Reg Edwards wrote:
"Ian White GM3SEK" wrote
There isn't really "an" equation for gain versus boom length,
because
boom length is only an indicator of the potentially achievable gain.
But
nothing "makes" a yagi deliver any particular gain figure.
=======================================
Ian,
Yes, there must be such an equation. Indeed, there must be a dozen of
them.
What I was trying to say was that there is not any single equation
relating gain to boom length. In the normal sense of the word
"equation", there is no equation at all.
I am aware that there are a multitude of things which are, or can be
optimised in the design of Yagis.
I am not interested in how gain can be maximised but what it has
actually turned out to be in practice over the years.
Ah, then you don't really want equations at all - you want historical
anecdotes.
Years ago, I used to collect gain data for long yagis... or at least,
such verifiable data as were available at the time... and plotted all
the dBd figures on the same piece of graph paper against log(boom
length).
The result was a scatter diagram showing a general increase of gain with
boom length. For well-designed families of long yagis (eg the DL6WU
series) it was possible to draw a good straight line; but there were
always a few yagis above that line, and many poorer designs below it.
It is a statistical function of the number of elements or of boom
length - which are much the same as each other.
It isn't "statistical" in any strict sense of that word. It's just a
collection of various isolated individual attempts to make a decent
yagi, and all the data include significant measurement errors.
It is just a historical fact which all experienced designers must have
a good idea of but, it seems, are reluctant to divulge.
Largely because it's all much less meaningful than you imagine.
You probably have a good idea yourself. What is it?
This was before the Internet and before computer modelling, so all I
have is an old piece of graph paper. I stopped adding to it in about
1985, when computer modelling became capable of far higher accuracy than
amateur measurements.
If anyone wants to try a modern correlation, there's lots of data in
the VE7BQH collection:
http://www.ifwtech.co.uk/g3sek/diy-yagi/ve7bqh.htm
VE7BQH's data are all for yagis that might be useful for VHF/UHF
moonbounce, so boom lengths start at 1.8wl and range up to 8wl. (This
turns out to be no use to Reg - see later - but it's an interesting
topic in its own right.)
If anyone is interested in doing it, use the L(WL) and GAIN(dBd)
columns. With Excel, it should take all of ten minutes to get the data
from the web page and into a "scatter X-Y" graph.
All of these modern long yagis are the results of computer optimization,
by people who already know what other designs are achieving. This tends
to make all the results bunch closely around the trend-line for the best
available performance. Unlike my old plot of stone-age yagis, very poor
designs don't make it into VE7BQH's table at all.
Back to Reg:
For 2, 3, 4 .... N elements?
Ball park accuracy is too good for it.
For short yagis, why not use the figures in N6BV's HFTA program? (ARRL
Antenna Handbook)
Antenna dBi Boom length @ 14MHz (ft)
Dipole 2.15 -
2-Ele. 5.5 8
3-Ele. 7.0 16
4-Ele. 8.5 26
5-Ele. 9.5 40
6-Ele. 11.0 60
8-Ele. 12.0 80
That is a fair set of "representative" figures.
I would like to include it in the notes to a practical, general
purpose, computer program which estimates received signal strength
from Tx power and ionospheric radio path distance. It could be titled
"How to use S-meters for Novices". ;o)
So - finally - it all comes out. If the context is "ionospheric", you're
not interested in long yagis at all. Why didn't you say so in the first
place?
--
73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek