Cooling Rate Prince Rupert's Drops
Date: Spring 2014
Does anybody know a formula for the cooling rate of Prince Rupert's Drop? If you have 200 grams of glass, how long would it take the core to cool to room temperature? Would the structure of a Prince Rupert's Drop cool slower?
Two hundred grams (1/5th of a kilo!) of glass is far to large to compare
with the fraction of a gram that makes up a Rupert Drop! You asked
how long it would take for the core of a 200-gram "chunk" of glass to
cool. The answer depends on the actual outside shape (and therefore
the surface area) of the glass, and the method of cooling. The short
answer is "a very long time"!
A Rupert Drop works because its small size allows its outer surface to
cool extremely fast, and this skin becomes hard while the center is still
liquid. The key here, is the large surface-area-to-volume ratio of the
drop. Then after the surface skin is cool and hard, the center more
slowly cools and shrinks. This shrinkage puts the already-cooled outer
skin in compression. As you may know, glass is extremely strong in
compression, so the compressive stresses in the outer skin protect the
drop from damage even when the drop is hit with a hammer. It is the
rapid cooling of the outer skin of the drop that matters here; the speed
with which the inner core cools is not too important.
A 200g chunk of glass is simply far to large to achieve the ultra-rapid
cooling rate that is necessary to get a sufficiently thick, compressively
stressed, outer skin for the large chunk of glass to act like a Rupert
This rapid cooling effect is used to make "tempered glass", which is
used in all car windows (except the front windshield). This very strong,
but thin glass is made by exposing a nearly-molten sheet of glass to
strong blasts of cold air. As with the Rupert Drop, the outer skin
hardens first, then is subjected to strong compressive stress as the
center more slowly cools.
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Update: November 2011