What if the wind blew twice as hard?

A wind turbine is like a giant pinwheel. The wind pushes its blades round and round.

What if the wind blew twice as fast? Would the turbine make twice as much electricity?

On a gentle day, the blades of a wind turbine turn slowly. On a blustery day, they whirl around. But how much more electricity does stronger wind really make?

You might guess that twice the wind gives twice the power. In this lab, a big turbine with 40-meter blades sits in a gentle 5 meters-per-second breeze. What happens to its electricity when the wind doubles to 10 meters per second?

A wind turbine extracts part of the kinetic energy of the air passing through the disk its blades sweep. Both the mass of air arriving each second and the energy each kilogram carries depend on the wind speed.

This lab holds a turbine's size (40 m blades), its power coefficient (Cp = 0.4) and its generator rating (15 MW) fixed, doubles the wind speed from 5 to 10 m/s, and asks how its electrical output scales.

A gentle wind blows. The big blades turn slowly.

The turbine makes a little electricity.

In the model, the 40-meter blades sweep a circle 80 meters across. A 5 meters-per-second breeze, about 18 kilometers per hour, carries about 0.385 megawatts of power through that circle. The blades turn 40 percent of it into electricity: about 0.154 megawatts.

The rotor turns about 8 times a minute. If this breeze blew steadily for a whole day, the turbine would make about 3.69 megawatt-hours.

With r = 40 m, A = πr² ≈ 5,027 m². At ρ = 1.225 kg/m³ and v = 5 m/s, P_wind = ½ × 1.225 × 5,027 × 125 ≈ 0.385 MW. The model's Cp of 0.4 gives 0.154 MW; the Betz limit would allow at most 0.228 MW.

With a tip speed ratio of 7, the rotor turns at 8.4 rpm. A full day of this steady wind yields 3.69 MWh. The model's cut-in speed is 3 m/s, so at 5 m/s the turbine is running.

Now the wind blows twice as fast. Whoosh!

The blades spin faster. The turbine makes eight times as much electricity!

Set the wind to 10 meters per second. The power in the wind jumps to about 3.08 megawatts, and the turbine makes about 1.23 megawatts: eight times as much, not twice. A whole day of this wind would make about 29.6 megawatt-hours.

Keep going. At 20 meters per second, the turbine makes about 9.85 megawatts, 64 times the gentle breeze. But above 25 meters per second, a stormy wind, the model's turbine shuts itself down and makes nothing at all.

At 10 m/s, P_wind = 3.08 MW and P = 1.23 MW, exactly 8 × 0.154 MW. Daily energy rises from 3.69 to 29.6 MWh and rotor speed from 8.4 to 16.7 rpm (rpm scales linearly with v at fixed tip speed ratio).

The cube law continues until the generator saturates: 9.85 MW at 20 m/s (64×). The model reaches its 15 MW rating at about 23 m/s, holds it, then parks the rotor above its 25 m/s cut-out, so at 25.5 m/s the output drops to zero.

Faster wind brings more air to the blades every second.

And each bit of faster air pushes harder. Two things grow at once, so the power grows a lot!

Two things happen at once when the wind doubles. First, twice as much air rushes through the blades every second. Second, each kilogram of that air carries four times as much energy, because moving energy grows with the square of the speed.

Twice as much air, each with four times the energy: 2 × 4 = 8 times the power. Our model is simple: it uses one steady wind, the same across the whole circle, and catches a fixed share of it.

Kinetic energy per unit mass is ½v² (OpenStax §7.2), and the mass flow through the disk is ρAv, so power is ½ρAv³. Doubling v doubles the mass flow and quadruples the energy per kilogram.

The model caps Cp at the Betz limit, 16/27 (about 59.3%): the theoretical maximum share of the wind's kinetic energy a turbine can use, worked out by Albert Betz in 1919. Energy Education (University of Calgary) notes that real turbines cannot reach it and commonly manage 35–45%. The model's limits: a steady, uniform wind, a fixed Cp (real Cp varies with wind speed and blade pitch), a single lumped loss term, and air density held constant. Real wind gusts and varies with height, so a real turbine's output fluctuates far more than this steady run.

Wind farms are built where the wind is strong and steady.

In a storm, real turbines turn their blades and stop, so they don't get damaged.

Because power grows so fast with wind speed, location matters a lot. The U.S. Energy Information Administration says utility-scale turbines need sites where the wind averages at least 13 miles per hour, about 5.8 meters per second, such as smooth hilltops, open plains and water. Wind is also generally faster higher above the ground.

The U.S. Department of Energy explains that turbines start making power at a cut-in speed, typically 6 to 9 miles per hour, and in very strong wind turn their blades to point into the wind and shut down to protect themselves. In 2025, wind made about 10.5% of U.S. utility-scale electricity.

EIA gives a minimum annual average of 13 mph (5.8 m/s) for utility-scale sites and notes that wind speeds generally increase with height. U.S. wind generation reached about 464 billion kWh in 2025, about 10.5% of utility-scale generation.

DOE describes the power curve: cut-in typically at 6–9 mph, rising output to the rated speed, constant rated power above it, and a cut-out speed that varies by turbine; in its example, an anemometer reading above 55 mph triggers shutdown. Above rated speed, the blades feather to reduce their surface area, and IEC standards require most turbines to withstand 112 mph sustained winds.