# Figuring the length of a radial by the diameter

#### digitalanalog

##### Member
Plenty of wave length calculators on-line.
so I can enter 45.000MHz and I can get the 1/4, 1/2, 5/8, 3/4 and full wave length of a radial in inches, feet, meters.
but I can not find a calulator that you enter the diameter of the radial.
The diameter of the radial will determine the length of the radial.

I have downloaded a bunch and also used a bunch on-line but none seem to have this function.

IE: Example.
45.000 MHz @ 1/4 wave length = 65.5 inches (aprox)
45.000 MHz @ 5/8 wave length = 164 inches (aprox)

so if the radial is 3/8 diameter for 45.000 MHz at 1/4 wave length, then what is the langth of the radial 65.5 inches ?
if the radial is 1/2 diameter for 45.000 MHz at 1/4 wave length.......I can not image the length being the same as the 3/8 diameter radial.

I cannot locate any calculators that allow you to enter the radial element diameter in to the calculator.

any help would be greatly appreciated.
not looking for a physics lesson, just some type of simple calculation.

#### majoco

##### Member
Where did you get this gem of information from.....
The diameter of the radial will determine the length of the radial.
... or are we getting two things mixed up here.

Coaxial cable has a 'velocity factor' where the speed of the wave down the cable is slowed by the various physical structures of the cable...
From.....
This slowing effect is almost entirely caused by the dielectric material; in coaxial cables, the insulation between the shield and the center conductor. For a closed-cell foam dielectric, for example, the VOP may approach 90%, meaning that a signal will travel at 90% of the speed of light. For solid Teflon®, the VOP is typically about 70%.
.....where "VOP" is the velocity of propagation. So the physical size of the cable will affect the length if you are looking for a specific phase shift along the cable.

But there are some statements, especially in Wiki, that are designed to confuse - such as...

To function as a ground plane, the conducting surface must be at least a quarter of the wavelength (λ/4) of the radio waves in diameter.
.....

Taken without reading the rest of the text, this is confusing but reading between the lines they are not talking about radial rods or wires but a flat or conical metal plate and IMHO it should be 1/4 wave radius, not diameter. Generally speaking, groundplane radials are often about 12% longer than the 1/4 wavelength.

But with a lot more browsing, either on the net or a selection of manuals I cannot find any reference to the wavelength of a rod changing with its diameter. The diameter of a radiating element will affect the bandwidth, generally lowering the resonant frequency as the diameter increases but by such a very small percentage of the original as to be imperceptible until you start talking about birdcage dipoles and things like that.

I'm prepared to admit that I'm wrong so let's hear about it!

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#### dlwtrunked

##### Member
...

But with a lot more browsing, either on the net or a selection of manuals I cannot find any reference to the wavelength of a rod changing with its diameter. The diameter of a radiating element will affect the bandwidth, generally lowering the resonant frequency as the diameter increases but by such a very small percentage of the original as to be imperceptible.
...
The diameter of a radiating element will affect the bandwidth and significantly if the elements have enough diameter. That is used to make antennas with a wide bandwidth--for example, the vertical radial in https://www.sirio.store/index.php?main_page=product_info&cPath=84&products_id=230 . This is not generally used in beam antenna due to weight and wind load difficulties.

#### prcguy

##### Member
I've had some Yagi design software that included element diameter and would recalculate the length based on diameter. Not sure where that software is at the moment. For small changes in diameter like going from 1/8" to 1/4" the change in element length is not that significant. Going from 1/8" to 1" dia will make a noticeable difference in element length.

#### digitalanalog

##### Member
I've had some Yagi design software that included element diameter and would recalculate the length based on diameter. Not sure where that software is at the moment. For small changes in diameter like going from 1/8" to 1/4" the change in element length is not that significant. Going from 1/8" to 1" dia will make a noticeable difference in element length.
Yes, this exactly what I am talking about.
I will look at Yagi designers to try and locate one that has that feature.
Thank You.

#### jonwienke

The effect of diameter on optimal length is small, less than 10%. For dipole and ground plane antennas, it's typically less than 2%. Unless you're making really fat elements, it's negligible.

#### Ubbe

##### Member
Logically a thicker element would have more capacitance and probably inductance that will lower its frequency. The thicker element will have resonance over a wider frequency range. A log periodic antenna will then have more elements that resonance at a frequency and gives more gain. A yagi or dipole will only have a larger frequency range.

/Ubbe