Solar Charging System

That's an awesome chart, thanks for the link. I looked into the source of the data and it's assuming a fixed panel averaged throughout the year. Luckily they have a handy calculator on their website:

http://rredc.nrel.gov/solar/old_data/nsrdb/1961-1990/redbook/atlas/

I put in Average July with a two-axis plate (since I rotate and tilt my panel during the day), and it came up with this:

In my region that's 8-10 "sun hours" per day, even more than I thought. June and August were about the same: 7-8. Since we only camp May-September it works out well for us.

As for the line-losses, check out this calculator:

http://www.reuk.co.uk/Line-Losses-Calculator.htm

My configuration shows 0.45% loss, so pretty insignificant (0.1Ah less).

First of all (sorry to be nitpicky), an amp is a measure of current which is the flow of electric charge. It's an instantaneous measurement and doesn't make sense to use over time ("amps per day" doesn't mean anything). If you want to describe an amount of electric charge then use amp hour (Ah).

On to the numbers themselves: 

Maybe you only get  4 hours of ideal sun, but there is still a full day of light that is generating a useful amount of electricity (even on a cloudy day). I would argue that the total amount of light hitting the panel during the entire day is equivalent to about 8 hours of full sunlight. You will need to re-position your panel occasionally to achieve this though.

As for efficiency, I lose about 12% from a hot panel (check STC vs PTC) and 8 percent from the charger, so I get 80% of the panel rating out of the charger.

After the charger our numbers will be different because I'm using an AGM battery (which I would highly recommend for solar use). Self-discharge is almost 0, and internal resistance is around 2%. Charging efficiency for an AGM is around 90% at room temperature. Also, if you're losing energy to line losses, you just need thicker cables.

So, the overall calculation is:

3.75A * 0.8 (panel and charger loss) * 0.9 (AGM loss) * 8 hours = 21.6 Ah

21.6Ah - 7Ah (LP detector) - 6Ah (fridge) - 0.09Ah (self-discharge) = 8.51Ah net charge.

That might not seem like much, but that's equivalent to (separately, not cumulatively):

water pump: 2 hours

furnace: 3 hours

led light: 40 hours

That's way more than I need to use in a day, so my solar charger is able to bring me back up to 100% every day. In fact, once it goes into maintenance mode (desulfation) then I plug in my phone charger and a couple duracell usb batteries to try and capture some of the surplus energy.

Something to consider with small solar systems - and this probably explains Footslogger's frustration with his - is lead-acid batteries will loose about an amp per day just in self-discharge.  The solar system must overcome that loss PLUS anything you actually use each day.  On top of that, you can expect to only get about 80% of the solar panel's rating - on a good day.  Those ratings indicate best-case scenarios, like very cold temperatures with snow reflecting the sun.  Add to that you can expect to loose up to 50% of the actual generated output in line losses, charger inefficiency, battery inefficiency, inverter inefficiency, etc.  That number might be closer to 40% loss if you are using 12 volts directly and not using an inverter.  Finally, most areas of the US get about 4 "solar insolation" hours per day on average over a year.  That number will be slightly higher over the summer when RV systems will be in use, say 4.5 hours.  Many people think "hey, its light outside 14 hours over the summer" so they think they'll get far more total amps from the system than they really will.  You have to account for the low angle of the sun, clouds, rain, etc.

 

So, a 45 watt system = 3.75 amp-hour * .80 = 3 amp-hour (on a good day)

Subtract 40%, 3 amp-hour * .60 = 1.8 amp-hour

4.5 hours * 1.8 amp-hour = 8.1 amps per day

Subtract self-discharge = 8.1 - 1 = 7.1 amps per day

 

As long as you use less than 7.1 amps per day AND you get full sun every day, then you will charge your battery - some, not much.  You will use more than 7 amps per day even with just the LP detector (2.3 amps per day on one model I just looked up) and the  "brains" of the fridge on LPG mode (6 amps per day).  Add an hour or three of lights and water pump use and you will be way above 7 amps per day.