I have no disputes with your math, but your starting figures are in error...
I am curious where you got these numbers. They seem a bit low to me. The dielectric constant of air is essentially 1.0, and there isn't enough resistance in stainless steel to cause that much of a drop in velocity factor on its own.
359 got to this one first, not that it will make that much of a difference in overall calculations, but channel 20 is not the middle frequency of the CB band, although a lot of people treat it like it is. Channel 19 is. The reason is there are five skipped "channles" along the lower frequency range of the CB band... The gaps between some frequencies are larger than the others, almost like they skipped some frequencies in the process. These gaps occur between channels 3 and 4, 7 and 8, 11 and 12, 15 and 16, and 19 and 20. These shift the center frequency some... 359 already did the math... Those gaps are from older RC (radio controlled) channels, although I think they are still allowed for RC use I don't think they are typically used for that anymore.
And something from later...
Actually you are missing the key item that affects the antennas readings on a vehicle, ground losses. It is possible to have such an antenna tuned to resonance on the car and still get a 1:1 SWR, the reason is that the ground losses from the inefficient ground system that is every vehicle in existance adds to the resistive part of impedance, so if that impedance is low like it naturally is for this type of antenna, ground losses will appear to get you closer to an SWR match, but this comes at the expense of performance...
Also, just as a note, tuning an antenna with a different natural impedance from the feedline you are using off of resonance will never net you a perfect 1:1 SWR to that feedline, but it can actually lower the SWR to some extent depending on the antenna, also at the cost of performance... This does not apply if you are using some form of matching network for the antenna.
The DB
bare in mind I'm from uk where frequencies don't have skips, so yeah a minor oversight. not to mention one most of your fellow Americans make too.
I haven't used midband for 35 years due to qrm from you guys and Italians/Spanish running mega power and mega splatter on Antiquated Modulation.
I have always found .98-.97 to be about right when building antennas, as opposed to the 95% quoted in many books and used on most antenna calculators, again its still minor, and doesn't change the fact the reason why 102" whips are too short.
I'm well aware of the alpha channels and why they were restricted and also why 23 comes after 24 and 25 frequency wise as they filled in the 30 Khz jump between 22 and 23 when they added the extra 17 channels to the original 23. I've been on cb since 78, i used fcc gear for the first year or so, a president ar7 to be precise.
velocity factor of air varies with, purity, altitude, weather, and other things too, unless you have 100% pure air which thanks to fannies at Chernobyl and your government detonating high altitude nuclear bombs, amongst many other things ain't gonna be the case, as W5LZ says its a ballpark figure , not often I agree with Doc. But was the reason i suggested 108" whips to tune out all these variable quantities.
where do you get dielectric constant of air is 1.0 ? Google it, I think you'll find others differ.
Even more important what makes you think its resistance that causes velocity factor, i think you'll find its more due to what surrounds conductor than what conductor is made off or how conductive it is, otherwise all coax being made from copper would have the same velocity factor, it doesn't, the dielectric dictates the velocity factor not the conductor, the more air it contains the higher the figure, but none are 1 or 100%, fibre optic cables have velocity factors too, but they are pretty shit at conducting electricity.
I never forgot to mention the ground losses, I chose not too, they are so unpredictable and depending on mounting location can even vary on different parts of the same vehicle. It wasn't worth mentioning as most people fail to grasp it anyway. I'm glad you do.
Just the same as you choose not to model lossy coils as its most likely beyond the capability of your modeling software's limitations. I ain't seen an antenna modelled yet that had the coil figured in. All I see are straight wires, not many of those in coils.
Do you model real ground conditions or just believe antennas hang in mid air, cause i ain't seeing masts or coax modelled either. Would be great if antennas behaved in the REAL world as they do in cyber space, but sadly they don't.
How do you know the guy who wrote the software hasn't fucked up programming it, because most of it looks seriously flawed to me. Which is why I don't bother my arse with it. Blind faith is very common, look at all the religious fuckwits in the world that follow without question and believe a wee man in the sky is looking down on their every move, don't mean they ain't deluded like those who think an A99 has more gain than a 3 element beam, blind faith again.
you say you can never match to 1.0:1 with tuning in reactance, tell a swr meter that, not to mention the fact not all coax is actually 50 ohms, many are 51 or 52 ohms and other values, also you can't be assured an antenna analyser is 100% accurate, especially Mississippi's finest junk ones. There's a small thing called manufacturing tolerance that ensures that. So it really depends how low your swr was to begin with.
We could nitpick all day but bottom line is, anyone buying a 102" will struggle to tune it, that was the main point I was trying to convey, so outwith all these minor niggles,
is there anything wrong with my Arithmetic,
Because I've got a very high grade in it in what once was the best education system in the world? I was tested in it at Glasgow university at 11 years of age and got an A, 5 years later when it counted at the exams, I sat in the hall for 10 minutes for 100 questions and got an A again, just to prove it wasn't a fluke the first time,
I got to meet Johny Ball a highly rated mathematician at Glasgow Uni, Zoe Ball's dad, the same Zoe Ball married to Norman Cook (Fatboy Slim) and he was amazed at my mental Arithmetic, which in those days my brain wasn't as fried from weed and I didn't trust calculators, as batteries run low and they are erratic when that happens.
I also proved a teacher wrong at secondary school who dragged me to head of maths dept, as I was apparently insolent because I demanded 100/100 instead of the 99/100 she gave me from marking from a book, he got her answer the first time because he used the formula in the book the same as she did, when i pointed out the book formula was wrong he done it my way and got my answer, did it a third time and got my answer, then told her there is a big difference between insolence and confidence, He made her apologise to me in front of 30 odd 16 year olds.
I was 13 years old and proved two teachers wrong, one of whom i admire greatly because he listened to reason and was open minded enough to realise a book might just be wrong, and a 13 year old might just be smarter than them both.
Just the same as Lou Franklin got it wrong in understanding and repairing cb radios, as he used the formula for 95% (which was commonly used for making wire antennas) velocity factor instead of 100%, that's why his length was 5% out, his proof reader missed it, i didn't, i also didn't miss his claim an Avanti Moonraker has a driven quad element when in fact it is driven by gamma matched Yagi element.
I question everything, especially where figures are concerned.
JAZZ 73
3.28 x Metres gives feet, 12 x feet gives inches.
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