# Tidal power **Tidal power**, or tidal energy, is [[Hydroelectricity|hydropower]] taken from the rise and fall of the [[Tide|tides]] and from the currents the tides drive. It comes in two families that obey two different equations. A barrage or a lagoon impounds water at high tide and releases it at low tide, so the resource is a *head*: the [[Potential_energy|potential energy]] of a basin standing above the sea. A [[Tidal_stream_generator|tidal stream generator]] is an underwater [[Wind_turbine|wind turbine]] planted in a fast channel, so the resource is a *flux*: the [[Kinetic_energy|kinetic energy]] carried past a swept area, `P = ½·ρ·A·v³`.[^k048-wind][^k048-hydro] In the microsim below the reader slides one current speed and flips a single toggle between water and air, and the same cubic law is evaluated twice. Kerlin's US-unit forms make the comparison brutal: for water, Betz-capped, `P[W] = 2.44·r²·f³` with r in feet and f in feet per second; for air at 1.2 kg/m³, uncapped, `P[W] = 0.00496·r²·v³`.[^k048-hydro][^spec-e44] A 10 ft rotor in a 10 ft/s current — 6.8 mph, a walking pace — yields 244 kW, while a ghost marker rides the other curve at 9.4 times the speed, the cube root of water's 833-fold [[Density|density]] advantage, to show that [[Wind_power|air]] needs a 64 mph hurricane for the same power.[^k048-hydro][^derived-tp] Two preset panels switch the equation that answers: `E = ½·ρ·g·A·h²` for the energy stored behind a barrage each tide, and `P = ρ·g²·H_s²·T_e/(64·π)` for the [[Wave_power|wave]] power crossing each metre of crest.[^spec-e44][^smyth] On the [[Energy]] flagship this article serves the *Tides and waves* section of Part V — Transformation, and its sim is the water sibling of the [[Wind_power|wind]] one: the same equation, a different ρ. ## Principle Tides are the ocean's response to the [[Gravity|gravitational]] pull of the [[Moon]] and the [[Sun]] on a rotating [[Earth]]. Energy taken from them is ultimately taken from the [[Angular_momentum|angular momentum]] of the Earth–Moon system, which makes tidal power the one renewable resource that is not sunlight in disguise — and the one that is exactly predictable years ahead, since it is set by orbits rather than by weather.[^murphy-app][^k048-wave] The flux form is the sim's spine. The power crossing a disc of area A in a fluid of density ρ moving at speed v is `P = ½·ρ·A·v³`, Kerlin's Eq. 8-1: doubling the speed multiplies the power by eight.[^k048-wind] No machine can take all of it, because the water must keep moving to get out of the way; the Lanchester–Betz–Joukowsky limit caps extraction at 59 % of the flux, and Kerlin applies that same ceiling to water turbines as to [[Wind_turbine|wind turbines]].[^k048-wind][^k048-hydro] In US units the uncapped form is Eq. 9-5, `P[W] = 4.13·r²·f³`, and the Betz-capped form Eq. 9-6, `P[W] = 2.44·r²·f³`; the check 4.13 × 0.59 = 2.44 closes.[^k048-hydro][^derived-tp] Example 9.2 puts r = 10 ft and f = 10 ft/s into Eq. 9-6 and gets 244 kW *before* turbine and generator losses, which run about 10 % in large machines.[^k048-hydro][^k048-turb] Density is the whole argument for the sea. Water is "over 800 times" denser than air; with the standard 1.2 kg/m³ for air the ratio is 833, so at equal speed water carries 833 times the power, and equal power needs 833^(1/3) = 9.4 times the air speed.[^k048-hydro][^derived-tp] That is why a tidal rotor can be small and slow where a wind rotor must be enormous and fast. The cube cuts the other way too: a 10 % error in the current estimate is a 33 % error in the power, so tidal-stream site surveys are dominated by measuring v, not by choosing the machine.[^k048-hydro] ## Methods Four arrangements are in use or under study, and they sort by which of the two resources they take. The first takes the flux, `P = ½·ρ·A·v³`, straight from an open current; the next two take the head, `E = ½·ρ·g·A·h²`, from an impounded basin; the fourth tries to manufacture a head where none exists. ### Tidal stream generator A tidal stream generator is the sim's default case: a rotor in an open current, governed by `P = ½·ρ·A·v³` and capped by [[Betz's_law|Betz's law]].[^k048-wind][^k048-hydro] Because ρ is large, the machine turns slowly and delivers its power as [[Torque|torque]] rather than speed, which moves the engineering problem from the blades to the drivetrain and the seabed mounting. Blade loading also sets a hard ceiling on tip speed: where the local [[Pressure|pressure]] on the suction side falls below the vapour pressure of seawater, [[Cavitation|cavitation]] begins and both thrust and blade surface suffer. Sites are therefore chosen for a narrow band of current — fast enough that v³ pays, slow enough that the rotor survives. Because power varies as the cube, a channel with twice the peak current is worth eight identical channels, and the practical resource collapses into a handful of straits and races rather than spreading along a coast.[^derived-tp] ### Tidal barrage A barrage closes an estuary with a dam of sluices and low-head [[Turbine|turbines]], fills the basin on the flood and empties it through the machines on the ebb. For a basin of plan area A and tidal range h the stored [[Potential_energy|potential energy]] per tide is `E = ½·ρ·g·A·h²`, because the average parcel of the trapped slab falls half the range.[^spec-e44] With seawater at 1,025 kg/m³ and g = 9.81 m/s², one square kilometre at a 5 m range holds 1.26×10¹¹ J = 34.9 MWh per tide; at 706 semidiurnal tides a year that is 24.6 GWh, an average of 2.8 MW per km² before any conversion loss and before the halving that one-way ebb generation costs.[^derived-tp] The square in h is the site-selection rule: double the range and the same basin is worth four times as much. The head is small, so the flow must be huge. Kerlin's Eq. 9-2, `P[W] = 84.6·Q[ft³/s]·h[ft]`, gives 72,000 ft³/s for 100 MW at a 5 m (16.4 ft) head — comparable to a large river, forced through the dam twice a day.[^k048-hydro][^derived-tp] That is why barrages are wide, why they use bulb turbines that pass great volumes at a few metres of head, and why the civil works, not the machinery, dominate the cost.[^k048-wave] ### Tidal lagoon A tidal lagoon is a barrage that impounds a piece of open coast inside its own wall instead of plugging an estuary, so the tidal range of the estuary and its ecology are left intact. The energy equation is unchanged, `E = ½·ρ·g·A·h²`, but the economics scale differently: a roughly circular lagoon of radius R has area πR² behind a wall of length 2πR, so energy per metre of wall grows in proportion to R.[^derived-tp] Big lagoons are therefore cheap per kilowatt-hour and small ones are not, which is why every serious proposal has been large. ### Dynamic tidal power Dynamic tidal power proposes a long dam running straight out from the coast, crossing no bay and enclosing nothing. The tidal wave travels along the shore, so at any instant the water on one side of such a dam stands higher than on the other, and turbines set along its length work on that difference. The concept converts a phase lag into a head where no estuary offers one, and it suits shelf seas with a strong along-shore tidal wave. No dynamic tidal power plant has been built, and the published performance figures are model results, so this page treats the scheme as a proposal rather than a technology.[^spec-e44] ## US and Canadian studies in the 20th century The Bay of Fundy and Passamaquoddy Bay, at the mouth of the bay on the United States–Canada border, have the largest tidal ranges on Earth, and they have been surveyed for power since the 1920s. Construction began at Passamaquoddy in 1935 as a federal relief project and was abandoned the following year, leaving the works that became Quoddy Village; joint United States–Canada commissions returned to the site repeatedly without a plant following.[^ijc-quoddy] The one North American machine that was built is the Annapolis Royal Generating Station on the Annapolis River in Nova Scotia, a 20 MW single-turbine barrage commissioned in 1984 and shut down in 2019.[^nspower] The arithmetic behind every one of these studies is the barrage equation: Fundy's range makes `h²` large enough that the head route is worth the civil cost, which is not true of most of the continent's coastline.[^derived-tp] ## US studies in the 21st century Twenty-first-century work in the United States moved from barrages to streams and from construction to measurement. The Department of Energy's marine energy programme has funded national resource assessments, instrumented test sites, and a small number of grid-connected demonstrations, of which the best known is the array set in the tidal reach of New York's East River.[^doe-marine] The effort is a measurement programme first because of the cube: since `P ∝ v³`, a 2.5 m/s channel is worth 4.6 times a 1.5 m/s one, so a national resource estimate is worth almost exactly as much as its measurements of v at a few dozen sites.[^derived-tp][^k048-hydro] ## Rance tidal power plant in France The Rance plant in Brittany, commissioned in 1966 with 24 bulb turbine-generators and a nameplate capacity of 240 MW, was the world's first industrial-scale tidal power station and was the largest for forty-five years.[^edf-rance] The estuary's range reaches about 13 m, and the impounded basin covers roughly 22 km².[^edf-rance] Putting those into `E = ½·ρ·g·A·h²` with a mean range near 8 m gives 7.1×10¹² J per tide — about 1,970 MWh, or 1.39 TWh a year over 706 tides.[^derived-tp] Reported annual output is near 0.5 TWh, roughly a third of that ideal, which is what two-way operation at partial head, turbine and generator losses, and the need to hold water for the grid rather than for the equation actually cost.[^edf-rance][^derived-tp] The gap between the two numbers is the honest content of the barrage equation: it is a ceiling, not a forecast. ## Tidal power development in the UK The Severn estuary has one of the largest tidal ranges in the world, and a Severn barrage has been proposed, studied and shelved for more than a century. The most recent government feasibility study concluded in 2010 that no scheme in the Severn should be taken forward at that time, on cost and environmental grounds, while leaving the resource formally recognised.[^decc-severn] British effort since has gone to tidal streams, above all in the Pentland Firth between the Scottish mainland and Orkney, where the MeyGen project installed four 1.5 MW seabed turbines and began delivering power to the grid in 2017.[^meygen] A proposed lagoon in Swansea Bay would have tested the third method at scale; it did not proceed.[^decc-severn] ## Current and future tidal power schemes The largest tidal plant now operating is the Sihwa Lake station in South Korea, 254 MW, opened in 2011 inside a sea wall built for other reasons: the cheapest barrage is an inherited dam.[^kwater] Tidal stream arrays remain small — a few tens of megawatts worldwide, in the Pentland Firth, the Bay of Fundy and a handful of European channels.[^meygen][^doe-marine] Against the planetary [[Energy|energy]] budget the ceiling is modest: total oceanic tidal dissipation is a small fraction of human primary energy use, and only the part concentrated in shallow estuaries and narrow straits is reachable.[^murphy-app] Tidal power's argument is not scale but timing: its output is a published timetable, which makes it easier to fit to a [[Electrical_grid|grid]] than either [[Wind_power|wind]] or sunlight.[^theis-098] ## Issues and challenges The physics is settled; the difficulties are all in the estuary, the metal and the money. In order, they are what the plant does to the water, what the water does to the plant, and what either of those costs — and none of them is a question the equations above can answer. ### Environmental concerns A barrage changes the thing it exploits. Reducing the tidal range inside the basin alters the intertidal zone on which estuarine [[Ecosystem|ecosystems]] depend, traps sediment that the tide used to move, and puts turbines across a migration route for fish. Tidal stream turbines leave the range alone and are far less intrusive, but they occupy exactly the fast channels that concentrate marine traffic and feeding, and they add [[Sound|underwater noise]] at the frequencies of the rotor and its drivetrain. Because the barrage's energy goes as `h²`, any mitigation that reduces the working range is expensive in a way that has no analogue in [[Wind_power|wind]].[^derived-tp][^k048-wave] ### Corrosion Seawater is an electrolyte, so every immersed structure is a potential cell and [[Corrosion|corrosion]] is continuous rather than occasional.[^corrosion-eng] Dissimilar metals in contact — a [[Bronze|bronze]] propeller on a [[Steel|steel]] shaft, [[Stainless_steel|stainless]] fasteners in a [[Cast_iron|cast iron]] housing — drive [[Galvanic_corrosion|galvanic corrosion]] at the junction, and the standard defences are electrical rather than chemical: [[Cathodic_protection|cathodic protection]] with sacrificial anodes or an impressed current, plus coatings and, where it can be afforded, [[Titanium|titanium]] or a duplex [[Alloy|alloy]].[^corrosion-eng] The cost falls on maintenance, because every inspection of a subsea machine is a marine operation. ### Fouling Marine organisms settle on any surface left in productive water. On a rotor, growth roughens the blade, thickens its section and shifts the point at which flow separates, so the machine's efficiency falls even though the current has not changed; on a barrage it blocks trash racks and cooling passages. Since the recoverable power is already capped at 59 % of the flux, a few percentage points lost to roughness is a direct cut in revenue, and fouling — unlike corrosion — returns on a seasonal schedule.[^k048-wind][^k048-wave] ### Cost Tidal power is capital-heavy and fuel-free, so its cost per kilowatt-hour is set almost entirely by the civil works, the discount rate and the [[Capacity_factor|capacity factor]]. A barrage generates only while a usable head exists, a stream turbine only while the current runs, and both go to zero four times a day at slack water; annual energy is rated power times 8,760 hours times availability, and for tidal machines the availability term is small.[^k048-hydro][^k048-turb] Against that, the plant is long-lived, the resource is free and its timetable is known, which is why tidal schemes tend to be justified on decades rather than on years.[^theis-098] ## Structural health monitoring A tidal machine works in a place people cannot easily reach, under a load that reverses twice a day, so it is instrumented instead of inspected. [[Sensor|Sensors]] on the blades, shaft and foundation report strain, [[Vibration|vibration]] and temperature; the raw streams are reduced by [[Fourier_analysis|spectral analysis]] to a handful of tracked resonances, and a shift in a natural frequency or a change in [[Signal_processing|damping]] flags a crack, a loosened bolt or a fouled blade before it becomes a failure.[citation needed][^shm-cn] The reversing load is what makes this worth doing: each tide is a full cycle, so the structure accumulates [[Fatigue_(material)|fatigue]] damage on a clock, and a [[Finite_element_method|finite element]] model updated against the measured frequencies converts that clock into a remaining-life estimate. The same argument applies with more force to the dam of a barrage, where dam failure is the main safety concern and the consequence of it is far larger than the loss of a turbine.[^k048-turb] ## See also - [[Wave_power]] — the other marine flux, `P = ρ·g²·H_s²·T_e/(64·π)` per metre of crest - [[Tidal_barrage]] - [[Tidal_stream_generator]] - [[Marine_energy]] - [[Dynamic_tidal_power]] - [[Tide]] — where the resource comes from - [[Wind_wave]] - [[Tsunami]] - [[Wind_power]] — the sibling sim, same equation with air's ρ - [[Betz's_law]] ## References [^k048-wind]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*. Chapter 5 (pp. 217–231): Eq. 8-1 `P = ½·ρ·A·v³`, the eightfold power gain for doubled speed, and the Lanchester–Betz–Joukowsky 59 % limit, p. 221. https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges [^k048-hydro]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*. Chapter 6 (pp. 232–248): Eq. 9-2 `P[W] = 84.6·Q·h`, p. 237; water "over 800 times" denser than air and the Betz cap applied to water turbines, pp. 241–242; Eq. 9-5 `P = 4.13·r²·f³` and Eq. 9-6 `P = 2.44·r²·f³`, p. 242; Example 9.2 giving 244 kW for r = 10 ft and f = 10 ft/s, pp. 242–243. https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges [^k048-turb]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*. Chapter 6: large turbine-generators reach about 90 % efficiency, p. 238; annual energy as rated power × 8,760 h × availability, p. 229; dam failure as the main safety concern, p. 245. https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges [^k048-wave]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*. Chapter 6, pp. 243–245: the tidal-barrage cycle and wave-energy converter types, given qualitatively; the extract carries no equations for either. https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges [^murphy-app]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Appendices, pp. 378–431 (tidal resource and planetary energy budget; page to pin). Chapter 6, *Alternative Energy*, pp. 183–322, frames the comparison of renewable resources against total human use. https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet [^smyth]: Smyth, William (2019). *All Things Flow: Fluid Mechanics for the Natural Sciences*. Surface-gravity-wave chapter (page to pin), for the dispersion relation and group velocity behind the deep-water wave-power flux. The form `P = ρ·g²·H_s²·T_e/(64·π)` is the standard engineering expression and is not printed in the extract; it is supplied here as a standard form. https://open.umn.edu/opentextbooks/textbooks/all-things-flow-fluid-mechanics-for-the-natural-sciences [^theis-098]: Theis, Tom; Tomkin, Jonathan, eds. (2015). *Sustainability: A Comprehensive Foundation*. Chapter 10, *Sustainable Energy Systems* (page to pin): dispatchability and the grid integration of variable renewable sources. https://open.umn.edu/opentextbooks/textbooks/sustainability-a-comprehensive-foundation [^corrosion-eng]: The galvanic-cell account of seawater corrosion, sacrificial and impressed-current cathodic protection, and alloy selection follow the standard treatment; on this wiki see [[Galvanic_corrosion]] and [[Corrosion_engineering]], whose Portal Book citations carry the electrode potentials. No Energy Portal Book covers marine corrosion (page to pin). [^spec-e44]: Matter & Energy Cluster contract, `_registry/plans/ENERGY_SECTIONS.md` row E44: the sim concept (water sibling of `Wind_power`), the fluid toggle between `P[W] = 2.44·r²·f³` and `P[W] = 0.00496·r²·v³`, the ghost marker at the equal-power speed ratio 9.4, the barrage preset `E = ½·ρ·g·A·h²` per tide and the wave preset `P = ρ·g²·H_s²·T_e/(64·π)` per metre of crest. The contract records the flux form of the wave preset as a documented gap. [^derived-tp]: Computed for this article from the equations on the page and the constants cited: 4.13 × 0.59 = 2.44; the air constant 0.00496 at ρ = 1.2 kg/m³, giving a density ratio of 833 and an equal-power speed ratio of 833^(1/3) = 9.4, so 10 ft/s of water matches 94 ft/s = 64 mph of air; 10 ft/s = 6.8 mph = 3.05 m/s; the barrage basin at ρ = 1,025 kg/m³ and g = 9.81 m/s², `E = ½·ρ·g·A·h²` = 1.26×10¹¹ J = 34.9 MWh per km² per tide at h = 5 m, × 706 semidiurnal tides per year (8,766 h ÷ 12.42 h) = 24.6 GWh/yr = 2.8 MW average; `Q = P/(84.6·h)` = 72,000 ft³/s for 100 MW at 16.4 ft; the Rance figure `E` = 7.1×10¹² J = 1,970 MWh per tide for A = 22 km² and h = 8 m, and 1.39 TWh/yr; the lagoon scaling πR²/(2πR) = R/2; the cube-law ratios (2.5/1.5)³ = 4.6 and 1.1³ = 1.33. [^edf-rance]: Électricité de France, technical documentation for the *Usine marémotrice de la Rance* (page to pin): commissioning in 1966, 24 bulb turbine-generators, 240 MW installed, basin area and tidal range, and reported annual output. No Portal Book covers the plant. [^kwater]: Korea Water Resources Corporation (K-water), project documentation for the *Sihwa Lake Tidal Power Station* (page to pin): 254 MW commissioned in 2011 within an existing sea wall. No Portal Book covers the plant. [^decc-severn]: United Kingdom Department of Energy and Climate Change (2010). *Severn Tidal Power: Feasibility Study Conclusions and Summary Report* (page to pin): the conclusion not to take a Severn scheme forward at that time, and the treatment of lagoon alternatives. [^meygen]: SIMEC Atlantis Energy, project documentation for *MeyGen*, Pentland Firth (page to pin): four 1.5 MW seabed turbines in Phase 1A and first grid delivery in 2017. No Portal Book covers the project. [^nspower]: Nova Scotia Power, station documentation for the *Annapolis Royal Generating Station* (page to pin): 20 MW commissioned in 1984 and taken out of service in 2019. No Portal Book covers the plant. [^ijc-quoddy]: United States–Canada International Joint Commission and United States Army Corps of Engineers, reports on the *Passamaquoddy Tidal Power Project* (page to pin): the 1935 start and 1936 abandonment of the federal works, and the later joint reviews. No Portal Book covers the project. [^doe-marine]: United States Department of Energy, Water Power Technologies Office, marine energy resource assessments and demonstration-project reporting (page to pin), including the East River tidal array. No Portal Book covers the programme. [^shm-cn]: Citation needed. The modal-tracking account of structural health monitoring for marine turbines — resonance shift and damping change as damage indicators, with a finite element model updated against measured frequencies — is standard practice, but no Energy Portal Book and no open text on this page's shelf states it; the record that would settle it is a marine-renewables condition-monitoring standard, page to pin. ## Further reading - Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapters 5 and 6 — the cubic law, the Betz cap and the US-unit hydro equations with worked examples. https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges - Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*, Chapter 6 and the Appendices — every renewable resource measured against total human demand. https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet - Smyth, William (2019). *All Things Flow: Fluid Mechanics for the Natural Sciences* — surface gravity waves, for the wave preset. https://open.umn.edu/opentextbooks/textbooks/all-things-flow-fluid-mechanics-for-the-natural-sciences - Theis, Tom; Tomkin, Jonathan, eds. (2015). *Sustainability: A Comprehensive Foundation*, Chapter 10 — energy systems and grid integration. https://open.umn.edu/opentextbooks/textbooks/sustainability-a-comprehensive-foundation ## External links - [*Future Energy: Opportunities & Challenges*](https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges) (Kerlin, 2013), the open text behind this page's equations - [*Energy and Human Ambitions on a Finite Planet*](https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet) (Murphy, 2021) - The Wikipedia pair's *External links* section lists the operator, agency and project sites for the plants named above; the Portal Books under *Further reading* are the open sources of this page. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Tidal_power.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Tidal power* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Tidal_power.html" data-title="Tidal power"></div> *Built from `MICROSIM_GUIDE/specs/sims/Tidal_power.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/Tidal_power) : [Wikitube](https://en.wikitube.io/wiki/Tidal_power) · pinned revision [1369272257](https://en.wikipedia.org/w/index.php?oldid=1369272257) · 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 E44 · sim pending (matter/Tidal_power).*