I'm not sure I understand the question,
Neither am I!
it has a 120 gallon tank
So to heat this 1000# of water 30 F takes 8.7 kwH.
96 sq ft
At 60% efficiency this can supply 5200 w at the average power supplied by sunlight. What is your nearest city/town?
the electric element kicks on even though it's going to be a sunny day.
To what likelihood? Here's where the gamble of saving a few cents is pitted against the likelihood of a lukewarm shower.
But, that's just the best that can be done sometimes we've gone 38 days of full clouds... sometimes we get 21 straight days of sun.
So I'd say, at the extremes, you need the kwH supplied by full sun to equal 38 days of showers @ some gallon usage @ some minimum temp.
Especially in winter after our showers the tank can be 90F and the solar will heat it to 115F if the stupid stupid element didn't kick on until later... in winter especially solar is a lot more efficient heating 90F water vs. 120F I'd rather have the solar do it's thing and have the element kick on at night for the remaining boost for my wifes shower in the morning. We pay $0.23/kW, I am having to run down at night to turn the breaker on and then before my wife takes her shower turning the breaker to the tank off more than I'd like, I'd rather a timer.
Can this http://www.amazon.com/Intermatic-WH21-Electric-Water-Heater/dp/B00002N5FP be used on my tank (it's on a 30A breaker to a 4500W 240v water tank)?