Reg,

I don't think there is a 'formula' that is used to predict gain based
on boom length. Several experienced experimenters with boom antennas
have stated that the number of elements varies the gain very little
for a given length, however, given some general design, a number of
elements is typically half the gain of the same design with twice as
many elements and twice the boom length.

In other words, a 6 element beam of some given element spacing has a
(number from the air) gain of 6db. A twelve element version with
twice the boom length will be in the ballpark of 12 db gain.

Given that some 1.5 lambda boom antennas are made for wide bandwidth
and others are fine tuned for maximum gain, one cannot have an
accurate, or ballpark formula for beams that fit all.

One example is a man who was advertising that his j-pole antenna
outperformed a 3 element beam. His comparison was to a 3 element beam
designed for 180 deg beam width. It had two reflectors and one driven
element, but no director. It had a gain of 2.5 db, if I remember
correctly. However, the typical 3 element beam a ham would use is 6-8
db gain and has one reflector, one driven element and one director.
It's beam width is much narrower than the 180 degrees desired by the
man trying to broadcast his bootleg FM BC station.

I hope this helps.

Let me know.

73
--
73 for now
Buck
N4PGW