Mac Oglesby wrote: > .... a dial to indicate > relative sunburn danger. Installed at a swimming pool or beach, this type > of dial wouldn't even need any hour lines - regions of color would alert > the sunbather as to when (s)he would burn most rapidly.
As an optical/solar physicist, I was intrigued by this, and the possible errors in its use. As long as the sunbather is in a horizontal position, and not particularly concerned about sunburn on the sides, just on the top, one could have a vertical post gnomon with concentric circular rings around it, giving zones of angle of incidence upon a horizontal plane. With the sun highest in the sky (smaller circles toward the center) the incident irradiance on the horizontal would be the most, giving the most exposure in the least amount of time, due to the smaller angles of incidence and the lessened optical distance through the atmosphere (measured by "air mass" with a vertical path being one air mass). The circles with larger diameters centered on the vertical post would receive shadows from the sun lower in the sky, at greater angles of incidence on the horizontal and more attenuated by the greater distance (air mass) through the atmosphere. The question of the affect of clouds is handled in a couple of ways. With a partly cloudy sky, one can have total horizontal radiation approaching that of the extraterrestrial value of 1350 W/m^2, because radiation is received from the direct sun and by reflection from white clouds surrounding the sun, producing what we know in optics as a crude form of what is called a "nonimaging concentrator." Sunburn risk is particularly bad when this particular could orientation occurs. With a hazy sky, the shadow will be a bit more fuzzy, indicating less direct beam radiation, but the total solar exposure can still be quite high. To be safe, there would not need to be a correction for this case. With darker clouds, obscuring the sun, the shadow would disappear, and the sun-bather would expect to receive less exposure, probably wisely. There are cases, however, where the diffuse sky radiation can produce sunburn even with the sun obscured by a cloud or two. If one were seated in a semi-reclined position, however, and facing the azimuth of the sun, the exposure would be greater for lower solar altitudes than for a totally prone position. I guess one could have a kind of correction table or diagram near the sundial, giving correction factors for exposure at other angles and directions of repose than horizontal. But then this would not truly be a sundial not needing correction. Ross McCluney Florida Solar Energy Center Cocoa, Florida USA
