you might want to just use a 1/4-wave vertical or a dipole
beams are good if you aim them where you want to hear
but if they're not aimed they are worse than a rubber-duck.
the gain in the forward direction is at the expense of other directions.

YOu don't usually use 1/4 verticals for over head passes of the sats.
They
have a big null overhead. Use a horizontal dipole or beter a dipole over
a
reflector. Think about 3/8 wavelength is the best distance for the dipole
over the reflector but need to check that .

I'll buy that - point is though - beam's a no


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