Glass batch calculation

Glass batch calculation or glass batching is used to determine the correct mix of raw materials (batch) for a glass melt.

The raw materials mixture for glass melting is termed "batch". The batch must be measured properly to achieve a given, desired glass formulation. This batch calculation is based on the common linear regression equation:

${\displaystyle N_{B}=(B^{T}\cdot B)^{-1}\cdot B^{T}\cdot N_{G}}$

with N_B and N_G being the molarities 1-column matrices of the batch and glass components respectively, and B being the batching matrix. The symbol "^T" stands for the matrix transpose operation, "⁻¹" indicates matrix inversion, and the sign "·" means the scalar product. From the molarities matrices N, percentages by weight (wt%) can easily be derived using the appropriate molar masses.

An example batch calculation may be demonstrated here. The desired glass composition in wt% is: 67 SiO₂, 12 Na₂O, 10 CaO, 5 Al₂O₃, 1 K₂O, 2 MgO, 3 B₂O₃, and as raw materials are used sand, trona, lime, albite, orthoclase, dolomite, and borax. The formulas and molar masses of the glass and batch components are listed in the following table:

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