8. Wind Power

Wind is the sun again, wearing a disguise.

Sunlight heats the Earth unevenly — land faster than sea, equator harder than poles. Warm air rises, cool air slides in beneath it, and that moving air is wind. Somewhere between 1% and 2% of the sunlight reaching Earth ends up as atmospheric motion, which is still an enormous amount of energy. A wind turbine simply intercepts a small disc of it.

The physics of how it does that is the most counterintuitive material in Part B — and the most satisfying.

Blades are wings, not sails

The instinctive picture is wrong. People imagine wind pushing the blades round, like air in a sail or water in a Pelton bucket. That kind of machine exists — traditional windmills and the spinning cups of an anemometer work by drag — and it is poor. A drag machine can never move faster than the wind driving it, and captures relatively little energy.

A modern turbine blade is an aerofoil: the cross-section of an aircraft wing.

Air meeting that shape is deflected, and the flow over the curved upper surface is faster and at lower pressure than the flow beneath. The pressure difference produces lift — a force acting roughly perpendicular to the oncoming airflow.

That perpendicular direction is the whole trick, and it answers our hook question. Because the lift force acts sideways rather than downwind, it pushes the blade along its circular path, not backwards. Nothing stops the blade from moving faster than the air producing the force. Blade tips routinely travel at five to seven times the wind speed, which is why an enormous turbine that looks lazy from a distance has tips moving at motorway speeds.

There is a nice consequence for the blade itself. Because it is already moving fast sideways, the airflow it actually experiences is the combination of the real wind and its own motion — arriving from a shallow angle that changes along the blade’s length. That is why blades are twisted: each section is set at the correct angle for the wind it personally meets. Look closely at a stationary turbine and you can see the twist from root to tip.

The tyranny of the cube

Two scaling laws govern everything about wind, and both are unusually harsh.

Power scales with the cube of wind speed. Not linearly. Not squared. Cubed.

Double the wind speed and you get eight times the power. A 25% faster site yields almost double. This single fact explains why:

• Developers fight over specific ridgelines and coastal strips.
• Turbines are built on tall towers — wind speed rises with height above the rough, slow-moving air near the ground.
• Wind resource surveys are done for years before anyone pours concrete: a small error in estimated average wind speed becomes a large error in estimated revenue.

Power scales with the square of blade length. The rotor sweeps a circle, and a circle’s area is πr². Double the blade length and you quadruple the swept area, and so quadruple the power captured from the same wind.

Put those together and you understand the relentless growth in turbine size. Longer blades capture more area and reach higher into faster wind, while the costs that do not scale — foundation, grid connection, access road, maintenance crew visits — are spread over far more output. Early commercial machines in the 1980s had rotors tens of metres across and were rated in the hundreds of kilowatts. Modern offshore machines exceed 200 metres in rotor diameter and are rated in the range of 10–15 MW each.

Turbines also have limits at both ends. Below the cut-in speed — typically around 3 m/s — there is not enough force to bother turning. Above the rated speed, the blades deliberately “pitch” to spill excess wind and hold output at the generator’s rating. And in a storm, above roughly 25 m/s, the turbine shuts down and feathers its blades entirely, because the cube law that made it money would now tear it apart.

Onshore and offshore

Onshore wind is cheaper to build and maintain, and is where essentially all of India’s capacity currently sits.

Offshore wind sits in the sea, where the wind is faster, steadier and less turbulent — no hills or buildings to disturb it — and where capacity factors are dramatically better. It is also far more expensive: marine foundations, submarine cables, and maintenance that requires a vessel and good weather. Europe and China have built offshore wind at scale; India has surveyed sites off Gujarat and Tamil Nadu and repeatedly announced targets, but has not yet built at commercial scale.

India’s wind

Wind supplied about 50 GW of India’s installed capacity and roughly 83 TWh — about 4.6% of generation — in FY 2024-25, growing to around 54 GW by late 2025.

Geography decides everything. As of mid-2025, Gujarat led with roughly 13.8 GW — its long coastline and open Kutch plains catch the monsoon flow — and Tamil Nadu followed closely with about 11.8 GW, thanks to a genuine natural accident. The Western Ghats run down the west coast like a wall; where that wall is broken, monsoon air pours through the gap and comes out onto the plains behind at high speed, exactly like water through a narrowed channel.

Two of those breaks matter for wind. The Palghat (Palakkad) gap, between Palakkad in Kerala and Coimbatore in Tamil Nadu, feeds the wind farms of the Coimbatore–Tirupur belt. Right at the southern end of the range, near Nagercoil, comes the last break of all — the Aralvaimozhi gap, also spelt Aramboli. That is the funnel behind Muppandal, in Kanyakumari district at India’s southern tip, which grew into one of the country’s largest wind farms: roughly 1.5 GW across thousands of turbines accumulated since the 1980s.

The seasonal pattern is a genuine gift. Indian wind generation peaks during the south-west monsoon, roughly May to September — precisely the months when heavy cloud suppresses solar output. Across a year, wind and solar partly cover for each other, which is why hybrid parks that share one grid connection between both technologies are increasingly the default. It does not solve the duck curve — nothing seasonal solves a daily problem — but it means a wind-and-solar grid is less lumpy than either alone.

How much does a turbine actually deliver?

A turbine’s rating — 2 MW, 3 MW, 15 MW — is what it makes in a good, steady wind. It is not what it makes on average, because the wind is not always good and steady. The honest number is the capacity factor from Module 7: actual output over a year, divided by what the machine would have produced running flat out the whole time.

You can work India’s out from the figures above, and it is worth doing yourself. A 50 GW fleet running at full rating for every hour of a year would generate 50 GW × 8,760 hours ≈ 438 TWh. It actually generated about 83 TWh in FY 2024-25. That is 83 ÷ 438 ≈ 19%.

Two things before you quote that number anywhere. First, some of those 50 GW were switched on partway through the year and so generated for only part of it, which pulls the average down. Second, India’s fleet still contains thousands of small, short-towered machines installed in the 1980s and 1990s, which sit in slower air than a modern 100-metre tower and capture far less. Module 7’s table gives about 20% for wind, and that is this same whole-fleet average — the sum you have just done is where it comes from. The livelier numbers you will meet elsewhere, around 25–30%, describe new machines on well-chosen sites; India’s own estimates of how much wind the country could still build assume about 30%. Every one of those figures is true of a different thing, and when someone quotes a capacity factor, the useful question is always which fleet, which year.

For a feel at the scale of one machine: a 3 MW turbine on a decent modern site, at 25%, delivers 3,000 kW × 8,760 h × 0.25 ≈ 6.6 million units a year (a “unit” being one kilowatt-hour, as in Module 1). Spread across the year that is an average of about 750 kilowatts flowing continuously, day and night — a quarter of the number painted on the nameplate. Neither figure is a lie. They answer different questions.

What a wind farm actually looks like

A wind farm is mostly empty space, and that surprises people who have only seen photographs taken with a long lens, which squashes the turbines together.

Machines are set several rotor diameters apart — for a rotor 120 metres across, that means hundreds of metres between neighbours, and more along the prevailing wind direction than across it. The reason follows straight from what a turbine does. It takes energy out of the air, so the air leaving it is slower and far more churned up than the air that arrived. That slowed, turbulent trail is the turbine’s wake, and it can stretch for a kilometre or more before the surrounding wind smooths it out again. A machine standing in another machine’s wake generates less, and is shaken harder while doing it, which wears it out sooner. Laying out a wind farm is the compromise between fitting more turbines onto the land you have leased and letting each one see clean wind.

All that spacing has a happy consequence: the ground in between stays in use. Only the tower bases, the access tracks and the substation are genuinely built on, so a wind farm’s real footprint is a small fraction of the area it spans. In Tamil Nadu and Gujarat, turbines stand in ordinary fields and grazing land with the farming carrying on underneath them — which is not remotely true of a coal mine or a large reservoir.

The objections, honestly

Wind is not a free lunch, and pretending otherwise is how projects get stopped.

Noise. Each blade makes a rhythmic swish as it passes the tower, and the machinery in the housing at the top hums. It is not loud from a distance, but it is unfamiliar, it never stops, and on a still night it carries. This is why planning rules generally set a minimum distance between a turbine and the nearest house.

Birds and bats. Turbines do kill them. The honest position is that the risk depends overwhelmingly on where the farm is built: a row of turbines across a migration route, or beside country used by eagles and vultures, is a serious problem, and the same machines a few districts away are close to a non-issue. Siting and survey work, not the technology, decide this one.

Landscape and land rights. A modern turbine is visible for kilometres, and some people simply do not want one on the ridge above their village. In India the sharper question is usually land: who owns the plot, who was using the grazing commons, and who in the village actually receives the lease rent.

Getting the power out. The windiest districts are rarely the ones with the biggest demand, so the electricity has to be carried a long way. When the lines out of a wind district are full, turbines are told to back off, and that energy is simply lost — nobody can store the wind for later. Part D is about exactly this problem.

🔥The Betz limit: why 59.3% is the ceilingAdvanced · optional

Here is one of the loveliest results in engineering, and you can reason your way to it without any equations.

Ask the greedy question: why not design a rotor that extracts all of the wind’s kinetic energy?

Follow the consequence. Kinetic energy is ½mv². To take all of it, you must reduce the air’s speed to zero. But air leaving your rotor at zero speed is stationary air sitting directly behind it — a wall. And the wind arriving behind it has nowhere to go, so it diverts around your rotor instead of passing through. Extract everything from a small amount of air and you end up processing almost no air at all. Output: nearly zero.

Now the opposite extreme. Barely slow the air at all, and enormous volumes flow through happily — but you take almost nothing from each kilogram. Output: also nearly zero.

Somewhere between “slow it too much and block the flow” and “slow it too little and take nothing” lies a maximum. In 1919 the German physicist Albert Betz found it. The optimum is to slow the wind to one-third of its original speed, and the fraction of the wind’s kinetic energy you can then capture is:

16/27 ≈ 0.593 — the Betz limit

No rotor of any design — three blades, twenty blades, vertical axis, shrouded, anything — can beat it. Modern turbines achieve roughly 75–80% of the Betz limit in their best operating range, meaning they capture something in the region of 45–50% of the wind’s energy. That is genuinely close to a hard physical ceiling; wind turbines are among the most thermodynamically mature machines we build.

Notice the structure of the argument. Like Carnot in Module 3 and Shockley–Queisser in Module 7, it is a limit derived from the nature of the process itself, not from any engineering shortcoming. Each of the three has taught us the same lesson from a different direction: every way of harvesting energy has a ceiling written into physics, and good engineering is the art of approaching it.

🔥🔥Deriving the cube law, and Betz properlyDeep · optional

Where v³ comes from. Consider a rotor of swept area A facing wind of speed v and air density ρ. In one second, the air passing through occupies a cylinder of length v and cross-section A, so the mass flow rate is:

ṁ = ρ · A · v

Each kilogram carries kinetic energy ½v². So the power passing through the disc is:

P = ½ · ṁ · v² = ½ · ρ · A · v³

The cube appears because two things scale with speed: how much energy each kilogram carries (v²), and how many kilograms arrive per second (v). Multiply them and you get v³.

A worked number. Take a modern onshore machine: rotor diameter 120 m, so A = π × 60² ≈ 11,310 m². With ρ = 1.225 kg/m³ and v = 10 m/s:

P = 0.5 × 1.225 × 11,310 × 1,000 ≈ 6.9 MW

Multiply by the Betz limit (0.593) and a realistic 0.8 of that, and you get roughly 3.3 MW delivered — a plausible rating for such a machine. The arithmetic genuinely works.

Betz, derived. Let the far-upstream wind speed be v₁ and the far-downstream speed v₂. Define the axial induction factor a such that the speed at the rotor is v₁(1 − a). It can be shown from momentum conservation that the rotor speed is the average of the two: v_rotor = (v₁ + v₂)/2, hence v₂ = v₁(1 − 2a).

Power extracted is the rate of loss of kinetic energy:

P = ½ ṁ (v₁² − v₂²), with ṁ = ρ A v₁(1 − a)

Substituting and dividing by the available power ½ρAv₁³ gives the power coefficient:

C_p = 4a(1 − a)²

Maximise: dC_p/da = 4[(1 − a)² − 2a(1 − a)] = 4(1 − a)(1 − 3a) = 0, giving a = 1/3 (the other root, a = 1, is the blocked case). Substituting back:

C_p,max = 4 × (1/3) × (2/3)² = 16/27 ≈ 0.593

And note what a = 1/3 means physically: the wind slows to two-thirds of its speed at the rotor and one-third far downstream. The intuition in the 🔥 block is not a simplification of the mathematics — it is the mathematics.

What comes next

That completes Part B: six ways to spin a shaft, one way that doesn’t spin at all, and three separate proofs that physics caps every one of them. Part C sweeps up the remaining menu — biomass, geothermal, tidal, and hydrogen, the most misunderstood topic in all of energy. Then Part D asks the question this whole tour has been building towards: how do you knit hundreds of these machines into a single continent-sized system that must balance itself every second of every day?