A very short antenna had about the same power gain and radiation pattern as a full half-wave antenna.
“My first interest in the short vertical antenna began when my thesis advisor at Harvard, Professor R.W.P. King, developed the full theory of the short antenna. In it he disclosed that a very short antenna had about the same power gain and radiation pattern as a full half-wave antenna. The main difference was that the resistive component, the radiation resistance, was very small in comparison. In turn, the short antenna has a very high capacitive reactance, which has to be cancelled by various loading techniques.
The theoretical results show that the power gain (when compared to an isotropic radiator) for a very short antenna, even one that is less than 1 foot high on 40 meters, is 1.5. This increases slowly to 1.513 for an 11-foot vertical. These gains are to be compared to about 1.62 for a resonant 1/4-wave vertical. This difference amounts to less than 0.4 dB or 0.07 S unit, based on 6 dB per S unit.
Base loading,[ as shown in Figure 2-3 above ], yields the lowest value. Top hat loading yielded the largest value of radiation resistance for a particular height. A top hat is also considered the most low-Q loading element. The reduction in height due to top hat loading (with a conducting wire around the perimeter) is approximately equal to twice the diameter of the top hat. A four-spoked wheel approximates, to a good degree, a solid disk. Doubling to eight spokes only improves the loading by about 9 per cent. Thus, a few radials on the top of a vertical, which are electrically connected by a perimeter conductor, are very effective.
The data were obtained by essentially cancelling out the reactance and measuring the resistive value with a simple impedance bridge. Because I used an extensive ground system together with base loading coils with Qs approaching 900, the resistance measured was actually that of the antenna itself. At the radial point the input resistance approaches the theoretical value of 35 ohms which strongly indicates low earth loss and reliable data.”
Summarized from a book by Dr. Jerry Sevick, The Short Vertical Antenna and Ground Radial, CQ Communications, 2003.
Fact checking Dr. Sevick there is a book published by ARRL written by Robert J. Zavrel, Jr. called Antenna Physics: An Introduction. From pp B.2: “A short vertical’s value will be about 6 ohms for a 1/8 wave physical height. For a perfectly top loaded 1/8 wave vertical, value becomes about 24 ohms…a fourfold increase in radiation resistance when compared to an unloaded simple vertical of the same physical height” These values agree very closely with those in Figure 2-3 above.
The above excerpts have been field tested in a 160 meter vertical antenna constructed in 2018. This vertical has been very successful and is still in use today. It has eight radials, each 100 ft long made of 4-ft wide welded wire fencing laid flat on the ground. The vertical element is made of 43 ft tall aluminum tubing tapered to average 1.5 inches in diameter. The top hat is made up from 6 102″ CB whip antennas with hookup wire connecting the tips.
Inside the box is a matching coil which is tapped with a coax feedline at the 50 ohm point. This setup is good up to about 300 watts. It needs to be hardened before it will get up the legal limit.