Almost 1%! Holy moly!

You're correct that the distribution is only approximately triangular.
But since a difference between a full quarter sine wave and a true
triangular distribution results in less than a 0.5 dB difference in
field strength, a 1% difference between a true triangular distribution
and the end of a sine wave will make a difference in gain, efficiency,
or feedpoint impedance that would be entirely negligible and in fact
impossible to measure. For that matter, the current distribution on a
wire of finite diameter isn't really a sine wave anyway, but a close
approximation (although very possibly not within 1%). So the current
distribution on a short antenna is triangular for any practical purpose.

Roy Lewallen, W7EL

Cecil Moore wrote:

Roy Lewallen wrote:

This is indeed an interesting result, even though it's small. As a
dipole or monopole gets shorter than a resonant length, the current
distribution changes from sinusoidal to triangular.


Actually, it just moves to a straighter portion of the sinusoidal
curve. The cosine curve from 75 degrees to 90 degrees does resemble
a triangle but it is not a straight line. Assuming a triangle from
75 deg to 90 deg is a simplified shortcut that introduces almost a
1% error at 82.5 deg.