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You're right, there are a lot of variables. Solar (photovoltaic) panels aren't super efficient, and that 20w rating is likely going to max out around 15-17.5w. Then there is a small loss when that power gets pushed into the battery (generates heat during the chemical reaction).
So lets assume you get 5 hours of sunlight at 17.5w... thats 1.325amps/hour (assuming 13.2v)... so you've stored 1.33x5=6.63amp/hrs. Now, during a full 24hr day, you run a 7.5w heater... 7.5w @13.2v = 0.568Ax24=13.64 amp/hrs.
You stored 6.63amp/hrs, and you used 13.64amp/hrs... so your battery lost ~7amp/hrs.
Next day, same thing... you're at a deficit. Following day, cloudy, so there isn't as much power produced... so even larger deficit.
Your battery should have an amp/hrs rating. For a regular car battery, you shouldn't go beyond 50% of this value... if you pull a car battery down below ~12-12.2V, sulfate crystals (from the sulphuric acid) start to form on the lead plates, resulting in a less efficient battery. For a deep cycle battery, you can drain more from it, but you still need to be sure to bring it back to full charge, and sulfate buildup can still occur. Battery maintenance and desulfation is a whole other can of worms... there are forums out there devoted to just that stuff!
Now a solar water heater captures much more of the energy from the sun's rays. Light is converted into heat much more readily than light is converted into electricity. You could also look into solar air heaters; insulate the coop, the use the sun to heat the air in the coop.
There are equations out there for calculating heat loss... you could (if you really felt like learning) calculate the difference in temp that you need to achieve (air temp is below freezing, you want water temp to be above freezing)... based on heat transfer through convection and conduction, you can calculate how quickly the water loses it's heat energy... which will tell you how much energy you much input to overcome the loss. But that's a couple months of college classes!
I will eventually have to deal with frozen water too; I'm in Northern Ontario (obviously), and our average winter temps are in the -20C to -30C. Hardiness Zone 3B. We are getting our chicks this spring, and I figure I'm insulating the heck out of my coop... min. R12 walls, R6 floor, R20 ceiling... controlled ventilation to minimize moisture but eliminate cold drafts on the chickens... then I may incorporate solar water heating as a small project to help keep the water warm.
Thank you for all the information. Let me ask you this... if I were too bump up the power, where do i need it first? Do I need a larger solar panel? Or do I need to add an addition deep cycle battery, or both? My coop is double walled, but I've already decided that I am going to take down the inner wall this spring and install insulation throughout. Then, put new interior walls back up. Its the one regret I have with my chicken house... I wish I had have insulated. We aren't nearly as cold as you here in winter, but we get about 2 months worth of days at or under freezing per year.
Keep in mind, my goal isnt to warm the house with solar, but keep a 2-3 gallon waterer unfrozen during freezing tempatures. If that means a 60 or 80 watt solar panel, then I'm willing to invest in that. If the solar system works, it will save me 60 days plus of replacing frozen water each year.
