But only if we are CowBoys (CB) :-)

As far as I can see, the radius of a capacity hat must be
the difference between the vertical's length and the
1/4 wave length of the desired band?

AIUI, the waves progressing in all directions in the capacity
hat cancel each other's fields resulting in no radiation, but
the transit time to the edge of the hat and back act as the
required element extension.