P shaft = ρ × g × Q × (gross head − head loss) × turbine efficiency, with ρ = 1,000 kg/m³ and g = 9.80665 m/s². Divide watts by 1,000 for kW. The optional example assumes 50 m gross head, 5 m head loss, 5 m³/s, 90% turbine efficiency and 4,380 hours/year. None is a surveyed site or supplier guarantee.

Annual energy assumes those conditions are simultaneous and constant for the entered hours. Seasonal flow, water rights, reservoir operation, environmental releases, turbine curves, cavitation, penstock transients, governing, speed matching and generator protection require site-specific design. The battery event still assumes the source is present throughout that event. No dam, turbine, gear ratio or 100 m rotor has been qualified here. Pumped storage is excluded: pumping energy would need its own debit.

Economics: budget turbine equipment under equipment, civil/penstock/interconnection works under installation, and water access/maintenance under operating costs. Include source opportunity cost where applicable; exclude sunk infrastructure only with a stated project boundary. An ordinary hydropower generator is the competing design. Positive generation does not demonstrate that Wegawomb improves it or makes a profit.

Source: DOE: head, flow, turbine and generator energy path · DOE: turbine selection depends on head and flow. These references support established hydro principles—not Wegawomb hardware performance.

• Magnetic–piezo: use modular annular banks with captive magnets, adjustable gaps, independently guided preloaded cartridges and travel stops. Provide bank isolation, replaceable cartridges and matched local conditioning before combining outputs. Bulk piezo power density, fatigue life and packing remain unknown; actuator force/travel ratings are not generator power ratings.
• Power electronics: individually rectify and protect each piezo channel, then use low-leakage conditioning and a load with demonstrated pulse acceptance. Match measured loaded voltage and available energy to startup thresholds. A controller's maximum current rating is not power supplied by the harvester. Avoid combining unmatched raw piezo outputs directly.
• Generator-led recovery: only use motion that would otherwise be dissipated. Benchmark the original machine, a supported regenerative drive/common DC bus, and the proposed hybrid at the same useful work. Extra piezo loading, controls and drag need their own measurement; the simple comparison below does not price them separately.
• Heat and mechanics: establish permitted torque, speed, current, ceramic stress, magnet retention, component temperature and fatigue life from selected hardware and tests. Require independent overspeed, overcurrent, overtemperature and emergency-stop protection, plus guarding and safe isolation. Measure component heat before sizing cooling; unrecovered mechanical energy is not all local heat.
• Scale gate: demonstrate repeatable loaded output and a useful advantage after added drive consumption, controls and standby. At facility scale, compare installed cost, maintenance, downtime and recovered energy with an ordinary regenerative drive or generator. No cost savings are claimed without real installed-cost and maintenance evidence.

The defaults are facility requirements hypotheses, not optimized hardware settings or a construction/safety approval. Zero firm-capacity credit remains appropriate until site availability is demonstrated. The annual schedule is illustrative; the short event does not prove annual energy yield.

Selected research material: copper indium thiophosphate, CuInP₂S₆ (CIPS). The facility conversion settings remain hypothetical; switching the material label does not establish output or transfer another ceramic’s specifications.

Temperature matters: Liu et al., Nature Communications (2016) reports a bulk transition near 315 K (41.85°C), and a transition near 320 K in the studied thin flakes. Composition, thickness and strain affect behavior; this is not a universal damage or service-temperature limit. The 35°C bulk target and 20 kW/°C cooling conductance here are explicit design assumptions, not qualified hardware. HQ Graphene sells research CIPS crystals; availability does not establish a packaged power cartridge.

• Wu et al., Small (2026): the published abstract reports AFM-based cyclic loading near 7 GPa beyond 10⁷ cycles. This is nanoscale mechanical-fatigue evidence, not loaded electrical-output endurance for a full-size cartridge. Electrical rejuvenation requires an external field; any such energy must be counted.
• Zhang et al., Advanced Functional Materials (2023): polarized CIPS produced 760 pA short-circuit current at 0.85% tensile strain. Short-circuit current is not delivered electrical energy.
• Io et al., Nano Energy (2022): a single-nanoflake device reported current and voltage responses. Separate maxima cannot be multiplied to infer useful output.

Unknown for this design: loaded energy per cycle, conversion map, allowable temperature, force and strain limits, packaged fatigue life, contacts and encapsulation. No material has been established here as delivering more usable energy than CIPS while also demonstrating durability under comparable loading.

• Rated torque = shaft power / angular speed. Equivalent tangential force = design torque / (radius × equally loaded paths). It is not the normal repulsive force between magnets; that needs a force–gap model or data. Rotational power reference.
• Solid-shaft diameter = cube root of 16 × design torque / (π × assumed allowable shear). This torsion-only lower bound omits bending, keyways, stress concentrations, critical speed, deflection, fatigue and load-sharing errors. It is not a procurement diameter. Torsion reference.
• Spring stiffness = incremental force / stroke. Incremental elastic energy = preload × stroke + ½ × incremental force × stroke. Throughput = this energy × cycles per second per spring × spring count; it is not electrical generation or a complete damped-cycle work integral. Spring-energy reference.
• Radial retention load = mass × angular speed² × radius, per drum. It does not give the net bearing load of a balanced rotor or a fastener/adhesive rating.
• Local heat envelope = entered fraction of rated transfer/conversion/conditioning losses plus active auxiliaries, counted once. Network losses, battery losses and upstream drive losses are outside this envelope. Unrecovered mechanical work is not necessarily heat in the chamber.
• Water flow = heat / (4,180 × water temperature rise), in kg/s. Required conductance = heat / allowed temperature rise above ambient. Uniform bulk warming starts at ambient with constant heat, conductance and thermal capacity; hot spots, pressure drop, pump/fan selection and loss of coolant remain unresolved. Cooling electricity must fit the existing auxiliary budget or be entered there; changing conductance here does not invent free cooling. Lumped thermal reference · Heat-transfer reference.

Inputs are explicit design hypotheses, not paper-derived Wegawomb performance. Download assumptions + results below to retain this sizing record.

• RodOri spring metamaterials: experimentally tunable stiffness and vibration response. The studied laboratory assembly spans about 3,200 to 6.79 N/m; those are not facility component ratings. Here, stiffness is an explicit editable hypothesis.
• Elastic Rod Origami: reconfigurable rod geometry motivates an adjustable frame and strain path. Electrical generation and Wegawomb-scale durability were not established.
• Porous liquid crystal elastomers: temperature-responsive acoustic behavior motivates an optional research layer. No acoustic-to-electrical gain is credited. Heating starts disabled at 0 W; any externally supplied heating must be entered as a debit. No validated temperature, acoustic or fatigue curve is supplied.

A small-motion, linear, force-driven oscillator is assumed: m x″ + (c mechanical + c electrical) x′ + k x = F sin(2πft). Natural frequency = √(k/m)/(2π). Mean absorbed power = ½ c total (2πf × displacement amplitude)². Equivalent electrical damping is an assumption, not a solved piezo circuit or a material conversion coefficient.

When the source cap is reached, ideal force control reduces the excitation. Real source impedance and control losses are not solved. The cases can draw different mechanical power; compare both input and output, not output alone. Mechanical and electrical damping remain the same in both cases, so tuning alone does not improve their conversion ratio.

The motion ceiling is an assumed linkage amplitude, not allowable ceramic displacement or a safety rating. Magnetic gap/force, preload, leverage, piezo stress, nonlinear snap-through, stored-energy transients, fatigue, acoustic response, manufacturing and cost need actual geometry, material data and tests. Heater and reconfiguration energy are externally supplied and subtracted; upstream drive consumption is a separate debit.

• Recoverable source and schedule: numeric examples entered; site survey not supplied.
• Materials and geometry: magnets, retained rotor, tunable linkage, guided preloaded piezo cartridges and protected electronics are concept roles; grades, dimensions and suppliers are not selected.
• Stress, temperature and fatigue limits: not established; no invented safety limits.
• Cooling: component heat measurements and rated hardware needed; total unrecovered work is not a cooler specification.
• Costs, profitability and novelty: not established; supplier quotes, comparable alternatives and a separate prior-art review are needed.

No missing evidence is replaced with a fabricated measurement. All editable design inputs have illustrative starting values; selecting real-measurement entry below deliberately opens a blank record.

• Captured annual energy = the minimum of the fleet’s annual source budget and min(source power, module count × assumed absorbed module power) × 8,760 × duty fraction.
• Converted energy = captured energy × transfer fraction × piezo conversion fraction × conditioning fraction. These fractions do not substitute for force–displacement, capacitance, frequency or load measurements.
• Equivalent full-power module-hours = captured energy / module input power. In facility mode, fixed auxiliary and entered upstream draw apply to all installed modules for scheduled operating hours; standby applies to the remaining hours. During a facility event all installed modules remain energized. Legacy large studies instead use ideal equivalent full-power staging. Constant efficiencies are not measured part-load curves.
• Net benefit = electricity delivered after network losses − auxiliary electricity imported − extra upstream electricity. Negative cases remain negative. Zero motion provides no recurring output.
• The direct-loading benchmark removes only the assumed magnetic-transfer loss. It does not prove that the same mechanical operating point is attainable without redesign.
• Repeated piezo output requires changing stress. A capacitor may smooth pulses, but stores—not creates—energy. Startup thresholds, power quality, pulse-level load matching and annual battery dispatch are not simulated. A separate constant-window battery screen accounts for capacity, power limits, charge/discharge loss and initial stored energy.
• The economics panel is conditional screening with editable costs and annual energy allocation, not a profitability forecast. Missing prices stay unknown; storage-event energy is not annual revenue.

• Analog Devices: LTC3588-1 — low-power conditioning and startup behavior; output-current limits do not predict harvested power.
• maxon: motors as generators — torque, speed, loaded voltage/current and operating limits.
• ABB: electrical braking guide — source duty and regenerative alternatives.
• US DOE: drive part-load efficiency — why a single efficiency assumption is not a performance map.

These references inform the engineering approach, not the numerical Wegawomb presets. Hardware performance and novelty remain unverified.

• Piezo Systems: piezoelectric generators — conversion, mounting and material limits, not Wegawomb performance.
• PI: mechanical preload and flexure guidance — integration principles; actuator ratings are not generator output ratings.
• ABB: permanent-magnet shaft generators — bulk-scale magnetic generation exists; this does not validate the proposed piezo addition.