The National Electrical Code specifies wire size for antennas (I realize the US 
NEC does not
apply to ON land), though the concern in the NEC is mostly mechanical - i.e. it 
will stay up, 
not fall and give someone an RF burn or electrical shock.
The NEC recognizes 3 categories:
Receive only antenna up to 35 feet: #18 hard drawn copper or copper clad steel.
Antenna with under 150 feet long span: #14 "
Antenna over 150 feet: #12                 "
While I have put antennas that don't meet these guidelines, they also tended to 
break within
a few years.  
>From the point of view of losses, even #24 would only take 5 or 10% off
efficiency for an 80m dipole.  Legal limit power in a 50 ohm antenna would be 
under 6 amps
which would require #18 to #20 in an extension cord, but a wire in free air has 
less heat
problems than bundled or in conduit so somewhat smaller wire would still stay 
cool enough.
        Darrel AK6I
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