Wind Turbine Blade Geometry
The different parts of a wind turbine blade include the root, tip, leading edge, and trailing edge. Generally speaking, the root is the widest and thickest, and is where most of the torque is generated. The tip is the narrowest and thinnest part of the blade, and is where most of the speed is generated. The blade tips will be travelling much faster than any other part of the blade because they have a larger distance to travel per rotation, and must keep up with the root or the blade will tear itself apart. Because speed is more important than torque when it comes to electrical generation, most of the blade is designed to be thin and narrow to reduce air resistance, while a small portion of the root - which travels slower - is wider to generate the startup torque needed to get the blades spinning in low winds.
Relative Wind Angle & Angle Of Attack
The relative wind angle refers to the apparent angle of the wind from the perspective of the blade as it’s spinning. To help visualize it, imagine that you’re driving on a straight stretch of road in a car, and notice a deer darting across a field to cross the road. If you’ve ever been in this situation, then it might have seemed like the deer was running straight at you. But it wasn't; you were just both headed for the same point from different directions. The line that can be drawn between you and the deer is the relative angle. When it comes to wind and turbine blades, this angle will be different throughout the length of the blade and is what produces the noticeable twist or ‘washout’ in its shape. If the angle of attack isn’t optimized for the relative wind angle throughout the length of the blade, then the blade will perform poorly.
Chord Geometry & Airfoil
The blade chord refers to the imaginary line that connects the blade’s leading edge with the trailing edge. The leading edge is the edge of the blade that faces the direction of rotation. Because of this, it’s usually the area of the blade that’s most susceptible to erosion from air resistance, precipitation, etc. The trailing edge is as it sounds, the thin, back edge of the blade where the twist distribution (washout) is most noticeable.
The blade chord is what provides the torque behind a spinning blade. The wider the blade chord (ie blade), the more wind it can harness and the more torque it will produce. But a person has to keep in mind that torque is only useful for startup when it comes to generating electricity, ie: startup torque. This is why only the root is made wide, so it can generate enough torque to get the blades spinning without interfering with top speed potential after they do. The wider the chord is, the more air resistance it experiences and the slower the top speed of the rotor will be. If the chord is too wide, then the blades will end up blocking the wind instead of harnessing it because the wind won't be able to pass through after a certain rpm - the blades will effectively form a wall and block it. The wind must pass through the rotor in order for the airfoil to harness it and generate lift. If it doesn't pass through the blades, then they don't generate lift, the wind piles up in front of the rotor, and the blades stall until they slow down enough to allow wind to pass through.
The blade chord is what provides the torque behind a spinning blade. The wider the blade chord (ie blade), the more wind it can harness and the more torque it will produce. But a person has to keep in mind that torque is only useful for startup when it comes to generating electricity, ie: startup torque. This is why only the root is made wide, so it can generate enough torque to get the blades spinning without interfering with top speed potential after they do. The wider the chord is, the more air resistance it experiences and the slower the top speed of the rotor will be. If the chord is too wide, then the blades will end up blocking the wind instead of harnessing it because the wind won't be able to pass through after a certain rpm - the blades will effectively form a wall and block it. The wind must pass through the rotor in order for the airfoil to harness it and generate lift. If it doesn't pass through the blades, then they don't generate lift, the wind piles up in front of the rotor, and the blades stall until they slow down enough to allow wind to pass through.
An airfoil is the aerodynamic cross-sectional profile of the blade, and is designed to convert the downwind drag force of a wind stream into a right-angled lifting force that causes the blades to rotate. There are many different types of airfoils, each producing their own lift coefficient based on a given angle of attack, camber, etc, but usually it’s somewhere around 80-85% for a 4-6° angle of attack.
The image below shows a variety of airfoils that have been used for small residential wind turbines over the decades, the most common being the SD7032 or similar.
Tip Speed Ratio
The TSR refers to the ratio of the speed of the blade tips to the speed of the wind that’s spinning them. Because the blades on a HAWT are always producing lift, they can be designed to spin much faster than the incoming wind is travelling, which is ideal for electrical generation because voltage generation is proportional to rpm; the higher the rotor rpm, the more voltage that can be produced from a given wind speed. The TSR is important because if the blades spin too slow at a given wind speed, then most of the wind will pass through the rotor with little being harnessed. So more wind speed will be required for the generator to reach a charging voltage and produce any useful power. But if the blades spin too fast, then they’ll block the wind and cause the blades to stall out prematurely. Thus, it's necessary to match the angular momentum of the blades to the wind speed and generator potential in order to maximize efficiency.
The TSR required for a particular rotor will depend on the average speed and type of wind (clean or dirty) that's to be harnessed in a given location, as well as the number of blades to be used. Generally, a TSR between 5 and 7 is recommended. Below 5, and the blades will likely stall prematurely. Above 7, and the blades will suffer more blade tip erosion and put the bearings and other components under more abuse, negating any potential cost efficiency advantages.
The TSR required for a particular rotor will depend on the average speed and type of wind (clean or dirty) that's to be harnessed in a given location, as well as the number of blades to be used. Generally, a TSR between 5 and 7 is recommended. Below 5, and the blades will likely stall prematurely. Above 7, and the blades will suffer more blade tip erosion and put the bearings and other components under more abuse, negating any potential cost efficiency advantages.
Number Of Blades
The number of blades used will also affect the torque and frequency generated. If a small number of blades are used, then the blades must travel faster to maximize the energy harvest, so they’re designed with a high TSR that will generate the high rpm’s needed. If a large number of blades are used, then the available torque will be increased but rpm’s will be slower because there’s more blade area occupying the swept area and limiting the amount of wind that can pass through the rotor after a certain rpm, so rotors with low TSR's and a large number of blades are limited to low wind speed/high torque applications, such as for water pumping or milling. This is why the old windmills that were used centuries ago for grinding grain used numerous blades (or vanes); they generated lots of torque for turning the wood and stone components within the mill, but also kept the rotor spinning at a relatively low and safe rpm.
Using more blades helps to balance the dynamic forces acting on a turbine and, as stated earlier, generates higher start up torque because there’s more blade area harnessing wind. But for electrical production, the frequency losses and subsequent power and efficiency losses negates any advantage in torque. Using 2 or even 1 blade with a counterbalance will allow the rotor to spin faster and make the turbine more efficient at generating electricity, but also makes it more susceptible to imbalance, wobbling, and faster structural degradation. This is why most wind turbines used for electrical generation have 3 blades instead of 2 or 4, because 3 is a good compromise between efficiency and structural integrity.
Using more blades helps to balance the dynamic forces acting on a turbine and, as stated earlier, generates higher start up torque because there’s more blade area harnessing wind. But for electrical production, the frequency losses and subsequent power and efficiency losses negates any advantage in torque. Using 2 or even 1 blade with a counterbalance will allow the rotor to spin faster and make the turbine more efficient at generating electricity, but also makes it more susceptible to imbalance, wobbling, and faster structural degradation. This is why most wind turbines used for electrical generation have 3 blades instead of 2 or 4, because 3 is a good compromise between efficiency and structural integrity.
Start Up Speed & Cut-in Speed
The start up speed is the wind speed that the blades start to spin in. The cut-in speed is the wind speed or the rotor rpm that the generator starts charging. Voltage output is proportional to rpm, so the faster the rotor turns, the more voltage the generator will produce. In order to provide power to a load, the generator rpm’s must rise enough to increase the output voltage to slightly more than the load’s rated voltage. This is the cut-in voltage. For example, if you want to charge a 12V battery that’s reading 13V on a multimeter, then the generator has to produce more than 13V to charge it.
Because the cut-in voltage depends on the rotor rpm, it’s necessary to account for it when designing the blades so that they’ll spin at the required speed when they should. For direct battery charging, the cut-in rpm is typically between 100-200, and the cut-in wind speed is usually somewhere between 3-4 meters per second (6-9 mph). This is largely due to the fact that the generator’s power curve needs to be designed to match that of the blade’s, which can only happen at a certain speed range.
To convert wind speed into rotor rpm, use the following equation:
RPM = 60 * V * TSR / (Pi * D)
Where:
V = velocity in meters per second
TSR = tip speed ratio
Pi = 3.1459
D = rotor diameter in meters
Example using a 3 meter rotor with a TSR of 7, performing in a 5 mps wind:
RPM = 60 * 5 * 7 / (3.1459 * 3)
= 60 * 5 * 7 / 9.44
= 222.5 rpm
Because the cut-in voltage depends on the rotor rpm, it’s necessary to account for it when designing the blades so that they’ll spin at the required speed when they should. For direct battery charging, the cut-in rpm is typically between 100-200, and the cut-in wind speed is usually somewhere between 3-4 meters per second (6-9 mph). This is largely due to the fact that the generator’s power curve needs to be designed to match that of the blade’s, which can only happen at a certain speed range.
To convert wind speed into rotor rpm, use the following equation:
RPM = 60 * V * TSR / (Pi * D)
Where:
V = velocity in meters per second
TSR = tip speed ratio
Pi = 3.1459
D = rotor diameter in meters
Example using a 3 meter rotor with a TSR of 7, performing in a 5 mps wind:
RPM = 60 * 5 * 7 / (3.1459 * 3)
= 60 * 5 * 7 / 9.44
= 222.5 rpm
Blade Element Momentum Theory
The most effective approach to blade design utilizes what's called blade element momentum theory (BEMT), which combines blade element theory with momentum theory , and is used to divide the span of a turbine blade into multiple elements or sections to calculate the local forces on each section of the blade at a specific wind speed, and establish optimal chord width, thickness, and angles accordingly.
BEMT is important for blade design because it accounts for the varying relative wind angle at different sections of the blade, and adjusts the angle of the blade so that its angle of attack is optimal throughout its length. Notice in the image above how the trailing edge twists along the blade to account for the different relative wind angles at each station. BEMT is also used to determine chord width and thickness at each section of the blade to optimize torque and speed for the work its intended to do.
BEMT is important for blade design because it accounts for the varying relative wind angle at different sections of the blade, and adjusts the angle of the blade so that its angle of attack is optimal throughout its length. Notice in the image above how the trailing edge twists along the blade to account for the different relative wind angles at each station. BEMT is also used to determine chord width and thickness at each section of the blade to optimize torque and speed for the work its intended to do.
Below is a list of the equations used in BEMT to design a blade to spec. However, an easy to use worksheet that will do all the calculations and generate a blade profile for you is available here, and includes a worksheet for designing a permanent magnet generator as well: https://www.resystech.com/the-diy-wind-turbine-design-guide.html
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Tip speed ratio per element: λi = λ(r/R)
Relative wind angle per element: φi = 2/3Tan-1(1/ λi)
Blade angle per element: σi = φi – α
Chord width per element: Ci = (VR2)/(βCLr λ λ)
Chord thickness per element: Cti = 1/8Ci
Where:
CL = lift coefficient = ~85% (approximation; actual factor depends on chosen airfoil)
Ci = chord width per element
Cti = chord thickness per element
σi = blade angle per element
φi = relative wind angle per element
λ = tip speed ratio
λi = tip speed ratio per element
R = rotor radius
r = radius per element
V = cut-in wind speed
A = rotor swept area
α = angle of attack
β = number of blades
Relative wind angle per element: φi = 2/3Tan-1(1/ λi)
Blade angle per element: σi = φi – α
Chord width per element: Ci = (VR2)/(βCLr λ λ)
Chord thickness per element: Cti = 1/8Ci
Where:
CL = lift coefficient = ~85% (approximation; actual factor depends on chosen airfoil)
Ci = chord width per element
Cti = chord thickness per element
σi = blade angle per element
φi = relative wind angle per element
λ = tip speed ratio
λi = tip speed ratio per element
R = rotor radius
r = radius per element
V = cut-in wind speed
A = rotor swept area
α = angle of attack
β = number of blades