Antenna Modelling and Stacking Distance

Recently as I've started to look at the WA5VJB Cheap Yagis I've started to become more interested in trying out some antenna modelling. In the last couple of days while I've been sick I've spent a bit more time on this and things are starting to make sense – although I have this feeling I've only barely touched the surface. I'm finding it very interesting and it's helping remove some of the mysteries of Yagis while also starting to give me some demonstrations of the theory I've read.
For my experiments I've been using 4nec2. This is a free UI to the publicly released NEC2 engine and is a great piece of software. Like most, at first I was a bit overwhelmed and wondered if I'd bitten off more than I can chew. But after poking around for a bit and reading some tutorials things have started to make sense. I've still got a lot to understand – but will need to wait until I have more time – and don't know why I have to do some things, but it's good fun none the less.
Anyway, one of the first real things I've been playing with is the idea of the simplicity of creating yagis. I've been a bit bothered lately by the lack of recommendations of elements lengths and spacings in the ARRL antenna book. I've found some hints as to recommended spacings, but none on the lengths. I was thinking this was an oversight as surely the spacings had to be perfect as did the lengths…. Well, 4nec2 has easily shown me that's not the case. Indeed you can still see gain increases with just two elements (one driven) the same length and just 1/4wl apart.
Then, using Symbols and the inbuilt optimiser you can then really hone in on spacings and lengths depending on what your design goals are. Really fascinating stuff. I recommend you give it a go and to get you started this tutorial will get you thinking. (Although, that is after you've found your way around 4nec2.)
After playing with that I then wanted to look if I could model the effects of two stacked yagis – using just two basic 2el yagis as described above. Well it proved amazingly easy. So to take it further I thought I'd use the optimiser to find the best spacing for them.
The ARRL Antenna book has a few graphs on the effects of spacing vs. boom length etc etc. But actually seeing 4nec2 model it was very interesting!!
The resulting optimised stack – which ended up at ~2/3wl spacing – can be seen below. Feel free to download and have a play. The patterns you can see is a comparison between just one of thee 2el yagis and then the optimised stacking of two of the 2el yagis – exhibiting the expected ~3dBi gain from stacking.



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