On Thu, Oct 14, 2010 at 11:00 AM, David Hobby <hob...@newpaltz.edu> wrote:
> Hi. Thanks for the details. I started thinking about > the problem. > >> It depends on the acceptance angle and the diameter of the light pipe. > > I'll give you that the spread for light come out of the > whole array and into the pipe is 30 minutes, the same as > the sun subtends in the sky. So that would be an average > deviation of something like 10 minutes, or .003 radians. > (Actually achieving that may be a headache, but I bet it > could be done if it mattered. Although I believe that > it doesn't matter that much, since even if light went into > the pipe with only small angular errors, the average incidence > angle would rapidly increase due to somewhat random reflections > off the walls. See below.) > >> This stuff: >> >> http://www.revelationlighting.co.uk/OLF%20Spec.pdf >> >> has a .99 reflectivity for angles less than 27 deg, > > That's pretty good reflectivity. Plastic tends to > crinkle, though, so you'll need some sort of backing > to help keep it flat. > > > and almost all the >> loss comes from the points not being sharp. > > Lost me there. What points? The 90 degree angles on the film. > At .999, which the >> optical guys say is not hard, and a 30 meter diameter light pipe, the >> loss is about 7%. One option is to fill the pipe with argon which >> reduces the Rayleigh scattering. > > Working backwards, you're assuming around ln(.93)/ln(.999) = 73 > reflections? For a 30 km light pipe, that's around one reflection > every 400 meters, for an average angle of 30/400 = .075 radians, > or 4 degrees. It would take a thorough analysis, but I'm betting > that successive reflections from the slightly crinkly walls of the > light pipe would gradually increase the average incidence angle, > pretty much like a random walk. Good point. > O.K., I'll buy that, if you can get .999 reflectance at angles > of a few degrees. > >> There is 4 GW coming down the pipe. At 7% loss, 280 MW. The area of >> a 30 meter x 20 km pipe is 2 million square meters so the loss would >> be 140 W per square meter. In open air it is only going to get >> slightly warm. > > O.K., but what about localized losses? Suppose there's a sharp > bend when the light pipe hits the jet stream, or something? > If the pipe bends something like 45 degrees over 300 meters, then > you'd have basically all the light hitting one side of the pipe > over around 100 meters. And it would hit at a 10 or 15 degree > angle, which probably decreases reflectivity to .995 or so? > Then you've got .005 of 4GW hitting an area of around 100*30 > square meters, giving .005*4GW/3000 = 7000 watts per meter. > So that's as hot as grabbing a 60 watt incandescent bulb? > > It might still work, but things are getting tricky. Yeah, again good point. We have a lot of stored heat in these things, so we can monitor the light pipe in real time. If it starts getting hot, just reduce the amount of light being fed in at the top. I don't think you would get that sharp a bend, but if you did, it's time to draw on stored heat till the light pipe straightens out. > For instance, after that one bend the average light ray > is going to be hitting the sides of the pipe at 10 or 15 degree > angles all the way down. (Unless you've got a mechanism to > "straighten out" rays that are bouncing off the sides too much? > I can't think of an easy one.) > > If you have a ray permanently at an angle of .2 radians, it > hits every 150 meters, which would be around 100 times over 20 km. > And if reflectivity is down to .995 at that angle, you're left > with .995^100 = 60% of the light at the bottom. > > Another problem could be "fluttering". If you have enough transient > surface waves running over the light pipe, each one giving large random > reflections to rays unlucky enough to hit it, you could rapidly > have almost all of the rays bouncing off the walls at 20 or 30 > degrees. That gives you more reflections per ray, each at larger > angles with lower reflectance. Something like that could really > cause big losses. > > It's an interesting problem. Thanks. It is indeed. Keith _______________________________________________ http://box535.bluehost.com/mailman/listinfo/brin-l_mccmedia.com
