A building's lifetime carbon has two parts. Embodied carbon is a one-time debt from making and erecting the structural materials; operational carbon accrues every year the building is heated, cooled and lit:
Total(t) = E_embodied + Ċ_op · t
E_embodied = Σ mass_material · EF_material
Ċ_op = FloorArea · EnergyIntensity(insulation) · GridCarbonIntensity
Mass timber can carry a net-negative embodied factor once the CO₂ locked into the wood during growth (biogenic storage) is credited against production emissions — swapping concrete/steel for timber lowers the column's starting height, sometimes below zero. Concrete and steel split the remaining structural mass 65/35.
Better insulation lowers the yearly heat loss that has to be replaced by the building's HVAC system — the same idea as the article's entropy relation ΔS = Q/T: a poorly insulated envelope must move more heat Q to hold the same indoor temperature, burning more energy and emitting more CO₂ every year. That is why the operational slope of the curve is controlled here by the insulation slider, while the material slider only ever changes the curve's starting height.
- Timber share — raises or lowers the embodied jump at year 0 (can go net-negative with a very high timber share).
- Insulation quality — flattens or steepens the operational climb; a well-insulated tower can cross a badly-insulated one within a couple of decades even if it started with more embodied carbon.
- Floors — scales both terms together, since more floor area means more material and more energy demand.
- Each tower's carbon column turns from green toward red as its cumulative total climbs toward a 50-year reference horizon.
Illustrative emission factors used here: concrete ≈ 0.13, steel ≈ 1.85, mass timber ≈ −0.9 kg CO₂e/kg (net of biogenic storage) — representative of published embodied-carbon ranges, not a single project's audited figures.