Windmills Are NOT Like Dams

Windmills can’t behave like dams because wind energy comes from motion: slowing the air to extract power inevitably reduces how much wind continues downstream. The key constraint is that the maximum extractable energy equals the drop in the wind’s kinetic energy, which scales with the square of speed. If a windmill reduces wind speed from v to v/2, then the outgoing kinetic energy is (v/2)² = v²/4, meaning the wind loses 3/4 of its kinetic energy—an energy-extraction “efficiency” of 75% for the wind that passes the turbine.

But that’s only half the story. The amount of wind passing through the turbine per second also changes, because the wind speed at the turbine itself sits between the incoming and outgoing speeds. Under the standard idealized model, the wind speed at the windmill is halfway between the two: for an incoming speed v and outgoing speed v/2, the speed at the rotor becomes (v + v/2)/2 = 3v/4. That means only 3/4 as much wind volume (and thus mass flow) passes through each second compared with the undisturbed flow. Combining these effects—extracting 3/4 of the kinetic energy from each parcel of wind, while only 3/4 as many parcels pass per second—yields an overall efficiency of (3/4)×(3/4) = 9/16 = 56.25%.

Repeating the same tradeoff for other speed reductions reveals a non-obvious optimum. If the windmill slows the wind to one-third of its incoming speed (outgoing speed v/3), the kinetic-energy drop is v² − (v/3)² = v² − v²/9 = 8v²/9, so 88.88% of the kinetic energy of the wind passing the turbine is extracted. Yet the wind speed at the rotor becomes halfway between v and v/3, which is (v + v/3)/2 = 2v/3. That reduces the mass flow rate to 2/3 of the original. The overall efficiency becomes 0.8888… × 2/3 ≈ 0.59259, or 59.259%.

Pushing the slowdown further (below one-third speed) increases the fraction of energy extracted from each parcel, but it starves the turbine of wind—too little mass flow passes per second—so total efficiency falls. Slowing the wind less than one-third does the opposite: more wind passes, but each parcel retains more kinetic energy, again lowering total efficiency. The result is a best-case ideal windmill that reduces wind speed to 2/3 of the incoming speed after the turbine (equivalently, outgoing speed v/3), achieving about 59% overall efficiency in extracting wind power.

Real turbines involve additional engineering constraints—wake losses, blade aerodynamics, and mechanical limits—so the 59% figure is an idealized upper bound rather than a guaranteed real-world performance number. Still, the central lesson holds: windmills face a fundamental physics tradeoff between extracting energy and keeping enough wind moving through the system.