Ignore the physical length of the folded dipole you ended up with. Electrically, it thinks it's a half wave. It's physically short because its "fat" in terms of a wavelength.
Calculate your relector and director lengths by the "traditional" method/s, NOT in proportion to the physical size of the folded dipole.
The old rule-of-thumb with a 3-element Yagi is to make the director about 3-4% shorter than a half wavelength at the design frequency, and the reflector about 5% longer than a half wavelength at the design frequency. You may have to shorten them a little because 20mm tube is a bit "fat" at 50 MHz. Old ARRL Antenna books had a table giving shortening figures for different diameter elements, if I recall correctly.
Don't be concerned if your folded dipole turns out to be a little shorter than the director !
I've been through this exercise before with commercial yagis built from 30 mm diameter tubing. Good luck with it.
Just remember that when you add the reflector and director to the setup, your SWR match will change on the folded dipole - in fact, if it doesn't change to some extent, then the director and reflector are not doing their job properly by mutual coupling to the driven element.
Expect the feed point impedance to drop lower when you add the parasitic elements.
Regardless of what you do with the director and reflector, with a three element yagi, you are not going to get the same impedance as you started with. I suspect it will probably about half the Z with a bit of reactance thrown in for good measure. If you can then measure the R + jX you can then design a matching section.
As mentioned, mutual coupling from the director and reflector will usually lower the DE impedance in a yagi ... however, if you are prepared to compromise forward gain by 2dB or so, a 3 element yagi can be designed to retain the impedance of your existing driven element if that is what is important.
As an example, the 3 element yagi depicted below has a 50 ohm feedpoint impedance with a split dipole. A folded dipole in this design should present 200ohms which can be connected to via a 4:1 half-wave coax balun to get a good match to 50 ohm coax cable.
Calculations and if I may use the term, other forms of 'guessing' will not cut it and give you the best results. What you will need to do is enter the dimensions into an optimisation tool. However, while there are some good free optimisation tools around today, none are very accurate with sharp bends and turns within the elements. The only real way you will acheive accurate results is by using an optimisation tool using the latest NEC4.1 calculation engine but this will cost you $500.00 without any software to put it in!
4nec2 is a free package (Google search) which comes with the free (and 30 year old) NEC2 calculation engine. better for this task would be MMana which uses the miniNEC calculation engines which is slightly better with loops providing your segmentation density is high. The third option is for you to give me the dimensions and sizes of the loops and the boom length you have and I will model it for you.
One point that was started above is that of the feedpoint impedance. I would need to know what you want that to be. It is not out of the question for this to end up at 50Ohm if you so wish it.
Not cut it? Heck, what did we all do before software was available? Trial & error, use a calculator, suck it and see. And the world still communicated! Half the fun in radio I find is experimenting, not sitting in front of a PC using the fruits of someone elses' intellect.
Good on Justin for having a go and he should be encouraged, not told that this method will not "cut it".
Oh dear, Richard could you not send me a photo of your car? I would love to see what a person drives that will not take advantage of 'the fruits of someone else's intelect'
A car is one thing but antennas entirely another. My point was simply that there is nothing wrong with the old fashioned pre-software approach to learning & design. It works- see Roger's post on the subject. I guess when I was 14 I didn't understand how the formula for a dipole 468/f(MHz) was derived but at least I started by building an antenna and finding out if it worked. Then I added a few extra elements and turned it in to a yagi... and all pre-software. They worked.
Software is great & I use it everyday but when it comes to developing a practical understanding of what makes a good antenna, nothing beats experimenting with real antennas.
Yes I do agree with you entirely and perhaps my post came across in the wrong way. A Yagi made of folded dipoles is very difficult to optimise at the best of times. In the days of hand trimming, 3 element dipole arrays (not folded) were about the maximum number of elements you could hope to optimise anywhere near efficiently (hence the early EME stacks consisting multiple of 3el Yagi arrays). While you could get a large beam to 'work' so can a tree be made to radiate in some degree.
My offer of hours of my time was to assist Justin in getting the best from the materials he has. He still has to build the antenna and obviously has an understanding of how they work from what has been stated already in the above posts.
Antennas are the one thing a Radio Ham can build himself and in so doing, can create something better than can be purchased commercially if time, the right tools and levels of knowledge are gained in order to achieve the results, something that has not be achievable for some time in the World the radio itself. Sadly we live in an age where most hams have ATU's in their shack 'can load up anything' and anything 'works' but until the optimum is achieved, we really do not know what we are missing.
Is this hobby not about teaching as well as learning?
Teaching comes in many forms. One of the most basic is to encourage experimentation. I guess I'm a bit old fashioned & like to think that one of the best ways to learn is experience, and antennas are one of the few items left that don't cost much to build so even a school child can experiment without it costing the earth, or potentially doing them harm. I think software is great for validation & for where experimentation isn't practical (like cars for most of us). 6m is a great band for experimental antennas- smallish, cheap, and with potentially excellent performance.
The first time I used a folded dipole was when I was 18 in a 15 element 2m yagi based on the ARRL Handbook dimensions of the time. I didn't have the necessary tools to make the folded dipole so a friend (who owned an antenna company!) made it for me but then left it to me to make the yagi work. I worked ZL a few times so I guess it worked- but then I found the boom was too light and the damn thing sagged! Software wouldn't necessarily teach me that- practical experience. Was it optimised? Probably not, but I learnt something. Having someone else offer to do it for you, as kind as that is, may not have the same degree of education though we all have to collaborate to move forward.
I don't see anything wrong with either method - each to their own in amateur radio, but the antennas I've built so far were easier to design in software, then go out and buy and cut the aluminium, and end up with something that works well first time with minimal adjustment. From my point of view, the tools are there, so why not use them? I don't know what the costs would have been in wasted aluminium for a 'suck it and see' method of experimentation, but I take my hat off to those that build antennas by this method and end up with something efficient and workable.
I am all for AR experimentation but you also have to be realistic. If you just need a simple beam for local contacts or intra-VK "Es" then a "suck and see" or "play and try" approach will be ok. Most of my early 6m yagis were based on Ch O TV antennas modified with the required formulas from the handbook, a tape measure, and a pair of snips. None of these antennas could be termed "optimized" but they were used for hundreds of contacts.
On the other hand, if your goal is working long-haul DX, and the experimental part is exploring modes of propagation along various paths, then you are going to need at least a 5 element yagi that has been optimised to squeeze out every bit of gain and directivity. In that situation you would be crazy not to make use of the software available, or use one of the excellent designs obtainable on the web.
Both "play and try", and software assisted antenna designing both have their place, both are educational, and both have an experimental aspect - horses for courses!
