Lesson 2 of 9 · about 19 minutes
Wind: The Cube Law, Capacity Factors and Siting
You'll be able to
- Use the wind power equation and the cube law to estimate a turbine's output
- Explain the Betz limit, cut-in and cut-out speeds and why average wind speed misleads
- Compare wind capacity factors nationally and in one state using EIA data
- Name the siting issues (wildlife, land, views, transmission, federal approvals) and find the records behind them
Wind made about 10 percent of U.S. utility-scale electricity in 2025, roughly 464 billion kilowatt-hours, according to EIA. Texas, Iowa, Oklahoma, Kansas and Illinois together produced about 52 percent of it. All of that comes from a simple trick: put a big propeller in moving air, let the air push the blades, and turn the slow, strong rotation into electricity.
Where the power comes from
Moving air has kinetic energy. The power flowing through a circle of air depends on the air's density, the circle's size and, above all, the wind's speed.
Power in the wind (watts) = 0.5 x air density x swept area x speed cubed
P = 0.5 x rho x A x v^3
rho at sea level = about 1.225 kg/m3
A = pi x (blade length)^2
The area term explains why turbines keep getting bigger. Blade length enters squared, so a rotor with blades 20 percent longer sweeps 44 percent more air. The speed term explains everything else.
The cube law, with real numbers
Worked example: one invented turbine on Butte Flats
The Butte Flats project uses turbines with 65-meter blades. Swept area:
A = 3.1416 x 65 x 65 = 13,273 m2
Power in the wind passing through that circle, at sea-level density:
| Wind speed (m/s) | Power in the wind (MW) | At 45% overall efficiency (MW) |
|---|---|---|
| 4 | 0.52 | 0.23 |
| 6 | 1.76 | 0.79 |
| 8 | 4.16 | 1.87 |
| 10 | 8.13 | 3.66 |
| 12 | 14.05 | capped at rated power |
Going from 6 to 12 m/s doubles the speed and multiplies the power by eight (1.76 to 14.05). The 45 percent figure is a stand-in for the turbine's real-world conversion; actual machines publish a power curve.
Now altitude. Air at about 1,200 meters elevation is roughly 11 percent less dense than at sea level. Multiply every number in the table by 0.89. A high plateau site needs a little more wind, or bigger blades, to match a coastal one.
Two limits keep real turbines below those raw numbers. The first is physics. In 1919 the German physicist Albert Betz showed that a turbine can capture at most 16/27 of the wind's kinetic energy, about 59.3 percent. Capture all of it and the air behind the rotor would stop, blocking new air from coming through. The second is engineering. Every turbine has a rated power, the most its generator can make. Above the rated wind speed, the blades pitch to spill extra wind. DOE says a typical controller starts the machine at roughly 7 to 11 mph and shuts it down above roughly 55 to 65 mph to avoid damage.
Why the average wind speed lies
Because of the cube, an hour at 12 m/s is worth eight hours at 6 m/s. Take a site that blows 4 m/s half the time and 10 m/s the other half. The average speed is 7 m/s. Plug 7 into the formula and you get 343 units (7 x 7 x 7). Average the cubes instead: half of 64 plus half of 1,000 is 532 units. The gusty site makes about 55 percent more energy than its average speed predicts. Developers measure wind for a year or more with met towers or lidar to get the full distribution. When a project brochure quotes only an average speed, it is leaving out the part that matters.
Capacity factor: the number to ask for
A 3-MW turbine does not make 3 MW all day. Capacity factor compares what it actually produced with what it would have made running flat out every hour of the year.
Capacity factor = actual MWh / (nameplate MW x 8,760 hours)
Example: a 100-MW wind farm produces 300,000 MWh in a year
300,000 / (100 x 8,760) = 300,000 / 876,000 = 0.342, or 34.2 percent
| Fleet | Capacity factor | Source year |
|---|---|---|
| U.S. wind, all utility-scale | 34.2% | 2025 |
| U.S. wind | 34.3% | 2024 |
| Idaho onshore wind | 31.5% | 2024 |
| Idaho onshore wind | 27.3% | 2023 |
| U.S. nuclear, for comparison | 91% | 2025 |
Idaho had about 1,128 MW of wind at the end of 2024, after adding 160 MW that year, and wind made about 15 percent of in-state generation. Newer turbines with taller towers and longer blades reach steadier, faster wind higher up, which is why new projects often post better capacity factors than old ones. A one-year number also bounces: Idaho's fleet went from 27.3 to 31.5 percent between 2023 and 2024 partly because of the weather and partly because of the new machines.
Siting: where the fights happen
Good wind and cheap land often sit far from the cities that use the power, so most wind arguments are about place.
Wildlife
The U.S. Fish and Wildlife Service estimates human-caused bird deaths each year: about 2.4 billion from cats, 599 million from building glass, 214 million from vehicles, about 25.5 million from power line collisions, and about 234,000 from land-based wind turbines (a range of 140,000 to 328,000). Those numbers date from 2017 and the wind fleet has grown since, so the turbine figure today is higher. Both sides misuse this table. Turbines are a small share of total bird deaths. But totals are the wrong lens for eagles, raptors and some migratory bats, where a handful of deaths can matter to a population. The fair framing names the species, the site and the mitigation (curtailing turbines at low wind speeds during bat migration, for example, or careful siting away from raptor flyways).
Land, views and neighbors
Turbines themselves and their roads cover a small slice of a project's lease area; most of the land can still be farmed or grazed. But a project's visual reach is huge, turbines are lit at night for aircraft, and nearby residents report noise and shadow flicker. County zoning setbacks are where these complaints become rules, so read the ordinance.
Federal approvals
Projects on federal land need federal sign-off, and that can flip. In December 2024 the Bureau of Land Management approved the Lava Ridge Wind Project in southern Idaho at up to 231 turbines on about 57,447 acres, for 1,000 MW. On August 6, 2025, Interior announced it would cancel that approval, citing what it called legal deficiencies in the approval, complaints from Idaho state agencies about a lack of consultation, and a policy of ending what it called preferential treatment for intermittent power sources. Supporters of the project pointed to jobs, lease revenue and new power supply; opponents pointed to its size and its effects on ranching, wildlife and nearby historic and cultural sites. Anyone following the project can get the record of decision, the environmental impact statement and the cancellation documents and read each one, then check BLM's project page for where the rescission stands now.
Transmission
Without lines, wind is stranded. Lawrence Berkeley National Laboratory's 2026 Queued Up report counted about 220 GW of wind among roughly 2,060 GW of projects waiting to connect to the grid at the end of 2025, and found that the median project built in 2025 took over five years from its interconnection request to operation. Only about 13 percent of capacity that applied from 2000 to 2020 was built. EIA reported that developers planned 11.8 GW of new wind for 2026, including the 3,650-MW SunZia project in New Mexico, which was built alongside its own long transmission line.
Common mix-ups
- Claim: A 100-MW wind farm powers a fixed number of homes all the time. What the evidence shows: "Homes powered" figures average the year's output. At 34 percent capacity factor the farm averages about 34 MW, and at any given hour it could be making 0 or 100.
- Claim: Turbines kill more birds than anything else. What the evidence shows: FWS estimates put turbines far below glass, cats, vehicles and power lines. The real concern is specific species and sites.
- Claim: Turbines spin at their rated output whenever the wind blows. What the evidence shows: Below rated speed, output falls with the cube of speed. Half the wind speed means one eighth the power.
Reporting angle
- For a proposed project, get the met tower or lidar wind study summary, the expected capacity factor, and the power purchase agreement terms if a utility is the buyer (often filed at the state utilities commission).
- Read the county conditional use permit, setback rules, decommissioning bond amount and road use agreement.
- On federal land, pull the BLM environmental impact statement, the record of decision and any later rescission. Check the Federal Register.
- Ask the developer and FWS about eagle take permits and bat curtailment plans.
- Ask the grid operator or utility which transmission line the project will use and whether that line exists yet.
Research angle
- EIA, where wind power is produced: Wind output by state.
- EIA Electric Power Monthly, Table 6.7.B: Wind capacity factors by year.
- EIA Idaho electricity profile: Idaho wind capacity and generation.
- U.S. Fish and Wildlife Service, threats to birds: Bird mortality estimates by cause.
- LBNL Queued Up: Wind projects waiting in interconnection queues.
- EIA on planned 2026 capacity additions: What is scheduled to come online.
Check yourself
1. If wind speed rises from 6 to 12 meters per second, how much more power is in the wind?
Power scales with the cube of speed. 2 x 2 x 2 = 8.
2. What does the Betz limit say?
If a turbine stopped the air completely, no new air could flow through. Albert Betz showed the theoretical maximum extraction is 16/27, about 59.3 percent.
3. What was the U.S. wind fleet's average capacity factor in 2025, according to EIA?
EIA's Electric Power Monthly Table 6.7.B lists 34.2 percent for 2025 and 34.3 percent for 2024.
4. Why can't you plug a site's average wind speed into the power formula to get average power?
The cube law rewards strong hours far more than it punishes weak ones. You need the distribution of speeds, not just the mean.
5. According to U.S. Fish and Wildlife Service estimates, which kills more birds each year in the U.S.?
FWS estimates roughly 599 million bird deaths a year from building glass versus about 234,000 from land-based turbines. Turbines still matter for specific species, like eagles and some bats.
6. In August 2025 the Interior Department moved to cancel approval of which Idaho wind project?
Interior's August 6, 2025 release said it would reverse the December 2024 approval of Lava Ridge, which allowed up to 231 turbines on about 57,447 acres.
Terms in this lesson
- Swept area
- The circle the blades sweep, pi times the blade length squared. Power grows in direct proportion to it.
- Cube law
- The power in moving air rises with the cube of its speed, so small speed gains mean large power gains.
- Betz limit
- The theoretical maximum share of wind energy a turbine can extract, 16/27 or about 59.3 percent.
- Cut-in and cut-out speed
- The wind speeds at which a turbine starts generating and at which it shuts down to protect itself.
- Nameplate capacity
- The maximum rated output of a generator, in megawatts. It says nothing about how often it runs at that level.
Sources
- EIA, Wind explained: Where wind power is harnessed checked 2026-10
- EIA, Electric Power Monthly Table 6.7.B, capacity factors (annual 2023 to 2025) checked 2026-10
- EIA, Idaho Electricity Profile 2024, state data tables (Tables 4A, 5, 15) checked 2026-10
- U.S. DOE, How a Wind Turbine Works (text version) checked 2026-10
- U.S. Fish and Wildlife Service, Threats to Birds checked 2026-10
- U.S. Department of the Interior, Interior Department Moves to Cancel Biden-era Approval of Lava Ridge Wind Project (Aug. 6, 2025) checked 2026-10
- EIA Today in Energy, record capacity additions planned for 2026 (Feb. 20, 2026) checked 2026-10
- Lawrence Berkeley National Laboratory, Queued Up: 2026 Edition checked 2026-10