Vertical doublet / dipole - on 10m an EDZ (2x 5/8) with 4.5 dBi gain, 30m its just under a 1/2 wave dipole, and 40m a little on the short side but will work ok.
Started off with the idea of building an elevated vertical with radials to cover the upper HF bands, using an Icom AH-4 ATU at the feed-point to match it.
A 5/8 wave vertical for 10m is around 20 ft long, a 1/4 wave on 30m is around .. 23 ft. This would cover the upper HF bands. I like to model antennas before I build them for the experience and to get an idea of what to expect.
Modeling an elevated vertical trying different length radials didn't look so good, high angle lobes would form on some bands and the gain was mediocre at best. Running radials everywhere was not entirely convenient either.
I searched around for other possibilities, ZS6AAA designed a Compact Quad Multi Band HF Antenna which fits on a 40 ft Spiderbeam fiberglass pole that covers 40m through 10m. In my case easier said than done, needs to be guyed at several points.
Back to verticals, I thought delete the radials and center feed it? How long can I make it before the lobes go silly on 10m - the highest band? 40 ft. I was quite amazed at what I had discovered - only to find it was in-fact nothing new. However..
On 10m it's a vertical EDZ (Extended Double Zepp) or a 2 x 5/8 with 4.5 dBi gain at 10 degrees, and on 30 m it's just shy of a 1/2 wave dipole and 0.82 dBi with lowest point 10 ft above average ground.
These patterns are much nicer than an elevated 1/4 or 5/8 wave ground plane antennas.
Model file: Vertical Doublet 4010.
I have a 40ft Spiderbeam pole which I mounted on the 2nd level rear deck placing the bottom 10ft above ground. A surplus ZS6BKW I shortened the legs down to 20ft and keept the 40ft 450 ohm window line section as is, window line leads away at around 45 degree angle across to a roof eave where I mounted a short piece of PVC pipe with small section removed for the window line to fit over and rest on keeping it above the roof.
The first version (based on https://www.hamoperator.com/HF/AH-4_Design_and_Operation.pdf) I had the window line split between the output and ground terminal of the AH-4 tuner. CM chokes are placed on the coax and control cable. I used 3/4" mix 31 snap ons with enough turns of cable for a snug fit.
I later found using a 1:1 ATU balun between the AH-4 and balanced line worked a lot better. The AH-4 got better matches, and an RFI problem on 17m went away. The ATU balun was from Balun Designs. The CM chokes on the coax and control cable are still a good idea and were left in place in as well.
Made a 50ft control cable extension using quality CAT5e joining the pairs to make a 4 wire cable. I put a CAT5e tail with the RJ-45 left on (cut a patch cable in half) the tuner end and the end of the supplied control cable, lets me change the length by using CAT5 couplers and different length cable in-between.
I put a 3 Meg Ω 5W metal film resistor across the window line to bleed off static charge buildup via ground lug which is common to the coax shield in the tuner, coax shield is grounded where feed lines enter the house - make sure you meet NEC / electrical code (Grounding and Bonding - ARRL is a good book for North America and in general / and where applicable - consult professionals as needed).
Pictures, taken before I added the 1:1 balun.
The AH-4 tunes all bands 80m to 6m no problem, but I would question the efficiency of this system below 40m.
Comparing it with my 80m OCFD at 55ft from my location near Seattle WA, the vertical does surprisingly well.
SSB: On 40m the OCFD is always better which is expected. On 20m and up the OCFD will pull out the weak signals a little better. Local nets on 10m where the vertical up-to 9 S-units better in some cases, I'm assuming others are using verticals on 10m.
On 6m the vertical has high angle lobes but works ok on local 6m FM repeaters, for better performance we could add 6m traps 5/8 wavelength (on 6m) down each leg which would make it a vertical EDZ on this band. Keeping in mind to account for the loading the traps add on HF, it may need to be shortened a little to keep 10m in check.
FT8: Running two instances of WSJT-X with two radios (IC-7100 on vertical, IC-7300 on OCFD) with one reporting my callsign with /P to make it easy to tell them apart on pskreporter and watching FT8 signals on 20m through 15m the OCFD hears around 20% more stations. There are a few cases both on SSB and FT8 where the vertical does better, likely in directions where the OCFD has a null. I should probably repeat the tests with the antennas swapped to see how much of that 20% is attributed to the IC-7300's SDR receiver..
Horizontal antennas 1/2 wavelength or more high are hard to beat due to the gain from ground reflections, this vertical is a close 2nd to the OCFD on the upper bands.
A permanent install would need to by guyed (using non conductive line) at the feed point with the window line supported / suspended from one - when the wind catches the window line things things start swinging and wobbling around more than I'd like.
Overall I'm quite pleased with this vertical, it's simple, light weight, no radials, and the results have surprised. Down sides are you need a good remote tuner, and a means to lead the window line away at 45 degree angle or higher if possible. In my case neither of these were an issue.
I can now also see why feeding balanced antennas with 450 ohm line to a good tuner is popular, it works well! Personally I've had little experience with this way of doing things.
A shorter version could also be used covering 17m to 6m, at 24 ft, it would be an EDZ on 6m, and just under 1/2 wave on 17m.
Related info:
