Presets
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Arch
Wedges of limestone-like stone, no mortar. The red line must stay inside the ring.
Lintel vs arch
Same stone, same span: the flat beam is loaded in bending, the arch in compression.
Timber frame
A pinned rectangle is a mechanism; one diagonal makes it two triangles.
Windmill and gears
Sails turn slowly; step-up gear pairs raise the speed to the millstone.
Layers
Model checks
The science
Arch statics (Heyman safe theorem)
Blocks have no tensile strength and do not slide. The arch stands if some line of thrust in equilibrium with the weight lies everywhere inside the ring (|M| ≤ N t/2 at every joint). A pointwise limit analysis gives the minimum thickness of a semicircular ring under self-weight, t/R = 0.1075; this page recomputes it live below.
Lintel
A flat beam of span L, section b×h, load P at midspan: M = PL/4, σ = 6M/(b h²). It cracks when σ reaches the tension strength (2 MPa, model value), i.e. P = 4 σt b h² / (6L).
Timber frame
A pinned rectangle has a mechanism (it racks); a diagonal at angle θ to the horizontal carries F = H / cos θ.
Windmill
P = ½ ρ A v³ Cp (Betz limit 16/27 ≈ 0.593), sail speed ω = λ v / R, each gear pair multiplies speed by Zdriver/Zdriven with efficiency 0.95 per mesh; flour output from 0.06 kWh/kg.
Honest simplifications: rigid blocks, no crushing or sliding in the arch; 2D plane strain per unit width; small-deflection beam theory; the frame sway animation is illustrative, not a dynamic solution; sail Cp is a typical value, not measured. Dimensions are toy-brick scale (1 stud = 8 mm) for the arch, lintel and frame, full-scale for the mill.
What to try
- Arch scene: raise Ring thickness from 0.5 to 3 studs and watch the capacity graph climb.
- Put the bags at 0.25 of the span, then at the crown: a crown load needs a thinner path.
- Arch vs lintel: how many bags crack the lintel? Compare with the formula in the graph.
- Frame: switch the brace off at 10 N of wind.
- Windmill: choose gears that give 80-120 rpm at 6 m/s.