I had an old broken 20 foot fishing pole that only had 16 feet of length so I decided to see if I could make an effective half size 40 meter antenna with it. Here is what I did. I used a capacitive hat to increase the radiation resistance of the antenna considerably. There are 8- 15 foot radials suspended a little less than a foot above ground. Finally, I made a small loading coil to tune the antenna up to the center of the band (7.100 MHz) for CW. I first tested a full size vertical to optimize the ground plane. By suspending the radials by only a few inches above ground, significant improvement was achieved . With 8 half size radials 10 inches above ground (compared to 4 on the ground), the measured loss went from about 20 ohms to 4 ohms. My loading coil has a measured Q at 7Mhz of about 300…with about 1 ohm of loss. The form was printed on my 3D printer out of HIPS..which is a low loss RF material. So my total system loss was about 5 ohms. With the HAT top load, the 17 foot antenna had a total impedance of 20 ohms. This means I had a total system loss of only 1.25 db…which is not bad. the full size antenna had a loss of about .5 db … so really the difference is negligible. Finally I matched the whole antenna to 50 ohms with a little L network connected at the base. I like to use crimp style bullet connectors for all wire connections because they provide quick disconnect and you can field repair(crimp) without need to solder anything(nice for portable setups).
I use it for QRP work on CW at about 1.1 watts. The antenna is a solid performer and it is very portable and easy to breakdown/setup. I can hear my signal on the many of the web based SDRs around the country. and have made numerous casual QSOs with it. Six or Seven radials work well also..you start seeing some more loss when you go to four radials but it is still usable even then.
View of Top Load( 2 -8 inch strips of thin aluminum)
View of loading coil and base assembly
The Loading coil
Unmatched Antenna Z at Resonance
The Final Matched Antenna Z
Circuit Salad 
Nice antenna, thank you! I’m going to experiment with shortened vertical antennas for 80m band too, however I don’t know a method to measure ground losses. Could you please tell how you did these measurements? 73 de R2AUK
what I did was create a full size antenna at the operational frequency with same ground plane layout and measured the Z…noting anything greater than approximately 36 ohm would be losses. Then I calculated the expected Z of the short antenna and then measured actual Z of the short antenna…the losses matched in both cases…giving me a reliable value