Sometimes, the heavens do align such that everything becomes possible.
First stroke of luck this week was finding someone willing to tell me about their WSPR system. G4HSB told me about his 2-ele quad and that it was firing along 300 degrees. He was using 0.2W output, as I was.
The second piece of luck was that we've had a long run of calm and relatively warm weather - perfect for mounting verticals in wet sand on the beach and standing around there, in the moonlight, for two hours!
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Beach WSPRing last autumn, when there was light to see!
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I had hoped to run a comparison of the two antennas as received by VE6JY, but unfortunately, I hit on a bit of bad luck as well, inasmuch as geomagnetic conditions were slightly rough on the evening and that station just wasn't hearing anyone from Europe at the time.
Oh, and there was the inevitable 'how did I forget that?' moment, when I realised I had left the USB battery keep-alive board at home! I overcame that problem by taking a charging cable from the car's radio set-up and then connecting my phone to charge from the battery pack to prevent it shutting down when the WSPRlite was in idle, between transmissions. It worked!
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Yellow line shows the 300 degree line from my beach location.
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After a beautiful, full moon couple of hours on the beach, it was time for the analysis. I start by taking the inherent 'design' gain of the 2-ele quad to be 11dB. It might be a dB or so higher than this in practice, but that's academic for this purpose. My 3-wire, elevated vertical is assumed to have a design gain of 1dB.
Because of the complexity of terrain modelling (read: it takes a lot of hard work to do), I'm not even going to attempt that for the quad; for my vertical, it's irrelevant (vertical radiation and a flat surface from source to infinity).
Here's the plot of how KD2OM, a well-known station for having good ears and always available, on a bearing of 290 degrees from G4HSB, heard both stations. Blue is my vertical, orange the quad.
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KD2OM hearing the vertical (BLUE) and 2-ele quad (ORANGE)
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I couldn't find a station that was further north in the US such that the 10 degree error in beam heading was reduced for G4HSB. But it turns out that, looking at a model for the quad, that the drop-off in gain (line and red dot indicate) is very low - only around 0.2dB or so. The model also predicts just over 12dB gain, but I'm still using 11dB for my calculations, because that, being a subtraction from the received signal, is a best-case scenario for the quad and allows for the possibility of a less-optimally spaced antenna. If you want to assume 12dB instead, just drop the orange line for G4HSB by 1dB in the plot above; it's somewhat pointless!
If I compute the mean for both antennas, there is 0dB difference; exactly the same output on average, though my vertical achieves significantly stronger signals, by around 7dB, on numerous occasions. The much stronger dips in the vertical's signal are likely indicative of a changing propagation path that is probably at somewhat higher angles relative to the horizon; the quad accesses a wider elevation range, though with a significant null, than the vertical, the latter putting out most of its radiation much closer to the horizon, including, often very importantly, angles at a small fraction of a degree to the horizon itself.
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2-ele quad model in MMANA-GAL (14MHz) at 60 feet boom height, good ground.
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Modelled radiation pattern for the sloped-radial, elevated vertical (14MHz), 1.4m feedpoint height, perfect ground. At a beach, where the ground conditions change rapidly from near-perfect to far less so, the azimuth pattern is much modified from that in the model and can be considered to have a beam-like pattern, the rear diminished and the front enhanced in gain (this is proven by experiment as well as logic!)
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So that was KD2OM's account. The only station that I did reach from the beach who was further away in the US and on a better-aligned 300 degrees to match the quad's beam direction, was KA7OEI-1, another high-quality 'regular' on the WSPR scene. Here's how that looked:
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Vertical (BLUE) and quad (ORANGE) heard by KA7OEI-1.
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Now the beach vertical wins out by a significant 4dB or so on average, almost certainly a product of the shallower angle of propagation to that station that may not be available to the quad, but is available to the vertical. I haven't drawn lines between the points in this plot, because there is a gap where my signal wasn't heard for a short while and the software doesn't cope well with gaps for some reason, drawing a misleading line in my favour. During this short period, the quad does get through to the receiver. That could be down to propagation changing to a higher elevation for a while, due to the rapidly-varying geomagnetic field at the time. There may be other explanations!
Do also note that the MMANA-GAL model shows what is certainly true - an antenna-and-ground gain of 6.65dBi, this partly being a product of a near-perfect image in the damp, saltwater-laden sand beneath the vertical. The quad, meanwhile, might benefit from ground reflections, depending on the site elevation and ground layout in the beaming direction. We can only allow for so much in practice!
Sure, if you are nowhere near the sea, this is all rather academic; you'll need a big antenna to achieve the same thing as a simple vertical at the beach. The point being that coastal and other watery environment operating is widely overlooked in the ham press, despite being a truly superb way to get places other sites cannot reach!