3 ms·

You can show with fluid mechanics is that all you need is a container, molten glass, and a steady source of rotational motion while the glass cools into a parab

You can show with fluid mechanics is that all you need is a container, molten glass, and a steady source of rotational motion while the glass cools into a parabola climbing the walls of the container, give or take a factor of two on the final shape depending on how you feel about density.

082349872349872 4y ago
How steady? Does a massive honking flywheel suffice, or does it require control?
- meltyness 4y ago
  Height varies quadratically with radial frequency and radius, mediated by gravitational acceleration, (rv)^2/?2g. I'll venture you want a small curvature with a great deal of uniformity, the model also discounts variable viscosity with temperature and bizarre patterns that would appear with inconsistent anything, I suspect you're gonna want a control system, and probably also to shave the tails to acquire a lens compatible with the paraxial model of magnification.
  - buescher 4y ago
    I recall seeing the technique used in the Amateur Scientist column in Scientific American, with epoxy or casting resin. The verdict was the result was "maybe for infrared"... found it: https://optica.machorro.net/Optica/SciAm/LiquidMirror/1994-02-fs.html https://optica.machorro.net/Optica/SciAm/LiquidMirror/1994-0... If you search around, you'll find people have kept trying and have got somewhat better results in the meantime. Fun stuff.
Someone 4y ago
https://en.wikipedia.org/wiki/Rotating_furnace https://en.wikipedia.org/wiki/Rotating_furnace discusses that. I think most mirrors cast this way still would need treatment. For example, the mirrors of the Giant Magellan Telescope (https://en.wikipedia.org/wiki/Giant_Magellan_Telescope#Mirrors https://en.wikipedia.org/wiki/Giant_Magellan_Telescope#Mirro...) are being cast using this method to get a rough (for modern astronomy. For example https://www.techbriefs.com/component/content/article/tb/supplements/pit/briefs/40525 https://www.techbriefs.com/component/content/article/tb/supp...: “after the casting, the surface “roughness” is about 2.5 millimeters, or a tenth of an inch, on average. “The polishing and constant measuring are what turn this amazing piece of glass into a mirror,” he said. “By the time we finish polishing, it will be accurate to better than 25 nanometers”) shape for them. That way, there’s a lot less glass to pour, the remaining glass cools down faster, and less glass has to be removed afterwards. (For the GMT, an additional complication is that six of the seven mirrors will be off-axis. I don’t know whether they spin them off-axis, or accept that more grinding will be necessary to give them their final shape) Instead of glass that solidifies, you can also use a container with mercury or another reflective liquid. https://en.wikipedia.org/wiki/Liquid-mirror_telescope https://en.wikipedia.org/wiki/Liquid-mirror_telescope: “Liquid-mirror telescopes are telescopes with mirrors made with a reflective liquid. The most common liquid used is mercury, but other liquids will work as well (for example, low-melting alloys of gallium). The liquid and its container are rotated at a constant speed around a vertical axis, which causes the surface of the liquid to assume a paraboloidal shape. This parabolic reflector can serve as the primary mirror of a reflecting telescope. The rotating liquid assumes the same surface shape regardless of the container's shape; to reduce the amount of liquid metal needed, and thus weight, a rotating mercury mirror uses a container that is as close to the necessary parabolic shape as possible. Liquid mirrors can be a low-cost alternative to conventional large telescopes. Compared to a solid glass mirror that must be cast, ground, and polished, a rotating liquid-metal mirror is much less expensive to manufacture.” Disadvantage is that you can only point the mirror straight up. Also, there’s evaporation of the mercury.

082349872349872 4y ago

How steady? Does a massive honking flywheel suffice, or does it require control?

meltyness 4y ago
Height varies quadratically with radial frequency and radius, mediated by gravitational acceleration, (rv)^2/?2g. I'll venture you want a small curvature with a great deal of uniformity, the model also discounts variable viscosity with temperature and bizarre patterns that would appear with inconsistent anything, I suspect you're gonna want a control system, and probably also to shave the tails to acquire a lens compatible with the paraxial model of magnification.
- buescher 4y ago
  I recall seeing the technique used in the Amateur Scientist column in Scientific American, with epoxy or casting resin. The verdict was the result was "maybe for infrared"... found it: https://optica.machorro.net/Optica/SciAm/LiquidMirror/1994-02-fs.html https://optica.machorro.net/Optica/SciAm/LiquidMirror/1994-0... If you search around, you'll find people have kept trying and have got somewhat better results in the meantime. Fun stuff.

Someone 4y ago

https://en.wikipedia.org/wiki/Rotating_furnace https://en.wikipedia.org/wiki/Rotating_furnace discusses that. I think most mirrors cast this way still would need treatment. For example, the mirrors of the Giant Magellan Telescope (https://en.wikipedia.org/wiki/Giant_Magellan_Telescope#Mirrors https://en.wikipedia.org/wiki/Giant_Magellan_Telescope#Mirro...) are being cast using this method to get a rough (for modern astronomy. For example https://www.techbriefs.com/component/content/article/tb/supplements/pit/briefs/40525 https://www.techbriefs.com/component/content/article/tb/supp...: “after the casting, the surface “roughness” is about 2.5 millimeters, or a tenth of an inch, on average. “The polishing and constant measuring are what turn this amazing piece of glass into a mirror,” he said. “By the time we finish polishing, it will be accurate to better than 25 nanometers”) shape for them. That way, there’s a lot less glass to pour, the remaining glass cools down faster, and less glass has to be removed afterwards. (For the GMT, an additional complication is that six of the seven mirrors will be off-axis. I don’t know whether they spin them off-axis, or accept that more grinding will be necessary to give them their final shape) Instead of glass that solidifies, you can also use a container with mercury or another reflective liquid. https://en.wikipedia.org/wiki/Liquid-mirror_telescope https://en.wikipedia.org/wiki/Liquid-mirror_telescope: “Liquid-mirror telescopes are telescopes with mirrors made with a reflective liquid. The most common liquid used is mercury, but other liquids will work as well (for example, low-melting alloys of gallium). The liquid and its container are rotated at a constant speed around a vertical axis, which causes the surface of the liquid to assume a paraboloidal shape. This parabolic reflector can serve as the primary mirror of a reflecting telescope. The rotating liquid assumes the same surface shape regardless of the container's shape; to reduce the amount of liquid metal needed, and thus weight, a rotating mercury mirror uses a container that is as close to the necessary parabolic shape as possible. Liquid mirrors can be a low-cost alternative to conventional large telescopes. Compared to a solid glass mirror that must be cast, ground, and polished, a rotating liquid-metal mirror is much less expensive to manufacture.” Disadvantage is that you can only point the mirror straight up. Also, there’s evaporation of the mercury.