Shape wet clay on a spinning wheel, keep the wall thick enough to stand, glaze it and run a virtual kiln schedule. Virtual only: not instructions for real kiln operation.
Same shape, different amount of clay: the volume-conservation solver gives the wall thickness; walls under 3 mm slump.
The science
Rotation. ω = 2π rpm / 60. A lump of mass m whose centre is a distance e off the axis needs a sideways force F = m ω² e to be held; the potter’s hand supplies it, and the torque the hand puts on the wheel is τ = μ F r (friction coefficient μ ≈ 0.35), so the motor power it must supply is P = τ ω.
Volume conservation. Wet clay is almost incompressible. The vessel (outer profile r(y), floor thickness tf, wall thickness t) must contain exactly V0 = m / ρ of clay (ρ ≈ 1900 kg/m³). The solver finds t by bisection on the revolution volume of the cross-section polygon (Pappus: V = 2π ∫ x dA); if you push the wall out the wall gets thinner. This is checked against an independent disc-stack integral of π(ro² − ri²) dy.
Slumping. The bottom of a vertical wall carries σ = ρ g h. Wet clay yields at a stress that drops with water content (illustrative law σy = 8000 e−0.18 (w−18) Pa, w in %). When σ > σy or t < 3 mm the pot slumps. Pushing the clay needs a finger force of about 3 σy A (indentation hardness ≈ 3σy, contact area A = 6 cm²).
Drying and firing. Linear shrinkage is about 6 % while drying and about 6 % more at maturity (cone 6, 1220 °C), so volume shrinks by 1 − s³ (≈ 31 %). A wall of thickness L heated at rate β on both faces develops a centre-to-surface difference ΔT = β L² / (8 a) (a = 5×10−7 m²/s), checked against an explicit finite-difference heat solution. Thermal stress σ = E α ΔT / (2(1−ν)) is compared with the tensile strength of the body; α is boosted near the 573 °C quartz inversion.
Glaze fit. Between the glaze setting point (about 550 °C) and room temperature the glaze and the body shrink by different amounts: ε = (αg − αb) ΔT, σ = Eg ε / (1 − ν). A glaze in strong tension crazes (fine crack network); one in very strong compression can shiver off at rims.
Simplifications. Axisymmetric pot, horizontal wall thickness, uniform glaze, constants are typical round numbers, steam release and the real quartz volume jump are not modelled (so real kilns need slower ramps than this model flags). Virtual craft only. Models built with Blender, scene by Three.js.