Plate Center Deflection Formula

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The Plate Center Deflection Formula is a simplified model that describes the amount of sagging w(t) at the center of a glass plate fixed at both ends when heated as a function of time t; it serves as the fundamental calculation formula for sagging design (Treatise §6.1). Equation: w(t) ≈ ρgL⁴t / (32ηh²). Here, ρ is the density of glass, g is the acceleration due to gravity, L is the span (the distance between supports in the mold), t is the holding time, η is the viscosity (a function of temperature), and h is the plate thickness. The dependence on the fourth power of the span and the square of the plate thickness is particularly important: doubling the span increases the deflection by a factor of 16, while doubling the plate thickness reduces the deflection to one-fourth.

This strong dependence has a direct impact on practical design. This equation reveals the physical basis for questions such as “Why are smaller slump molds more prone to deformation?” and “Why can thinner glass be formed at lower temperatures?” In actual slump testing, the mold shape (convex, concave, or support method) and effective-thickness correction modify the parameters of the equation, but the fundamental relationship between span and glass thickness remains unchanged. By combining this with HSM (heated microscope) and kiln calibration, it is possible to estimate the viscosity-temperature curves for each glass system and theoretically predict the optimal slump temperature.

Related Concepts

スランピング（slumping）・自重クリープ（creep）・実効厚み（effective-thickness）・HSM加熱顕微鏡（hsm-heating-microscopy）・粘度-温度曲線（viscosity-temperature-curve）