Appendix — figure atlas
Capacity scaling atlas
Every curve below is drawn by evaluating the locked equation register across the full validated capacity window, Q = 0.1 MW → 1 GW, on log–log axes. Nothing is fitted to the picture: the lines are the same functions the workspace calls when it prices a project, so a figure and a scenario result can never disagree. Dashed lines are accepted external benchmarks, never model output.
Solid = model output · dashed = accepted external benchmark · every axis carries its unit and time basis.
Part 1
Economics of scale
Capital intensity, operating cost and output all follow power laws in Q. On log–log axes a power law is a straight line, and its slope is the scale exponent θ — the single number that decides whether a bigger plant is cheaper per kilogram.
Straight lines with slope θ < 1: doubling capacity costs less than double. SOEC sits highest because its stack is the least mature; AEL is the cheapest per installed kilowatt across the whole window.
C(Q) = a · Q^θ · [M€2024] · θ = scale exponent, dimensionless
The same curves normalised by capacity. This is the figure that answers 'how much cheaper does the next megawatt get?'
c(Q) = 10³ · C(Q)/Q · [€2024/kW]
Fixed operation and maintenance only — electricity, water and stack replacements are charged in their own engines so no cost is counted twice.
O(Q) = a · Q^θ · [M€2024/yr]
Output is exactly linear in Q — slope 1 — so every intensity indicator per kilogram is a pure ratio of the curves above to this one.
ṁ(Q) = Q·10³ · CF · 8760 / SEC · [kg H₂/yr] · SEC in kWh/kg
The three anchor points the engines are validated against. Any scenario that lands far from these at 100 MW indicates an input error, not a discovery.
LCOH = (CRF·CAPEX + OPEX + electricity + water) / annual kg · [€/kg]
Point values read off Figure 1B at the reference capacity, for quick comparison against vendor quotations.
c(100 MW) = 10³ · C(100)/100 · [€/kW]
Part 2
Climate, water, land and biodiversity
Environmental loads are annualised at the environmental capacity factor and reported per year, not per kilogram, so that a 1 GW project and a 1 MW pilot can be compared on the same axis without hiding four orders of magnitude in a ratio.
All four routes are straight lines of slope 1 — the carbon intensity per kilogram does not improve with size, only with cleaner electricity. That is the single most important message in this atlas.
GWP100 = Σ_g m_g · CF_g · [t CO₂e/yr] · CF_g = characterisation factor
The lifecycle curve sits far above the 9 L/kg stoichiometric-plus-treatment floor because it includes the water embedded in the electricity supply.
W(Q) = w · Q · [m³/yr] · per-kg basis = W/ṁ [L/kg]
Land is dominated by the renewable generation attributed to the plant, not by the electrolyser hall. The SMR benchmark is roughly twenty times smaller because its energy arrives as a pipeline, not as a field.
A(Q) = a_land · Q · [ha] · exposure in km², A = π r²
Potentially disappeared fraction of species, integrated over a year. Reported on the source endpoint basis; production boundary only, storage and transport excluded.
B(Q) = b · Q · [PDF·yr/yr]
Part 3
Noise, annoyance and health burden
The noise chain is the one place where an impact genuinely switches on at a threshold. Below Q ≈ 3.86 MW the 55 dB(A) contour never reaches a receptor, so annoyance and DALYs are exactly zero — not small, zero. Above it the dose–response curve takes over.
A logarithmic axis in dB would be a logarithm of a logarithm, so the level is plotted linearly against log Q — the straight line is the 7.5 dB per decade slope of the source law.
Lp(Q,r) = 90.6 + 10·β·log₁₀Q − 20·log₁₀r − IL · [dB(A)]
Regulatory and literature reference levels the boundary curve is judged against. These are inputs to the assessment, never outputs of it.
Benchmark set — WHO, EPA, oil & gas practice, measured electrolysis source term
Area grows with the three-quarter power of capacity, because sound pressure falls with the square of distance while the source term grows with Q^0.75.
A₅₅(Q) = π · r₅₅(Q)² · [km²]
Point values from Figure 3C, plus the 300 m field-exposure circle used as a screening comparator.
A = π r² · [km²]
The vertical wall at 3.86 MW is physical, not numerical: it is the capacity at which the 55 dB(A) contour first extends past the plant boundary.
P_HA(Q) = ρ · ∫ %HA(L(Q,r)) dA · [persons/yr]
Disability-adjusted life years from chronic high annoyance. The band is the disability-weight uncertainty, which dominates every other source of error in this indicator.
DALY(Q) = DW · P_HA(Q) · [DALY/yr] · DW dimensionless
Even a gigawatt plant carries under one DALY per year at the central disability weight — small, but not zero, and it must be disclosed.
DALY = DW · P_HA · [DALY/yr]
Part 4
Employment, skills, safety and value added
Social indicators are reported on the project lifetime where the source defines them that way — employment in job-years, not headcount — because a headcount without a duration is not an indicator.
The green route carries more employment per megawatt than blue at every scale, and the net curve exceeds direct because indirect activity outweighs displacement in the source studies.
J(Q) = j · Q · [job-years/project]
A scenario layer, not a measured indicator: it inherits all the uncertainty of the employment curve and adds an assumed hours-per-worker figure the user should override with local data.
H(Q) = h_worker · J(Q) · [thousand h/project]
This figure deliberately stops at exposure hours. Converting to fatalities requires a jurisdiction-specific rate, and the platform refuses to invent one.
F = r_h · WH / 10⁶ · [expected fatalities] · WH in worker-hours
The benefit curve and the burden curve on one axis. Four to five orders of magnitude separate them, which is the honest framing of the social trade-off.
Persons served = LHV·ṁ / 3500 kWh · exposed = P_HA(Q)
Kept deliberately in its source currency until a single frozen GBP→EUR2024 coefficient is adopted, so that no silent conversion error propagates into the decision file.
GVA(Q) = g · Q · [GBP million/project] · labour compensation ⊂ GVA
Part 5
Storage economics, degradation and the CAPEX envelope
Three families of curve that do not run on capacity Q at all. Storage prices run on stored mass M, degradation runs on operating time, and the CAPEX envelope is a band rather than a line — because a single number for capital cost would be a false precision.
Cavern cost falls with the roughly minus-one-half power of stored mass, so a large cavern is cheap per kilogram and a small one is not worth excavating. Tanks are modular: the price per kilogram is the same at one tonne and at one thousand.
p(M) = a·M^−b · [€/kg] · tank p = 0.346·P + 286, pipe p = 607
The same laws integrated to a capital number. Below one hundred tonnes the cavern curves are drawn but not offered: the geology, cushion gas and deliverability requirements make them infeasible, not merely expensive.
C(M) = p(M)·M / 1000 · [M€2024] · M in tonnes H₂
Each stack replacement resets the efficiency loss to zero; the balance of plant keeps ageing until its own twenty-year overhaul. The mean of the system curve, 3.3 %, is exactly the δ̄ that divides mean annual output in the lifecycle LCOH — nothing here is decorative.
g_sys(t) = 0.75·g_stack(t mod t_stack) + 0.25·g_BoP(t mod 20) · δ_max = 10 %
Each stack replacement resets the efficiency loss to zero; the balance of plant keeps ageing until its own twenty-year overhaul. The mean of the system curve, 3.2 %, is exactly the δ̄ that divides mean annual output in the lifecycle LCOH — nothing here is decorative.
g_sys(t) = 0.75·g_stack(t mod t_stack) + 0.25·g_BoP(t mod 20) · δ_max = 10 %
Each stack replacement resets the efficiency loss to zero; the balance of plant keeps ageing until its own twenty-year overhaul. The mean of the system curve, 3.5 %, is exactly the δ̄ that divides mean annual output in the lifecycle LCOH — nothing here is decorative.
g_sys(t) = 0.75·g_stack(t mod t_stack) + 0.25·g_BoP(t mod 20) · δ_max = 10 %
The band is the honest answer to 'what will it cost'. A point estimate inside a ±35 to ±55 percent envelope is a reading aid, not a quotation, and the platform flags every evaluation that falls outside the calibrated interval instead of silently extrapolating.
C(Q) = A·Q^β ± envelope % · [M€2024] · validity 1–1 000 MW
How to read these figures
Slope is the physics
On log–log axes the slope of a line is the exponent θ in y = a·Q^θ. Slope 1 means strictly proportional; slope below 1 means economy of scale; a bend means a regime change.
Dashed is external
Solid lines are model output. Dashed and dotted lines are published benchmarks or regulatory limits, drawn so the model can be judged, never fitted to.
Units are on the axis
Every y-axis carries its unit and its time basis. Annual quantities are per year at the stated capacity factor; lifetime quantities say so explicitly.
Thresholds are real
Where a curve starts abruptly, an exposure threshold has been crossed. The platform never smooths a threshold to make a chart look continuous.