# Wind turbine A **wind turbine** is a machine that converts the [[Kinetic_energy|kinetic energy]] of moving air into rotating shaft power, almost always to drive an [[Electric_generator|electrical generator]] mounted on a tall tower and feeding an [[Electrical_grid|electrical grid]]. The tower is not merely a mast. Wind speed rises with height above the ground, and because power goes as the cube of speed, height is a power multiplier: Thomas Kerlin's Eq. 8-2 gives the approximate profile `v_h = v₀·(h/h₀)^(1/7)`, so the power ratio between two heights is `(h/h₀)^(3/7)`.[^kerlin-222] A turbine is therefore a vertical sampling instrument as much as a rotor — its disc is a slice through a wind that is not the same at the top as at the bottom. In the microsim below the reader has one control, hub height h, from 160 to 1,000 ft on a log scale, with the rotor radius fixed at the 145 ft of a real 2.5 MWe machine and a reference wind of 12.5 mph at 33 ft — the Class 3 threshold.[^kerlin-220][^kerlin-223] The tower grows, tracer particles stream faster at the top of the frame than at the bottom, and the swept disc is coloured by v(z)³. Three readouts answer the question. `P/P₃₃ft = (h/33)^(3/7)` reaches 2.48 at a 275 ft hub. The disc-averaged v³ is 0.991 of the value at hub height, so treating the whole rotor as if it saw the hub wind overstates the power by less than 1 %. And the top-to-bottom speed ratio across the disc is 1.18 — the blade tip sees 18 % more wind at the top of its circle than at the bottom, 1.65 times the power density, once every revolution.[^derived-wt][^spec-e42] On the [[Energy]] flagship this article serves *Wind shear and hub height* in Part V — Transformation, the sibling section to [[Wind_power|wind power]], whose cubic-and-Betz sim this one reuses in three dimensions. ## History Machines that take work from the wind are ancient, but the tall, three-bladed, upwind horizontal-axis machine is a twentieth-century convergence, and nothing about it is obvious in advance. Sail-wing mills, multi-bladed farm pumpers, two-bladed teetering rotors and vertical-axis designs were all built and all worked. What selected the modern form was the combination of the cube law and the shear profile: once the goal became electricity for a [[Electrical_grid|grid]] rather than mechanical work, the value of putting a large, fast, lightly loaded rotor as high as possible outweighed every argument for simplicity at ground level. ## Wind power density Wind power density is power per unit of swept area, `P/A = ½·ρ·v³` in watts per square metre, and it is the right way to describe a site because it removes the machine from the question, leaving only air [[Density|density]] and speed.[^kerlin-221] Height enters through the one-seventh law. Kerlin states Eq. 8-2 as approximate and tabulates its cube in Table 8-2; the printed table and the expression disagree in the last digit by up to 0.01, which the sub-manual flags rather than reconciles.[^kerlin-222][^manual10] | height (ft) | speed ratio, printed | speed ratio, from Eq. 8-2 | power ratio, printed | power ratio, from Eq. 8-2 | |---|---|---|---|---| | 10 | 1.00 | 1.000 | 1.00 | 1.000 | | 20 | 1.10 | 1.104 | 1.35 | 1.346 | | 50 | 1.26 | 1.258 | 1.99 | 1.993 | | 100 | 1.39 | 1.389 | 2.69 | 2.683 | | 200 | 1.53 | 1.534 | 3.62 | 3.611 | | 500 | 1.74 | 1.749 | 5.36 | 5.347 | | 1,000 | 1.92 | 1.931 | 7.21 | 7.197 | The shape of that table is the argument for tall towers, and it is an argument about diminishing returns. Going from 100 ft to 1,000 ft — a factor of ten in steel, foundation and crane — buys only 39 % more wind speed, because the exponent is 1/7. But it buys 2.68 times the power, because the exponent that matters is 3/7.[^kerlin-222][^derived-wt] Height is expensive and speed is cheap; the cube is what makes the trade worth making at all. The same law explains Table 8-1's two columns: the ratios between its 33 ft and 164 ft wind-class speeds run from 1.24 to 1.28, against (164/33)^(1/7) = 1.257.[^kerlin-220][^derived-wt] Kerlin is explicit that Eq. 8-2 holds only approximately, and at 1,000 ft it is an extrapolation well past any of his tabulated data.[^kerlin-222] ## Efficiency No rotor can take all the power in the stream it intercepts, because air stripped of all its [[Kinetic_energy|kinetic energy]] would stop and block the disc. The Lanchester–[[Betz's_law|Betz]]–Joukowsky limit sets the ceiling at 16/27 = 0.593, which Kerlin rounds to 59 % and applies to wind and water turbines alike.[^kerlin-221][^derived-wt] A real machine's power coefficient C_p, the fraction of the stream [[Power_(physics)|power]] it takes, peaks near 0.45 to 0.50 at its design tip-speed ratio and falls away on either side, and drivetrain and generator losses come on top of that.[^kerlin-221] Efficiency is also height-dependent in a way the sim makes visible. Because the rotor spans a sheared wind, the correct power is the average of v³ over the disc, not the cube of the average. For the 275 ft hub and 145 ft radius of Kerlin's machine that average is 0.991 of the hub value — a 0.9 % overestimate if the shear is ignored, small enough to neglect in an energy estimate and far too large to neglect in a fatigue calculation.[^derived-wt] ## Types ### Horizontal axis The horizontal-axis machine puts the rotor at the top of the tower, where the wind is fastest, and yaws it to face the wind. Three blades upwind of the tower is the near-universal answer: three balances the rotor without the teetering hub a two-bladed machine needs, and upwind avoids the pressure pulse a blade feels passing behind a tower. ### Vertical axis Vertical-axis machines accept wind from any direction and keep the [[Electric_generator|generator]], gearbox and brake at ground level, which makes maintenance far easier. Kerlin gives the decisive objection in one clause: they sit "where wind velocity is lowest".[^kerlin-225] Everything the one-seventh law rewards about a tall tower it takes back from a rotor that begins at the ground — and the cube turns a modest speed deficit into a large energy deficit. ### Unconventional types Ducted, shrouded and oscillating devices reappear regularly in [[Fluid_dynamics|fluid-dynamic]] guises, as do [[Airborne_wind_energy|airborne]] systems that replace the tower with a tether and fly a wing at heights no mast can reach. The airborne case is the only one that attacks the right variable: the readouts in the sim keep climbing past 1,000 ft, and a kite is the only way to get there without building the structure underneath it. ## Design and construction ### Components A modern machine is a tower, a nacelle and a rotor. The tower is a tapered [[Steel|steel]] tube on a concrete foundation, an exercise in [[Civil_engineering|civil engineering]], sized more by the overturning moment of the rotor thrust than by the weight above it. The nacelle carries the main shaft and bearings, an optional gearbox, the generator, the yaw drive and the control system. The rotor carries pitchable blades that feather to spill power above rated wind and to stop the machine above cut-out. Blade pitch is the primary control; yaw keeps the disc square to the wind; the brake is for parking, not for regulation. ### Turbine monitoring and diagnostics Because the machines are numerous, unmanned and awkward to reach, condition monitoring is not a refinement but the operating model. Vibration, [[Temperature|temperature]] and oil-debris sensing on the main bearing and gearbox convert an unscheduled crane hire into a planned one, which on a large machine is the difference between a bad year and an ordinary one. ## Technology ### Blade materials Blades are [[Composite_material|composites]] — glass or carbon fibre in epoxy — because the requirement is stiffness and [[Fatigue_(material)|fatigue]] life at the lowest possible mass, and mass at the blade tip is paid for all the way down the structure. The load case the sim illustrates is the reason fatigue dominates: a blade passing from the bottom to the top of its circle moves through an 18 % change in wind speed and a 65 % change in power density, and it does so once per revolution for twenty years.[^derived-wt] That is of order 10⁸ cycles. ### Costs At a fixed wind, blade length scales as the square root of power, so doubling a machine's rating from 2.5 to 5 MWe lengthens its blades from 145 ft to 145 × √2 = 205 ft.[^kerlin-231][^derived-wt] Mass and cost, however, scale faster than length, so the economies of upsizing are real but bounded, and each generation of larger machine needs a materials or structural change rather than a scale drawing. ### Non-blade materials A 2.5 MWe machine embodies about 500 tonnes of steel, so a fleet producing one quad a year — about 45,000 machines — represents roughly 2.25 million tonnes of it.[^kerlin-223][^kerlin-229] The concrete foundation is comparable in mass. These are the numbers that decide a wind fleet's material footprint, not the [[Neodymium|neodymium]] in the generator, though the magnet materials decide its supply-chain politics. ### Material supply Direct-drive machines trade the gearbox for a large permanent-magnet generator and therefore for rare-earth content; geared machines trade magnet supply for a gearbox that is the most failure-prone component in the nacelle. Neither choice is obviously right, which is why both are still built. ## Wind turbines on public display Decommissioned and demonstration machines standing at visitor centres, campuses and museums serve a purpose the specification sheet cannot: they make the scale legible. A 145 ft blade lying on the ground is an argument about cranes, roads and bridges that no diagram conveys. The pair maintains the list of individual display machines. ## Small wind turbines Small machines are penalized twice by the same physics. They sit low, where Eq. 8-2 says the wind is slowest — a 33 ft hub has 1/2.48 of the power density of a 275 ft hub at the same site — and their swept area scales as the square of a small radius.[^kerlin-222][^derived-wt] Mounting one on a building is worse still, because the air there is turbulent and obstructed rather than merely slow. Small wind earns its place where the comparison is not with a large turbine but with no wire at all. ## Wind turbine spacing Each rotor leaves a slower, [[Turbulence|turbulent]] wake, and a downwind machine sees both less wind and a rougher one. Through the cube, a 10 % speed deficit in a wake is a 27 % power deficit, so spacing is set by the cost of land against the value of energy lost to array effects. The wake also matters for loads: a rotor operating half in a wake and half in clean air sees an asymmetry every revolution, exactly like the shear asymmetry the sim colours, and the two add.[^derived-wt] ## Operability ### Maintenance Scheduled maintenance is cheap and unscheduled maintenance is not, because the cost is dominated by access — a crane, a vessel, a weather window. This asymmetry drives everything from the choice of gearbox to the decision to leave a fault on a machine until the next planned visit. Cold-climate blades need heaters, which does not change the aerodynamics but does change the energy budget and adds a system that can fail.[^kerlin-225] ### Repowering Replacing old machines on an existing site with fewer, larger, taller ones usually raises output more than any new site would, because the permits, roads and grid connection already exist and the new hub height moves up the (h/33)^(3/7) curve. Repowering is the cheapest height a project will ever buy. ### Demolition and recycling The tower and nacelle are [[Steel|steel]], copper and cast iron, and recycle straightforwardly. The blades do not: a thermoset [[Polymer|polymer]] composite cannot be melted back into its constituents, which is why blade disposal is the industry's one genuinely unsolved end-of-life problem and why thermoplastic and separable-resin blades are an active research line. ## Comparison with other power sources ### Advantages No fuel, therefore no fuel price, no fuel supply chain and no combustion products — the contrast with a [[Rankine_cycle|steam-cycle]] plant is total. Short construction times and modular capacity, so a project can be built in stages. Land that is shared rather than consumed, since farming continues between the towers. ### Disadvantages Output is set by the weather rather than by demand, and the cube amplifies every fluctuation. The [[Capacity_factor|capacity factor]] of around 30 % means nameplate capacity overstates energy by more than a factor of three.[^kerlin-229] The machines are visible, audible and in the way of things people value, and — unlike the impacts of a [[Fossil_fuel|fossil]] plant — theirs land almost entirely on the people nearest them. ## Records The record that matters physically is height, because that is the variable the exponents reward, and the record that follows is rotor diameter, because at a fixed wind blade length scales as √P.[^kerlin-231] Kerlin's contemporary reference machine — 2.5 MWe, a 275 ft tower and 145 ft blades — has long since been passed, and the direction of travel is exactly what the (h/33)^(3/7) readout predicts.[^kerlin-223] Individual record holders are catalogued by the pair; the equation on this page says only which way the record must move. ## See also - [[Wind_profile_power_law]] — the one-seventh law the sim animates - [[Wind_shear]] — the same profile seen from aviation - [[Wind_power]] — the root article and the cubic-and-Betz sim - [[Betz's_law]] - [[Wind_farm]] - [[Capacity_factor]] ## References [^kerlin-220]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapter 5 (pp. 217–231), pp. 220–221: Table 8-1, the seven wind classes quoted at 33 ft and 164 ft, and the Class 3 threshold of at least 12.5 mph at 33 ft. https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges [^kerlin-221]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapter 5, p. 221: Eq. 8-1, `P = (1/2)·rho·A·v^3`; doubling v multiplies P by 8; the Lanchester–Betz–Joukowsky limit caps extraction at 59 %, with turbine and generator losses on top. [^kerlin-222]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapter 5, p. 222: Eq. 8-2, `v_h = v_o·(h/h_o)^(1/7)`, stated as approximate, and Table 8-2, which tabulates the speed ratio and its cube, the power ratio `(h/h_o)^(3/7)`, at 10, 20, 50, 100, 200, 500 and 1,000 ft. [^kerlin-223]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapter 5, p. 223: a contemporary machine of 2.5 MWe with a 275 ft tower, 145 ft blades and about 500 tonnes of steel. [^kerlin-225]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapter 5, p. 225: vertical-axis machines keep the generator at ground level but sit "where wind velocity is lowest"; cold-climate blades need heaters. [^kerlin-229]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapter 5, p. 229: annual energy is rated power × 8,760 h × availability, with 30 % as the worked availability; 1 quad/yr needs about 45,000 machines of 2.5 MWe and about 2.25 million tonnes of steel. [^kerlin-231]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapter 5, p. 231: at a fixed wind speed, blade length scales as the square root of power (Exercise 8-4, unworked: a 5 MWe machine needs 145 × √2 = 205 ft blades). [^derived-wt]: Computed for this article from Eq. 8-2 and the cited book values on this page: the Eq. 8-2 column of the Table 8-2 comparison (1.104/1.346, 1.258/1.993, 1.389/2.683, 1.534/3.611, 1.749/5.347, 1.931/7.197), which differs from the printed table by up to 0.01 in the last digit; (164/33)^(1/7) = 1.257 against Table 8-1's printed 1.24–1.28; the 100 ft → 1,000 ft gains of 39 % in speed and 2.68 in power; `P/P_33ft = (275/33)^(3/7)` = 2.48, and its reciprocal as the small-turbine penalty; the hub speed 12.5 × (275/33)^(1/7) = 16.9 mph; the top-to-bottom ratio across a 145 ft-radius disc on a 275 ft hub, (420/130)^(1/7) = 1.182, whose cube is 1.65; the disc-averaged v³ of 0.991 of the hub value, from the area-weighted mean of (z/h)^(3/7) over the disc; the Betz value 16/27 = 0.5926 against the book's 0.59; and the wake arithmetic, 0.9³ = 0.729, a 27 % power deficit for a 10 % speed deficit. The C_p range of 0.45–0.50 and the order-10⁸ blade cycle count are representative engineering figures, not book values. [^manual10]: Wikitube MICROSIM_GUIDE sub-manual 10, *Earth, Energy and Environment*, §3.3 (wind shear: why towers are tall) and §A.2: the extract calls Table 8-2's rows "exactly" the formula, but the printed last digits differ from Eq. 8-2 by up to 0.01 in both columns, so the two are reported side by side here rather than reconciled, and tests are to be run at ±0.015. [^spec-e42]: Matter & Energy Cluster contract, `_registry/plans/ENERGY_SECTIONS.md` row E42: sim concept (`wind.shear`, three.js geometry), hub height h from 160 to 1,000 ft on a log scale growing the tower, the swept disc coloured by `v(z)^3` under `v_h = v0·(h/h0)^(1/7)`, readouts `P/P_33ft = (h/33)^(3/7)`, the disc-averaged v³ against the hub value (0.991 at 275 ft) and the top-to-bottom speed ratio (18 % at 275 ft — a load cycle every revolution), with `ParticleSystem` tracers. ## Further reading - Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*, Chapter 5, pp. 217–231 — wind classes, the cubic law, the one-seventh shear law and the fleet arithmetic. https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges - Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*, Chapter 6, Alternative Energy, pp. 183–322, for the wind resource set against total demand. https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet ## External links - [*Future Energy: Opportunities & Challenges*](https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges), Kerlin (2013) — Eq. 8-2 and Tables 8-1 and 8-2 are the source of every height figure on this page - The Wikipedia pair's *External links* section lists manufacturers, record registers and individual display machines, which this page's shelf does not carry. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/variants/Wind_turbine.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Wind turbine* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Wind_turbine.html" data-title="Wind turbine"></div> *Built from `MICROSIM_GUIDE/specs/variants/Wind_turbine.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/Wind_turbine) : [Wikitube](https://en.wikitube.io/wiki/Wind_turbine) · pinned revision [1372572948](https://en.wikipedia.org/w/index.php?oldid=1372572948) · 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 E42 · sim pending (matter/Wind_turbine).*