that has been floating around a while that is frequently used to get the length of a ½ wave dipole in feet: 468/f MHz. This would give us 468 / 14.0 = 33.4’. When I have used this formula, the antenna is frequently too short. For the general exam, you are safe if you just use the formula I showed previously. The 468 number came some from empirical testing and the development of a table of correction factors. So if you use the 468 formula to build an actual dipole, consider adding 3% to 5% to ensure the antenna will be long enough. You may have some extra wire but just wrap it back on the antenna and leave it there. It won’t affect the antenna and you will be able to change the frequency if you want to.

Vertical Antennas are usually half the length of a dipole. That is because the ground plane forms a mirror image of the vertical radiator completing the dipole! So, all you need to do to find the approximate length of a vertical radiator is use the same calculations for a dipole then divide it by 2. So the vertical for 14.000MHz would be 35.31’ / 2 ≈ 17.7’.

Did you know the characteristic impedance of a dipole is 72Ω not 50Ω? Did you know the impedance changes as the height above ground changes? Did you know that dipole impedance changes with the configuration of the legs?

Some of the things we will be talking about on the Elmer Net. 😃