The Kinetic Energy of Wind Turbines

The Kinetic Energy of Wind Turbines For this Science Saturday our science geek Charlie Keeble explains the science of wind turbines and how they capture the power of the wind. Are they are effective and green as they seem to be?    Wind turbines are a clever and effective way of harnessing the power of the wind to generate electricity. They convert the kinetic energy of wind into electricity by the motion of the wind turning the blades of the turbine. They come in a wide range of sizes and their power output depends mostly on the density and speed of the wind in one part of the world.

Wind power has been used for centuries long before electricity was even invented. In Upminster, there is a windmill that was originally built in 1803 for milling flour. I went to Upminster Windmill once to examine the inner workings of the windmill and see how useful the wind can be to power machinery. The inner workings of the windmill use the rotation of the sails to drive a series of cogs and gears to power the milling machines. Grinding grains into finer forms of flour that can be used by bakers to make bread. As a keen baker, I was fascinated by the process used to make the ingredients for all those lovely cakes and biscuits I make. It was a wonderful and enjoyable trip to know the benefits of wind technology.

The Upminster Windmill Modern wind turbines are very similar in principle to windmills in that they convert the energy of the wind into a rotational motion. This is used to generate electricity by taking kinetic energy and converting it via a generator into electricity. Kinetic energy is energy from motion and it’s measured by half of the mass of the wind by the square of its speed.

Expressed mathematically this goes as 1/2mv2 and the energy taken out by the wind turbine reduces the wind speed behind it. Now the mass of the wind and its speed can drive the turbines faster and generate more electricity provided the wind is dense and fast flowing, which only occurs in certain locations. From the end of the pier at Southend on Sea, I spotted the Kentish Flats Offshore Windfarm in the distance. This massive wind energy facility comprises 45 Danish Vestas V90-3MW horizontal-axis wind turbines generating a total power output of 139.5 megawatts (MW) of electricity. That is enough to meet the electricity needs of 15 thousand to 35.5 thousand homes. The turbines have a hub height of 70 metres and their rotors have a diameter of 90 metres, which gives them a maximum height of 115 m at the highest blade tip.

But despite the promises of clean and renewable electricity from the power of natural forces it’s not practical or efficient to rely on wind turbines. They are flaws in the designs of wind turbines that have been proven by incidents that have plagued them. Wind turbines are not perfect and they have been shown to suffer from engineering problems. Such as collapsing in fiercely strong winds, and overloading the national grid and causing dangerous power surges if they spin too fast. Inevitably they disrupt the migration patterns of birds when they fly into the path of the blades and kill them. Also since wind is an intermittent force of nature it doesn’t continuously make the blades spin all the time. Placing them in suitable locations is a very tricky business because where there are areas of strong wind patterns they have to be built and transported to these locations. They also have to be in places where they can be maintained and operated by service personnel otherwise they degrade and fall into disrepair. But the biggest inefficiency in wind turbines lies in the kinetic energy of the wind itself. In 1919 a German physicist called Albert Betz discovered something that is not widely spoken about by renewable energy enthusiasts. He found that there was a limit to the amount of energy that a wind turbine could extract from its motion driven by the wind no matter the size of the blades. This is called the Betz law and it’s factored into the power capacity of the wind turbines.

This reveals why wind turbines do not actually run at 100% efficiency. In aerodynamics, Betz law indicates the maximum amount of power that can be extracted from the wind. This is derived from the principles of conservation of mass and the momentum of the airstream flowing through a wind turbine. According to Betz law, no turbine can capture more than 59.3% of the kinetic energy of the wind. There is also another limit to Betz law where most wind turbines can only manage to achieve a peak of 75-80% of the Betz limit. This means that the power output of the turbines does not equal the kinetic energy of the wind. If we apply the Betz limit to the power output of Kentish Flats Offshore Windfarm the electricity supply generated is not as much as the energy company claims it to be. If the maximum energy it produces is 139.5 MW of electricity then that is the figure from 59.3% of the kinetic energy of the wind. Additionally, the extra 41.7% that is not produced from the wind farm brings the total kinetic energy of the wind to be 197.7 MW. That is quite a big loss in potential energy that can not be captured. Also under the 75% peak of the Betz limit the maximum capacity of the Kentish Flats turbines is 104.6 MW.      

Environmental activists claim that the wind can provide a very reliable source of electricity as the wind is essential to providing an energy infrastructure free from fossil fuels. But as the engineering and the science of wind power has shown it is far from efficient. It can work in small local areas, but it can not be scaled up effectively to provide enough electricity for large cities. Even if they are built well enough the wind turbines have a life span of about 20 years and they need to be serviced with thousands of litres of oil to keep the gears greased. Also, the blades tend to wear down from the mechanical stresses of wind and movement until they have to be replaced. On the subject of scaling up wind power, it is not practical to use it to power entire counties or indeed the country because the energy return on the energy invested to make them is very low. They have to be part of a diverse array of energy sources in order to be acceptable, so there is something to back them up when the wind isn’t blowing. Advocates for wind energy should look to small-scale wind turbines to prove their effectiveness. One way to do this is to look towards past wind technology like the classic windmill design at Upminster. One intriguing design of wind turbines that looks more efficient is vertical-axis turbines. These have the main rotor shaft set transverse to the wind while the main components that generate electricity like the generator, gearbox and controller are stationed at the base of the turbine. This means that the technicians don’t have to maintain it by climbing the tower.

Vertical-axis turbines can also be built in a design similar to that of windmills in which the blades can be like sails or helically shaped that twist and turn as the air moves them around. There are many advantages to this such as the blades have a much wider surface area that they catch more wind, they can move with lower wind density and speeds in the same way as sailing ships do, and they don’t have to be so tall that they avoid getting in the way of bird’s flying or blighting the landscape. In fact, they can be as short as 40 metres (a third of the height of a Kentish Flats turbine) and still generate enough electricity for a small town. Studies have shown that vertical-axis wind turbines are 15% more efficient than horizontal-axis wind turbines as they produce less turbulence for noise and visual pollution.      

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