Velocity factor? No, capacitive loading.

Most hams who build dipoles know that 468 is the magic number when it comes to building dipoles. That is to say, the length, in feet, of a half-wave dipole antenna is:

L (ft) = 468 / f (MHz)

That number is about 5% shorter than what you’d expect if you used the formula:

wavelength (in meters) = 300 / frequency (MHz)

Now, I was always told that the reason for this is that the speed of a radio wave in a wire is slower than a radio wave in free space. I bought into this explanation and even included it in my No-Nonsense Technician Class License Study Guide. Walt, K6WRU, disagrees with this.

In his critique of the latest edition of the study guide, he pointed out that a dipole antenna is not shorter because of the velocity factor of the wire, but instead, “It is caused by capacitive loading due to the proximity to ground. It varies with height, which is a big clue about the capacitive loading.” You can find a more complete explanation by reading this StackExchange item.

This is not to say that velocity factor isn’t a real phenomenon, just that it isn’t a factor when cutting a length of wire for use in a dipole. A single conductor doesn’t have this distributed inductance and capacitance—at least not to the extent that it would cause a 5% change in the velocity factor. Coaxial cable does have a velocity factor less than 1, and that velocity factor is dependent the cable’s distributed inductance and capacitance, and that, in turn, is dependent on the cable’s dielectric.

Comments

  1. Actually a large part of the 5% is the end effect and not the capacitive loading of the antenna due to surrounding enviroment (wich only becomes significant below 1 to 0.5 wavelength). You can check this very easily by testing the resonance of a dipole on the 3rd harmonic, you will see that in reality it will not be at exactly 3 times the fundamental but a bit higher. This happens because at the 3rd harmonic the antenna looks electrically like 3 dipoles in series, out of wich only 2 ends are open and suffer the end effect. If it were a distributed ground capacity shifting the resonance, the antenna would resonate at exactly 3 times the fundamental.

  2. Walt is correct. Velocity factor is more a consideration in insulated transmission systems like coax – important when calculating lengths of matching sections at different frequencies.

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