Costs
=====

**Implementation status:** Production economics block Partial (fuel and
removal costs). CASCADE's *Cost* page is additionally implemented in full
— all 22 governing equations, including the effective cost per MJ
:math:`\hat{C}`, the relative-cost decomposition :math:`\tilde{C}` for all
five strategies, marginal abatement cost :math:`MAC_{stype}`, and the
per-payload-distance costs :math:`\Delta C^{mass}/\Delta C^{pax}` on the
engine's own RTK/RPK denominators from ``payload.ts`` — standalone under
DL-134; the production path still emits the legacy absolute series.
CASCADE states no currency year for its cost inputs
(``COST_CURRENCY_NOTE``).
**Source:** ``src/engine/cascade.ts:computeLCA`` (economics block),
``src/engine/removals.ts:offsetBlend`` (removal costs),
``src/engine/fuel-costs.ts`` (Workstream-B 2050 stacks),
``src/engine/cost-model.ts`` (full CASCADE cost model, DL-134),
``src/engine/cost-series.ts``
**Test evidence:** ``tests/fuel-costs.spec.ts``,
``tests/removal-capacity.spec.ts``,
``tests/suite-h-cost-context.spec.ts``, ``tests/sbatch-cost.spec.ts``

Fuel costs and breakeven oil price
----------------------------------

Jet-A1 cost per tonne is crude plus crack spread, with a carbon adder:

.. math::

   C_{jet} = (p_{oil} + 12) \times 7.74, \qquad
   C_{jet,tot} = C_{jet} + p_{CO_2} \times 3.16

($/bbl → $/t via 7.74 bbl/t; 3.16 tCO₂ per tonne of fuel at the displayed
rate convention; defaults oil $85/bbl, CO₂ $30/t). The LH₂
energy-equivalent cost uses the LHV ratio (120 / 43.2 MJ/kg):

.. math::

   C_{LH_2} = \frac{p_{H_2}\,[\$/\mathrm{kg}] \times 1000}{120 / 43.2},
   \qquad
   C_{LH_2,carbon} = p_{CO_2} \times 3.16 \times
   \frac{CI_{LH_2,del}}{CI_{JetA1,WTW}}

and the breakeven oil price solves for cost parity including the CI-scaled
carbon adder:

.. math::

   p^{*}_{oil} = \frac{C_{LH_2} + C_{LH_2,carbon} - C_{jet,carbon}}{7.74}
   - 12

A five-bucket ASK cost comparison (oil $60–200/bbl) evaluates per-ASK costs
for Jet-A1, Jet-A1+CO₂, SAF, LH₂ and LH₂+SC (superconducting discount
0.8 %/pt of SC gain) — used to read off the first year LH₂ beats Jet-A1.

Removal costs and MACC-like output
----------------------------------

Removal costs follow the learning curves on
:doc:`carbonOffsetsRemovals` (:math:`C_k(y)`), and the engine reports the
capacity-constrained total spend ($B/yr) and the weighted-average $/tCO₂.
HyFlux does **not** construct a full marginal abatement cost curve (MACC);
the per-pathway cost/capacity pairs and the blended average are the
MACC-like output currently surfaced.

Workstream B — 2050 fuel-cost stacks
------------------------------------

``fuel-costs.ts`` (DL-033) reconstructs 2050 component cost stacks per fuel
in 2024 US$/GJ (LHV), each component a triangular {low, central, high}
range. Percentile combination sums component percentiles — the documented
**fully-correlated** approximation (the dominant component of every e-fuel
is the same electricity price; this honours the required correlation within
each fuel and yields the widest, conservative spread). Three metrics per
fuel:

.. math::

   C_{GJ} = \sum_i c_i, \qquad
   C_{JGE} = C_{GJ} \times 0.131354\ \mathrm{GJ/JGE}, \qquad
   C_{shaft} = \frac{C_{GJ}}{\eta_{prop}}

with :math:`\eta_{prop} = 0.40` (turbine) or 0.55 (fuel-cell +
superconducting LH₂ chain). The shaft renormalisation is the point of the
workstream: per-gallon comparisons ignore conversion efficiency. Verified
finding (§19 Q5): per jet-gallon-equivalent, e-methane ($4.83) beats LH₂
($5.40) at p50, but per unit of propulsive output the ranking **inverts**
— LH₂ FC+SC ($74.7/GJ shaft) beats e-methane turbine ($91.9). Disclosed
Boeing 2050 anchors (Jet-A $0.89–3.72/gal, bio-CH₄ ≤ $5.44/gal, e-SAF ≤
$19.96/gal; currency year unstated by Boeing) are bracketed by the model
envelopes.

Known deviations / limitations
------------------------------

* The full CASCADE cost model (22/22 equations incl. MAC and cost per
  tonne-km / seat-km) exists standalone (``cost-model.ts``, DL-134) but is
  not wired into ``computeLCA`` — the production output remains the legacy
  absolute series. Aircraft acquisition learning curves and NPV are not
  CASCADE-published equations and remain out of scope.
* Electricity price inputs are triangular literature ranges ($20/40/80 per
  MWh), not market forecasts.
* The percentile-sum method is the full-correlation limit (an upper bound
  on spread). The §7.3 prerequisite is now satisfied: the gated Monte
  Carlo engine (``monte-carlo.ts``, DL-039) draws one shared
  electricity-price sample per iteration to correlate the e-fuel chain
  (electricity ↔ H₂ ↔ e-CH₄ ↔ e-SAF), all other components independent
  (documented assumption), deterministic seeded PRNG; MC spreads ≤ the
  percentile-sum interim is asserted as a cross-method check
  (``tests/mc-scthermal.spec.ts``).
* Carbon price is a flat user input with no trajectory.