PEM
- About 80 °C, starts in under a minute, follows load.
- Flat plates stacked in hundreds, like the Toyota Mirai’s 370-cell stack.
- Low-grade heat: big radiators.
- Main candidate for aircraft propulsion.
First time here?
The fuel-cell twinin ten minutes
This site is a digital twin of hydrogen fuel cells: computer models of PEM and solid-oxide cells, kept honest against measurements and published data. Use it to size a fuel-cell system, compare the two chemistries, and see exactly how much of each number has been checked.
What a digital twin does
Measure, model, check, plan
- MeasureVoltage, current, temperature, gas flows and impedance from a test rig, or published data.
- Model the physicsEquations for the cell voltage, heat, water and gas, solved for the conditions measured.
- Check and quantify uncertaintyCompare predictions with data the model never saw, and keep every alternative that still fits.
- Plan the next testRank rig conditions by how much they would teach the model per minute of testing.
Where to start
A tour of the site
- Fuel-cell explorerA 3D model of a whole power system. Cells are drawn solid and to scale, the rest of the system as grey X-ray. Slide the power and read the key numbers.
- Live SOFC calculatorDrag the cell voltage and watch current, power and efficiency change on the curve.
- PEM vs SOFC for aircraftBoth chemistries sized for the three steps of hydrogen-electric aviation, with sources.
- Evidence boardWhat has been shown, what has not, and where the model still loses. Every card links to the file it came from.
- WorkbenchReplay a PEM rig run, watch the twin predict and update, and see the next tests it would run.
- Nyquist BenchFit equivalent circuits to the SOFC impedance record, in the browser.
- API and command lineThe same models as JSON over the web, or as the fctwin command and a Python library.
- Battery twinThe sister twin for battery packs, with the same navigation and evidence rules.
Fuel cells in two minutes
Two ways to turn hydrogen into electricity
SOFC
- 600–1,000 °C, slow to start, best at steady load.
- Ceramic cells, often tubes; very efficient, tolerant of fuels.
- High-grade heat that a turbine can use.
- Candidate for APUs, ground power and hybrids.
How to read the results
Every number says how far to trust it
Status labels in the API and tables
MODEL_OUTPUT_NOT_VALIDATED | Straight from a twin model; no independent test confirms it. |
SCREENING_ESTIMATE | A sizing estimate for discussion: stack only, simplified losses. Not design data. |
CALIBRATED_ONE_POINT_NOT_VALIDATED | Adjusted to match one published point (the Mirai-class PEM cell). |
SCREENING_ASSUMPTION_NOT_VALIDATED | A stated screening assumption inside a published range (the reference and high-performance SOFC cells). |
POSTERIOR_FROM_PUBLIC_DATA_NOT_VALIDATED | A Bayesian fit to public data, with uncertainty bands; still not a validation. |
The model switches
- PEM · Mirai-class stack (default) refits one coefficient to a public Toyota Mirai point; Lab cell is the twin’s frozen lab model.
- SOFC · reference cell (default) gives 0.6 W/cm² at 0.8 V; high-performance lab cell 1.0 W/cm², an advanced laboratory level; Lab rig cell is the twin’s own 7 mm research tube.
- Cell, stack, system. W/cm² is cell power per active area; kW/kg is stack or whole-system power per mass. They are different boundaries and are never converted: SOFC cells can approach PEM per area, but today’s SOFC stacks are several times heavier per kW. Mass defaults to today’s hardware; “Development targets” shows roadmap figures, clearly labelled.
Try it
Size a 2 MW regional aircraft in five minutes
- Open PEM vs SOFC for aircraft and leave the switch on Side by side.
- In the Fuel-cell explorer, choose Step 2 · 2 MW, a regional aircraft of 9–100 seats.
- Read the metrics table: PEM needs about 255 m² of cells and 96 kg/h of hydrogen; SOFC about 333 m² and 94 kg/h (default models).
- Turn the 3D view to see the stacks to scale beside a 1.8 m person; the grey boxes are the balance of plant.
- Switch PEM model to Lab cell and SOFC model to Lab rig cell: the same aircraft now needs far more cell area. That gap is why calibration matters.
- Scroll to Size your own case and type your own power, then check the Sources at the bottom.
Words you will see
Glossary
- Digital twin
- A computer model of a physical system that is kept in step with measurements from it, used to predict, explain and plan.
- PEM fuel cell
- Proton-exchange membrane cell. Runs near 80 °C, starts in under a minute, follows load; used in cars such as the Toyota Mirai.
- SOFC
- Solid-oxide fuel cell. Runs at 600–1,000 °C, more efficient and fuel-flexible, but slow to start; suits steady duty.
- Cell, stack, BoP
- A cell is one membrane and its electrodes; a stack is hundreds of cells in series; balance of plant (BoP) is everything else: compressor, cooling, humidifier, power electronics.
- Current density (A/cm²)
- Current per square centimetre of cell. Higher means more power from the same area, at a lower voltage.
- Polarization curve
- Cell voltage against current density. The basic fingerprint of a fuel cell.
- Power density (W/cm²)
- Voltage × current density: power per square centimetre of cell.
- Efficiency (LHV)
- Electrical energy out divided by the hydrogen’s lower heating value. Roughly cell voltage ÷ 1.25 V.
- kW/kg
- Power per kilogram, for the stack or the whole system. The key aviation metric.
- BoP kW per stack kW
- Power the balance of plant uses, mostly the air compressor, for each kW the stack makes.
- Impedance (Nyquist plot)
- How the cell responds to a small AC signal over frequency; separates resistance and electrode processes.
- Calibration vs validation
- Calibration adjusts a model to data. Validation tests it on data it never saw. This site keeps them apart.
- Posterior, hold-out
- A posterior is a model’s parameters with their uncertainty after seeing data. A hold-out check predicts data left out of the fit.
Questions
FAQ
Is the twin validated?
No. It is a development candidate. The evidence board shows exactly what has been checked; independent physical validation is pending.
Where do the numbers come from?
From the twin’s models, run when the site is built, and from public sources cited on each page. Each evidence card links to the file and its checksum.
Why can I switch the PEM and SOFC models?
The twin’s own cells are lab cells. The Mirai-class PEM shows a commercial stack cell; the SOFC reference and high-performance cells span the published 0.5–1 W/cm² range. The answer changes, so the page lets you see both.
Can I use it in my own work?
Yes, through the web API or by installing the code (pip install -e . then fctwin --help). Treat outputs as screening estimates.
What is not modelled?
Altitude, start-up energy, thermal cycling, mass from first principles, and certification. Balance-of-plant shapes in 3D are placeholders.