Arctic Airships, Part 1 - Generating Electricity
This is the first question in my Arctic Airships series of questions. The second one is Arctic Airships, Part 2 - Navigation.
The premise:
An Earth-like planet plunged into an ice age roughly 2,000 years prior to the story. The ice sheets extend to a latitude of about 50 degrees above and below the equator, though I this story (so far) takes place in the planet's Northern Hemisphere. At a latitude of about 67 degrees north are a series of ten or so small villages, each with a population of 500 people.
The technology is roughly that of the late Victorian era - so no automobiles. In fact, there is no clear boundary between icy land and frozen-over water, and it would be extremely dangerous to travel overland in any way. Submarines have not been developed, nor have airplanes; a lack of fossil fuels means that internal combustion engines are nonexistent.
The airships:
The transportation system between villages is an informal fleet of semi-rigid airships. Each is privately owned, and may range in size from 100 feet to 500 feet (30-152 meters) - nothing spectacular. They are a motley bunch, ragged and as patchwork as can be; the one thing that ties them together is that they provide the villages' primary source of power. The one big stride forward has been in photovoltaic cells, and the airships are outfitted with them along much of their body. Wind and hydropower are impractical for various as-yet undetermined reasons; fossil fuels are nonexistent and nuclear power is way too advanced, so this is the only power source for the villages. The engines run on electricity; there are anywhere from four to ten engines on each airship, depending on its size.
The villages are space about 10 miles apart on average - not a lot. The airships provide a sort of taxi service, bringing passengers and freight. The majority of the time, though, they stay aloft, gathering the Sun's energy (ground-based stations are impractical because of the icy terrain, and for some reason airspace near the ground is unstable; cruising altitude is the only place to be).
Do the airships provide a feasible method of generating power? If so, about how many would be needed to provide the villages with enough electricity, (bearing in mind that the airships consume electricity and stay aloft for long periods of time, as well as that there may not be as much sunlight here as in other parts of the world)?
Clarifications:
The solar power generation rates and airship engine efficiency rates are comparable to the solar power and airships of today. The engines are comparable to high-class electric motors in both size and efficiency, such as Solar Impulse.
Power is released at each village via charging cables when the airship docks. Electricity is stored onboard in the form of rechargeable batteries which have an essentially infinite lifespan. The energy is needed only for household use - there's no large-scale industry in this world, just small pockets of people. The houses are decently insulated and pretty energy-efficient insofar as they retain heat very well.
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