But they are not, so the rest of your supposition is false. Anyone that watches the 6:00 o'clock local news and weather can tell that when you have one cloudy day, the chances of the next day also being cloudy are higher. Similarly, when one day is sunny, the probability of the next day also being sunny are higher than 50/50.
(and yes, I have evidence for that 'article of faith'. Look on NOAA's web site for any given weather reporting station and do the stats on cloudy days for a year or two)
without, a 50 watt panel might produce 3a x 3h or 9ah.
9ah x 12v = 108 wh (not 150wh) into the battery, of which 86wh (7ah) might be available for use (20% conversion inefficiency). That's less than his needed 12ah, so a 75 watt panel would be more appropriate in NY, but I do not know where the OP is located.
The sad truth is that solar weather is probabilistic, like 100-year floods or coin flips. No matter how much energy storage we provide, if we wait long enough, there will always be a long enough cloudy day sequence to exhaust our energy store and leave the house cold or the lights out, unless we have some other backup system, eg a woodstove or a generator.
I think what that means is that the clouds parted and exposed the solar disk for 14 minutes total over that time period (and having spent my holidays there, I cannot doubt its accuracy). It's not representative of the total amount of solar energy that penetrated the clouds and reached the surface of the earth. A little bit of math provides a quick sanity check:
14 minutes of full sun = 233 Wh/m^2
233 Wh/m^2 = 13.7 Wh/m^2/day over 17 days
13.7 Wh/m^2/day = approximately 2 W/m^2 during daylight hours
That's a tad darker than Barrow, Alaska (in the Arctic Circle) in late January, and no way was Detroit that dark. Indeed, if you check NREL's data on the subject, Detroit averages 1300 Wh/m^2/day in December despite the fact that long cloudy spells like the one you described are the norm for the area at that time of year. You can also check NREL's 30 years of hourly data to see that peak horizontal insolation in Detroit is usually greater than 200 W/m^2 and nearly always exceeds 100 W/m^2, even on Detroit's cloudiest days.
Another FYI, 'Total sunshine' is not required to generate appreciable power.
Today it has been cloudy for the 9 hours (so far) of daylight. My 10 kW system has been far from it's most productive for this time of year today. It has only produced 21 kWh today Feb. 4, 2006. On on the other side of the coin, on Feb. 1, 2006 it made 44 kWh on a beautiful Fresno winter day. So far this year the least I have produced was 0.568 kWh (truly terrible) on one cold rainy dark day in January. (Which is why I'm on the grid.) :-)
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