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‘You basically have free hot water’: how Cyprus became a world leader in solar heating
(www.theguardian.com)
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The math depends on where you're living, but what would you mathematically compare here, available required roof area and roof load limits?
Because the SWH, if put in a place like Cyprus, consumes next to no electricity. Pumps and electronics, but even that is pretty nil if the tank is on the upper floors. So let's assume a mild sunny climate where the electrical heaters of both the heat pump and the solar heater are off. The heat pump requires power and the water heater doesn't. As for cloudy days, with proper insulation, a SWH can keep the tank piping hot for a few days.
Personally i don't see how a heat pump could beat a SWH in costs and benefits over time. Off the gate it already starts at a disadvantage on environmental impact and upfront costs. When it's sunny, it loses to solar heating, as it's free vs very efficient. It probably regains some ground during inclement weather and very cold winter days. There's also the degradation of the solar panel, which happens at a faster rate than the degradation of the solar heater. So i guess in the end it boils down to how bad the weather gets where you live and yeah, do the math. There's probably a graph of bad weather days with a point where the SWH becomes less attractive than solar powered heat pumps. But for Mediterranean climates, no contest I'd say. You require less area on the roof for a SWH.
And this is only considering available roof area/weight limits, because being honest they're both free sun energy. But you could use the solar power/money/environmental impact elsewhere.