# Do wind turbines convert the kinetic energy of air?

It is often said that wind turbines convert the kinetic energy of the wind into electricity. But in respect to horizontal wind turbines with airfoil shaped blades this is imho not the case.

Wind turbine designers try to minimize drag. A perfect wind turbine has an infinite lift-to-drag-ratio (drag is infinitesimal) where the kinetic energy of the air molecules behind the rotor is equal to the kinetic energy in front of the rotor.

Unlike traditional windmills and most vertical axis wind turbines, horizontal wind turbines with airfoil blades do not try to "catch the wind" (try to transfer the kinetic energy of the air onto the blades) but use lift to induce rotation.

What is really happening?

## 2 Answers

The principle of conservation of energy is your friend.

The wind turbine generates electricity.

That energy has to come from somewhere.

The other energy in the system is the kinetic energy of the wind.

Therefore, the wind turbines convert the kinetic energy of the wind into electricity, and the kinetic energy of the air downwind of the rotor is less than the kinetic energy upwind of the rotor. Your "perfect" wind turbine would be useless.

The lift generated by the wind over the blade moves the blade around. That takes energy from the wind to achieve. The energy is delivered into the generator.

There's a comprehensive book called "Wind Energy - The Facts", and the technology chapter covers the specific aerodynamics. Your closest decent library should have a copy.

See also "Wind Turbine Blade Design", Peter J. Schubel and Richard J. Crossley, Energies 2012, 5, 3425-3449; doi:10.3390/en5093425

• I'm confused about what is the front of the rotor and what is the back side. I thought that the back side has lower pressure to rotate the rotor. In that case, the back side has the higher kinetic energy (Bernoulli's principle). – LDC3 Oct 26 '14 at 15:55
• @LDC3 I've rephrased "back" and "front" to "downwind" and "upwind" respectively, to clarify. – 410 gone Oct 26 '14 at 16:56

First, it's not only drag that slows down the air, every force has to be matched by an equal and opposite force including lift. Second, friction is not the sole cause of drag, indeed there's drag on an airfoil in an inviscid fluid due to pressure.

So why we need sophisticated airfoil design when traditional windmills can work and how modern wind turbines work?

In this picture $v_1$ is wind speed at far upstream, $v$ is wind speed at rotor (wind speed is different at upstream and downstream and it has some intermediate value at rotor), $u$ is linear velocity of the blade. $w$ is the apparent wind speed (wind speed relative to the blade). The apparent wind is stronger than the true wind but its angle is less favourable. You see that when rotating, angle of attack $\alpha$ is close to zero. A flat plate at zero angle of attack produces nothing but drag, while an airfoil can produce considerable lift even at zero angle of attack (while cruising wing of an airliner has almost zero angle of attack).

The lift $F_L$ has a component along rotor plane which contributes to a positive torque along the rotor axis, while the drag $F_D$ has a component along the rotor plane tends to decrease that torque. That's why we should decrease the drag.

The closer to the tip of the blade you get, the faster the blade is moving through the air and so the greater the apparent wind angle is. To compensate for this they twist the blade.

The planform shape is chosen to give the blade an approximately constant slowing effect on the wind over the whole rotor disc (i.e. the tip slows the wind to the same degree as the centre or root of the blade). This ensures that none of the air leaves the turbine too slowly (causing turbulence), yet none is allowed to pass through too fast (which would represent wasted energy).

Because the tip of the blade is moving faster than the root, it passes through more volume of air, hence must generate a greater lift force to slow that air down enough. Fortunately, lift increases with the square of speed so its greater speed more than allows for that. In reality the blade can be narrower close to the tip than near the root and still generate enough lift. The optimum tapering of the blade planform as it goes outboard can be calculated; roughly speaking the chord should be inverse to the radius.

In reality a fairly linear taper is sufficiently close to the optimum for most designs, structurally superior and easier to build than the optimum shape.

So these airfoils allow us to generate lift even at high rotational velocities, but why not operate the turbine at low speeds? Because power is speed $\times$ force and to obtain the same power we need to operate them at higher forces which increases the load on the structure necessitating costly materials. And to increase the lift we need more chord length which increase weight of the blades, increasing the load on the structure again.

Furthermore remember that the equal and opposite force is exerted on the fluid. As the blades generates torque, they would have an equal but opposite effect on the air. So the air downstream would have a swirl. That swirl represents lost power so reduces the available power that can be extracted from the wind. Lower rotational speed requires higher torque for the same power output, so lower blade speed results in higher wake swirl losses.

• How did you draw your wind turbine. – OHLÁLÁ Oct 2 '15 at 7:33
• @OHLÁLÁ with asymptote asymptote.sourceforge.net – Azad Oct 2 '15 at 8:15