When looking at solar industry ratings, keep in mind that to acheive that rating, the panel has to be in the conditions they are rated (i.e. sun 90 degrees to the panel on a clear day, and a panel temperature no higher than 77F degrees). To get the rated output with a horizontally mounted panel, that's solar noon, on July 22nd, on a boat 1 degree (60 nautical miles) south of Key West Florida, with an ambient temperature in the 50's Farenheit. When it's that cool at that latitude at that time of year, we might say hell has frozen over.
The further north from that position you go, the further from July 22nd, and the further from solar noon, and the cloudier the day, the lower the panel output current. The further from temperatures in the 50's, the lower the panel output voltage. Watts=amps X voltage, so power goes down as either goes down.
I can't find the panel you're talking about to see the specs. While it isn't the same type panel you're talking about, here's a 10W monocrystaline Shell/Siemens ST10
. I like Shell/Siemens because their flyers give you an idea of best real-world output in a section titled Typical Data at Nominal Cell Operating Temperatures. It says the ST10 10W panel is really about a 6.8W panel.
Here you can see that at 68 degrees F ambient, with a slight breeze, the ST10 output voltage is down to 13.7V (due to the panel temperature), .1V lower than the typical output of a Magnetek or Univolt. At higher ambient temperatures, it will be even lower, and by the time voltage drop across the cables is taken out, it will be even little lower than that.
I believe you'd be lucky to get a 13.2V "float" charge at the batteries from the ST10. Dividing the 6.8W by 13.7, you get about 1/2A real-world peak current, or only enough daily power to run a 1.4A 12V
light bulb for 2 hours.
Two of these would be good for keeping the batteries up during storage, except perhaps in the winter, and even a third might be marginal then. And at this low of a power input into the batteries, you don't really need a controller.
For a small vintage Airstream, you already have a lot of battery capacity. If you run one two-bulb incandescent lamp (1.4A per bulb) for 5 hours in the evening (really four hours but an hour of bathroom light too), that's about 15AH, the water pump doesn't use much, maybe 1-2AH. Add an hour of bathroom vent fan and you're still under 19AH/day, with no radio, TV, or other electrical use like modern RVs have with all their circuit boards and modern radios.
If you left on a Saturday and came back on the following Sunday, that's 8 nights, taking your batteries from fully charged down to maybe 30% charge, with no solar or generator. No radio, no TV. Yeah, that depth of discharge is hard on the batteries. Even with 2 rainy days, the 3 ST-10 panels producing maybe 6-7AH/day total over 5 of the 7 camping days, would keep discharge to no lower than about the 50-60% level. So yes, on a much older Airstream, those 3 panels could make a significant difference, if nothing else, in your battery life.
I can't help you with the TV power calculation because I don't know what size or wattage it is. Do you use an amplified or unamplified antenna with it?
And if you can get me a link to a specs page for the panels you're looking at, I could give you a little more accurate picture.