Weird Harold wrote:Even without metal for "silvering" it would take less glass and less perfection to build a reflective array than it would a refractive compound lens. Adequate mirrors could be made from opaque glass or simple non-metallic paint on glass sheets.
You also have to consider solar-tracking -- your proposed design would only provide decent power for about an hour either side of Noon unless you build a boiler that can track the focal point. A mirror-array has a lot less mass for any given amount of solar concentration and consequently can be made to track the sun with a lot less effort; one slave in a tread-wheel pivoting an acre or so of mirrors, or something similar, would be manageable. Tracking your multi-ton, multi-element rooftop installation would require a lot more effort.
Think about the precision required for a very large array of reflective mirrors that can track the sun. Part of the reason this type of solar mirror array isn't commercially successful yet is because it's expensive. The more precise and efficient you want it to be, the more expensive it is and the more expensive your energy will be, either money-wise or resource-wise.
Additionally, the lens method would certainly use a linear element to absorb heat, and the focal point would shift throughout the day, much like trough-style reflective solar elements today.
Additionally, and this idea just popped into my head, there would be nothing stopping you from having the system be three sided, not one sided. The building could be built like a greenhouse, arched, and the lenses would be shifted through the course of the year. On Earth, if you are in the Northern hemisphere, as Winter approaches, your flattest lenses would be adjusted south, row by row. Yes, you would lose a lot of energy, but you could make it work reasonably well.
OK, this is definitely making it into paper in what I'm writing. During the winter it will probably just heat water, perhaps even enough water to keep a house warm. In the summer, it might provide power for, say, processing crops or making tools, or whatever.
Mirror solar systems also concentrate solar power by having a concave surface facing the sun, and concentrating power at an exposed surface between them and the sun. This makes them more vulnerable to bad weather. On the other hand, lens solar systems can concentrate light from many shapes, and some of the most efficient will be concave, with the object of the concentrated light being protected and insulated under the structure that holds the lenses in place.
If you're going to do small-to-moderate-sized primitive solar thermal energy without the ability to make cheap, efficient mirrors, I really think lensing power would be more effective than reflecting it. If you can make cheap, efficient mirrors, it becomes a different scenario entirely. If you can make cheap computers and cheap servos, then massive arrays of mirrors becomes even more attractive.
Since they can make corrective lenses, Safehold clearly has a fairly advanced glass industry. They are probably at the cusp of having mirrors be better than lenses for solar energy.
With the glassmaking industry being what it is, and with heliographs being used, I'm a bit surprised no Mother Church members have thought about trying to use lenses to burn Charisian sails. Trying to do it at sea probably wouldn't work that well, but setting up mirrors, lenses, etc in placed where you expect an attack?.