Is there a general rule as to the optimum way copper should be
distributed on a longwire antenna for maximum propagation? E.g.,
should the first half be heavier gauge than the second half? How much
heavier?

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There is only one general rule. The wire MUST be thick enough to withstand
the longitudinal tension due to its own weight and the amount of sag in the
middle. Otherwise propagation will suddenly cease.


Tapered copper wire, to match diameter to the current distribution along
antenna wires (one band only), is available only by special order for space
exploration and defence purposes. If it WAS available, for a given amount
of copper, the improvement in signal strength would amount to less than
1/140th of an S-unit. The same improvement could be achieved with an
enormous cost saving just by changing wire gauge from 18 to 14 awg.
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Reg, G4FGQ