Are you referring to the 1/4 wave matching stub? This is to allow a low impedance feed point since an end fed 1/2 wave antenna presents a very high impedance (theoretically infinite). The zeppelin antennas accomplish this with a 1/4 section of feed line. The theory is the same just the scale is different.I've never understood what the bit sticking out of the bottom is for. The original Jpole was devised in the early 1900's to be hauled behind an airship and therefore had no mounting pole - this was one of the criteria to be overcome and the Jpole did it. Now it seems to have sprouted a mounting which is unnecessary.
and F.G. Rayer's original article for the "Slim Jim" - no conductive mounting pieces. My slim jim is constructed around a 32mm PVC pipe with 3mm ali rod - works a treat.
No. No antenna design will give you a 9-degree vertical radiation pattern, omni horizontal radiation pattern, and 80MHz of bandwidth withreasonably low SWR.
Pick any two.