Maximum Distance for Solar Mirror

<...What can be the maximum distance for a mirror from the tower?...>

Given that there are some alarming schemes for doing it from space, there doesn't seem to be a maximum.

Is this relevant for a flat mirror as well?

"Is this relevant for a flat mirror as well?" As long as you don't wish to concentrate or focus, then a flat mirror is always relevent.

The mirrors you see in the pictures are not producing power....so effectively zero percent of the area covered by mirrors is producing power.

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Maximum distance? How much time do you have?

I think that we must take into acount that the sun rays hit air molecules, water vapor, and dust!

The lower the mirrors are, they will heat more the surrounding air, and less the collector.

This is the reason why in the lower valleys is the air hotter than on the high mountains, though the sun's radiation is much stronger on the heights!

But how much?

'...But how much?...'

The solar radiation reaching the top of the atmosphere is somewhere around 1300 W/m² to 1400 W/m²

In a tropical region, on a clear day, around high noon about 1000 W/m² will have made the the transit through the atmosphere to sea level.

Once you account for things such as many areas not being in tropical regions, and noon only being a relatively short part of the 24 hour day, the average over the entire surface is below 200 W/m²

My question was how much affects the distance on the radiation.

If the mirror would be placed in vacuum, then there would be no radiation losses, but for practical needs can we figure a mirrors array which is 1000m' away from the solar tower?

'..My question was how much affects the distance on the radiation..'

I understand, which is why I thought you might start with the data on a typical reduction in solar radiation from about 1350 W/m² to 1000 W/m² as a result of the reflectance and absorption of the entire atmosphere.

You also initially asked the maximum distance a mirror could (effectively) be used related to solar power. Since there are several realistic proposals (based on existing technology) for space based mirrors used for just such purposes, mirrors are probably useful at least to that distance.

Asking a more specific question will facilitate a more specific answer you apparently desire. Local atmospheric condition including temperature range, altitude and humidity; mirror type, size and shape; incident angle, cleanliness of the mirror, as well as wavelengths of concern (solar thermal, or concentrating photovoltaic?) will all have some affect on performance.

Main limit for distance comes from nonparallel radiation of sunlight. The distance calculated by Usbport is some kind of upper limit. To have better usage of mirror surface and collector surface, I would accept something like distance< 30 x diameter of mirror. Loses of sun energy due to absorption by air at above distance will be much smaller than other loses.

By proper control of angles of all mirrors (by computer), You can get radiation on collector equivalent to about 1/2 of mirror's total surface x 7 hours shining (depends on construction, geographical location, quality of mirrors...)

Why not take a mirror outside, reflect it to a certain distance, and measure the reflected sunlight.

GA.

Simple and effective.

Effective? Reflective? Whatever....

The atmospheric absorption isn't really all that much, actually. The loss we see is due mostly to the 100 miles of air above us (or more, when the sun is near the horizon; it goes via the secant of the zenith angle). Look up 'air mass'. And of that 100 miles the lowest 20 causes the majority of the loss. But if you're looking at distances of a few thousand feet there is not much absorption except on very foggy or dusty days. The biggest loss is actually in the mirror coating. A good coating has a reflectivity of maybe 85 per cent (15 per cent loss). A very good coating would be close to 97 per cent (only 3 per cent loss). There will be some loss due to dirt on the mirror surfaces, too.

The sun maintains an angular diameter in the sky of a half a degree. So from the viewpoint of the reflecting mirror, the target at which the mirror is aimed needs to have an angular width of 1 degree plus the linear diameter of the mirror. So if the target is 1000 feet from the mirror, the target should have an approx diameter of D = 1000 * sin (1 degree). If my math is right, that would mean your target should be 17.5 feet across. Plus the diameter of the mirror. If the mirror is a 4 foot square, the diagonal is 5.6 feet, so the target should be 23.1 feet across. These are rough calculations, but this should give you an idea of how to look at the problem.

It's a question of geometry and packing density. For the type of solar collection you are referring to the mirrors are computer controlled to always maximize the amount of incident energy reflected up to the collector at the top of the tower. As you get further from the base of the tower the mirrors have to be further from the previous row or there will be a shadow on it from that row. As a practical matter the number of concentric rows is limited by the stability and accuracy of the mirror control mechanism. The loss due to the dust ans atmospheric pollution you allude to is much smaller than the loss of output caused by said dust and pollution settling on and dirtying said mirrors.