This paper formulates and solves the problem of optimum annealing of glass in which one seeks to minimise either residual stress or annealing time. An approximate analysis shows that residual stress is a weighted integral of cooling rates and that an optimum schedule is obtained when the cooling rate is inversely proportional to the square root of the weighting function. Several multibreak annealing schedules are investigated. It is found that a practical and nearly optimum schedule in this class is a two-break schedule that cools glass most slowly in a 65 deg C interval and most rapidly outside this interval. It yields an optimum stress significantly lower than that of a constant-rate annealing schedule. Furthermore, the optimum is not very sensitive to minor changes in the schedule.
