Your Questions About Wind Turbine Efficiency

adminsta answers:

First off Air Density at sea level (p) = 1.226 kg/m^3

Power = 1/2 * Density(p) * Area * (Velocity^3)average * efficiency

Betz limit states a turbine can capture no more than 59.3 percent of the potential energy in wind.

Therefore I believe the efficiency is 75% of 59.3%… Which, is what you have stated there.

So that answers your next question.

Power = 1/2 * 1.226 kg/m^3 * (pi*50^2) * (15 m/s) ^3 * N
Power = 16.25×10^6 W * efficiency

For including the efficiency (Betz) it would be

Power = 16.25 MW * 59.3% * 75%
Power = 9.63 MW

For the last part.. Side force?? Is the turbine not facing directly into the wind? Or is it asking for the side force on the blades?

adminsta answers:

Your friend is, indeed, telling an outlandish story.

Most likely some of the generators are off-line because the demand for electricity is low (at that time) — especially the demand for that particular wind-farm energy. That wind farm sells power to the grid at a certain rate, which is probably slightly higher than the other power plants in the area, so it is probably used as a “buffer” or reserve capacity.

Every time I toured Hoover dam (I lived in Las Vegas for 10 years), never, did I see all of the generators running at one time. The most I ever saw was 40% of capacity. I asked the tour guide why, and they referred me to a plant engineer (who was fortunately standing near by). He told me that the power authority out of Phoenix would place orders the night before based on estimated demand, and the dam operators would setup that generating capacity for the next day (i.e. Open sleuce-gates, get turbines spinning and stable, switch on electrical lines, etc.).

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adminsta answers:

Hey Young, good question. If you take a moment to read through all these different answers, you’ll see that there are a lot of different positions on this subject. The short answer is the most efficient wind turbine design is the horizontal axis single blade turbine. Most people have never heard of or seen one in North America, they were common years ago in many parts of Europe where the winds were very light, and so efficiency was a chief concern. The single blade extended only in one direction away from the hub, and on the opposite side was a large bowling ball shaped counter weight. The reason this type is most efficient is that the one airfoil has complete use of the passing air. When you add a second blade, you can capture the wind twice as often, but the combination of two blades to swing through the air, and the turbulence left behind from one blade interferes with the second one in its path, much like a boat leaving a wake behind for another one to pass through. The next most efficient design is the 2 blade, but it is nearly as efficient as the single blade, better for slightly higher and less steady winds. They work best in areas where the wind blows mainly in one direction all day and the rotor head does not have to change direction often. When you are in a situation where the wind changes direction frequently, like the upper midwest, the three blade units are the best, because no matter what orientation the blades are in, the gyroscopic moment on the tower is steady while the unit is turning to a different direction. This is the main reason the 3 blade units are so common in North America. The 5 or 10 percent loss in efficiency is more than offset by the longer longevity of the tower and equipment, they run much smoother. Once you get beyond the 3 blades, additional blades do not offer any additional advantages, but each additional blade costs a bit more in efficiency losses. For this reason, most wind turbine manufacturers today primarily make 3 blade units. There are a few 2 blade units out there, Southwest windpower has one I believe for home use. There are also a few very small units for remote applications with 6 or 8 blades, but these are made purely for extremely high wind applications, like an artic weather station or onboard an ocean going vessel.

The two people who are considered the gurus on this subject are Mick Sagrillo and Paul Gipe. Paul has written a book called, “Wind Power for Home and Business,” and Mick has authored several papers and articles and written several books on renewable energy as well, and continues to teach workshops in Wisconsin on the subject. We were fortunate enough to go to one of his classes at the Midwest Renewable Energy Fair several years ago. I would suggest looking for Paul’s book at the library, or anything by Mick, or surfing to one of the websites below, it’s all very interesting reading, and you’ll be getting better information on the subject this way. Take care, Rudydoo

adminsta answers:

The aerodynamics of a horizontal-axis wind turbine are not straight forward. The air flow at the blades is not the same as the airflow far away from the turbine.The very nature of the way in which energy is extracted from the air also causes air to be deflected by the turbine. In addition the aerodynamics of a wind turbine at the rotor surface exhibit phenomena that are rarely seen in other aerodynamic fields..

[edit] Axial momentum and the Betz limit

Energy in fluid is contained in four different forms: gravitational potential energy, thermodynamic pressure, kinetic energy from the velocity and finally thermal energy. Gravitational and thermal energy have a negligible effect on the energy extraction process. From a macroscopic point of view, the air flow about the wind turbine is at atmospheric pressure. If pressure is constant then only kinetic energy is extracted. However up close near the rotor itself the air velocity is constant as it passes through the rotor plane. This is because of conservation of mass. The air that passes through the rotor cannot slow down because it needs to stay out of the way of the air behind it. So at the rotor the energy is extracted by a pressure drop. The air directly behind the wind turbine is at sub-atmospheric pressure; the air in front is under greater than atmospheric pressure. It is this high pressure in front of the wind turbine that deflects some of the upstream air around the turbine.

Albert Betz was together with Lancaster the first to study this phenomenon. He notably determined the maximum limit to wind turbine performance. The limit is now referred to as the Betz Limit. This is derived by looking at the axial momentum of the air passing through the wind turbine. As stated above some of the air is deflected away from the turbine. This causes the air passing through the rotor plane to have a smaller velocity than the free stream velocity. The degree at which air at the turbine is less than the air far away from the turbine is called the axial induction factor. It is defined as below.

Aequivfrac{U_1-U_2}{U_1}

a is the axial induction factor. U1 is the wind speed far away from the rotor. U2 is the wind speed at the rotor.

The first step to deriving the Betz limit is applying conservation of axial momentum. As stated above the wind loses speed after the wind turbine compared to the speed far away from the turbine. This would violate the conservation of momentum if the wind turbine was not applying a thrust force on the flow. This thrust force manifests itself through the pressure drop across the rotor. The front operates at high pressure while the back operates at low pressure. The pressure difference from the front to back causes the thrust force. The momentum lost in the turbine is balanced by the thrust force. Another equation is needed to relate the pressure difference to the velocity of the flow near the turbine. Here the Bernoulli equation is used between the field flow and the flow near the wind turbine. There is one limitation to the Bernoulli equation. The equation cannot be applied to fluid passing through the wind turbine. Instead conservation of mass is used to relate the incoming air to the outlet air. Betz used these equations and managed to solve the velocities of the flow in the far wake and near the wind turbine in terms of the far field flow and the axial induction factor. The velocities are given below.

U2 = U1(1 ? A)

U4 = U1(1 ? 2a)

U4 is introduced here as the wind velocity in the far wake. This is important because the power extracted from the turbine is defined by the following equation. However the Betz limit is given in terms of the coefficient of power. The coefficient of power is similar to efficiency but not the same. The formula for the coefficient of power is given beneath the formula for power.

P=0.5rho AU_2(U_1^2-U_4^2)

C_pequivfrac{P}{0.5rho AU_1^3}

Betz was able to develop an expression for Cp in terms of the induction factors. This is done by the velocity relations being substituted into power and power is substituted into the coefficient of power definition. The relationship Betz developed is given below.

Cp = 4a(1 ? A)2

The Betz limit is defined by the maximum value that can be given by the above formula. This is found by taking the derivative with respect to the axial induction factor, setting it to zero and solving for the axial induction factor. Betz was able to show that the optimum axial induction factor is one third. The optimum axial induction factor was then used to find the maximum coefficient of power. This maximum coefficient is the Betz limit. Betz was able to show that the maximum coefficient of power of a wind turbine is 16/27. Airflow operating at higher thrust will cause the axial induction factor to rise above the optimum value. Higher thrust cause more air to be deflected away from the turbine. When the axial induction factor falls below the optimum value the wind turbine is not extracting all the energy it can. This reduces pressure around the turbine and allows more air to pass through the turbine, but not enough to account for lack of energy being extracted.

The derivation of the Betz limit shows a simple analysis of wind turbine aerodynamics. In reality there is a lot more. A more rigorous analysis would include wake rotation, the effect of variable geometry. The effect of air foils on the flow is a major component of wind turbine aerodynamics. Within airfoils alone, the wind turbine aerodynamicist has to consider the effect of surface roughness, dynamic stall tip losses, solidity, among other problems.

[edit] Angular momentum and wake rotation

The wind turbine described by Betz does not actually exist. It is merely an idealized wind turbine described as an actuator disk. Its a disk in space where fluid energy is simply extracted from the air. In the Betz turbine the energy extraction manifests itself through thrust. The equivalent turbine described by Betz would be a horizontal propeller type operating with infinite blades at infinite tip speed ratios and no losses. The tip speed ratio is ratio of the speed of the tip relative to the free stream flow. This turbine is not too far from actual wind turbines. Actual turbines are rotating blades. They typically operate at high tip speed ratios. At high tip speed ratios three blades are sufficient to interact with all the air passing through the rotor plane. Actual turbines still produce considerable thrust forces.

lambdaequivfrac{ROmega}{U_1}

One key difference between actual turbines and the actuator disk, is that the energy is extracted through torque. The wind imparts a torque on the wind turbine, thrust is a necessary by product of torque. Newtonian physics dictates that for every action there is an equal and opposite reaction. If the wind imparts a torque on the blades then the blades must be imparting a torque on the wind. This torque would then cause the flow to rotate. Thus the flow in the wake has two components, axial and tangential. This tangential flow is referred to as wake rotation.

Torque is necessary for energy extraction. However wake rotation is considered a loss. Accelerating the flow in the tangential direction increases the absolute velocity. This in turn increases the amount of kinetic energy in the near wake. This rotational energy is not dissipated in any form that would allow for a greater pressure drop (Energy extraction). Thus any rotational energy in the wake is energy that is lost and unavailable.

This loss is minimized by allowing the rotor to rotate very quickly. To the observer it may seem like the rotor is not moving fast; however, it is common for the tips to be moving through the air at 6 times the speed of the free stream. Newtonian mechanics defines power as torque multiplied by the rotational speed. The same amount of power can be extracted by allowing the rotor to rotate faster and produce less torque. Less torque means that there is less wake rotation. Less wake rotation means there is more energy available to extract.

[edit] Blade Element and Momentum Theory

The simplest model for Horizontal Axis Wind Turbine Aerodynamics is Blade Element Momentum (BEM) Theory. The theory is based on the assumption that the flow at a given annulus does not effect the flow at adjacent annuli. This allows the rotor blade to analysed as separate sections, where the resulting forces are summed over all sections to get the overall forces of the rotor. The theory uses both axial and angular momentum balances to determine the flow and the resulting forces at the blade.

The momentum equations for the far field flow dictates that the thrust and torque will induce a secondary flow in the approaching wind. This in-turn affects the flow geometry at the blade. The blade itself is the source of these thrust and torque forces. The force response of the blades is governed by the geometry of the flow, or better known as the angle of attack. Refer to the Airfoil article for more information on how airfoils create lift and drag forces at various angles of attack. This interplay between the far field momentum balances and the local blade forces requires one to solve the momentum equations and the airfoil equations simultaneously. Typically computers and numerical methods are employed to solve these models.

There is a lot of variation between different version of BEM theory. First off one can consider the effect of wake rotation or not. Second one can go further and consider the pressure drop induced in wake rotation. Third the tangential induction factors can be solved with a momentum equation, an energy balance or orthognal geometric constraint, the later a results of Biot-Savart law in vortex methods. These all lead to different set of equations that need to be solved. The simplest and most widely used equations are those that consider wake rotation with the momentum equation but ignore the pressure drop from wake rotation. Those equations are given below. A is the axial component of the induced flow, a’ is the tangential componenet of the induced flow. ? Is the solidity of the rotor, ? Is the local inflow angle. Cn and Ct are the coefficient of normal force and the coefficient of tangential force respectively. Both these coefficients are defined with the resulting lift and drag coefficients of the airfoil.

A=frac{1}{frac{4sin^2phi}{C_nsigma}+1}

a’=frac{1}{frac{4sinphi cosphi}{C_tsigma}-1}

[edit] Corrections to Blade Element Momentum Theory

Blade Element Momentum (BEM) theory alone fails to accurately represent the true physics of real wind turbines. Two major shortcomings are the effect of descrete number of blades and far field effects when the turbine is heavily loaded. Secondary short-comings come from dealing with transient effects like dynamic stall, rotational effects like coriolis and centrifugal pumping, finally geometric effects that arise from coned and yawed rotors. The current state of the art in BEM uses corrections to deal with the major shortcoming. These corrections are discussed below. There is yet an accepted treatment for the secondary shortcomings. These areas remain a highly active area of research in wind turbine aerodynamics.

The effect of the descrete number of blades is dealt with by applying the Prantl tip loss factor. The most common form of this factor is given below where B is the number of blades, R is the outer radius and r is the local radius. The definition of F is based on actuator disk models and not directly applicable to BEM. However the most common application multipies induced velocity term by F in the momentum equations. As in the momentum equation there are many variations for applying F, some argue that the mass flow should be corrected in either the axial equation, or both axial and tangential equations. Others have suggested a second tip loss term to account for the reduced blade forces at the tip. Below shows above momentum equations with the most common application of F.

F=frac{2}{pi}cos^{-1}(e^{-(frac{B*(R-r)}{2rsinphi})})

a=frac{1}{frac{4Fsin^2phi}{C_nsigma}+1}

a’=frac{1}{frac{4Fsinphi cosphi}{C_tsigma}-1}

The typical momentum theory applied in BEM is only effective for axial induction factors up to 0.4 (thrust coefficient of 0.96). Beyond this point the wake collapses and turbulent mixing occurs. This state is highly transient and largely unpredictable by theoretical means. Accordingly, several emperical relations have been developed. As the usual case there are several version, however a simple one that is commonly uses is a linear curve fit given below, with ac = 0.2. The turbulent wake function given excludes the tip loss function, however the tip loss is applied simply by multiplying the resulting axial induction by the tip loss function.

C_t=4(a_c^2+(1-2a_c)a) when a > ac

[edit] Other Methods of Aerodynamic Modelling

BEM is widely used due to its simplicity and overall accuracy. Limited success has been made with computational flow solvers based on Reynolds Averaged Navier Stokes (RANS) and other similar three dimensional models. This is primarily due to the shear complexity modeling wind turbines. Wind turbine aerodynamics are dependent on far field conditions, several rotor diameters up and down stream, while at the same time being dependent on small scale flow conditions at the blade. Coupled with body motion, the need to have fine resolution and a large domain makes these model highly computationally intensive. For all practical purposes this approach is not worth it. As such these methods are relagated to research.

One method that is commonly applied is Biot-Savart law. The model assumes that the wind turbine rotor is shedding a continuous sheet of vortices at the tip, and sometimes the root or along the blade as in lifting line theory. Biot-Savart law is applied to determine how the circulation of these vortices induce a flow in the far field. These methods have largely confirmed much of the applicability of BEM and shed insight on the structure of wind turbine wakes. Vortex methods have limitations due to its grounding in potential flow theory, as such cannot model viscous behavior. These methods are still computationally intesive and still rely on blade element theory for the blade forces. Just like RANS vortex methods are found soley in research environments.

[edit] Tower height

The wind blows faster at higher altitudes because of the drag of the surface (sea or land) and the viscosity of the air. The variation in velocity with altitude, called wind shear, is most dramatic near the surface.
Wind turbines generating electricity in California.
Wind turbines generating electricity in California.

Typically, in daytime the variation follows the 1/7th power law, which predicts that wind speed rises proportionally to the seventh root of altitude. Doubling the altitude of a turbine, then, increases the expected wind speeds by 10% and the expected power by 34%. Doubling the tower height generally requires doubling the diameter as well, increasing the amount of material by a factor of eight.

At night time, or when the atmosphere becomes stable, wind speed close to the ground usually subsides whereas at turbine hub altitude it does not decrease that much or may even increase. As a result the wind speed is higher and a turbine will produce more power than expected from the 1/7th power law: doubling the altitude may increase wind speed by 20% to 60%. A stable atmosphere is caused by radiative cooling of the surface and is common in a temperate climate: it usually occurs when there is a (partly) clear sky at night. When the (high altitude) wind is strong (a 10-meter (33 ft) wind speed higher than approximately 6 to 7 m/s (20-23 ft/s)) the stable atmosphere is disrupted because of friction turbulence and the atmosphere will turn neutral. A daytime atmosphere is either neutral (no net radiation; usually with strong winds and/or heavy clouding) or unstable (rising air because of ground heating — by the sun). Here again the 1/7th power law applies or is at least a good approximation of the wind profile.

For HAWTs, tower heights approximately two to three times the blade length have been found to balance material costs of the tower against better utilisation of the more expensive active components.

[edit] Blade count
The NASA Mod-0 research wind turbine in Ohio tested a one-bladed rotor configuration
The NASA Mod-0 research wind turbine in Ohio tested a one-bladed rotor configuration

The determination of the number of blades involves design considerations of aerodynamic efficiency, component costs, system reliability, and aesthetics. Noise emissions are affected by the location of the blades upwind or downwind of the tower and the speed of the rotor. Typically one bladed rotors will operate at higher tip speed ratios. Given that the noise emissions vary by the 7th power of blade speed, a small increase in speed can make a big difference.

Wind turbines developed over the last 50 years have almost universally used either two or three blades. Aerodynamic efficiency increases with number of blades but with diminishing return. Increasing the number of blades from one to two yields a six percent increase in aerodynamic efficiency, whereas increasing the blade count from two to three yields only an additional three percent in efficiency. Further increasing the blade count yields minimal improvements in aerodynamic efficiency and sacrifices too much in blade stiffness as the blades become thinner.

Component costs that are affected by blade count are primarily for materials and manufacturing of the turbine rotor and drive train. Generally, the fewer the number of blades, the lower the material and manufacturing costs will be. In addition, the fewer the number of blades, the higher the rotational speed will be. This is because blade stiffness requirements to avoid interference with the tower limit how thin the blades can be. Fewer blades with higher rotational speeds reduce peak torques in the drive train, resulting in lower gearbox and generator costs.
The 98 meter diameter, two-bladed NASA/DOE Mod-5B wind turbine was the largest operating wind turbine in the world in the early 1990s
The 98 meter diameter, two-bladed NASA/DOE Mod-5B wind turbine was the largest operating wind turbine in the world in the early 1990s

System reliability is affected by blade count primarily through the dynamic loading of the rotor into the drive train and tower systems. While aligning the wind turbine to changes in wind direction (yawing), each blade experiences a cyclic load at its root end depending on blade position. This is true of one, two, three blades or more. However, these cyclic loads when combined together at the drive train shaft are symmetrically balanced for three blades, yielding smoother operation during turbine yaw. Turbines with one or two blades can use a pivoting teetered hub to also nearly eliminate the cyclic loads into the drive shaft and system during yawing.

Finally, aesthetics can be considered a factor in that some people find that the three-bladed rotor is more pleasing to look at than a one- or two-bladed rotor.

[edit] Rotation control

Tip speed ratio
The ratio between the speed of the wind and the speed of the tips of the blades of a wind turbine. High efficiency 3-blade-turbines have tip speed/wind speed ratios of 6 to 7.

Modern wind turbines are designed to spin at varying speeds (a consequence of their generator design, see below). Use of aluminum and composites in their blades has contributed to low rotational inertia, which means that newer wind turbines can accelerate quickly if the winds pick up, keeping the tip speed ratio more nearly constant. Operating closer to their optimal tip speed ratio during energetic gusts of wind allows wind turbines to improve energy capture from sudden gusts that are typical in urban settings.

In contrast, older style wind turbines were designed with heavier steel blades, which have higher inertia, and rotated at speeds governed by the AC frequency of the power lines. The high inertia buffered the changes in rotation speed and thus made power output more stable.

The speed and torque at which a wind turbine rotates must be controlled for several reasons:

* To optimize the aerodynamic efficiency of the rotor in light winds.
* To keep the generator within its speed and torque limits.
* To keep the rotor and hub within their centripetal force limits. The centripetal force from the spinning rotors increases as the square of the rotation speed, which makes this structure sensitive to overspeed.
* To keep the rotor and tower within their strength limits. Because the power of the wind increases as the cube of the wind speed, turbines have to be built to survive much higher wind loads (such as gusts of wind) than those from which they can practically generate power. Since the blades generate more downwind force (and thus put far greater stress on the tower) when they are producing torque, most wind turbines have ways of reducing torque in high winds.
* To enable maintenance; because it is dangerous to have people working on a wind turbine while it is active, it is sometimes necessary to bring a turbine to a full stop.
* To reduce noise; As a rule of thumb, the noise from a wind turbine increases with the fifth power of the relative wind speed (as seen from the moving tip of the blades). In noise-sensitive environments, the tip speed can be limited to approximately 60 m/s (200 ft/s).

Overspeed control is exerted in two main ways: aerodynamic stalling or furling, and mechanical braking. Furling is the preferred method of slowing wind turbines.

Turbine size
A person standing beside medium size modern turbine blades.
A person standing beside medium size modern turbine blades.

For a given survivable wind speed, the mass of a turbine is approximately proportional to the cube of its blade-length. Wind power intercepted by the turbine is proportional to the square of its blade-length. The maximum blade-length of a turbine is limited by both the strength and stiffness of its material.

Labor and maintenance costs increase only gradually with increasing turbine size, so to minimize costs, wind farm turbines are basically limited by the strength of materials, and siting requirements.

Typical modern wind turbines have diameters of 40 to 90 meters (130-300 ft) and are rated between 500 KW and 2 MW. Currently (2005) the most powerful turbine is rated at 6 MW

adminsta answers:

I’ll try to be more constructive than the foregoing respondents.

If you mean a 400kW (output) wind turbine, then the efficiency of the generator part (not including the turbine) would be around 93 to 95%.

adminsta answers:

For the efficiency calculation the formula

Power in wind = (density of air ) x (turbine blade diameter)2 x( velocity of wind)3 x (a constant)

Power in wind = d x D2 x v3 x c

Notice that the power in the wind depends on the density of the air, the diameter of the turbine blades squared (D times D), and the velocity of the wind to the third power (V times V times V). There is also a constant in there which I’ll discuss in the very next paragraph.

What about that constant, C? It’s there because what we are really interested in is the Area swept by the blades of diameter, D. The area is calculated by multiplying the number Pi (approximately 3.14159) times the diameter squared divided by 4. So part of the constant, C, is just the constant number Pi divided by 4 pulled out to show us that the important variable in the area formula is D. The other part of the constant, C, can be whatever unit conversion numbers are needed to make sure the numbers come out right. For now, we won’t go further into that. The point is that the variables that determine the wind power blowing into a wind turbine are air density, blade diameter (resulting in a certain swept area), and wind velocity.

You have probably noted that power (not energy) is dependent on the velocity times itself 3 times (V x V x V). Whoa! In other words, if the wind speed doubles, the power available from the wind increases by a factor of eight. The diameter is significant too. Doubling that increases the power by 4 times. Faster is better, and bigger is better (if you can afford it and can build it strong enough).

Of course, the wind doesn’t blow all the time in most places and when it blows too hard the turbine blades can break or spin so fast they break off (not good when each blade can weigh several tons). In that case, the blades are usually “feathered” to reduce stresses on them and to slow them down. This means we can’t take advantage of really high wind speeds.

Turbine Efficiency

If the turbine could convert all the wind’s power to mechanical power we would say it was 100% efficient. But as you probably know, the real world is never so generous. To even achieve 50% is unlikely, and would be a very efficient machine. A 50% efficient turbine would convert half of the power in the wind to mechanical power.

Hope this will solve your problem

Regards

For other references

Efficiency Varies with Wind Speed
A given wind turbine has a “design point” that generally defines its peak efficiency at the wind speed for which the system is designed. At wind speeds above and below the design speed the efficiency is the same or less – maybe much less. If a turbine’s best efficiency is 40% at a wind velocity of 9 meters per second (about 20 mph), it will be 40% only at that wind speed. At all other wind speeds it will be something worse. That wind turbine will generally operate at lower than its best efficiency, because wind speeds are never constant or average.

The electric power actually produced will be still lower because the generator efficiencies are also less than 100% (generally in the mid- or low-90′s at best), and there are further losses in the conversion electronics and lines. But this is true of all power technologies. When all these losses are figured in, you might, if you are lucky, be getting 35% or so of the wind’s energy actually delivered as useful electrical energy to the end user in the very best conditions. The average might only be in the twenties.

In the formula above, then, we have to add one more number that I don’t show. That number is an efficiency number that would have to supplied by the manufacturer of the wind turbine, or experimentally determined by you if you make it yourself. It will not be one number, but a variable that is a function of wind speed.

adminsta answers:

Hey Paul, that has become a fairly common question just in the last 6 months, I think I’ve answered it 4 times now. You can go back into yahoo answers and look for resolved questions similar to yours, or just go to the website I’ll list here and see it for yourself.

A wind turbines efficiency is not hard to determine, you need to know the air density, wind speed, swept area and power output. Usually engineers in the field are working the problem the other way, they know the efficiency, then they use that, wind speed, density and swept area to calculate the power output instead, but the formula works both ways.

The American Wind Energy Association has done some great work in this area, and they have a really good explanation for what you are asking for. You can go to their website I have listed below, or easier yet is to google, “Wind Turbine Efficiency Formula,” and look for a link to their website. Click on that and it takes you straight to the correct page at their website that explains the entire formula in fairly simple terms. While you are there, look for a reference to something called the, “Betz Limit.” No matter how well designed a wind turbine is, there is a theoretical limit of efficiency of about 39%. So if you see advertisements for wind turbines with efficiencies beyond this, you can discount them, and believe me, there are plenty. I see ads all the time for small turbines with swept areas not much more than a good size ceiling fan claiming to produce 2000 watts. That would make them about 350% efficient. So far nobody has been able to replicate the mileage that they advertise.

We live in a home that is powered by the wind and sun, so I’ve been forced to learn all this stuff the hard way. Some people choose to grow their own tomatoes instead of buying them at the store, even though it might be cheaper to purchase them. They have to know about soil ph, watering, bugs and dirt. People who grow their own electrons have a similar curse. Good luck Paul, and take care, Rudydoo

adminsta answers:

As previously stated, prop effieiency is in the neighborhood of 70%. The mose efficient generators convert kinetic energy to electricity with about a 90% efficiency. These losses are additive, so that means about 60% efficient.

adminsta answers:

It would reduce the efficiency of the chimney (you don’t get anything for nothing).

It would probably not create much energy either.