I watched a transit of Venus through an ~8" reflector made by Aerobie|Aeropress inventor Alan Adler, who precisely strained spherical mirrors. The editor of Sky & Telescope was very enthused, but the technique never caught on, apparently because CNC grinding of paraboloids got cheap. Alan is now using his extra mirrors under homemade tungsten tops that spin for twenty minutes. What is the optimal shape to trade air drag for moment of inertia? It turns out to be hard to model air drag. --rwg On 2017-10-23 14:37, Richard Howard wrote:
Large telescope mirrors start as extremely accurate sections of a sphere made by carefully randomized grinding of two surfaces against each other. The only two surfaces that fit together in all orientations are spheres.
Starting with a rough glass sphere and a rough hemispherical hole in a plate, continued random grinding produces a perfect sphere (and a perfect hemispherical hole).
BTW, the thermal approaches have the difficulty of dealing with the thermal expansion of glass. A 8" sphere could take many months to anneal without shattering. Corning museum has a nice video of making of the largest glass paperweight (~13" diameter and over 109 lbs).
--R
On Mon, Oct 23, 2017 at 1:58 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
It was perhaps 58 years ago, in our High School auditorium, the speaker gave us a demo of this prestressed glass phenomenon. It was in the shape of a chemist's Florence flask, the rounded kind. He first used the flask to hammer a nail, no problem. Then he dropped in a speck of carborundum. It's harder than glass, and produces a tiny nick on impact. The flask just exploded.
-- Gene
On Monday, October 23, 2017, 1:29:12 PM PDT, Bill Gosper < billgosper@gmail.com> wrote:
Interesting 16/sec ball bearing production process: https://www.youtube.com/watch?v=19duYMdiXi0 Falling raindrops form cabochons: https://www.youtube.com/watch?v=a9CRrGvQwe0 1961|2 freshman chemistry lecturer demoed Prince Rupert's Drops, and then something more interesting. (Prince <othername>'s Drops? Google fails me.) Hollow, thick-walled glass blobs, open at one end. He hammered nails with one, then wrapped it in a towel, dropped in some carborundum crumbs, BAM! --rwg
On 2017-10-22 11:57, Dan Asimov wrote:
Henry got that right — in fact, something quite interesting happens, as Wikipedia says:
----- Prince Rupert's Drops (also known as Dutch or Batavian tears) are toughened glass beads created by dripping molten glass into cold water, which causes it to solidify into a tadpole-shaped droplet with a long, thin tail. These droplets are characterized internally by very high residual stresses, which give rise to counter-intuitive properties, such as the ability to withstand a blow from a hammer or a bullet on the bulbous end without breaking, while exhibiting explosive disintegration if the tail end is even slightly damaged. In nature, similar structures are produced under certain conditions in volcanic lava. -----
more at https://en.wikipedia.org/wiki/Prince_Rupert's_Drop.
—Dan