Capex · anchor points and interpolation

Three anchor stacks from Fig C15 of the parent essay drive the capex model:

40 kW  → $14K/rack (air 8, facility 6)
100 kW → $44K/rack (air 4, cold-plate 5, manifold 3, QD 1, CDU 8, facility 12, controls 3, install 8)
250 kW → $87K/rack (air 7, cold-plate 12, manifold 5, QD 2, CDU 18, facility 22, controls 6, install 15)

Each capex slice interpolates linearly between adjacent anchor stacks: 40→100 uses the 40 and 100 stacks, 100→250 uses the 100 and 250 stacks. Total-per-rack is the sum, so it stays consistent with the three published anchor totals. Above 250 kW the 100→250 slope continues; treat that regime as directional.

Capex adjustments

Coolant supply temperature. 45 °C removes 15% from the facility-loop slice (dry-cooler free cooling). 32 °C adds 20% (chiller required). Linear between. The adjustment appears as a separate row in the composition table so the arithmetic reconciles with the essay anchor visibly.

Two-phase multiplier. 1.35× applied to cold-plate + TIM, CDU share and controls when two-phase is selected. The model treats two-phase as economically relevant above ~180 kW/rack and disables the toggle below that; the 180 kW threshold is a model assumption, not an industry-standard boundary.

Redundancy. Base CDU count = ceil(total IT load / CDU capacity per unit). N leaves it as the base count. N+1 adds one hall-level spare CDU. 2N doubles the count. CDU capex scales with the number of installed CDUs, so N+1 adds one CDU's worth of capex and 2N doubles the CDU capex slice — redundancy is not just a spare on the shelf, it is fully-installed capacity. Real deployments may apply N+1 by row, zone or CDU group; this model uses the simpler hall-level abstraction.

Opex · formulas

Effective PUE      = base PUE − (pump_fraction_1p × 0.40)   when two-phase is selected
                   = base PUE                                   otherwise
   (two-phase drops pump electricity to 0.6× the single-phase level; that saving
    lowers effective PUE so total facility electricity falls accordingly)
Facility electricity = IT_MW × (effPUE − 1) × utilisation × 8760 × $/kWh × 1000
   (this is the ONLY electricity line; PUE is treated as inclusive of pumps + fans + chillers)
Pump electricity    = pump_fraction × IT_MW × utilisation × 8760 × $/kWh × 1000
   (sub-component of facility electricity; two-phase applies 0.6× to pump_fraction)
Non-pump overhead   = Facility electricity − Pump electricity
   (chillers, fans, controls, facility infrastructure)
Preventive maint.   = maint_pct × capex_total
Coolant refresh     = refresh_pct × 0.03 × capex_total
   (0.03 = coolant slice as fraction of stack; author estimate)
Water               = tsup < 40 ? IT_MW × 0.012 × 8760 × water_price : 0
   (0.012 m³/MWh IT is a typical evaporative rate)
Total opex          = Facility electricity + Maintenance + Coolant refresh + Water
   (pump is a sub-component of facility electricity, NOT added again on top)

Boundaries and caveats

Thermal load ≈ IT load. A simplified steady-state approximation. Pumps, fans, chiller consumption at low tsup are captured through PUE, not modelled separately.

CDU classification. Technology-side vs facility-side is a modelling choice. Other reasonable classifications put CDU on the facility-side (interface component owned by the facility MEP contractor). Treat the 48/52 split as one lens.

Two-phase vs immersion. Two-phase DTC and immersion are architecturally distinct above ~250 kW/rack, not variations of one architecture. The two-phase toggle here only sits inside DTC; immersion is out of scope.

Not modelled. Flow-rate + delta-T at the cold plate. Coolant fluid choice (water-glycol vs dielectric). White-space floor loading. Dual-loop A/B redundancy for tier-4 workloads. Component lead-time sensitivity. Any of these can move the numbers materially; treat this tool as a first-pass scenario framework, not a mechanical/electrical design study.

Change any anchor unit cost or opex assumption in Advanced to reflect a hyperscaler-specific reference design, negotiated CDU pricing, site energy price or a specific climate. See Data Centre Cooling · a double-click on Direct-to-Chip for the underlying architecture, vendor scorecards and value-migration analysis.