Thanks, Dennis, for posting the details of the solar charging and alarm systems. I've been looking into solar power for my place here, and read an article a while back in Home Power magazine that covered sizing solar arrays based on the loads they would need to power. Using that and a little knowledge from high school electricity class (bet they don't teach that one very many places these days), I worked through an example for your video camera.
...My cams are 750mili amps........So figured the wattage necessary and figured that a 10 watt solar panel would work and a small battery for like a lawn mower would be just fine........WRONG
If the camera (or what ever load you're using from the battery) needs 0.75A, and runs 24 hours a day, that's .75 x 24 = 18 Amp/hours of battery capacity needed to keep it running. Most of my motorbike batteries are at least that size, so I can see where that would have been a reasonable guess on capacity.
But that's only the comes outta side. Ya gotta do the goes inta side, too, and for solar there's some guess work involved as you found out.
Our camera needs 0.75A, and at 12 Volts, that's 0.75 x 12 = 9 Watts. (W (power) = I (Amps) x V (Volts))
Over 24 hours that adds up to 24 x 9 Watts = 216 Watt hours of power to keep running day and night.
Now remember that the sun only shines in the day time, and the length of the day varies throughout the year. And sometimes clouds cut down on the intensity of the sunlight reaching the array. The solar power folks have come up with a term called "daily peak sun-hours" to help determine the amount of electricity available through a solar array at locations throughout the country. Here's an article that explains the term, and gives a reference for determining it at your location:
ASK THE EXPERTS: Peak Sun-Hours | Home Power Magazine
For Atlanta, GA, a little south of Sugar Hill, the daily peak sun-hours is about 4.75.
So to determine the size of the solar panel that will keep up with the camera, divide the camera's power use by the daily peak sun-hours:
216 Whr / 4.75 hr = 45.5 W
This assumes that the panel isn't in the shade at any time during the day, and that the converter is 100% efficient. You can correct for either of those being off by multiplying the above figure by the percentage of each factor. This number is an estimate that takes into account the yearly variation in day length as well as local weather conditions, so on long, clear summer days you'll have more power than the camera needs, but it may fall a little short on cloudy winter days. If I read your account correctly, Dennis, you've got 50W total of panels, but 30 of them are shaded in the summer. Owing to the longer days in the summer when 30W of production is shaded, your array is still keeping the battery up. And when the days shorten, the leaves drop and allow more of that previously shaded 30W to come into play. If you really want suspenders to go with your belt, up size the battery to get you through long periods of cloud cover and long nights during the winter, just as you've already done.
Harbor Freight sells a 45 Watt solar panel kit that includes a 12 volt regulator and two lights, and it just happens to be on sale now for $199. No experience myself with it, and unlike some of the HF stuff, this one seems well liked. HF might be convenient, but for two hundred bux you can probably do better at some of the surplus places on line.
FWIW, I'm using a deep cycle marine battery from WalMart on my electric gate, and after three years of unattended operation it's still going strong. Of course it'll probably bite the dust shortly since I've just mentioned it. I found a plastic battery box at WalMart and have it anchored into the ground to keep the battery from sprouting legs. I did that by digging a couple of feet down below the box and burying a length of chain in concrete as I filled the hole back up to the bottom of the battery box, the upper lip of which is a couple inches above the surrounding ground. When the top is on the box I wrap the ends of the chain over each other and hook them together with a pad lock. Yeah, anybody with a good pair of bolt cutters will still get the battery, but the setup so far has kept mostly honest people honest.