Another recent POTA activation turned out to be a useful learning experience for me. It was a moderately cold February day. The temperature had dipped to -20degC overnight, but by afternoon it had risen to a relatively balmy -7degC. It was also the occasion of the Polar Bear QRP Ops February Polar Bear Moonlight Madness Event (PBMME) so I had to get out and get on the air.
I chose a conservation area near my home in Owen Sound Ontario for the activation and set up my usual hitch mount vertical antenna. The operating session was conducted in my winter quarters – the shack-in-a-truck. I adjusted the length of the MFJ-1979 telescopic vertical whip for best SWR on 20m and made sure my power was wound down to 5 watts, then spotted myself on pota.app and started calling CQ on 14068.5 KHz.
I don’t usually do activations on weekends because of contests and, frankly, competition for the attention of hunters from other POTA activators. The 14060 – 14069 band segment often used by POTA CW activators was busy as expected; it took me 3 or 4 CQs before I got a response.
The first QSO was with a station in Puerto Rico; the second was with a station in Washington State. Clearly my 5 watts was making the distance. I logged a total of 20 stations before packing up for the day.
When I got home I received an email from fellow Polar Bear QRP operator Craig WB3GCK in eastern Pennsylvania. Craig had heard stations working me, but couldn’t hear me. When I looked at my log it was clear that I had not logged any QSOs with stations in the northeast. I usually work multiple stations in NY, NJ, PA, OH and other nearby states such as WI and IL. The reason seemed fairly straightforward – the band must have been “long”. That realization prompted me to do a little simple math to analyze what was happening.
My first step was to model my antenna using EZNEC. From that I determined that maximum radiation from my antenna was at an elevation of 25 degrees. The antenna has no gain so any component of the signal propagated at a higher angle would be attenuated. Since I was working QRP that meant any stations within close range probably wouldn’t hear me (as was indeed the case).
Then a bit of simple trigonometry to determine the minimum range I could expect to reach revealed the answer. The ionospheric F2 layer varies in height between about 250 and 400km. To keep the math simple I assumed the Earth is flat (it is – isn’t it?). Curvature of the Earth’s surface would likely result in a longer range anyway so the flat Earth model could be considered a best case calculation.
The distance between my station in Owen Sound Ontario and WB3GCK in eastern Pennsylvania is 665km. If the height of the F2 layer were at its lowest – 250km – the -3dB points of my signal would be received at a distance of between 500 and 2800km and Craig would have heard me. On the other hand, if the height of the F2 layer were at its highest – 400km – my signal would have been refracted back down between 1600 and over 4000km away – well beyond eastern Pennsylvania.
The simple formula I used is d=h/tan(25) where d is half the distance between transmitting and receiving stations, h is the height of the refracting F2 layer and 25 is the propagation angle for maximum signal radiation. There are many assumptions incorporated into that simple analysis but the result of the model matches empirical observations. QED (Quod Erat Demonstrandum – thus it has been proved) – as we used to write in college physics and math exams. Those college exams were half a century ago so please excuse me if my old grey noddle got the math wrong.
Ok, math hat off, toque back on. Ham radio can be more than just a whole bunch of fun; it can also be a great learning experience. I had more fun than you can wave a 20m whip at – both from making great contacts in the cold of winter and in the satisfaction of having improved my understanding of radio communication.
Ham Radio Outside the Box 