Not to sound like an obsessed nut, but I went out and bought a special antenna for capturing airplane data. Specifically, I bought the FlightAware 1090MHz ADS-B Antenna from Amazon. Heh. I didn't look too closely at the pictures and thought it would be walkie-talke antenna size. When a three foot long box arrived with a 26 inch antenna, I realized the coax connector in the picture was actually a large N coax connector instead of the tiny SMA connector I had in mind. I didn't have the right connectors, so I had to order a special cable to try the antenna. The initial tests of the antenna inside the house were good (saw a few flights beyond 100 Miles), but naturally I wondered how well it would do outside the house.
One of the nice things about working with the Pi is that I can just hook it up to a USB battery pack and take the thing wherever I want. This turned out to be great for testing the antenna. I attached the antenna to some PVC pipe, cabled it into the battery-powered Pi, and then duct taped the whole thing to the top of a ladder. While the whole thing was wobbly, I could pick up the ladder and drag it to different spots in the back yard. I'd then go to the Pi's web page from my tablet and watch the map to see how many planes I was getting.
I wasn't very rigorous about the tests, but it seemed like I got better performance when I moved the antenna from our patio to the back yard. The results seem logical because on the patio the house is still in the way of most of our air traffic (which is west and south). The downside of all this is that there isn't a good place to mount the antenna (or route its cable) on the back of the house. Plus my wireless network evaporates a few feet into the backyard. In any case, I'm going to put the antenna and the Pi in the garage for now, until I get more time to mount it properly up top.