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Aerodynamics of Wind Turbines: Drag

Both aircraft engineers who build aircraft wings and propellers, and wind turbine engineers who design rotor blades are concerned with aerodynamic drag. Drag is always important when an object moves rapidly through the air. Aircraft should have good fuel economy, and wind turbine rotor blades must have high tip speeds to work efficiently. Therefore it is critical, that both aircraft wings and rotor blades have low aerodynamic drag.

Drag Arrow
Airfoil with wind arrowsThe black arrow above the picture shows the direction of the drag force, when the cross section of the airplane wing or rotor blade is moving towards the right.

 

 

Drag Increases with the Area Facing the Wind
Drag increases in proportion to the frontal area of an object facing the wind. The frontal area is the area of the hole in a wall if the object were thrown through a wall in a cartoon. It is a good idea to design objects that have to move quickly through fluids with low energy use to have small cross sections facing the current. That is the reason why submarines, missiles, cars, or bicyclists' helmets often are built using elongated drop shapes.

Drag Depends on the Shape of the Object

Semisphere open towards the wind

A Parachute shape has a very high drag coefficient of 1.42

Different shapes have very different drag. The size of the drag for a given shape is usually measured by the drag coefficient, CD, which is defined as the drag force per square metre frontal area of the object. *)
The picture shows a hollow hemisphere open towards the wind, just like the cup of a cup anemometer or like a parachute. Such a shape has a very high CD of 1.42, whereas its CD is only 0.38 if you turn it 180° around a vertical axis. A modern automobile typically has a CD in the range 0.27-0.35. A runner has a CD about 0.5, a racing bicyclist about 0.4. An airfoil shape used on aircraft wings or rotor blades, typically has an extremely small CD about 0.04. **)

*) For aircaft airfoils the drag coefficient is usually defined relative to the wing area.
**) The drag coefficients are valid for Reynolds numbers above 10
4, a subject which is further discussed at the bottom of this page.

 

 

Drag Increases with the Square of the Wind Speed
Both lift and drag increase with the square of the wind speed.
The reason why drag is much more of a problem for a racing bicyclist than for, say, a runner, is that a fast runner will be moving at speed of some 6 m/s (21 km/h, 13 mph), whereas a racing bicyclist is moving at a speed of some 12 m/s (42 km/h, 26 mph).
A modern car (drag coefficient 0.34) with a 110 kW (150 HP) engine will be using about 4.6 kW (6 HP) of power to overcome air drag and 11 kW (14 HP) for mechanical propulsion (rolling resistance etc.) when it is being driven at a constant 80 km/h (22.2 m/s, 49 mph). When driving at its top speed of 210 km/h (58 m/s, 128 mph) it will be using 82 kW (112 HP) to overcome drag and the remaining 28 kW (38 HP) to overcome rolling resistance etc.

High Lift to Drag Ratio Needed for airfoils for Rotor Blades
The rotors on modern wind turbines have very high tip speeds for the rotor blades, usually around 75 m/s (270 km/h, 164 mph). In order to obtain high efficiency, it is therefore essential to use airfoil shaped rotor blades with a very high lift to drag ratio, i.e. rotor blades which provide a lot of lift with as little drag as possible. This is particularly necessary in the section of the blade near the tip, where the speed relative to the air is much higher than close to the centre of the rotor.
For wind turbines with a low tip speed it is not necessary to use top quality airfoils. The "Western" type windmill rotors can easily be manufactured from flat metal plate.

Drag Increases with the density of air
Both lift and drag increase in proportion to with the density of air. Cold air will thus give more drag than hot air. You may find the density of air at different temperatures in the Reference Manual to study how important this effect is.

Drag Coefficient Varies with the roughness of the object surface
Just as it is case for lift, drag may vary quite dramatically with the surface roughness of the object. Normally it is desirable to have smooth, clean surfaces in order to minimise drag. There are some curious exceptions to this rule, as you can see on the page about Research and Development in Wind Energy.

 

 

OwlDrag Force Formula
The drag force for a given object can be found using the formula below:

FD = CD 0.5 A v2

FD = The drag force measured in N (Newton).
CD = The drag coefficient, measured in N/ m2, i.e. the drag force per square metre frontal area of the object shape. You will have to find this figure in a table. This value is usually found through (very expensive) wind tunnel measurements.
Warning: Airfoil tables frequently give the drag coefficient per square metre wing or rotor blade area, rather than per square metre frontal area. You can recalculate that figure, since you know the relative thickness of the airfoil.
= The density of the fluid measured in kg/m3. In the case of dry air at sea surface level at 15° C the figure is 1.225 kg/m3. You can find air densities for other temperatures in the Reference Manual.
A = Frontal area of the object in m2.
v = Relative wind speed in m/s, i.e. the speed of the fluid moving past the object. If the object itself is moving while facing a headwind, you have to add the headwind speed to the speed of the object to obtain v.
The formula for the drag force is fairly logical when you compare it with the formula for the power of the wind. The reason why it is v2 which is used in the formula is that we are dealing with a force. If we had looked at the power loss from drag instead, we should have multiplied by v3.

 

OwlOwlDrag Depends on the Reynolds Number
In reality, there is not just one, but two kinds of drag: Pressure drag, and friction drag. At very low speeds, and for small objects, say dust particles, the friction drag dominates. At high speeds and/or large object sizes pressure differences dominate. The drag coefficient for an object will therefore depend on which type of flow is dominating. A microscopic parachute will not work like a large parachute.
Fortunately we are able to predict which type of flow we are dealing with if we know the so-called Reynolds number for the experiment. (Named after the British engineer Sir Osborne Reynolds 1842-1912).
The Reynolds number is defined as

Re = v L / (μ / )

Re = The Reynolds number, which is dimensionless, i.e. it is a ratio of two quantities with the same unit.
v = The relative velocity of the fluid in m/s.
L = The characteristic length, in this case the largest cross section of the frontal area in m.
μ = The viscosity of the fluid in Ns/m2. The viscosity of air, also called the dynamic viscosity of air is 1.8 x 10- 5 at 15° C and atmospheric pressure at sea level. The value for the viscosity of air at other temperatures may be found in the Reference Manual.
= The density of the fluid in kg/m3.
The value in the denominator of the fraction (μ / ) is called the kinematic viscosity of air. When the kinematic viscosity is high, the laminar flows dominate.
Thus, if the Reynolds number is very small, below 1, one can ignore pressure drag and concentrate on friction drag. If the number is large, above 100, one can ignore the friction drag and look at pressure drag only. Close to the surface of the object friction drag and viscosity are always important.

If you are interested in more detail on this subject, you should consult a textbook on fluid mechanics such as the ones mentioned in the bibliography.

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Updated 11 September 2002
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