Wind Turbine Energy Lab

A rotor can never take more than 16/27 ≈ 59.3% of the wind's kinetic power — the Betz limit — and real machines fall further short of even that. Set the wind speed, rotor diameter, air density, power coefficient Cp and drivetrain efficiency η and watch the electrical output climb along a power curve gated by cut-in, rated and cut-out wind speeds, with a loss bar showing exactly where the rest of the kinetic power goes. Feed that intermittent output into a battery — capacity, load and round-trip efficiency — and watch the state of charge ride out calm spells over a day. It all runs on your device.

You are in the Physics lab.

Elapsed (sim-day)00:00 / 24:00
Energy produced0 kWh
Stored in battery0 kWh (0%)

Turbine

Wind in, electricity out — and the losses along the way.

Electrical power
Betz-limit power
Net capture (Cp·η)
Rated power
Turbine
Power curve — output vs wind speed
Energy loss breakdown
Power output

Storage

Smoothing an intermittent supply against a steady load.

Autonomy
Unmet-load time
Capacity factor
Battery charge — fills as the day plays
No rotor beats 59.3% of the wind. The Betz limit, 16/27, caps the fraction of kinetic power any turbine can extract — slow the wind to a stop and no more air gets through to push on the next blade; barely slow it and almost nothing is taken, so the ceiling sits in between. Real machines fall short of even that: the power coefficient Cp measures how close the blades get to Betz, and the drivetrain efficiency η takes a further cut through the gearbox and generator. What survives both is intermittent — governed by wind, not demand — so a battery absorbs the surplus and covers the gaps, at a cost in round-trip efficiency and a capacity factor well under 100%.

Reading the simulation

What the gauge, the curve and the loss bar are telling you — then what the battery does with the result.

1

The rotor and the gauge

The turbine spins faster as wind speed climbs, and the gauge beside it fills toward the rated power — the ceiling the machine is built for. Push the wind speed past the cut-out slider and the rotor stops: real turbines feather their blades and shut down in a storm rather than risk damage, so the gauge drops back to zero exactly where it should.

2

The power curve and the loss bar

The power curve plots output against wind speed: flat at zero below cut-in, climbing as the cube of wind speed to rated, flat at the rated power up to cut-out, then zero again. The loss bar breaks that same instant down into four slices of the wind's kinetic power: the share no rotor can ever reach (Betz), the further shortfall between your Cp and the Betz ceiling, what the drivetrain eats via η, and what's left as net electrical capture — the smallest slice, and the only one you actually get.

3

The battery rides out the gaps

The Storage card feeds a simulated day of wind — built from your mean wind speed — through the same turbine into a battery serving a constant load. The state-of-charge trace climbs when generation beats the load and falls when it doesn't; if it would fall below zero that stretch counts against unmet-load time. Autonomy is simply capacity divided by load, and capacity factor compares the energy actually delivered over the day to what the turbine would deliver running at rated power the whole time.

How It Works

A hard ceiling on extraction, a curve shaped by cut-in and cut-out, and a battery to bridge what the wind won't hold still for.

1

The Betz limit sets a hard ceiling

The kinetic power in wind moving through a rotor's swept area is P = ½ρAv³ — it scales with air density, swept area, and the cube of wind speed. No rotor can extract all of it: slowing the wind completely would block the air stream, so the physical maximum, proven by Betz, is 16/27 ≈ 59.3%. That ceiling is set by the airflow itself, not by blade design.

2

Cut-in, rated, cut-out

Below cut-in there isn't enough wind to turn the rotor usefully, so output is zero. From cut-in to rated wind speed, electrical output is η·Cp·P, rising with the cube of wind speed. Above rated, the turbine deliberately sheds power — pitching its blades — to hold output flat and protect the gearbox and generator, until cut-out, where it shuts down entirely rather than risk damage in a storm.

3

Storage turns an intermittent supply into a steady one

Because generation follows wind, not demand, a battery is what actually lets a constant load be served: it charges on the surplus and discharges through the gaps, at a round-trip efficiency below 100%. Its capacity sets how many hours of autonomy it buys against the load, and over a full day the capacity factor — actual energy over rated-power energy — tells you what fraction of the turbine's nameplate rating the wind really delivered.

How a wind turbine works

Moving air pushes the blades — shaped like aircraft wings — turning a hub at 10–25 rpm; a gearbox steps that up to the generator, which makes electricity; a transformer raises the voltage for the grid, and a battery can bank the surplus for calm spells. Below cut-in the rotor won't start; past cut-out the blades feather to a stop for safety.

Blade Rotor + hub Nacelle Tower
Blades → hub → gearbox & generator (in the nacelle) → transformer → grid. This lab models the whole chain as a single efficiency, so you watch energy and losses at the system level.
How big? Modern turbines rival landmarks — taller means longer blades in faster, steadier wind.
305 ft Statue of Liberty 466 ft Avg. turbine 574 ft Tallest onshore 853 ft GE Haliade-X 1,063 ft Eiffel Tower
What is the Betz limit?
The Betz limit is the theoretical ceiling on how much of the wind's kinetic power any rotor can extract: 16/27, about 59.3%. A rotor that slowed the wind to a stop would block the air behind it from flowing through at all, and one that barely slowed it would extract almost nothing, so the maximum lies in between, at the wind losing exactly one third of its speed across the disc. No blade design, however good, can beat that fraction — it is a limit on the airflow itself, not on engineering.
How does a turbine's power curve work?
Below the cut-in wind speed the rotor produces nothing — there isn't enough force to turn it usefully. Between cut-in and the rated wind speed, output climbs with the cube of wind speed, since kinetic power scales as . Above rated wind speed the turbine pitches its blades or otherwise sheds power to hold output flat at the rated power, protecting the generator and gearbox. Past the cut-out wind speed the turbine shuts down entirely to avoid damage in a storm, so output drops back to zero.
Where does the wind's energy go before it reaches the wall?
Start with the wind's kinetic power through the swept area. A fixed share, 1 − 16/27, is unreachable by any rotor — the Betz limit. Of what remains, a real rotor's power coefficient (Cp) falls short of that Betz ceiling because blades are imperfect aerodynamic shapes, and the drivetrain — gearbox and generator — loses a further share set by its efficiency (η). What's left after all three deductions is the net electrical power actually delivered, shown as the smallest slice of the loss bar.
How does battery storage help with wind's intermittency?
Wind power tracks wind speed, not demand, so a constant load often needs more or less than the turbine is generating at any instant. A battery absorbs the surplus when generation exceeds load and discharges to cover the shortfall when it doesn't, charging and discharging at a round-trip efficiency below 100%. Its capacity divided by the load sets an autonomy in hours; if the battery empties before generation returns, that stretch counts as unmet-load hours. Capacity factor — actual energy delivered over a period divided by what the turbine would deliver running at rated power the whole time — summarizes how much of the nameplate rating the wind actually supplies.