Vertical-axis wind turbine

The forces and the velocities acting in a Darrieus turbine are depicted in figure 1. The resultant velocity vector, ${\displaystyle {\vec {W}}}$, is the vectorial sum of the undisturbed upstream air velocity, ${\displaystyle {\vec {U}}}$, and the velocity vector of the advancing blade, ${\displaystyle -{\vec {\omega }}\times {\vec {R}}}$.

${\displaystyle {\vec {W}}={\vec {U}}+\left(-{\vec {\omega }}\times {\vec {R}}\right)}$

Figure 1: Forces and velocities acting in a Darrieus turbine for various azimuthal positions

Thus the oncoming fluid velocity varies during each cycle. Maximum velocity is found for ${\displaystyle \theta =0{}^{\circ }}$ and the minimum is found for ${\displaystyle \theta =180{}^{\circ }}$, where ${\displaystyle \theta }$ is the azimuthal or orbital blade position. The angle of attack, ${\displaystyle \alpha }$, is the angle between the oncoming air speed, W, and the blade's chord. The resultant airflow creates a varying, positive angle of attack to the blade in the upstream zone of the machine, switching sign in the downstream zone of the machine.

It follows from geometric considerations of angular velocity as seen in the accompanying figure that:

${\displaystyle V_{t}=R\omega +U\cos(\theta )}$

and:

${\displaystyle V_{n}=U\sin(\theta )}$

Solving for the relative velocity as the resultant of the tangential and normal components yields:

${\displaystyle W={\sqrt {V_{t}^{2}+V_{n}^{2}}}}$ [7]

Thus, combining the above with the definitions for the tip speed ratio ${\displaystyle \lambda =(\omega R)/U}$ yields the following expression for the resultant velocity:

${\displaystyle W=U{\sqrt {1+2\lambda \cos \theta +\lambda ^{2}}}}$ [8]

Angle of attack is solved as:

${\displaystyle \alpha =\tan ^{-1}\left({\frac {V_{n}}{V_{t}}}\right)}$

Which when substituting the above yields:

${\displaystyle \alpha =\tan ^{-1}\left({\frac {\sin \theta }{\cos \theta +\lambda }}\right)}$[9]

The resultant aerodynamic force is resolved either into lift (L) - drag (D) components or normal (N) - tangential (T) components. The forces are considered acting at the quarter-chord point, and the pitching moment is determined to resolve the aerodynamic forces. The aeronautical terms lift and drag refer to the forces across (lift) and along (drag) the approaching net relative airflow. The tangential force acts along the blade's velocity, pulling the blade around, and the normal force acts radially, pushing against the shaft bearings. The lift and the drag force are useful when dealing with the aerodynamic forces around the blade such as dynamic stall, boundary layer etc.; while when dealing with global performance, fatigue loads, etc., it is more convenient to have a normal-tangential frame. The lift and the drag coefficients are usually normalised by the dynamic pressure of the relative airflow, while the normal and tangential coefficients are usually normalised by the dynamic pressure of undisturbed upstream fluid velocity.

${\displaystyle C_{L}={\frac {F_{L}}{{1}/{2}\;\rho AW^{2}}}{\text{ }};{\text{ }}C_{D}={\frac {D}{{1}/{2}\;\rho AW^{2}}}{\text{ }};{\text{ }}C_{T}={\frac {T}{{1}/{2}\;\rho AU^{2}R}}{\text{ }};{\text{ }}C_{N}={\frac {N}{{1}/{2}\;\rho AU^{2}}}}$

A = Blade Area (not to be confused with the Swept Area, which is equal to the height of the blade/rotor times the rotor diameter), R = Radius of turbine

The amount of power, P, that can be absorbed by a wind turbine:

${\displaystyle P={\frac {1}{2}}C_{p}\rho A\nu ^{3}}$

Where ${\displaystyle C_{p}}$ is the power coefficient, ${\displaystyle \rho }$ is air density, ${\displaystyle A}$ is the swept area of the turbine, and ${\displaystyle \nu }$ is the wind speed.[10]

VAWTs offer a number of advantages over traditional horizontal-axis wind turbines (HAWTs):

• Omni-directional VAWTs may not need to track the wind. This means they don't require a complex mechanism and motors to yaw the rotor and pitch the blades.[12]
• Gearbox replacement and maintenance are simpler and more efficient, because the gearbox is accessible at ground level instead of requiring the operator work hundreds of feet in the air. Motor and gearbox failures generally are significant operation and maintenance considerations.
• Some designs can use screw pile foundations, which reduces the road transport of concrete and the environmental impact of installation. Screw piles can be fully recycled at end of life.
• VAWTs can be installed on HAWT wind farms below the existing HAWTs, supplementing power output.[13]
• VAWTs may operate in conditions unsuitable for HAWTs. For example, the Savonius rotor, which can operate in irregular, slow wind ground-level contexts, is often used in remote or unattended locations although it is the most 'inefficient', drag-type, VAWT.
• Reduced noise compared to HAWTs[14]
• Reduced danger for birds[15]

When the velocity of a VAWT wind turbine grows, so does the power, however at a certain peak point, the power progressively decreases to zero even while the wind turbine velocity is at its greatest. Such that, disc brakes are used to slow the velocity of a wind turbine at high wind conditions. However, sometimes due to disc brake overheating, the turbine can catch fire.[16]

VAWTs often suffer from dynamic stall of the blades as the angle of attack varies rapidly.[17][18][19]

The blades of a VAWT are fatigue-prone due to the wide variation in applied forces during each rotation. The vertically oriented blades can twist and bend during each turn, shortening their usable lifetimes.

Other than the drag-types, VAWTs have proven less reliable than HAWTs,[20] although modern designs have overcome many early issues.[21][22]

A 2021 study simulated a VAWT configuration that allowed VAWTs to beat a comparable HAWT installation by 15%. An 11,500-hour simulation demonstrated the increased efficiency, in part by using a grid formation. One effect is to avoid downstream turbulence stemming from grid-arranged HAWTs that lowers efficiency. Other optimizations included array angle, rotation direction, turbine spacing, and number of rotors.[23]

In 2022 Norway's World Wide Wind introduced floating VAWTs with two sets of counter-rotating blades. The two sets are fixed to concentric shafts. Each has an attached turbine. One is attached to the rotor, the other to the stator. This has the effect of doubling their speed relative to each other versus a static stator. They claimed to more than double the output compared to the largest HAWTs. HAWTs require heavy drivetrains, gearboxes, generators and blades at the top of the tower, necessitating heavy underwater counterbalances. VAWTs place most of the heavy components at the bottom of the tower, reducing the need for counterbalance. The blades sweep a conical area, which helps reduce the turbulence downwind of each tower, increasing the maximum tower density. The company claims it will build a 400 m (1,300 ft) 40-megawatt unit.[24]

Light pole wind turbine

The Windspire, a small VAWT intended for individual (home or office) use was developed in the early 2000s by US company Mariah Power. The company reported that several units had been installed across the US by June 2008.[25]

Arborwind, an Ann Arbor, Michigan, based company, produces a patented small VAWT which has been installed at several US locations as of 2013.[26]

In 2011, Sandia National Laboratories wind-energy researchers began a five-year study of applying VAWT design technology to offshore wind farms.[27] The researchers stated: "The economics of offshore windpower are different from land-based turbines, due to installation and operational challenges. VAWTs offer three big advantages that could reduce the cost of wind energy: a lower turbine center of gravity; reduced machine complexity; and better scalability to very large sizes. A lower center of gravity means improved stability afloat and lower gravitational fatigue loads. Additionally, the drivetrain on a VAWT is at or near the surface, potentially making maintenance easier and less time-consuming. Fewer parts, lower fatigue loads and simpler maintenance all lead to reduced maintenance costs."

A 24-unit VAWT demonstration plot was installed in southern California in the early 2010s by Caltech aeronautical professor John Dabiri. His design was incorporated in a 10-unit generating farm installed in 2013 in the Alaskan village of Igiugig.[28]

Dulas, Anglesey, received permission in March 2014 to install a prototype VAWT on the breakwater at Port Talbot waterside. The turbine is a new design, supplied by Wales-based C-FEC (Swansea),[29] and will be operated for a two-year trial.[30] This VAWT incorporates a wind shield which blocks the wind from the advancing blades, and thus requires a wind-direction sensor and a positioning mechanism, as opposed to the "egg-beater" types of VAWTs discussed above.[29]

Architect Michael Reynolds (known for his Earthship house designs) developed a 4th-generation VAWT named Dynasphere. It has two 1.5 kW generators and can produce electricity at very low speeds.[31]

• Unconventional wind turbines
• Cross-flow fan

Wikimedia Commons has media related to Vertical-axis wind turbines.

• Cellar Image of the Day Shows a VAWT transverse to the wind, yet with the axis horizontal, but such does not allow the machine to be called a HAWT.