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Friday, January 30, 2009

Fans and Wind Power

Fans and Wind Power

The wind, like water, is a natural source of power. With water, we use its attraction by gravity as it descends from the mountains to the sea. With wind, we use the kinetic energy of the air. The energy of either fluid per unit volume can be expressed as the sum of three terms, ρgz + p + ρV2/2, corresponding to elevation, pressure and velocity. One form can be converted into another quite freely, but the sum must remain constant, or even decrease due to dissipative forces like friction. It is convenient to divide each term by ρg, the weight per unit volume or specific weight, so that they have the dimensions of length. Then, energy is called head of the fluid in question.

The most significant difference between air and water in regard to energy is that they are very different in density. Water is about 800 times as heavy as air, volume for volume. This means that energy is much more tightly packed in water, so that water machines can be conveniently small. Air machines, on the other hand, must handle large volumes of air, and so are large and cumbersome. Air weighs about 0.075 pcf (70°F, 29.92 inHg) or 1.293 x 10-3 g/cm3 (0°C, 760 mmHg). Air is also compressible, approximately obeying the ideal gas law pV = nRT, where R is the molar gas constant, 8.31441 x 107 J/K-gmol or 1545.33 ft-lb/R-lbmol. K = °C + 273.15 and R = °F + 491.7. Water, on the other hand, is incompressible in normal situations. Air is about 10 times more viscous than water, its kinetic viscosity being about 0.15 cm2/s. The discussion here applies directly to air, but the behavior of water is very similar.

The most popular unit of pressure for air machines in U.S. engineering has been the inch of water gauge. An inch of water is 1.867 mmHg, or 0.036 psi, or 1.489 mb (1489 dyne/cm2). Gauge pressure is pressure above atmospheric, which is considered to act at all points equally, so that it vanishes from equations. To find pressure in inches of water, multiply air head in feet by 0.1442, or air head in metres by 0.473.

Flow velocity in air or water is often measured with a Pitot Tube, as shown in the figure at the left. The impact tube faces directly into the flow, while the static tube is perpendicular to the flow. Both functions can be combined in a single unit. From Bernoulli's equation, pt = ps + ρV2/2. In U.S. engineering units, ρ = w/g, where w is pcf and g is 32.1725 ft/s2. Therefore, V is proportional to the square root of the pressure difference Δp. For air, if V is in fps and p is in inches of water, then V = 66.8√Δp, assuming air weighs 0.075 pcf (in Denver, it is closer to 0.060 pcf). For water, the coefficient is 2.32. In practice, the pitot tube must be traversed to measure the velocity in annular areas of equal volume of a circular duct. It is often assumed that the average velocity V is 0.83 of the velocity at the centre of the duct, but this is approximate.

Henri Pitot immersed a bent glass tube in the Seine to determine the velocity of its water in 1730. The Pitot tube has been used in hydraulics since then. Perhaps its greatest common application is as an airspeed indicator for aircraft.

Let's estimate how much wind power is available to us. The average wind in Denver is 7.5 mph or 11 fps. The corresponding velocity head is (11)2/(2)(32.2) = 1.879 ft of air. Multiplying by the specific weight, 0.075 pcf, the energy is 0.1409 ft-lb/ft3. Assume a windmill of 50 ft diameter. The area will be 1964 ft2, and so 21,600 ft3 of air will be gathered per second, or 3040 ft-lb/s. Since 1 hp is 550 ft-lb/s, this is 5.5 hp. The maximum efficiency of the windmill will be no greater than 65%, the efficiency of a propeller fan, so the useful output of our 50 ft windmill will be about 3.6 hp or 2.7 kWh. To capture greater power, we need either a higher wind velocity or a larger windmill. If the windmill is 150 ft in diameter, 3 times larger, and the wind speed is four times larger at 30 mph, then the power output would be multiplied by 576 to 2073 hp or 1555 kWh. This illustrates at least two important things: wind power is not very dense, and requires large machines to capture it; and it varies rapidly with the force of the wind (as V3). The past month (July 2003) in Denver has been practically windless, and would generate very little power.

Water mills come to us from antiquity, but windmills do not. Wind has been used as the motive power for boats for millennia. This application uses only the pressure of the wind on a sail, and the techniques for controlling it were highly developed. It does not require machinery, except for the minor machinery for handling rigging. In this article, we consider only the use of the wind in producing mechanical power. The basic theory of turbines, of which fans and windmills are examples, is given in Turbines.

Fans are used to move air (or other gases) in large volume at low gauge pressures. A windmill is a fan in reverse. A fan consists of a wheel or impeller, and a housing. Sometimes the housing is absent, and we have just the impeller, as in an aircraft propeller. The two principal types of fans are the axial-flow and the centrifugal. We will talk mainly of propeller-type axial flow fans here, but the general principles will apply to both types. The ducting and other appurtenances associated with a fan are called the system, which may be absent when a fan is used in the free air just to generate a breeze. If the system is at the output of a fan, the fan is called a blower, while if the system is at the input, the fan is an exhauster. The moving part of the fan is the impeller or wheel, and the stationary part the housing. A propeller fan may have a housing as simple as a circular aperture, called the shroud, which nonetheless makes the fan more efficient. At the other limit, the fan may be enclosed in a duct and work against static pressure.

An arrangement for a fan test is shown at the right. The flow resistance of the duct can be varied at input or output. If A is the area of the duct, then Q = VA, where V is the flow velocity. If the input and output are completely unrestricted, then the pressure difference is zero and the flow is a maximum. If the duct is blocked at each end so that the flow is zero, the pressure difference Δp will be a maximum. The most important variables for a fan are its discharge at outlet in cfm or m3/s, which together with the area of the fan gives the output velocity V, and the total pressure difference Δp. For propeller fans, this pressure difference is in the range 0.5 to 1.5 inches of water. The velocity pressure at the output is ρV2/2, and the static pressure at the output is the total pressure less the velocity pressure. The output power is the total power in the output, W = (ps + ρV2/2)Q. The efficiency is this power divided by the input power W', e = W/W'.

There may be an egg crate straightener about 6 duct diameters from the input. This is a lattice of square passages of side 0.075 to 0.15 of the duct diameter, and three times as long as the length of a side. This and other details are mentioned in the standard specifications for fan tests of the Association of Heating and Ventilating Engineers, or the ASME, which are excellent sources of information about fans.

Fan characteristics as determined by a test in a duct are shown at the left. These are just the general shapes of the curves, not the results for any particular fan. At zero flow the fan maintains a pressure difference of pmax. At free discharge, the fan produces a flow of Qmax. The pressure curves give the results for intermediate cases. ps is the static pressure, as would be measured by a manometer with an opening in the wall of the duct. pt is the total pressure, as would be measured by a Pitot tube. The difference between them is pv, the kinetic energy measured in pressure units. The input power and the efficiency are shown as percentages at the right. The power curve is not quite a straight line. Most problems involving fans in ducts can be solved with the use of the characteristic curves. For example, the head loss due to friction in the system is a parabola open upwards. The intersection of this curve with the pt curve will give the flow Q under those conditions.

Imagine the fan blades as elements of a helix, moving the air like an Archimedean screw. In one turn, let the helix advance a distance L, called the pitch of the fan. If θ is the inclination of a blade, then L = πD tanθ, or L/D = π tanθ. The amount of air moved in one revolution will then be (πD2/4)L, and if the impeller makes n rev/min, then the discharge Q = (πD3/4)(L/D)(n) cfm. A certain propeller fan mentioned in a handbook has the characteristics n = 1150 rpm, D = 2 ft, Q = 5000 cfm. For this fan, A = 3.142 ft2, and V = 26.52 fps. From these figures, L/D = 0.69, or θ = 12.4°. This is a quite reasonable figure. The actual pitch of the blades is larger, since there is back flow or slip. For a slip of 50%, the blade inclination would be 24°. Slip is usually less than this, around 40% to 30%. In any case, the effective L/D is probably more or less typical for the fan design.

If D is held constant, and n is varied, we see that Q is proportional to n. Since V is proportional to Q, and Δp is proportional to V2 (we presume that Δp is just the velocity pressure at the output in free discharge), it follows that Δp is proportional to n2. Finally, the power output is proportional to Q and to V2, so W is proportional to n3. These relations for varying n and constant D are called "Fan Law No. 1."

The tip velocity of a fan blade is a good reference velocity for the other velocities involved. This is V' = ωD/2 = nD/19.10 fps. If we vary D, but keep the tip velocity constant, then n varies inversely with D. In these conditions, Q will be proportional to D2, assuming L/D constant. Since the area is also proportional to D2, the velocity will be constant, as well as Δp. The power output W will be proportional to the discharge times the square of the constant V, so it will be proportional to D2. These relations are "Fan Law No. 2." Vector summation of the blade velocity at any radial position and the speed of approach of the air will give the angle of attack on the blade. Blades are usually twisted (greater pitch for smaller radius) to equalize the effect over the effective area. Small blades may be flat and thin, but large blades should have a rounded leading edqe and a feathered trailing edge. An airfoil section is often used for propeller blades. For an aircraft propeller, the blade angle is from 10° to 28° at 0.75R. The tip velocity should not exceed the local speed of sound to avoid the creation of shock waves.

We can think of other conditions as well. For example, let us vary D, but now keep the angular velocity constant, so that the tip velocity is proportional to D. In this case, Q varies as the cube of D, Δp as the square of D, and W as the fifth power. This can be combined with Fan Law No. 1 to show that when D and n are both varied independently, Q ≈ D3n, Δp ≈ D2n2 and W ≈ D5n3.

The frictional loss from air flow in a duct can be estimated by the pipe flow equations. If L is the length of a circular duct of diameter D, then the head loss is h' = 0.015(L/D)(V2/2g), where I have chosen what seems to be a reasonable value for the constant, usually written 4f and the one found in the Moody Chart and other references. For other duct shapes, replace D by 4R, where R is the hydraulic radius (area/perimeter). For air, the "wetted perimeter" is just the perimeter, of course. A square duct of side a has R = a/4.

Torque is the rate of change of angular momentum, just as force is the rate of change of linear momentum. When a fluid exerts a torque on a turbine runner, the reaction is a change in angular momentum of the fluid. The air that leaves a fan is rotating, the reaction to the torque that turns the impeller. Fluid is given angular momentum by the guide vanes which, ideally, is destroyed by the torque exerted on the runner. With some machines, however, the water at the exit may still have considerable angular momentum, and the energy in this motion is energy that does not appear at the shaft. Where velocity in the exit fluid is part of the desired output (as with a fan), vanes to straighten out the flow help to recover some of the energy that would otherwise be lost.

Fans for use under low pressure differences generally have a small hub, with the blades occupying most of the cross-sectional area. As the pressure differential increases, it becomes more efficient to concentrate the blade area near the periphery of the impeller. The hub then becomes larger, and the blades are stubby vanes on its surface. This is seen at the forward end of a jet engine, where the fan forms the compressor that efficiently decelerates the air relative to the engine, raising its pressure. Energy is added by burning fuel in the compressed air. Its velocity increases as it returns to atmospheric pressure, forming a jet the reaction to whose momentum provides the thrust. The exhaust drives a turbine that extracts some energy to operate the compressor.

The centrifugal fan is a very simple device. It consists of an impeller with blades that can be simply radial, though there are certain benefits to curved blades. It is fed from the centre, and the output is taken from a scroll case on the outside. The air is simply whirled around and centrifugal force causes the pressure to rise on the outside. It is a curious machine in that, unlike most power machines, it cannot be run in reverse to produce a torque. There are, of course gas turbines that can produce work efficiently, but they are very different from a centrifugal fan run in reverse.

An aircraft propeller is a fan with free discharge, whose purpose is to add velocity to the air it encounters. A jet engine, or even a rocket engine, has an identical function, so will be included in the following discussion. The reaction to the momentum added to the air is the thrust of the propeller, that pulls the aircraft through the air. This propels the aircraft although it has no connection with the ground, a somewhat marvellous phenomenon. The familiar blast of air behind a rotating propeller is called the slip-stream. When a single-engine aircraft is moving through the air, the velocity of the air behind the propeller is greater than the speed of the aircraft, and so produces greater parasitic drag than would otherwise be expected. Propellers on the wing, or behind the fuselage, do not produce this added drag.

Let's analyze the action of the propeller, using the conservation of energy, momentum and mass. As usual, we will be able to make considerable progress. In the figure, the dotted line marks out a cylindrical region containing the air influenced by the propeller, the slip stream. At the left, velocities relative to the aircraft are shown, while at the right are the absolute velocities. V is the speed of the aircraft, and the relative velocity of approach of the air. V' is the speed of the air behind the propeller. Since V' > V for positive thrust, the area of the slip stream is smaller in the wake of the propeller than in front of it. The absolute velocity in the slip stream is ΔV = V' - V. It extends from a diameter of 0.2D on the axis to 0.8D - 0.9D.

Let us assume that the propeller produces a pressure difference Δp that is turned into a velocity difference in a short distance. The thrust can now be expressed in two ways, T = (πD2/4)Δp = QρΔV. The energy equation in the relative motion gives V2/2g + Δp/ρg = V'2/2g. Solving for Δp, we get Δp = ρΔV(V + ΔV/2). Then, using the relation between Δp and ΔV given by the thrust formulas, we find Q = (πD2/4)(V + ΔV/2). Using this in ΔV = T/Qρ, we get a quadratic equation for ΔV, with the solution ΔV = V[√(1 - K) - 1], where K = 8T/πD2V2. This formula relates ΔV to the thrust, propeller diameter and aircraft velocity.

It is seen that the aircraft leaves behind an energy ΔV2/2g in the slip-stream. This energy soon mixes with the other air in turbulence. This loss is a necessary part of the propulsion, since if ΔV = 0 there is no thrust. The propulsive efficiency η of the propeller is the ratio of the total useful ouput, TV = QρVΔV, to the input energy, which will be the sum of the useful work and the energy left in the slip-stream. The result is η = 1/(1 + ΔV/2V) = 2/(1 + V'/V). V' cannot be less than V, of course, so η <>

Propeller and jet propulsion can be compared on the basis of thrust and propulsive efficiency. The thrust is T = ρQ(V' - V), so it depends jointly on the area of the slipstream and the velocity difference. If V = 200 mph, for example, V' should not greatly exceed 200 mph. If V' = 300 mph, then η will be 0.8, a reasonable figure. For an adequate thrust, this means a large flow Q, since the velocity difference will only be 100 mph. This can be achieved by a large propeller diameter D. A jet engine, however, has a much smaller area and would not be able to provide the required Q with the given V'. On the other hand, if V = 500 mph, then V' = 750 mph would give the same propulsion efficiency of 0.8 and a velocity difference of 250 mph. Now the required T can be obtained with the dimensions of a jet engine, since the higher velocity increases both factors contributing to T.

Thrust can also be expressed as T = ηP/V, where P is the power supplied to the propeller. If P is in hp and V is in mph, the thrust in pounds is T = 375ηP/V. The tip velocity of the propeller is V" = ωD/2 = πnD, where n is rps. A design ratio often used with propellers is N = V/nD, where V is in fps, D is in ft, and n is in rps. This dimensionless ratio is also N = πV/V". The tip velocity should be kept well below the speed of sound to avoid the ceation of shock waves. In practice, N is usually between 0.8 and 1.1, which implies V"/V = 3 to 4. If propellers are provided with multiple blades, the same flow Q can be obtained at a slower speed. If there are M blades, then we have V = MV"/3, taking the smaller end of the range. The speed of sound is about 340 m/s or 760 mph, so if V" is restricted to 50% of the speed of sound, V = 127M mph. For a two-bladed propeller, this means a limit of 264 mph, for a three-bladed propeller, 381 mph, and for a four-bladed propeller, 485 mph. This seems to agree with practice. The maximum velocity of flow over the propeller is greater than the tip speed.

In all of this, we have neglected the rotation of the propeller, and the vortex motion in the wake. The propeller gives angular momentum to the air in the slip stream, and the propeller tip sheds vortices in a helix. This added motion will reduce the propulsion efficiency, but does not play a large role.

If the efficiency is calculated in the relative motion, the maximum efficiency available is only 50%, since an amount of energy equal to the useful energy is contributed to the wake. In this coordinate system, the propeller is not moving, and so cannot produce useful work by means of the thrust. The energy that in the absolute system is useful work here goes into the wake. In fact, if you make an energy balance in the relative system, you will find that the energy contains two terms, one of which is exactly the thrust energy in the absolute system, and the other is the energy left in the wake. Of course, in this system both appear in the wake.

The aircraft is also supported in the air by the reaction to an air jet, in this case air forced downward by the wings. A helicopter even uses a fan for this purpose, and its analysis is the same as we have just presented. All this is possible because air is actually pretty heavy, with each cubic metre weighing about a kilogram. It seems insubstantial to us, but air has considerable inertia.

The Windmill

Wind as a land power source does not have as long a history as water as a land power source. Its low energy density and its unreliability are sufficient reason for this. Horizontal windmills were known in Persia, perhaps by the 8th century BCE, and the idea was carried to the Far East by prisoners of Genghis Khan, where it was considerably developed in China to drive irrigation machinery. These mills have nothing to do with the European windmill. The first documentation of windmills in Europe dates from 1185 (or 1105), with only the name mentioned, though by 1300 they were becoming common in Northern Europe. They spread to other places, where they developed many local peculiarities during their adaptation. The machinery was obviously developed from that of the Roman water mill, and the availability of millwrights was necessary to its creation. Their major use was always to turn the heavy millstones for grinding grain into flour, but before electricity was available they found many other applications, such as land drainage, pumping, sawing and ore crushing.

The European windmill consisted of sails, usually four in number, attached to sail stocks that rotated a stout horizontal windshaft. There was a large brake wheel on the windshaft with cogs driving a wallower, usually a lantern gear, that rotated the main shaft. In early mills, the main shaft rotated the upper millstone, or runner, which rested on the bedstone. Medieval mills had symmetrical sails, with the stock in the centre supporting transverse sail bars, usually braced on their outer edges with hemlaths. The canvas sail strips were threaded above and below alternate sail bars and tied tightly. The later common sail was entirely on the trailing edge of the sail, and the canvas was laid on top of it and tied down. Cords allowed the sails to be reefed as necessary, depending on the wind. Setting the sails was an arduous and difficult job. Eventually, canvas was replaced by rotating slats controlled by springs. Later, the slats could even be adjusted while the sails were in motion. Previously, the mill had to be stopped for this to be done. The leading edges of the stocks were later given fairings for smoother air flow, which made a considerable improvement. Sail spans of 50 to 70 feet were common. The windmill was built entirely of timber, connected by mortises and trenails (wooden pegs), and used as little costly wrought iron as possible. Since the wood was not exposed to water, as in the case of a water mill, it did not suffer from rot.

The basic machinery of wooden wind and water mills is shown at the right. The similarity is obvious. The millstones that turn grain into flour were about 4 ft in diameter, and rotated at 120-125 rpm. The preparation of millstones by grooving was an art. They had to be very carefully adjusted to just not touch, kept apart by the grain that was being ground. Moving stones could not be allowed to run "dry." Good stone for millstones was rare. In England, the best was a hard sandstone from the Pennines known as "millstone grit." A stone from the Rhine was superior to this, as was the "French burr" made from volcanic rock. The water mill drove the runner from below, by means of a spindle whose mace head turned the iron rynd let into the runner. The windmill drove from above, as shown. A wooden vat surrounded the millstones (not shown). On top of it, the horse supported the hopper from which grain was discharged into the eye of the runner. To drive more than one set of millstones, a "head and tail" arrangment could be used, with two crown wheels on the wind- or watershaft. A large spur gear could be mounted on the vertical shaft, running several sets of stones around its periphery. Metal gearing allowed even more complicated ways to distribute the power, and to attach accessories such as sack lifts.

The sails had to be directed into the wind by moving the windshaft. The first mills were post mills, small houses called bucks that contained the machinery and rotated on a stout post at the centre. The floor of the buck was supported by the crown tree, which rotated on a pintle in an enclosure called the roundhouse, when it was not open to the air. The tail pole extended from the rear of the buck, and was moved to point the sails into the wind and tied to one of a ring of stakes. The simplicity of this kind of mill meant that it never entirely disappeared, especially for small mills.

Another method was to mount the windshaft in a rotating cap. Only the cap rotated, while the power came down the main shaft at any cap position, since it was at the centre. In the tower mill, which arrived in the 15th century, the timber cap was mounted on a masonry or brick tower, usually round. The mills of La Mancha that excited Don Quixote were of this type, whitewashed and with slowly rotating sails. About this time, the horizontal windshaft was replaced by a windshaft that was inclined upwards slightly. This gave a much better stress distribution in the cap, and also more clearance below. The gearing was no problem, since all that was necessary was to incline the cogs on the crown wheel. The smock mill is so-called because its flaring tower, which could be of shingled or weatherboarded timber and octagonal in cross-section, looked like a rural smock. As these mills became taller to reach stronger winds, it was necessary to build a gallery around the tower so the miller could attend to the sails, and also arrange the tail pole to adjust the orientation. Dutch mills had a characteristic way of bracing the tail pole from a cross-piece on the cap by outrigger-like struts. Later, some mills were turned by a worm gear or winch inside the mill. The reader is probably familiar with the appearance of these mills, many of which have been preserved (except, alas, in the United States, where I believe they are all long gone).

When a windmill was not in operation, the sails were placed in an X position to equalize forces on the stocks. When the mill was ready to begin operation, the sails would be moved vertically one by one so the miller could reach them to set the sails, as long as this was necessary. The brake wheel held the sails immovable by the action of a weight. To allow the sails to move, the brake was "pulled off." In case of emergency, the sails could be stopped quickly by releasing the rope.

It was not only necessary to face the mill into the wind just so the sails would be turned efficiently, but also for important stability reasons. The mill was built to resist force from the front, and was in danger if tail-winded by a strong gust or thunderstorm. If the wind rose suddenly, and the brake could not hold the windshaft, friction rapidly set the mill on fire, especially if the miller ran out of grain to put between the millstones. Unusually strong winds are dangerous to windmills today, a hazard water mills do not face.

In 1745 Edmund Lee invented the fantail, or fly, a small windmill with an axis perpendicular to the windshaft. If the wind had a component from the side, the rotation of this wheel drove machinery that rotated the cap accordingly. In this way the mill was automatically kept facing the wind. The fantail was widely adopted in England and on the Continent, except, curiously, for the Netherlands, where the braced tail pole was retained.

A famous and excellent kind of windmill that can still be commonly seen, though less than formerly, is the American wind pump, simply called a "windmill" in the United States. It has an annular sail, which is very strong and durable, composed of many radial vanes. A tail vane keeps the sail faced into the wind. this vane is hinged so that it can be latched parallel to the sail when the mill is not intended to work. A cranked windshaft moves the vertical pump rod up and down to operate the pump in the well beneath it directly. The machinery is mounted at the top of a tower made from angle iron in the better machines, of wood in the lesser. This mill pumps water for cattle in isolated locations, and will work unattended, pumping whenever there is sufficient wind from any direction. Large mills of this type even provided locomotive water for the Union Pacific (as a photograph shows) at certain locations where the installation of a steam engine was not warranted. There could be a device that folded the tail if the wind exceeded 30 mph, or even speed governors. One example of a small mill had a 6' wheel and a 19' redwood tower. Among manufacturers were the Fairbury Windmill Co. of Fairbury, Nebraska and the Chicago Aermotor Co. A Fairbury windmill with an 8' wheel and 33' tower, restored by Bill Alexander, is shown at the left. Today, electricity has taken over most similar tasks once performed by the wind. Even the provision of small amounts of electricity for battery charging is now usually done with solar cells. However, windmills are made with geared heads for driving generators. Because of the variation in speed, the control of output voltage must be carefully considered.

An 8' wheel has an area of 50.2 ft2. The maximum operating wind velocity is 30 mph, or 44 fps, which gives 2.25 ft-lb/ft3. The total power available in the wind intercepted is then 4976 ft-lb/s or about 9 hp. At an efficiency of 50%, this means that a maximum of 4.5 hp is available. With an average wind of 15 mph or so, about 0.56 hp should be available, which can still pump a lot of water. The rapid variation of output with wind speed is one of the difficulties in applying wind power. Windmills are most useful for winds of Beaufort Force 4 to Force 6, or 15 to 30 mph. Over this range, their power varies by a factor of 8. Weaker winds will not provide sufficient power, while stronger winds may be damaging, and require that either the vanes be feathered or the wheel turned parallel to the wind.

The horizontal windmill was mentioned above in connection with its early appearance in Persia. On a small scale, horizontal windmills are still common, in devices like the cup anemometer. The drag coefficient of a hemisphere or cone presenting its convex side to the wind is less than when it presents its concave side, so if two or more such cups are mounted on an axis, they rotate in the wind. A similar device is the ventilating stack with a rotating, S-shaped vane on top. The wind-operated prayer wheel of Central Asia seems to have been a device of this kind, possibly suggesting the Persian windmills. There was no gearing inside a Persian mill. It is a very long way between prayer wheels and wind-operated toys to a mill that can turn heavy millstones. Larger examples were in towers with walls and openings that act in the same was as jets, acting on a runner inside with fixed vanes. These devices are not efficient, but have the advantage that they do not have to be turned into the wind, working equally well with wind from any direction. Note that they are actually impulse turbines, while the European windmill is closer to being a reaction turbine.

Wind is getting its own back, however, in wind farms to generate electricity. A good example is the North Hoyle wind farm 7 km off the North Wales coast between Prestatyn and Rhyl. 30 turbines will be installed, with a total nominal capacity of 60 MW. The hub of windshaft is 67 m above the sea, and the sails are 80 m in diameter, sweeping out 5027 m2. The windshaft is inclined by 6°, and the blades are coned by 2°. Each of the three glass-fibre reinforced epoxy blades is 39 m long, with a chord 3.52 m at the root and 0.48 m at the tip, and a twist of 13°. The pitch of the blades is regulated hydraulically. A blade can rotate 95° in all, and is full feathered for stopping. The windshaft is yawed by a ring gear and pinions, just like a cap mill, but electrically driven. The controls keep the windshaft rotating at a nominal 18.1 rpm, provided there is sufficient wind. The nacelle at the top of the post is also glass-fibre reinforced epoxy. It contains the gearbox and the alternator. The gearbox is planetary and helical, giving a fixed ratio of 1:92.6 for 50 Hz operation and 1:111.1 for 60 Hz operation. The alternator is a 4-pole induction generator with 690V output, and can generate either 50 Hz or 60 Hz. An induction generator is like an induction motor run in reverse. The rated speed of the rotor is 1680 or 2016 rpm. With slip, the stator field rotates at either 1500 or 1800 rpm, producing 50 Hz or 60 Hz power. The controls keep the windshaft rotating at a nominal 18.1 rpm, provided there is sufficient wind.

Unlike synchronous alternators, induction generators cannot supply reactive power, so connecting them to the grid involves control difficulties. Also, rated power can be produced only about 20% to 30% of the time, which calls for some kind of power storage. Even pumped hydroelectric has been suggested, but it is an expensive solution.

The average wind at the site is given as 10 m/s, which is a brisk 48 mph. At this speed, wind contains 61.25 J/m3. The flow is 50,270 m2/s, so the total power in the intercepted wind is about 3 MW. This would make the efficiency of the unit 67%, which seems a bit high. The wind speed for producing 2 MW is not given, so perhaps 2 MW is an optimistic estimate of the actual power. The turbine will stop at 25 m/s, and restart when the wind falls to 20 m/s. At 20 m/s, the power of the wind will be 24 MW, so getting 2 MW should be no problem, but the efficiency will drop to 8%. Efficiency is rather unimportant, since wind costs nothing. The efficiency could be improved somewhat by increasing the number of blades to 4 or even 6, but this would also increase the force on the structure in a high wind. Wind turbine blades are probably limited to 2 or 3 for this reason. At the North Hoyle site, the 50-year 10 minute gust is 46 m/s, and the 50-year 2-second gust is 60.3 m/s. This 60 m/s gust is 134 mph, well in the hurricane range, and something rightly to be feared.

Since the output of this wind farm is about that of a good hydroelectric turbine and alternator (80,000 hp), the economics of the enterprise are, it would seem, doubtful. Wind power burns no fuel, however, and is a hazard only to birds and ships. At sea, it is at least out of sight. Together with the higher winds over the ocean, this is an excellent reason for offshore wind farms. Modern windmills are actually very much like the older ones, but differences in materials and how the turbines are used makes them look different. The old mills were built almost entirely of wood, which determines the appearance of the structures and machinery, while new ones are metal and plastic. The sails of a modern windmill are aerofoils, and can be feathered automatically to control the torque and speed. In the older mills, this was done by reefing the sails, or later by controlling rotating slats. Fairings on the leading edges of the old sails brought them closer to aerofoils, and the angle of attack could sometimes be varied as well. The sails and windshaft of a new windmill are mounted on top of a post, just as in a post mill, with the orientation controlled by electric motors instead of a tail pole. Mechanical power does not have to be transmitted to the ground for grinding grain, but is used close to the sails by putting the alternator directly on the windshaft (with gearing). Thinner sails can be used because of the greater angular velocity; in the older mills, speed had to be kept low for several reasons. The same necessity of intercepting a large area to gather sufficient power is common to both. Modern windmills are distinctly less attractive than the old ones, verging on visual pollution of the landscape when used en masse on account of the low power density, but they are no worse than advertising, electric transmission wires and four-lane highways.

J. Reynolds, Windmills and Watermills (New York: Praeger, 1970). Very well illustrated; covers all kinds of historic mills.

S. Strandh, A History of the Machine (New York: A&W Publishers, 1979). pp. 108-111. Well-illustrated. The Chinese horizontal mill and the Mediterranean jib-rigged sails are shown.

R. L. Daugherty and J. B. Franzini, Fluid Mechanics, 6th ed. (New York: McGraw-Hill, 1965). pp. 162-165.

J. K. Salisbury, ed., Kent's Mechanical Engineer's Handbook, 12th ed. (New York: John Wiley & Sons, 1950). Power Volume, pp. 1-57 to 1-96; 15-18 to 15-22; 15-38 to 15-40.

The site Windmill World has many links to windpump information, most of them broken and some of the nasty American variety that leaves webturds. Be sure not to enable cookies when using this link. There are still a few honest sites and good pictures, if little technical information.

An excellent wind power website is National Wind Power.

Peter Fairley, Steady as she Blows, IEEE Spectrum, August 2003, pp. 35-39.

What are Vertical-Axis Wind Turbines(VAWTs)?

What are Vertical-Axis Wind Turbines(VAWTs)?

by Eric Eggleston and AWEA Staff

It can be very difficult to find information on vertical axis wind turbines (VAWT). Here's a basic summary of VAWT technology.

"VAWTs come in two flavors: lift-based and drag-based designs"

A cup anemometer is
a drag-type vertical
axis wind turbine

VAWTs come in two flavors: lift- and drag- based designs. Drag-based designs work like a paddle used to propel a canoe through the water. If you assume that the paddle used to propel your canoe did not slip, then your maximum speed would be about the same speed you drag your paddle. The same holds true for the wind. The three-cup anemometers commonly used for measuring wind speed are drag-based vertical-axis wind turbines. If the velocity of the cups is exactly the same as the wind speed, we can say that the instrument is operating with a tip speed ratio (TSR) of 1. The ends of the cups can never go faster than the wind, so the TSR is always 1, or less.

A good way of determining whether a VAWT design is based on drag or lift is to see if the TSR can be better than 1. A TSR above 1 means some amount of lift, while TSR below 1 means mostly drag. Lift based designs can usually output much more power, more efficiently.

_____________________________________________________________

wpe68.gif (9876 bytes)

Stacked Savonius
rotor

The Savonius: A Useful, Drag-Type VAWT

Yet drag-based VAWTs can be useful. They can be made many different ways with buckets, paddles, sails, and oil drums. The Savonius rotor is S-shaped (when viewed from above) and apparently originated in Finland. A good Savonius turbine might exceed a TSR of 1, but not by much. All of these designs turn relatively slowly, but yield a high torque. They can be useful for grinding grain, pumping water, and many other tasks; but are not good for generating electricity. RPMs above 1000 are generally best for producing electricity; however, drag-based VAWTs usually turn below 100 RPM. One might use a gearbox, but then efficiency suffers and the machine may not start at all easily.

Should you have already built a low-RPM VAWT and wish to calculate its power output, you might try getting your machine to lift something heavy (safely). One horsepower equals 550 ft-pounds/sec. If it lifts 100 pounds 5.5 feet in one second, it is one horsepower. Another way to measure output would be to sample the torque and RPM:

Horsepower = torque x rpm / 63000

Torque in. (inch x pounds) (1 hp = 746 watts)

_____________________________________________________________

vawtbush.bmp (23350 bytes)

DOE's 500-kW variable
speed Darrieus machine

Darrieus Lift-Type Vertical-Axis Machines

There are also lift-based vertical-axis types like the "eggbeater" Darrieus from France (first patented in 1927.) Each blade sees maximum lift (torque) only twice per revolution, making for a huge torque (and power) sinusoidal output -- just like cranking on a bicycle -- that is not present in HAWTs. And the long VAWT blades have many natural frequencies of vibration which must be avoided during operation. For example, a 500-kW two-bladed vertical-axis turbine we have on site has two or three rotational speeds that must be gone through quickly to get up to operating speed and several modes within the operational band which the control must avoid. A well-designed HAWT has none of these problems.

VAWTs are very difficult to mount high on a tower to capture the higher level winds. Because of this, they are usually forced to accept the lower, more turbulent winds and produce less in possibly more damaging winds.

Guy cables are usually used to keep the turbine erect. They also impose a large thrust loading on the main turbine bearings and bearing selection is critical. Like all types of turbines, replacing main bearings requires that the turbine be taken down.

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giromill.bmp (24638 bytes)

McDonnell Aircraft
Vertical Axis Giromill

cyclotur.bmp (18718 bytes)

ASI/Pinson
Cycloturbine

Other Lift-Type Vertical Axis Configurations

Darrieus' 1927 patent also covered machines with straight vertical axis blades called Giromills (photo at left).

A variant of the Giromill called the cycloturbine (below left) uses a wind vane to mechanically orient a blade pitch change mechanism.

There are not many easy-to-find references devoted to vertical-axis turbines. The wind energy group of Sandia National Labs in Albuquerque, New Mexico, has done a lot of research on Darrieus vertical-axis technology. Straight-bladed VAWTs were explored by the National Wind Technology Center at NREL. (See Links.)

VAWTs have not performed well in the commercial wind turbine market. The cylcoturbine was marketed commercially for several years. The Giromill never progressed beyond the research stage. In the summer of 1997, the last U.S. Darrieus VAWT company went bankrupt.

Basic Principles of Wind Resource Evaluation

Wind resource evaluation is a critical element in projecting turbine performance at a given site. The energy available in a wind stream is proportional to the cube of its speed, which means that doubling the wind speed increases the available energy by a factor of eight. Furthermore, the wind resource itself is seldom a steady, consistent flow. It varies with the time of day, season, height above ground, and type of terrain. Proper siting in windy locations, away from large obstructions, enhances a wind turbine's performance.

In general, annual average wind speeds of 5 meters per second (11 miles per hour) are required for grid-connected applications. Annual average wind speeds of 3 to 4 m/s (7-9 mph) may be adequate for non-connected electrical and mechanical applications such as battery charging and water pumping. Wind resources exceeding this speed are available in many parts of the world.

Wind Power Density is a useful way to evaluate the wind resource available at a potential site. The wind power density, measured in watts per square meter, indicates how much energy is available at the site for conversion by a wind turbine. Classes of wind power density for two standard wind measurement heights are listed in the table below. Wind speed generally increases with height above ground.

Classes of Wind Power Density at 10 m and 50 m(a)


10 m (33 ft) 50 m (164 ft)

Wind
Power
Class

Wind
Power
Density
(W/m2)
Speed(b)
m/s (mph)
Wind
Power
Density
(W/m2)
Speed(b)
m/s (mph)
1 <100 <4.4> <200 <5.6>
2 100 - 150 4.4 (9.8)/5.1 (11.5) 200 - 300 5.6 (12.5)/6.4 (14.3)
3 150 - 200 5.1 (11.5)/5.6 (12.5) 300 - 400 6.4 (14.3)/7.0 (15.7)
4 200 - 250 5.6 (12.5)/6.0 (13.4) 400 - 500 7.0 (15.7)/7.5 (16.8)
5 250 - 300 6.0 (13.4)/6.4 (14.3) 500 - 600 7.5 (16.8)/8.0 (17.9)
6 300 - 400 6.4 (14.3)/7.0 (15.7) 600 - 800 8.0 (17.9)/8.8 (19.7)
7 >400 >7.0 (15.7) >800 >8.8 (19.7)

(a) Vertical extrapolation of wind speed based on the 1/7 power law
(b) Mean wind speed is based on the Rayleigh speed distribution of equivalent wind power density. Wind speed is for standard sea-level conditions. To maintain the same power density, speed increases 3%/1000 m (5%/5000 ft) of elevation.
(from the Battelle Wind Energy Resource Atlas)

In general, sites with a Wind Power Class rating of 4 or higher are now preferred for large scale wind plants. Research conducted by industry and the U.S. government is expanding the applications of grid- connected wind technology to areas with more moderate wind speeds.

Wind Energy

How Can I Calculate the Amount of Power Available at a Given Wind Speed?


Contributed By Eric Eggleston, 5 February 1998

Because air has mass and it moves to form wind, it has kinetic energy. You may remember from science class that:

kinetic energy (joules) = 0.5 x m x V2

where:
m = mass (kg) (1 kg = 2.2 pounds)
V = velocity (meters/second) (meter = 3.281 feet = 39.37 inches)

Usually, we're more interested in power (which changes moment to moment) than energy. Since energy = power x time and density is a more convenient way to express the mass of flowing air, the kinetic energy equation can be converted into a flow equation:

Power in the area swept by the wind turbine rotor:

P = 0.5 x rho x A x V3

where:
P = power in watts (746 watts = 1 hp) (1,000 watts = 1 kilowatt)
rho = air density (about 1.225 kg/m3 at sea level, less higher up)
A = rotor swept area, exposed to the wind (m2)
V = wind speed in meters/sec (20 mph = 9 m/s) (mph/2.24 = m/s)

This yields the power in a free flowing stream of wind. Of course, it is impossible to extract all the power from the wind because some flow must be maintained through the rotor (otherwise a brick wall would be a 100% efficient wind power extractor). So, we need to include some additional terms to get a practical equation for a wind turbine.

Wind Turbine Power:

P = 0.5 x rho x A x Cp x V3 x Ng x Nb

where:
P = power in watts (746 watts = 1 hp) (1,000 watts = 1 kilowatt)
rho = air density (about 1.225 kg/m3 at sea level, less higher up)
A = rotor swept area, exposed to the wind (m2)
Cp = Coefficient of performance (.59 {Betz limit} is the maximum thoretically possible, .35 for a good design)
V = wind speed in meters/sec (20 mph = 9 m/s)
Ng = generator efficiency (50% for car alternator, 80% or possibly more for a permanent magnet generator or grid-connected induction generator)
Nb = gearbox/bearings efficiency (depends, could be as high as 95% if good)

If there is any single equation that the beginning wind enthusiast should memorize, this is it.


Basic Aerodynamic Operating Principles of Wind Turbines

The Figure illustrates the basic aerodynamic operating principles of a horizontal axis wind turbine.

The wind passes over both surfaces of the airfoil shaped blade. It passes more rapidly over the longer (upper) side of the airfoil, creating a lower- pressure area above the airfoil. The pressure differential between top and bottom surfaces results in a force, called aerodynamic lift. In an aircraft wing, this forces causes the airfoil to "rise," lifting the aircraft off the ground. Since the blades of a wind turbine are constrained to move in a plane with the hub as its center, the lift force causes rotation about the hub. In addition to lift force, a "drag" force perpendicular to the lift force impedes rotor rotation. A prime objective in wind turbine design is for the blade to have a relatively high lift-to-drag ratio. This ratio can be varied along the length of the blade to optimize the turbine’s energy output at various wind speeds.

Is Low Frequency Noise a Problem for
Wind Turbines?

Provided by Neil Kelley
U.S. National Renewable Energy Laboratory

1) Because of the low rotational rates of the turbine blades, the peak acoustic energy radiated by large wind turbines is in the infrasonic range with a peak in the 8-12 Hz range. For smaller machines, this peak can extend into the low-frequency "audible" (20-20KHz) range because of high rotational speeds and multiple blades.

2) The levels of infrasound radiated by the largest wind turbines are very low in comparison to other sources of acoustic energy in this frequency range such as sonic booms, shock waves from explosions, etc. The danger of hearing damage from wind turbine low-frequency emissions is remote to non-existent. Generally there little acoustic energy much above about 4000 Hz so ultrasound is not a problem. <100>

3) Impulsive noise generation is generally confined to turbines whose rotors operate downwind of the support tower (downwind machine). In this case, impulses are generated by the interaction of the aerodynamic lift created on the rotor blades and the wake vortices being shed from the tower elements. Turbines that have their rotors upstream of the tower, except in very rare circumstances, do not generate impulses since there is nothing blocking the flow upwind of the rotor. The low-frequency noise generated from an upwind turbine is primarily the result of the interaction of the aerodynamic lift on the blades and the atmospheric turbulence in the wind. Because atmospheric turbulence is a random phenomenon, the radiated low-frequency noise also exhibits a random or non-coherent characteristic. Impulsive noise generated by the tower wake/rotor interaction, on the other hand, tends to be much less random or coherent and therefore much more detectable when it interacts with an intervening resonant structure.

4) In my paper published in the AWEA WindPower '87 conference proceedings ("A Proposed Metric for Assessing the Potential of Community Annoyance from Wind Turbine Low-Frequency Noise Emissions," SERI/TP-217-3261, Nov 1997 or Proceedings of WindPower '87, San Francisco), I discuss the development of a criteria for assessing potential annoyance. It is interesting to note that low-frequency sounds with a random characteristic are much less likely to induce human annoyance than those which are impulsive. Typically the random low-frequency noise induces annoyance only at much higher acoustic energy levels than impulsive sounds.

5) While downwind wind turbines inherently are pre-disposed for producing impulsive noise because of the wakes from tower structural elements, careful designs can reduce such emissions to below detectable levels and therefore will cause no community annoyance. The overwhelming majority of wind turbines that have been installed in Europe are of the upwind rotor design and therefore low-frequency noise has not been considered a major issue there. By contrast, the primary concern there has been the much higher frequency broadband and discrete frequency noise associated with the unsteady aerodynamic forces on the blades, often in the blade tips.

Basic Principles of Wind Turbine
Power Production

Power CurveThe output of a wind turbine varies with the wind's speed through the rotor. This relationship is usually shown graphically in a power curve (Figure).

The "rated wind speed" is the wind speed at which the "rated power" is achieved and generally corresponds to the point at which the conversion efficiency is near its maximum. In many systems, the power output above the rated wind speed is mechanically or electrically maintained at a constant level, allowing more stable system control.

Note that at lower wind speeds, the power output drops off sharply. This can be explained by the cubic power law, which states that the power available in the wind increases eight times for every doubling of wind speed (and decreases eight times for every halving of the wind speed).

Using the power curve, it is possible to determine roughly how much power will be produced at the average or mean wind speed prevalent at a site. In the example above, the turbine would produce about 20% of its rated power at an average wind speed of 15 miles per hour (or 20 kilowatts if the turbine was rated at 100 kilowatts). This is somewhat lower than most modern wind turbines.

How Does A Wind Turbine's Energy Production Differ from Its Power Production?

While wind turbines are most commonly classified by their rated power at a certain rated wind speed, annual energy output is actually a more important measure for evaluating a wind turbine's value at a given site.

We know that . . .

Energy = Power x Time

This means that the amount of time a wind turbine produces a given power output is just as important as the level of power output itself. And wind turbine operators don't get paid for producing a large amount of power for a few minutes (except in rare circumstances.) They get paid by the number of kilowatt-hours (kWh) their turbines produce in a given time period.

The best crude indication of a wind turbine's energy production capabilities is its rotor diameter--which determines its swept area, also called the capture area. A wind turbine may have an impressive "rated power" of 100 kW, but if its rotor diameter is so small that it can't capture that power until the wind speed reaches 40 mph (18 m/s), the wind turbine won't rack up enough time at high power output to produce a reasonable annual energy output.

Expected energy output per year can be reliably calculated when the wind turbine's capacity factor at a given average annual wind speed is known. The capacity factor is simply the wind turbine's actual energy output for the year divided by the energy output if the machine operated at its rated power output for the entire year. A reasonable capacity factor would be 0.25 to 0.30. A very good capacity factor would be 0.40.

NOTE: Capacity factor is very sensitive to the average wind speed. When using the capacity factor to calculate estimated annual energy output, it is extremely important to know the capacity factor at the average wind speed of the intended site.

Lacking a calculated capacity factor, the machine's power curve can actually provide a crude indication of the annual energy output of any wind turbine. Using the power curve, one can find the predicted power output at the average wind speed at the wind turbine site. By calculating the percentage of the rated power (RP) produced at the average wind speed, one can arrive at a rough capacity factor (RCF) for the wind turbine at that site. And by multiplying the rated power output by the rough capacity factor by the number of hours in a year, (8,760), a very crude annual energy production can be estimated. For example, for a 100 kW turbine producing 20 kW at an average wind speed of 15 mph, the calculation would be:

100 kW (RP) x .20 (RCF) = 20 kW x 8760 hours = 175,200 kWh

Actually, because of the effect of the cubic power law, the annual energy output will probably be somewhat higher than this figure at most windy sites. This is determined by the wind power distribution, which shows the percentage of time the wind blows at various wind speeds over the course of an average year. Lacking precise data on a given site, there are two common wind distributions used to make energy calculations for wind turbines: the Weibull distribution and a variant of the Weibull called the Rayleigh distribution that is thought to be more accurate at sites with high average wind speeds.

Energy output is also greatly influenced by more subtle features of a wind turbine's design, including

  • cut-in speed, or the wind speed at which it begins to produce power (if the turbine's cut-in speed is significantly below a site's average wind speed, problems are inevitable)
  • the power it produces at moderate wind speeds, determined largely by blade airfoil shape and geometry
  • the cut-out speed (the wind speed at which the turbine may be shut down to protect the rotor and drive train machinery from damage) or high wind stalling characteristics.
  • operating characteristics such as low speed on-off cycling, shut-down behavior, and overall reliability, which together determine the turbine's availability to produce power when the wind speeds are in its operating range
  • the efficiency of drive train components, such as the generator and gear box.
These more subtle features should not be underestimated when looking for ways to improve energy output. In recent years, the U.S. wind industry has begun using seemingly insignificant refinements in blade airfoil shapes to increase annual energy output from 10 to well over 25 percent. These increases have helped to dramatically lower the cost of wind-generated energy and increase the number of areas in the U.S. at which wind plants are feasible.

Building my own blades.

Part of the allure of building a windmill is to carve the blades. The craftsman in me drools over the prospect. I love carving wood. But I didn't know where to start, so I found a web site with some books on the subject and ordered a few books. Two in particular were quite valuable. These were both by Hugh Pigott; Windpower Workshop and Brakedrum Windmill Plans. The web site I bought these from was picoturbine.com. They are also available from otherpower.com. Hugh Piggot has a very helpful web site at Scoraigh Wind Electric which includes alternator information also.

Blade materials

I used basswood (linden) for the blades. I don't believe it is the best wood to use, that would be quartersawn sitka spruce. Sitka spruce is hard to come by here in Colorado and I'm not up to any trips to the coast for a while. I'm certainly not going to buy expensive wood sight unseen. Basswood has numerous good qualities however. It is soft (easy to carve), has little difference between flatsawn and quartersawn sections, and is more available than sitka sprice. It takes finishes well and is very light in weight. It is not brittle like redwood or western red cedar and so shouldn't shatter quite as easily. I purchased three 8' planks of rough 2x6 basswood lumber with the intent of making at least 10' diameter blades. I discovered that I could stagger the blades such that I could build a smaller 7' diameter set first, just like the ones in Hugh's Brakedrum windmill book. So I chose the less desirable ends of the three planks and cut the outlines of the blades.

Templates for the Blades

I've created a .pdf file which should print out to full size templates for the blades I made using Hugh's book. These are available here. There is some chatty info I've included as well. Below is a photo of the templates in use on a blade in the carving process.






Carving the Blades

I carved the blades by hand after cutting the shape roughly on a band saw. I made a template for the overall outline, shown to the right of the photo below. The blades were first cut to this outline and then the shape and angle of the twist was drawn on each one.


Two sides of the blades shown in different stages of cutting. Note the airfoil profile on the near ends.








Three stages of carving shown from the leading edge (back side) of the blade. Note the burn marks from bandsawing the basswood. The blade needs to be sharp and with few hook teeth per inch.







The same three stages from the trailing edge of the blade, again with the back side up.

Attaching the blades together

I pretty much went by Hugh Piggott's Windpower Workshop book (pg 57) for attaching the blades to the hub. See that for a diagram. Most of the screws were applied from the back side of the hub. The weights were applied from the front side (see balancing the blades, below).

Finishing the blades

I decided to use 3 coats of oil based primer followed by 4 or more coats of oil based epoxy resin high gloss enamal. I wanted the superior adhesion of the oil based paint (over latex) and I wanted the extra hardness of the enamal. I brushed each coat heavily taking care not to get many runs. I sanded with 220 grit open coat silicon carbide sandpaper between coats. There were still brush marks on the final coats, so I may spray the last few coats to achieve the desired smoothness and mirror finish.

Balancing the Blades

While all aspects of building a windmill are important, this one is crucial. Without proper balancing, a wind machine will exhibit signs of instability, affecting performance and safety. An unbalanced blade can wear out bearings quickly, run noisily, stall out prematurely and even shatter.

There are several aspects to balancing wind generator blades. I prefer to have the rotating axis of the blades in the exact center of the circle described by the blades. This is relatively easily done by making each blade the same exact length and aligning them on the hub so that the tips of the blades are all the same distance from the center of the hub. It is necessary to measure the distance of the tips from each other, to make sure they are equidistant from the other blades as well. See Hugh Piggott's Brakedrum windmill book for a good description of this. For a hub, I followed Hugh Piggot's suggestion and sandwitch the blades between two (exterior grade) plywood circles, ~11" in diameter.

Balancing means adding weights somewhere. Initial testing showed that one of the blades was considerably heavier than the other two. This appeared to be the actual density of the wood, so I was stuck. I had to add a lot of weight to the other side(s). I decided that I didn't want to put holes in the blades themselves and so I purchased about 2 lbs of ¼" round lead fishing weight. This is like a ¼" string of lead spagetti. I drilled ¼" holes in the plywood circles and epoxied lead spagetti into the holes. In the photo below, the heavy blade is on the right. Note the numerous dots (the holes filled with lead) on the opposite side of the plywood circle. I used the setup shown below to finish the balancing. By spinning the blade and noting where it stopped, I was able to discover the heavy areas and compensate with lead on the other side.


Blades mounted in the makeshift bearing shaft (really long nail) for dynamic balancing. Note the longer basswood planks against the wall for the next set of blades. (10' diameter planned)






View of the front of the blades up, showing the flat front side, curved back side and twist.

How Hydropower Works

How Hydropower Works


Hydropower is using water to power machinery or make electricity. Water constantly moves through a vast global cycle, evaporating from lakes and oceans, forming clouds, precipitating as rain or snow, then flowing back down to the ocean. The energy of this water cycle, which is driven by the sun, can be tapped to produce electricity or for mechanical tasks like grinding grain. Hydropower uses a fuel—water—that is not reduced or used up in the process. Because the water cycle is an endless, constantly recharging system, hydropower is considered a renewable energy.

This illustration of the water or hydrologic cycle shows how water evaporates into clouds, precipitates, forms rivers that flow downhill into the ocean, and begins the cycle again.

The Water (Hydrologic) Cycle

When flowing water is captured and turned into electricity, it is called hydroelectric power or hydropower. There are several types of hydroelectric facilities; they are all powered by the kinetic energy of flowing water as it moves downstream. Turbines and generators convert the energy into electricity, which is then fed into the electrical grid to be used in homes, businesses, and by industry.


Types of Hydropower Plants

There are three types of hydropower facilities: impoundment, diversion, and pumped storage. Some hydropower plants use dams and some do not. The images below show both types of hydropower plants.

Many dams were built for other purposes and hydropower was added later. In the United States, there are about 80,000 dams of which only 2,400 produce power. The other dams are for recreation, stock/farm ponds, flood control, water supply, and irrigation.

Hydropower plants range in size from small systems for a home or village to large projects producing electricity for utilities. The sizes of hydropower plants are described below.

Impoundment

The most common type of hydroelectric power plant is an impoundment facility. An impoundment facility, typically a large hydropower system, uses a dam to store river water in a reservoir. Water released from the reservoir flows through a turbine, spinning it, which in turn activates a generator to produce electricity. The water may be released either to meet changing electricity needs or to maintain a constant reservoir level.

Drawing showing a cross section of an impoundment dam and hydropower plant. Transmission lines conduct electricity to homes and businesses. Dam stores water. Penstock carries water to the turbines. Generators are rotated by the turbines to generate electricity. Turbines are turned by the force of the water on their blades.

An impoundment hydropower plant dams water in a reservoir.

Diversion

A diversion, sometimes called run-of-river, facility channels a portion of a river through a canal or penstock. It may not require the use of a dam.

Photo of an aerial view of a river with a waterfall and no dam. The hydropower intake and outlet are labeled. The intake is above the waterfall; the outlet is below it.

The Tazimina project in Alaska is an example of a diversion hydropower plant. No dam was required.

Pumped Storage

When the demand for electricity is low, a pumped storage facility stores energy by pumping water from a lower reservoir to an upper reservoir. During periods of high electrical demand, the water is released back to the lower reservoir to generate electricity.

Sizes of Hydroelectric Power Plants

Facilities range in size from large power plants that supply many consumers with electricity to small and micro plants that individuals operate for their own energy needs or to sell power to utilities.

Large Hydropower

Although definitions vary, DOE defines large hydropower as facilities that have a capacity of more than 30 megawatts.

Small Hydropower

Although definitions vary, DOE defines small hydropower as facilities that have a capacity of 100 kilowatts to 30 megawatts.

Micro Hydropower

A micro hydropower plant has a capacity of up to 100 kilowatts. A small or micro-hydroelectric power system can produce enough electricity for a home, farm, ranch, or village.

Drawing shows a micro hydropower plant. Intake gates allow water to flow through the Penstock Powerhouse to the turbine.

>Micro Hydropower Plant

Types of Hydropower Turbines

There are two main types of hydro turbines: impulse and reaction. The type of hydropower turbine selected for a project is based on the height of standing water—referred to as "head"—and the flow, or volume of water, at the site. Other deciding factors include how deep the turbine must be set, efficiency, and cost.

Terms used on this page are defined in the glossary.

Impulse Turbine

The impulse turbine generally uses the velocity of the water to move the runner and discharges to atmospheric pressure. The water stream hits each bucket on the runner. There is no suction on the down side of the turbine, and the water flows out the bottom of the turbine housing after hitting the runner. An impulse turbine is generally suitable for high head, low flow applications.

Photo of a Pelton hydropower turbine.

Pelton hydropower turbine
Credit: GE Energy

  • Pelton

    A pelton wheel has one or more free jets discharging water into an aerated space and impinging on the buckets of a runner. Draft tubes are not required for impulse turbine since the runner must be located above the maximum tailwater to permit operation at atmospheric pressure.

    A Turgo Wheel is a variation on the Pelton and is made exclusively by Gilkes in England. The Turgo runner is a cast wheel whose shape generally resembles a fan blade that is closed on the outer edges. The water stream is applied on one side, goes across the blades and exits on the other side.

  • Cross-Flow

    A cross-flow turbine is drum-shaped and uses an elongated, rectangular-section nozzle directed against curved vanes on a cylindrically shaped runner. It resembles a "squirrel cage" blower. The cross-flow turbine allows the water to flow through the blades twice. The first pass is when the water flows from the outside of the blades to the inside; the second pass is from the inside back out. A guide vane at the entrance to the turbine directs the flow to a limited portion of the runner. The cross-flow was developed to accommodate larger water flows and lower heads than the Pelton.

Reaction Turbine

A reaction turbine develops power from the combined action of pressure and moving water. The runner is placed directly in the water stream flowing over the blades rather than striking each individually. Reaction turbines are generally used for sites with lower head and higher flows than compared with the impulse turbines.

Photo of a Propeller hydropower turbine.

Propeller hydropower turbine
Credit: GE Energy

  • Propeller

    A propeller turbine generally has a runner with three to six blades in which the water contacts all of the blades constantly. Picture a boat propeller running in a pipe. Through the pipe, the pressure is constant; if it isn't, the runner would be out of balance. The pitch of the blades may be fixed or adjustable. The major components besides the runner are a scroll case, wicket gates, and a draft tube. There are several different types of propeller turbines:


    Photo of a Bulb hydropower turbine.

    Bulb hydropower turbine
    Credit: GE Energy

    • Bulb turbine

      The turbine and generator are a sealed unit placed directly in the water stream.

    • Straflo

      The generator is attached directly to the perimeter of the turbine.

    • Tube turbine

      The penstock bends just before or after the runner, allowing a straight line connection to the generator.

    • Kaplan

      Photo of a Kaplan hydropower turbine.

      Kaplan hydropower turbine
      Credit: GE Energy

      Both the blades and the wicket gates are adjustable, allowing for a wider range of operation.

  • Francis

    Photo of a Francis hydropower turbine.

    Francis hydropower turbine
    Credit: GE Energy

    A Francis turbine has a runner with fixed buckets (vanes), usually nine or more. Water is introduced just above the runner and all around it and then falls through, causing it to spin. Besides the runner, the other major components are the scroll case, wicket gates, and draft tube.

  • Kinetic

    Kinetic energy turbines, also called free-flow turbines, generate electricity from the kinetic energy present in flowing water rather than the potential energy from the head. The systems may operate in rivers, man-made channels, tidal waters, or ocean currents. Kinetic systems utilize the water stream's natural pathway. They do not require the diversion of water through manmade channels, riverbeds, or pipes, although they might have applications in such conduits. Kinetic systems do not require large civil works; however, they can use existing structures such as bridges, tailraces and channels.

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