## About Velocity Factor

**One of the problems in describing a particular concept is that scientists, engineers, and hobbyists (that’s us ham folks) all talk using different terms**.

The term **velocity factor** is one such term. Us hams think of it as how our signals slow down in various wires and cables. It’s a practical concept that we need to consider at times… such as when tuning an antenna for use at specific frequencies.

For example, after last night’s **McARCS **meeting, **Steve, KJ6EIF** was pointing out how much he had to trim the length of his bicycle’s 2M antenna to account for the shrink wrap insulation that held the copper wire against its fiberglass pole. *The difference in length was significant!*

By comparison, engineers think of this same concept in different terms. They think of the **dielectric constant** of specific insulating materials through which electromagnetic fields pass. This is of critical importance in the insulators used in capacitors and coaxial cable.

Finally, scientists and physicists think of it as the **refractive index**, which is based on the **permittivity** and **permeability** of specific materials. This is related to how EM (electromagnetic) waves move in various materials. It’s why light travels slower in air than a vacuum, and why it travels even slower in water or glass.

So, all of these boil down to **the fact that EM waves travel different speeds in different materials**. Based on various tables, I’ve calculated some of the speeds in millions of meters per sec, plus or minus:

**299.8**in a vacuum (maximum speed)**299.7**in air**288**in bare copper wire**285**in ladder line (lead-in cable)**237**in good quality coax**230**in water**200**in ordinary glass**198**in cheap coax**125**in diamond

I should point out that all these numbers are rough… and depend on many other variables… the specifics of the material, temperature, frequency, etc.

I should also note that we’re talking about the **speed of waves here, not the speed of electrons**. While EM waves move extremely fast, the electrons on average move very slow. A good way to understand this difference is to consider your garden hose. If it’s full of water, and you crack open the spigot just a bit, the flow is very slow. But, because the hose is already full of water, you’ll see water flow out the end of the hose immediately.

So, the **velocity factor is the ratio of the speed of waves in a material compared to the maximum speed**, that of a vacuum. Taking the above numbers for good coax, divide 237 by 299.8, and you’ll get **0.79**. That is, the wave in good coax will move 79% of the speed it does in a vacuum. And, that’s why you need to account for this difference in your various antenna designs.

Finally, “the why” of how this happens is a complex topic, and in fact I think it’s very poorly explained in most references that I’ve come across. For us hams, we can use the widely published numbers, and get quite close to the results we need.

Where did you ever get the idea that the speed of a wave in a copper wire (surrounded by air) is 3% slower than c? All of the other cases you mention involve a dielectric SURROUNDING the conductor (where the EM wave is) which certainly does slow down wave propagation by the factor n = sqrt(epsilon_relative). But a copper wire hanging in space? No. No possible rationalle for that. (But surveying the volume of misinformation circulating on the web, I don’t doubt that one could become confused).

– JM

Where did it say 3%? It’s 299.7 for air vs 299.8 for vacuum. That’s more like 0.03% – close to the theoretical 0.06% for relative permittivity of air.

I’m talking about the 3rd line, where it talks about “bare copper wire.” As far as I know, standing waves on a bare copper wire in space will be at the vacuum wavelength. THAT was the issue. The other dielectrics, when surrounding a wire, are given correctly.

Jeff, very good… thanks for clarifying your point. From what I know, air is not the same as a vacuum. Although it’s not very dense compared to most dielectrics, air still has an effect due to the atoms/electrons within it. Sure, it’s not much of an effect, but there is one. Let me know if you find anything that shows otherwise. Thanks.

I think it’s far more complicated. A bare wire in space is like the center conductor of a coax with the shield at infinity. Each infinitesimal piece of wire possesses series inductance plus resistance together with shunt capacitance and conductance. These all together determine a speed for travelling waves. But I could be wrong. w8mqw

Now I am really lost!!! All these years I have been cutting my aluminum poles using the formula eg… 300/434.5 /.95= then /by .5 or .25 , that is 1/2 or 1/4 etc, I should get 0.7268. Now I am confused. Do I now use 300/434.5 *.95 instead… I get 0.65

Magnus