# Flywheel energy storage **Flywheel energy storage** holds energy as the [[Rotational_energy|rotation]] of a mass. A motor–generator spins a rotor up, the rotor keeps spinning, and the same machine run backwards takes the energy out again as electricity. The stored quantity is the rotational [[Kinetic_energy|kinetic energy]] E = ½·I·ω², where I is the [[Moment_of_inertia|moment of inertia]] of the rotor about its spin axis and ω its [[Angular_frequency|angular speed]].[^idema-inertia] Because the energy goes as the square of ω, nearly all of it lives in the last few thousand revolutions per minute, and the whole engineering problem is how fast the rotor can be spun before it tears itself apart. In the microsim below the reader sets the speed in rpm on a logarithmic slider, the rotor radius, and the material — steel, aluminium alloy or carbon fibre — and watches three readouts: the stored energy in kilowatt-hours, the rim speed v = ω·R, and the fraction of the material's limit the rim stress has reached. The equation that answers is the hoop stress of a thin rotating rim, σ = ρ·v², which combines with E = ½·I·ω² to give the specific energy E/m = K·σ/ρ. That result is the point of the page: **specific energy depends on strength over density, and not on size at all.** A rim twice as large stores more energy only in proportion to its own extra mass. On the [[Energy]] flagship this article sits in Part VII — Energy transfer, section *Flywheels* (row E64), one of the three children of the C42 storage group, alongside the root article [[Energy_storage]] and its high-energy counterpart [[Hydrogen_storage]]. A flywheel occupies the opposite corner of that group's Ragone plane: very high power, very short duration. ## Main components A flywheel store has four parts and a container. The **rotor** carries the energy and is the part the stress law constrains. The **motor–generator** is a single electrical machine that runs in both directions, converting between shaft power and terminal power; its efficiency and its magnetic drag appear twice, once on the way in and once on the way out.[^mitofsky] The **bearings** carry the rotor's weight and set the standby loss. The **housing** is both a vacuum enclosure, because aerodynamic drag on a rim moving at hundreds of metres per second is severe, and a containment structure for the case in which the rotor fails. Power electronics sit between the machine and the grid or load, because the rotor's speed — and so the machine's frequency and voltage — falls continuously as energy is withdrawn. That variable-speed operation is a feature, not a defect: it is what lets a flywheel deliver useful energy over a wide speed range rather than only at one operating point. ### Possible future use of superconducting bearings Bearings are the flywheel's standby loss. A mechanical bearing rubs; an active magnetic bearing does not, but needs sensors, amplifiers and control electronics that draw power continuously and fail unsafe if power is lost. A bearing built on a [[High-temperature_superconductivity|high-temperature superconductor]] is passive: flux pinning holds a permanent magnet in a stable position with no control loop at all, so the rotor levitates without instrumentation.[^super-note] The cost moves rather than disappearing — the [[Cryogenics|cryogenic]] plant that keeps the [[Superconducting_magnet|superconductor]] cold draws power whether the store is charged or not, which is exactly the trade the [[Superconducting_magnetic_energy_storage|superconducting magnetic store]] makes for the same reason. ## Physical characteristics ### General A flywheel is the mechanical analogue of a [[Capacitor|capacitor]]: it takes charge quickly, gives it back quickly, holds it badly for long periods, and does not wear out from being cycled, because nothing chemical happens inside it. Its two ratings are almost independent — the rotor sets the energy, the motor–generator and power electronics set the power — so the same rotor can be specified for a megawatt for ten seconds or a hundred kilowatts for a hundred. ### Form of energy storage The stored energy is E = ½·I·ω², and the moment of inertia is I = Σ m·r² over the rotor's mass, which for common shapes is written I = β·m·R² with a dimensionless shape number β.[^idema-inertia] A thin hoop has β = 1 because all its mass sits at R; a solid cylinder has β = ½; a solid sphere has β = 2/5.[^idema-inertia] The same β appears in the classic rolling race, where the acceleration of a body rolling down an incline is a = g·sin θ/(1 + β) and mass and radius cancel entirely — a reminder that shape numbers, not sizes, govern rotational problems.[^idema-roll] Writing ω = v/R, the energy becomes E = ½·β·m·v², where v is the rim speed. Rim speed, not rpm, is therefore the physical variable, and this is why the sim's rpm slider is coupled to the radius: 10,000 rpm on a 0.1 m rotor and 2,000 rpm on a 0.5 m rotor are the same machine. ### Specific energy For a thin rim spinning freely the tensile hoop stress is σ = ρ·v², a standard result of rotating-ring mechanics and the only equation on this page that no Energy Portal Book covers.[^hoop] Setting v² = σ/ρ in E/m = ½·β·v² gives E/m = K·σ/ρ, with K = β/2, so a thin rim reaches K = ½. The mass cancels; so does the radius. **The specific energy of a flywheel is half its material's specific strength, and nothing else.** For a uniform-thickness disk the peak stress moves to the centre and takes the standard form σ_max = ((3 + ν)/8)·ρ·v², which with ν = 0.3 gives K ≈ 0.61 — better than a rim, because more of the material is working below its limit.[^hoop] Shape factors for real profiles all sit within a factor of about two of ½. | Rotor material | ρ (kg/m³) | σ (MPa) | σ/ρ (kJ/kg) | E/m at K = ½ | |---|---|---|---|---| | [[Carbon_steel|High-strength steel]] | 7,800 | 1,000 | 128 | 17.8 Wh/kg | | [[Aluminium_alloy|Aluminium alloy]] | 2,700 | 500 | 185 | 25.7 Wh/kg | | [[Carbon_fiber_reinforced_polymer|Carbon fibre composite]] | 1,600 | 2,000 | 1,250 | 174 Wh/kg | *ILLUSTRATIVE. The E/m column is computed from K·σ/ρ; the density and strength columns are external reference figures for the sim's three presets and are not drawn from any Portal Book.[citation needed] What the sim actually varies is the ratio σ/ρ, and the ordering — composite above aluminium above steel — is what the ratio says, even though steel is by far the stronger material in absolute terms.* That last point is the one readers most often get backwards. Steel is twice as strong as the aluminium alloy here and stores less per kilogram, because it is nearly three times as dense. [[Specific_strength|Specific strength]], not strength, is the figure of merit, which is why rotors migrated to wound [[Composite_material|composites]] as soon as the fibres became available. ### Tensile strength and failure modes Because stress rises as v² while energy rises as v², the margin against burst and the stored energy are the same quantity seen twice. Run a rotor at 88 % of its limiting rim speed and it holds 77 % of its burst energy; there is no operating point that is both safe and full. A worked case: a 200 kg steel rim of radius 0.5 m at 6,000 rpm has ω = 628 rad/s and v = 314 m/s, giving I = 50 kg·m², E = 9.87 MJ = 2.74 kWh, and E/m = 49.3 kJ/kg (derived) — about 77 % of the stress limit in the table above, and about 13.7 Wh/kg. Failure is the design driver. If that 2.74 kWh is released in ten milliseconds the burst is a 987 MW event (derived), which is why flywheel stores are put in pits, in armoured housings, or underground. [[Fatigue_(material)|Fatigue]] and [[Creep_(deformation)|creep]] set the real service limit well below the single-cycle burst strength, since a store cycled tens of thousands of times a year sees its rim stress swing on every cycle. ### Energy storage efficiency A flywheel's round-trip efficiency has three terms, and only one of them is about the rotor. The motor–generator loses a few percent in each direction; the power electronics lose a little more; and the rotor itself loses continuously to **windage** and **bearing drag** while it simply waits. Aerodynamic drag scales with the square of rim speed and with gas density, so a hard vacuum is not a refinement but a requirement at 300 m/s. Friction is on the standard list of thermodynamic irreversibilities, and every joule it removes is gone.[^yan-irrev] The general rule of the storage root article applies without exception: storage by conversion is always lossy.[^kerlin-lossy] The consequence is a sharp split between the two efficiencies. Cycle a flywheel in seconds and the round trip is excellent, because the standby loss has had no time to act. Leave it charged overnight and the standby loss dominates, and the round trip collapses. Duration, once again, picks the store. ### Effects of angular momentum in vehicles A spinning rotor stores [[Angular_momentum|angular momentum]] L = I·ω as well as energy, and angular momentum is a vector.[^idema-gyro] The 200 kg rim above carries L = 31,400 kg·m²/s. With its axis horizontal and the vehicle yawing at 0.5 rad/s, the rotor demands about 15,700 N·m from its mounts, τ = L × Ω about an axis perpendicular to both (derived) — felt as a pitching moment through the turn. The same relation, τ = dL/dt, is why a top precesses instead of falling, at a rate ω_p = m·g·r/(I·ω): the faster it spins, the slower it precesses. Earth does the same thing, its 23.4° tilt sweeping a cone in about 25,000 years.[^idema-gyro] Vehicle designs remove the nuisance in three ways: mount the spin axis vertically so that yaw is about the same axis and produces no cross-torque; gimbal the rotor so it can keep its orientation while the vehicle turns; or use a counter-rotating pair whose angular momenta cancel. Note that L = I·ω holds only about a symmetry axis; an off-axis rotor needs the full inertia tensor.[^idema-gyro] ## Applications Flywheels appear wherever a job needs large power for a short time, or a very large number of cycles, or both. ### Transportation Vehicle flywheels recover braking energy and give it back on the next acceleration — a duty that is all power and no duration, and therefore the one flywheels are best suited to. The store is sized by the energy of one stop, and the machine by the power of one stop, which is why a vehicle flywheel can be small even on a heavy vehicle. ### Uninterruptible power supplies A flywheel between the mains and a critical load rides through a voltage sag or a short outage and holds the load up for the seconds a standby generator needs to start. This is the application where a flywheel's poor standby efficiency does not matter at all, because the store is topped up continuously and is expected to discharge for only a few seconds a year. ### Test laboratories Pulsed test facilities draw power far above their supply connection for a fraction of a second. A flywheel decouples the two: it is charged slowly over minutes from a modest feed and emptied in a fraction of a second into the test article, which is exactly the arbitrage the E = ½·I·ω² store makes cheap. ### Physics laboratories Large experimental machines use the same trick to avoid disturbing the grid they sit on: the motor–generator becomes the pulse supply, and the grid sees only a steady charging load.[^mitofsky] ### Aircraft launching systems Catapult launch is a pure high-power problem: a large mass brought to flying speed in a couple of seconds. A rotating store charged between launches and emptied into a linear motor matches that duty exactly, and is controlled electrically rather than by a valve. ### NASA G2 flywheel for spacecraft energy storage A spacecraft flywheel can do two jobs with one rotor: store the energy collected by the [[Solar_cell|solar]] array through the sunlit part of the orbit, and provide attitude-control torque through the same angular momentum that any store necessarily carries. That combination replaces both the [[Electric_battery|battery]] and the reaction wheels, and it exploits the vehicle's natural vacuum. [[NASA|NASA]] Glenn's G2 test unit is the pair's worked example, and the programme detail belongs to the pair. ### Amusement rides A launched roller coaster is a catapult with a shorter track. The ride draws a modest feed between trains, stores it in a rotor, and empties it into a linear motor in two or three seconds — the same power-arbitrage duty, sized for passengers rather than aircraft. ### Pulse power Welding, forming, electromagnetic launchers and plasma experiments all want megawatts for milliseconds. The flywheel's advantage over a [[Capacitor|capacitor]] bank here is energy density, and its disadvantage is that it cannot deliver its energy in microseconds — the machine and the electronics set a floor on discharge time that the rotor does not. ### Motor sports Racing use is short-duration braking recovery under a strict mass budget, the case where the σ/ρ ordering of the table above decides the design outright: the rotor is composite, small, and spun as fast as containment permits, because every kilogram of rotor and housing is a kilogram not spent elsewhere. ### Grid energy storage On the grid a flywheel bank is a frequency-regulation asset rather than an energy asset. It answers second-to-second imbalances between generation and load, charging and discharging thousands of times a day — a duty that would consume a battery's electrodes and does nothing at all to a rotor.[^theis] For bulk shifting across hours the grid uses [[Pumped-storage_hydroelectricity|pumped hydro]] or batteries instead.[^kerlin-batteries] ### Wind turbines A flywheel in a [[Wind_turbine|wind turbine]] nacelle smooths the torque pulsations of the rotor and buffers gusts, which reduces fatigue loading on the drivetrain and steadies the electrical output. The store is measured in seconds, not hours; the turbine's own rotor is itself a large flywheel and supplies part of the same effect for free. ### Toys The friction motor in a toy car is a flywheel store: a child pushes it along the floor, gearing spins a small steel disk to a few thousand rpm, and the disk drives the wheels back. It is the whole technology in miniature, losses included — the toy runs down in seconds for want of a vacuum and decent bearings. ### Toggle action presses A mechanical press is the oldest industrial use of the principle. A small continuous motor spins a heavy wheel through the idle part of the stroke, and the toggle linkage spends that stored rotation in the fraction of a second the punch is in the work — so the motor is sized for average power and the press for peak force. ## Comparison to electric batteries Against a [[Electric_battery|battery]], a flywheel wins on power, on cycle life, on temperature tolerance and on state-of-charge measurement, which for a rotor is simply a speed reading rather than an inference from voltage. It loses on specific energy and, decisively, on standby loss. The table above puts a good composite rotor near 174 Wh/kg at K = ½ for the rotor material alone, before any housing, machine or electronics are counted, while a battery cell's figure is for a complete cell — the comparison flatters the flywheel considerably.[^haverkort-batteries][^kerlin-batteries] The deeper difference is what cycling costs. A battery stores energy in a chemical reaction that also, slowly, destroys the electrodes, so its life is counted in cycles. A flywheel stores energy in a velocity field and its life is counted in stress cycles of the rim and hours on the bearings, neither of which depends on how deeply it is discharged.[^haverkort-batteries] The result is a clean division of labour, visible as a diagonal on the storage root article's Ragone plane: the flywheel takes the seconds, the battery takes the hours, and the fuel takes the seasons.[^murphy-ke][^murphy-app] ## See also - [[Flywheel]] - [[Moment_of_inertia]] - [[Rotational_energy]] - [[Energy_storage]] - [[Kinetic_energy]] - [[Specific_strength]] - [[Composite_material]] - [[Grid_energy_storage]] ## References [^idema-inertia]: Idema, Timon (2018). *Mechanics and Relativity*. Part I, "Classical mechanics", pp. 66–67: the moment of inertia `I = Σ m·r² = ∫ ρ·r²·dV`; Table 5.1 of shape factors (hoop MR², solid cylinder ½MR², solid sphere ⅖MR², rod about its end ⅓ML², plate 1/12·M(a²+b²)); the parallel- and perpendicular-axis theorems; and the rotational kinetic energy `K_rot = ½·I·ω²` with `W = ∫ τ·dθ`. Portal Book 080, https://open.umn.edu/opentextbooks/textbooks/mechanics-and-relativity [^idema-roll]: Idema (2018), *Mechanics and Relativity*, pp. 70–71 (a solid cylinder rolls down an incline at a = (2/3)·g·sin θ, derived three ways; the general form a = g·sin θ/(1 + I/(m·R²)) shows mass and radius cancelling). Note that the book's prose garbles the solid-cylinder inertia; Table 5.1's ½MR² is the value to use. Portal Book 080. [^idema-gyro]: Idema (2018), *Mechanics and Relativity*, pp. 68 and 71–72 (L = I·ω holds only about a symmetry axis; τ = dL/dt; the precession rate ω_p = m·g·r/(I·ω) for a symmetric top; Earth's 23.4° tilt precesses in about 25,000 years, with an 18.6-year lunar nutation). The 31,400 kg·m²/s and 15,700 N·m figures on this page are computed from I·ω and τ = L×Ω. Portal Book 080. [^hoop]: Standard form supplied, and flagged: the rotating-ring hoop stress σ = ρ·v², and the uniform-disk peak stress σ_max = ((3 + ν)/8)·ρ·v², are textbook results of rotating-body mechanics that no Energy Portal Book in this set covers — sub-manual 10 has no flywheel topic, and sub-manual 02 §7.1 supplies the inertia and energy halves only. Both forms, and the K ≈ 0.61 that follows from ν = 0.3, should be checked against a strength-of-materials text before being promoted to a unit test. [^murphy-ke]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Chapter 5, pp. 89–93 (Table 5.2 lists `½·m·v²` as the energy form behind wind and ocean-current power; 1 kWh = 3.6 MJ; "power is the speedometer and energy the odometer"). Portal Book 097, https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet [^murphy-app]: Murphy (2021), Appendices, pp. 378–431 (battery, gravitational and kinetic-energy storage compared; page to pin). Portal Book 097. [^kerlin-lossy]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*. Chapter 3, p. 188 ("storage by conversion is always lossy"). Portal Book 048, https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges [^kerlin-batteries]: Kerlin (2013), *Future Energy*, Chapter 9, pp. 354–466 (batteries, their duty cycles and their limits; page to pin). Portal Book 048. [^haverkort-batteries]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Chapter 7, "Batteries", pp. 110–129 (cell energy density, and the ageing of electrodes that ties battery life to cycles; page to pin). Portal Book 053, https://open.umn.edu/opentextbooks/textbooks/electrolysers-fuel-cells-and-batteries-analytical-modelling [^yan-irrev]: Yan, Claire Yu (2022). *Introduction to Engineering Thermodynamics*. Chapter 6, p. 269 (the list of irreversibilities: friction, unrestrained expansion, mixing, heat transfer across a finite ΔT, electrical resistance, inelastic deformation, chemical reaction). Portal Book 115, https://open.umn.edu/opentextbooks/textbooks/introduction-to-engineering-thermodynamics [^mitofsky]: Mitofsky, Andrea (2018). *Direct Energy*. Part I, "Survey of Energy Conversion Devices", pp. 33–254 (electrical machines treated as reversible converters between shaft power and terminal power; page to pin). Portal Book 055, https://open.umn.edu/opentextbooks/textbooks/direct-energy [^theis]: Theis, Tom; Tomkin, Jonathan, eds. (2015). *Sustainability: A Comprehensive Foundation*. Chapter 10, "Sustainable Energy Systems" (short-duration storage and grid regulation alongside variable renewable supply; page to pin). Portal Book 098, https://open.umn.edu/opentextbooks/textbooks/sustainability-a-comprehensive-foundation [^super-note]: No Energy Portal Book in this set treats superconducting bearings; the description here is limited to what follows from flux pinning — a passive, control-free equilibrium — and from the standing power draw of the cryogenic plant, and asserts no performance figures. ## Further reading - Idema, *Mechanics and Relativity* (2018), Part I, §5 (moment of inertia, rotational energy, angular momentum and precession) — Portal Book 080. - Murphy, *Energy and Human Ambitions on a Finite Planet* (2021), Chapter 5 and the Appendices — Portal Book 097. - Haverkort, *Electrolysers, Fuel Cells and Batteries: Analytical Modelling* (2024), Chapter 7 — Portal Book 053. - Kerlin, *Future Energy: Opportunities & Challenges* (2013), Chapter 9 — Portal Book 048. ## External links - [Mechanics and Relativity](https://open.umn.edu/opentextbooks/textbooks/mechanics-and-relativity) (Idema, 2018) — Portal Book 080; the rotational-dynamics chapter behind this page's energy and inertia relations - [Energy and Human Ambitions on a Finite Planet](https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet) (Murphy, 2021) — Portal Book 097 - The Wikipedia pair's external links list manufacturer and programme pages for the installations named above <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Flywheel_energy_storage.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Flywheel energy storage* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Flywheel_energy_storage.html" data-title="Flywheel energy storage"></div> *Built from `MICROSIM_GUIDE/specs/sims/Flywheel_energy_storage.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Flywheel_energy_storage) : [Wikitube](https://en.wikitube.io/wiki/Flywheel_energy_storage) · pinned revision [1373054797](https://en.wikipedia.org/w/index.php?oldid=1373054797) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Energy]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Energy row E64 · sim pending (matter/Flywheel_energy_storage).*