OWA Yagi Antennas are well known and introduced by WA3FET. A nice design for the Region 2 was published by Greg Ordy, W8WWV . It is a 4 el Yagi, where 2 elements form the OWA cell added by a reflector and a director.
I changed W8WWV´s design for and adapted it to the region 1 and 3 needs in the narrowed 40 m Band from 7.0 to 7.2 MHz.
Design goal was a flat SWR curve eleminating the need of antenna tuning units, antenna gain and as I am operating mainly in cw the focus was an improved f/b ratio in the lower portion of the band.
The design shows a lower antenna gain the W8WWV´s design but the only reason is that the simulation results shown are based on a antenna heigth of 20m (abt. 60 ft instead of the 120ft. assumed in W8WWV´s simulations). This design shows a 13.2 dBi firstname.lastname@example.org MHz and an antenna height of 40m. This is about 0.3 dB lower than W8WWV´s design
The simulation is based on 4NEC2 with extended NEC2 kernel and is not veryfied in real world yet!
Here´s what you might get:
The entire Region 1/3 40m band can be covered with a reflection loss of < -27 dB corresponding VSWR < 1:1.1.
The front to back ratio of the W8WWV design peaks impressively at 7.1 MHz. At 7.0 MHz there´s a 20dB f/b and at 7.2 MHz is´t at about 23 f/b. It must be clearly said the both gain and f/b strongly depend on the height of the antenna. As 20m is more common at least for the average ham in europe I optimized for this height. As mentioned before I also emphasized the cw part of the band.
Here´s the vertical antenna diagrams for different frequencies:
The backlobe in the SSB portion of the band is acceptable for me.
f/b @ 7.0 MHz: 29dB
f/b @ 7.1 MHz: 21 dB
f/b @ 7.2 MHz: 17 dB
The antenna gain almost a constant 12 dBi @ 7.0 MHz slightly rising to 12.2 dB @ 7.2 MHz.
The geometrical layout is standard:
The element tapering and the dimensions will be added after confirmation by a prototype which is currently build up.
The shown design is based on a supported 15m boom and 4 fullsize elements (hopefully) without element supports. The calculated weight of the antenna is about 120 kg.
 40m OWA Yagi update (2019) by Greg Ordy, W8WWV: https://www.kkn.net/n6tr/40/K3LR_40mOWAYagiUpdate1.pdf