Technoeconomics on a napkin

Can a factory deliver custom freeze-cast terracotta at the price of flat extruded panels? This page is the steady-state algebra of such a factory: freeze dryers and kilns, the molds and people between them, and the price per square metre that carries a margin. The Manual tab lets you set every number; the Optimize tab asks, for a demand you name, which machines and how many. The two tabs keep separate inputs.

Units: euros per square metre of façade. A square metre is 10.54 pieces of 30 × 30 cm on an 8 mm joint; a building is 580 m². The dashed line is the deck's USD 80/ft² (€797/m²). The grey band is flat extruded terracotta ex-works, €100–330/m²; the top is a real USD 33/ft² quote, the bottom is inferred.

The piece

Mass follows the effective solid depth: a solid 10 cm piece is nine litres, a hollow-backed one about five and a half. At 60 % solids every litre holds 1.5 kg of clay and 0.4 kg of ice. N = 10.54 pieces per m².

Piece → materials line
Clay per piece mclay
9.0 L × 60 % × 2.5 kg/L
13.5 kg
142 kg of fired clay per m²; also drives firing and the tunnel kiln's tonnes
Materials
(13.5 × €0.25 + 0.40 × €2.5) × N
€46/m²

Freeze dryers

Batch machines: so many molds per load, so many hours per load, so many chambers. Their yearly capacity is the first of the two throughput limits; their owning cost is shared over whatever the plant actually makes.

Chamber:
Dryers → two lines
Chamber capacity Cch
55 × 8,760 ÷ 34 h × 72 % × 540
5,509,525 / yr
used 88 %: the kilns are the bottleneck
Drying energy
110 kW × 34 h ÷ 540 × €0.15 = €1.04 × N
€11/m²
Freeze-dryer capital
55 × €0.925M × 0.186 ÷ 4,866,667 started = €1.94 × N
€20/m²

Kilns

The second throughput limit. Shuttle kilns fire a chamber-full per cycle; a tunnel kiln fires tonnes a day continuously and burns about half the gas per kilogram. The plant makes the smaller of the two capacities.

Kiln:
Kilns → two lines, and the throughput
Kiln capacity Ckiln
1 × 250 t × 1000 ÷ 13.5 kg × 365 × 72 %
4,866,667 / yr
this is the bottleneck
Throughput Q
min(5,509,525 dryers, 4,866,667 kilns)
4,866,667 started / yr
4,623,333 sold at 95 % yield = 438,588 m² = 756.2 buildings a year
Firing energy
13.5 kg × 2.5 MJ ÷ 38 × €0.50 × N
€5/m²
Kiln capital
1 × €15.00M × 0.186 ÷ 4,866,667 = €0.57 × N
€6/m²

Molds and masters

Each piece is cast in a silicone mold that survives a number of casts; each design needs a printed master. A mold can never make more casts than a design repeats in a building, whatever the silicone can take.

Molds → one line
Molds & masters
(€204 ÷ 60 + €60 ÷ 168) × N
€40/m²
81,111 molds and 28,968 masters a year

Labor, scrap and shipping

People → three lines
Touch labor
€1.92 × N
€20/m²
≈ 127 production staff at 1,600 h a year
Scrap
(€15.59 of production lines per started piece) × 0.053 × N
€9/m²
Freight
€1.50 × N
€16/m²

Plant, overhead and price

What is left once the machines are paid for: the building around them, the people who are not on the floor, the selling, and the margin. Fixed sums are divided by the square metres the plant sells, so they dominate a small plant and vanish in a large one.

Plant → four lines, then the price
Plant capital
€40.0M × 0.186 ÷ 4,866,667 × N
€16/m²
Fixed overhead
€3.00M ÷ 438,588 m²
€7/m²
Before SG&A and margin
€46 + €11 + €20 + €5 + €6 + €40 + €20 + €16 + €9 + €16 + €7
€196/m²
Price
€196 ÷ (1 − 12 % − 40 %)
€408/m²
SG&A €49 + margin €163 on top; €79 above the band top

The three napkins, restated for a plant

Everything above is one function: price per square metre of a plant, steady state. The napkins are three ways of setting its inputs, and now they carry the whole plant, not one chamber.

Napkin A: parity is possible

The hollow-backed line: 55 FD1800s, a tunnel kiln, 5.5 cm of clay per piece, 660 molds per 26 h load, 95 % yield. Price at 40 % margin €287/m², inside the band, with SG&A and overhead inside the price. Mass is what makes it work: 79 kg/m² against the panel's 57.

Napkin B: parity is impossible

The same line making the solid 10 cm piece: €408/m² at 40 % margin, above the band top. Twice the clay, a longer cycle, and the kiln becomes the bottleneck at 250 tonnes a day. An extrusion line at €50–80/m² of cost is out of reach for either piece.

Napkin C: the skeptic

48 h drying, 250 molds a load, 45 % running, €60M of plant, money at 15 %, 5 min of labor, 30-cast molds, 80 % yield: €1,617/m². The deck's USD 80/ft² becomes the break-even. Load it and watch which bars grew: the two capital lines and scrap, all of them the same division, machines over pieces.

€/m²PilotSeed lineLine, solidLine, hollowSkepticYours
Materials (clay + binder)€105€67€46€25€46€46
Drying energy€43€11€11€7€54€11
Freeze-dryer capital€365€56€20€11€143€20
Firing energy€13€11€5€3€5€5
Kiln capital€84€19€6€3€42€6
Molds & masters€81€53€40€33€75€40
Touch labor€251€96€20€20€40€20
Packaging + freight€5€11€16€16€16€16
Scrap€303€40€9€6€144€9
Building, racking, mold shop capital€270€47€16€9€169€16
Fixed overhead (people, rent)€4,580€334€7€4€42€7
SG&A€1,525€186€49€34€194€49
Margin€5,084€620€163€115€647€163
Price€12,709€1,551€408€287€1,617€408
Buildings a year0.13.1756.21,368.3122.3756.2
Capital in the ground€0.3M€1.3M€105.9M€105.9M€125.9M€105.9M

What decides it

Two divisions. Machines over pieces: every capital line is a fleet's yearly cost divided by the pieces the plant makes, and the plant makes the smaller of what the dryers and the kilns can do. Fixed sums over square metres: overhead divided by output, which is what makes a pilot cost thousands per square metre and a line hundreds. Everything else is a price times a mass or a minute. So the commodity question is: at what plant size, with what drying time and what piece, do those two divisions fall under the band? The Optimize tab searches that directly.

Over time

The plant above is a steady state. Getting there is a path: a pilot, a seed line, then production lines, with touch labor learning along the way. Every doubling of cumulative pieces cuts minutes per piece by a fixed share; solar modules did about 20 % per doubling, lithium-ion batteries about 18 %.

Starts from the simulator's pilot touch times, 30 minutes per piece at 2,000 cumulative pieces, and floors at 2.5 min (your slider above). Labor rate 46 €/h.
01002003001k10k100k1M10Mfloor 2.5 min/piece = €20/m²labor, €/m²cumulative pieces made (log)

The two figures below are from the time-dependent forecast (vault note “Price Floor and Commodity Parity — Forecast 2026-09-08”), which runs the simulator's cost model and its discrete-event scheduler year by year with phased fleets and learning. They use that note's assumptions, which predate this page, and they are here because the steady-state algebra cannot say when: an experience curve, and the margin scissors between price and cost.

Production cost against cumulative pieces on log-log axes
Experience curve. Production cost against cumulative pieces sold, log-log. The realised slope is about 11 % per doubling, conservative against solar and batteries.
Price paths against full cost, and the operating margin each implies
Margin scissors. Hold USD 80/ft², or cut toward the 40 %-margin floor from 2033; the lower panel is the operating margin each path implies.