EZNEC can be used to verify the relationship of conductor
diameter to velocity factor. Once the conductor diameter
exceeds a certain limit, the standing wave current at the
ends of that conductor undergo a 180 degree phase change,
indicating a longer length than resonance.

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A cylinder has a flat circular end. Antenna wires and rods are
cylinders. You should be reminded that the true length of the antenna
is its straight length PLUS the radius of the flat circular end.
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Reg.