How Does Your Wind Farm Grow?

Calculating what the global saturation point for wind energy would be and if we can generate enough wind power to power half the globe.

WHO: Mark Z. Jacobson (Department of Civil and Environmental Engineering, Stanford University, Stanford, CA)
Cristina L. Archer (College of Earth, Ocean, and Environment, University of Delaware, Newark, DE)

WHAT: Predicting the effectiveness of scaling up wind power to provide half the world’s power requirements by 2030.

WHEN:  September 25 2012 PNAS, Vol 109, No. 39

WHERE: Proceedings of the National Academy of Sciences of the United States of America

TITLE: Saturation wind power potential and its implications for wind energy

I learnt about a new law today; Betz’s Law. Betz was a guy who decided to calculate exactly how much energy could be extracted from the wind by a turbine at any given time mathematically (as you do). He worked out that no turbine can take any more than 59.3% of the energy from the wind. To be able to conceptualise this, you have to think about wind like a physicist. The first law of thermodynamics states that you can’t create or destroy energy; you can only convert it to different forms. Therefore, all wind is just energy in a certain form, and in any system there is a point where the transformation is most efficient and beyond there it takes a lot of effort to get any more energy from the system.

There’s a really cool project being done in the US, where a website has taken data from the National Digital Forecast Database and created a visual representation of what wind would look like if you could see it move. It’s strikingly beautiful, and looks a lot like a Van Gogh painting.

Wind Map by Fernanda Viegas and Martin Wattenberg of

The question this paper looks at is: since there is a limit to the amount of energy you can take from a turbine, what is the maximum wind power that can be extracted from a geographical area? They called it the ‘Saturation Wind Power Potential’.

They came up with some interesting findings, as well as probably having a lot of fun along the way because they used 3D Models to do it (I’m telling you, my chemistry molecular model kit was much more like playing with Lego than actual ‘science’). They got into the detail and calculated the potential wind power at 10m off the ground, 100m off the ground (the standard height of a wind turbine) and 10km off the ground in the jet stream.

They then looked at whether it would be possible to scale up wind power globally to meet 50% of the world’s power needs by 2030. Actually measuring the wind power potential for more than 1 Terrawatt (TW) of energy is not possible as there isn’t enough wind power installed yet. But they did mathematically work out that we would need 4million 5 Megawatt (MW) turbines to supply half of the world’s electricity needs in 2030 (5.75TW).

They did four simulations with different turbine densities, because how close together wind turbines are affects their ability to produce power. Put them too close together and they start stealing their neighbour’s wind power. Overall, up to 715TW, the increased number of turbines increases the amount of power in a linear straight line. Once you get above that it slows down and flattens out – once again you need to put much more effort in to get power out.

Predicted wind power saturation potential (from paper)
Grey line – global wind power potential, black line – wind power potential on land only

The saturation point, where no matter how many more turbines you add, they’ll just be stealing energy from each other and not adding anything to the total, was 2,870TW of power globally. Interestingly, they found the wind power available in the jet stream (10km above the ground) was 150% greater than the wind power available 100m above the ground.

There were also some big changes to the results depending on the density. If we placed 4million 5MW turbines and packed them in at 11.3 Watts per m2 (W/m2), they would be too close together and the collected power wouldn’t match the target for half the world’s power by 2030. If you spread them out to 5.6W/m2 the output is still too low. However, once you’ve got them spaced at 2.9W/m2, they produce enough power to meet the required demand.

4million turbines meet demand when they’re 2.9W/m2 apart or further (from paper)

So it turns out wind turbines don’t like it when you cramp their style. But, you can pack them in a bit tighter, only if you then have enough space between your wind farm and your neighbour’s wind farm. It’s a bit like playing wind farm Tetris.

What does this mean though? It means that we can ramp up world wind power production to levels that will meet half our power needs in 2030, which can be integrated with hydro, solar and other renewables with smart grids to power our cities and lifestyles without burning fossil fuels. But it also means we need to think about where we are putting wind farms and how much space they need to be as efficient as possible. We need that renewable energy, so we can’t cramp the wind turbines’ style!


One thought on “How Does Your Wind Farm Grow?

  1. Pingback: How Does Your Wind Farm Grow? | Amy Huva

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