On Thursday, January 31, 2013 11:52:10 PM UTC-6, Michiel Kappeyne wrote:

I want to build a Slim Jim antenna for receiving airband (118-136MHz)

out of 3/8" or 1/2" soft copper tubing.

I'm not really a fan of those type of antennas. You would
likely be as well off to just make a simple 1/4 ground plane
with sloping radials. Easy match to coax, and super easy to
build. Can be as simple as a SO-239 connector with 5 stiff
wires attached.
All the bandwidth issues, etc are not worth worrying about
for receiving. You will likely never hear the difference
between a vertical length of wire, vs a fat copper tube
for receiving air band.
Another issue with most J-poles, and other antennas of it's
ilk are the total lack of decoupling from the feed line.
There is no point in worrying about extra gain or bandwidth,
when the design of the antenna does not take decoupling of
the feed line into consideration. The lack of decoupling will
skew the pattern up off the horizon, and make any extra gain
from a longer element length apply only to higher angles.
This could be good for airplanes in flight, but bad for
tower comms.
The decoupling of a 1/4 ground plane is not perfect, but it's
generally a good bit better than the usual J pole.
And it can be improved by adding more radials, or an extra
set of radials 1/4 wave below the feed.

Myself, I would just build a simple SO-239 ground plane,
"google for illustrations", hang up from the ceiling with
a short piece of fishing line and a tack, and be done with it.
It will likely function as well as most of the J pole designs,
with a lot less work involved. And it's a direct match to
coax, which means no matching losses. The sloping radial
version is a better match, than one with the radials at
90 degrees from the vertical element. And the gain of the
sloping radial ground plane will usually be within .3 db
of a 1/2 wave vertical. And this assumes the 1/2 wave is
properly decoupled. Most are not.. So it would not be totally
unusual to see the simple ground plane actually do better
in many cases.
If one is going to use a 1/2 wave vertical for VHF, one
needs to take decoupling of the feed line into consideration.
Most don't it seems..