A SELF-STARTING, SINGLE-BLADE, UNBALANCED, EXPANDING RADIUS, VERTICAL AXIS WINDMILL WITH CENTRIFUGAL PENDULUM, PASSIVE,
DYNAMIC PITCH-CONTROL, COUPLED TO A VARIABLE-STROKE PISTON PUMP

  Copyright 1/25/2008  Peter Sharp, Oakland, CA       sharpencil@sbcglobal.net

 

The Whirlwing Windmill is still experimental. Much more testing is required to determine its potential. It breaks many of the rules used for designing conventional windpumps.
 

The purpose of the Whirlwing Windmill is to be as simple and cheap as possible so that it can be purchased and maintained by very poor farmers who earn a dollar a day. The cost might be so low that it could make small scale wind energy the first choice for pumping, even in areas with only moderate winds. No patent. The windmill can be built without fully understanding how it works.
 

I have not yet constructed a complete windpump model, and I hope to do so when I can afford the time, and when I can find a test site. I have, however, done a lot of experimenting with model blades so as to determine their operating characteristics. The first model was invented around 1975.
 

The pump I recommend is the Canzee hand pump. It has no piston seal and it is therefore very durable and easy to make and service. It uses rubber flaps for the one-way valves. It was invented by Richard Cansdale (his company is SWS Filtration Ltd., UK, www.swsfilt.co.uk; Richard@swsfilt.co.uk). The Canzee hand pump is now used in Madagascar.
 

A full scale version of this Whirlwing Windmill is currently being built and tested by Dr. Wirachai Roynarin, an engineer at RMUTT in Thailand (wirachairoynarin@yahoo.com ). He is an expert on vertical axis wind turbines. I sent him a small model of just the windmill (no pump). I can send other qualified researchers the same model plus an information packet.
 

When the single V blade is orbiting, the blade and its elastic cords look like a vertical jump rope with the blade at the midpoint of the jump rope. Horizontal cables and vertical poles support the vertical jump rope. As the wind speed increases, the blade’s orbit diameter expands greatly.
 

As the unbalanced blade orbits, the centrifugal force acting on the blade creates an oscillating force. That oscillating force is used to operate a variable-stroke piston pump. To be useful, and safe, the oscillation frequency must be kept low, and that requires a very large blade orbit. Most deep-well piston pumps require a low number of strokes per minute, usually around 60 or less.
 

The Whirlwing Windmill would be coupled to a variable-stroke piston pump. In other words, the piston can rise and fall a variable distance. Most piston pumps can operate this way. The piston is lifted and lowered by a vertical cable above the well head. The unbalanced motion of the blade serves to pull on the piston cable (or rope) so as to raise and lower the piston, and alternately raise and lower the pump counterweight. The pump counterweight balances the weight of the water in the delivery pipe.
 

This windmill uses a single V blade and the same pitch-control system as the Sharp VAWT (1982 US patent # 4,334,823). Sicard VAWT (1977 US patent # 4,048,947) blade units could also be adapted for use with this windmill since they operate on the same pitch-control principle. (The European Patent Office has copies of these patents, plus drawings, available on-line.) The V blade permits an even simpler blade unit construction since the usual rocking arms (pendulum arms) of the Sharp VAWT blades are eliminated. The blade's counterweight is located ahead of the vertex of the V blade. The enclosed angle of the V is roughly 120 degrees.
 

The blade and its counterweight together create the horizontal, centrifugal pendulum to control blade pitch. The blade controls its own pitch angle like a mechanical computer. It continuously adjusts to its apparent wind (the vector addition of the true wind plus the blades forward speed). Aerodynamic forces and centrifugal forces find a balance. That balance continuously changes as the blade orbits so as to adjust the pitch angle of the blade, and therefore the angle of attack of the blade. The pitch control is passive and dynamic, meaning that the pitch schedule changes to match the tip speed ratio. The tip speed ratio (TSR) is the blade’s ground speed divided by the speed of the wind. The Whirlwing V blade typically moves at about 3.0 times the speed of the wind, so its TSR is 3.0. (Horizontal axis wind turbines typically have a TSR around 6.0.)
 

The mass of the blade and its counterweight is radially outward of the blade’s pivot axis (an imaginary line joining the leading edge tips of the V blade). That creates a horizontal, centrifugal pendulum, meaning that the pendulum responds primarily to centrifugal force rather than to gravity. Centrifugal force attempts to hold the blade outward in a fixed position like a fixed blade. But aerodynamic forces attempt to force the blade to face directly into the blade’s apparent wind, like a wind vane. Those two forces, the centrifugal restoring force and aerodynamic pitching force, act in opposition to each other. Together, they reach a dynamic balance. That dynamic balance determines the instantaneous pitch angle of the blade. The blade produces thrust at all times except when it is heading directly upwind or directly downwind.
 

When the blade begins to pitch (swing fore or aft), the centrifugal restoring force increases (like pulling a normal pendulum to the side) and the aerodynamic pitching force decreases, until the two forces reach a balance. In general, as the pitch of the blade increases, the angle of attack of the blade decreases. The centrifugal restoring force, for a V blade, can be increased by adding weight to the blade or by increasing the blade span (which moves the blade’s center of mass farther outward).
 

Sharp blade units, whether straight or V blades, use a counterweight (or two) out in front of the blade. Its function is to balance the blade so that the center of mass of the blade-plus-counterweight (blade unit) is a little in front of the leading edge of the blade. The center of mass is the pendulum bob of the centrifugal pendulum.
 

Since aerodynamic forces act at the center of lift of the blade (usually ¼ chord), that creates an aerodynamic moment arm that extends from the center of lift of the blade to the pitch axis. The torque applied to the aerodynamic moment arm by the blade acts to pitch the blade. The centrifugal pendulum’s center of mass has a moment arm that extends from the center of mass of the blade-plus-counterweight to the pitch axis. The torque applied to the centrifugal moment arm by the center of mass (the bob of the centrifugal pendulum) acts to resist the pitching of the blade.
 

If the distance between the pitch axis and the center of mass is too small, there will not be enough centrifugal restoring force. The blade will pitch too much. The angle of attack will be too small. If the distance is too large, there will be too much restoring force. The blade will not pitch enough. The angle of attack will be too high at low tip speed ratios. A practical length for the distance (which is the same as the length of the centrifugal pendulum arm) is roughly one chord length, but that will vary somewhat with the mass of the blade-plus-counterweight.
 

This pitch control system works best if the diameter of the VAWT is fixed. But it is also quite robust. It can keep the blade from stalling even if the diameter varies widely. It can not keep the blade at its optimum angle of attack, but it can at least keep the blade from stalling. So for a variable diameter VAWT like the Whirlwing, the proportions of the blade-plus-counterweight (blade unit) are selected to work best at an intermediate diameter. At smaller diameters, the blade will pitch less than optimum, and at larger diameters, the blade will pitch more than optimum. For the Whirlwing, all that matters is that the blade does not stall, and the pitch control system accomplishes that.
 

The blade is typically balanced to be slightly nose heavy so that the blade will appear to toe outward slightly (about 3 degrees). Actually, the blade has zero pitch when it is in that position because the blade is tangent to its orbit at the center of lift of the blade (about ¼ chord from the leading edge). (The fixed blades of H-rotors are typically mounted so that the blades are tangent to their orbit at the center of lift of the blade.)
 

During the downwind pass of the blade, the blade pitches (swings) forward of its pivot axis. During the upwind pass of the blade, the blade pitches (swings) rearward (aft) of its pivot axis.
 

This type of pitch control system is surprisingly accurate when the VAWT diameter is fixed. Both centrifugal force and aerodynamic lift increase by the square of the blade’s ground speed and air speed respectively. So the strength of this type of centrifugal spring increases as the wind speed increases the rpm of the windmill. A centrifugal pendulum type of centrifugal spring is a variable rate spring. Conventional metal springs could be used to control the pitch of the blade accurately only if the wind speed never changed, and the diameter never changed. But they do.
 

Bayly and Kentfield (1981) calculated that this type of pitch-control (which they refer to as “freely hinged blades”) is capable of producing a coefficient of performance (Cp) of .45. (The best horizontal axis wind turbines have a Cp of about .47.) Their full-scale test model achieved .37. (The theoretical limit, the Betz limit, is .593.) They suggested that the reason for the lower Cp was that the Reynolds number was not high enough. In other words, the wind turbine was not quite large enough to achieve maximum efficiency.
 

The best article on their research is by J. A. C. Kentfield, titled “A Cycloturbine with Automatic, Self Regulating, Blade-Pitch Control”, contained in the FOURTH ASME WIND ENERGY SYMPOSIUM, Dallas, Texas, 1985, pgs. 147–154, of The American Society of Mechanical Engineers, and sponsored by The Solar Energy Division, ASME, edited by A. H. P. Swift. Dr. Kentfield is currently a Professor of Engineering Emeritus at the University of Calgary, Canada. Dr. Kentfield independently invented the Sicard wind turbine (1978) after Sicard had patented it in 1977. Dr. Kentfield greatly improved it. But when Dr. Kentfield discovered that he could not patent his invention, he did not further develop the Sicard/Bayly-Kentfield VAWT.
 

When the wind gusts, that drops the tip speed ratio of the V blade. The blade can then be observed to “flip” when transitioning from its upwind pass to its downwind pass. This is characteristic of the quick pitch reversal that an optimum pitch schedule requires at low tip speed ratios (below 2).
  

N. C. K. Pawsey (online Ph.D. thesis, 2002, University of New South Wales, Australia) expresses concern that the thrust of Sharp VAWT blade (the V blade is a variation of the Sharp VAWT blade) will cause excess pitching forward (toe-in). That concern is not justified because the thrust vector is derived from the blade’s aerodynamic pitching force vectors. And in any case, moving the counterweight forward slightly could be used to create more toe-out to counter any forward pitch bias (toe-in). (Incidentally, Pawsey’s rolling-cam pitch-control system may be inherently flawed because, when heading directly upwind, the high aerodynamic drag of the blade tries to roll it aft, whereas the blade needs to roll forward to create the necessary toe-out for the upwind pass. The result is a damping effect on pitch reversal and a lowering of efficiency. In contrast, that same high drag aids the pitch reversal for Sharp VAWT blades at that point since the blade needs to swing aft to create toe-out for the upwind pass.) To find the Pawsey thesis, search for “Pawsey thesis unsw” and go 40% down the long list.
 

Blade balancing is done while the V blade is horizontal and suspended from its pivot points. The counterweight arm should point downward from horizontal about 2 to 3 degrees. This balances the blade so that when it is vertical and manually revolved (orbiting) in still air, the blade chord is tangent to the blade’s orbit at the center of lift of the blade (at about ¼ chord). That is the zero pitch angle.
 

The V shaped blade is able to withstand high centrifugal forces without bending. Most of the forces within this windmill are in tension, so very little material is required, thus reducing the cost.
 

I categorize the Whirlwing Windmill as a lift-type VAWT that uses a passive, dynamic, pitch-control system based on a centrifugal spring of the centrifugal pendulum type. The Whirlwing is unique in that it makes use of an expanding orbit radius. There are other types of centrifugal springs (such as Pawsey’s rolling cam or Kirke’s radially sliding mass), but none has yet proved to be as efficient as a centrifugal pendulum.
 

The Whirlwing blade sweeps a very large area of wind for its small size. However, that does not increase its power proportionally to the swept area because both the rotor solidity and the tip-speed ratio are too low most of the time as compared to a conventional 3-bladed VAWT. The rotor solidity is the area of the blades, as viewed from the side of the blades, divided by the area (cross section) that the blade sweeps.
 

The Whirlwing parts are easy to make, and they have low tolerances. The blade can be crudely made and still perform adequately. These attributes can radically lower the cost of the windmill.
 

The V blade is suspended on elastic cords above and below it. As the speed of the blade increases, the orbit radius of the blade increases. This expanding radius keeps the rpm of the blade low, which is what a piston pump requires. Since the tip-speed ratio (TSR) of the blade is about 3.0, the orbit radius must be quite large compared to the span of the blade (probably 5 times the blade span or more).
 

I expect that a full-scale (small scale) windmill of this type would use a V blade with a span of about 2 meters, weighing perhaps 5 kilograms or less, including the blade’s counterweight. The maximum orbit diameter of the blade would be large enough to keep the rpm low, such as 60 rpm. For example, if the furling wind speed is 10 m/s, and the tip-speed ratio is 3.0, the orbit diameter would need to be about 10 meters. In other words, the blade's speed would be 30 m/s, and so the circumference of the orbit would be 30 meters. 30 meters divided by pi gives an orbit diameter of 9.5 meters.
 

Crops could be conveniently grown beneath this windmill, so it should take up little space.
 

The swept area of the windmill would be about 2 meters X 10 meters = 20 square meters. But that also means that the coefficient of performance (Cp) would be low due to the abnormally low solidity ratio of the rotor and the only moderate tip-speed ratio of the blade. (The solidity ratio may be defined as the chord length of the blade divided by the diameter of the blade's orbit.) The solidity ratio could be as low as 3%. Some single blade, high tip-speed ratio (8 to 12), horizontal axis wind turbines have solidity ratios that are that low, but this single blade, vertical axis windmill has only a moderate tip-speed ratio (typically about 3.0).
 

When stopped, the blade hangs vertically, and there is little or no slack in the lower elastic cord. The V blade is self-starting in light winds due to random oscillations. Due to the way it is balanced, the blade naturally falls into an oval orbit that quickly becomes a nearly circular orbit. During start-up, as the blade swings from side to side randomly, the blade tends to swing around its pivot axis when tension in the elastic cables prevents the pivot axis from swinging any more to one side. That initiates an oval orbit. Centrifugal force then quickly converts the oval orbit into a nearly circular orbit.
 

Once the blade is orbiting, its unbalanced motion serves to pull horizontal cables that run over pulley blocks and then attach to the pump, and to the pump counterweight. If the blade is not orbiting fast enough, it will just continue to orbit until the windspeed and centrifugal force are strong enough to begin to operate the pump. So, in effect, the windmill functions as if it had a built-in clutch. The support cables and the pump cables are at right angles to each other and are joined at their midpoints. The upper elastic cord passes over a small pulley wheel attached to the midpoint where the horizontal cables cross. The size of the oscillations is restrained by the horizontal support cables. One is located well above the blade and other is located well below the blade.
 

(Note: All of the lower horizontal cables may be eliminated to further simplify this design. The lower elastic cable is then anchored to the ground).
 

The horizontal support cables merely oscillate from side to side at their midpoint. Their purpose is to prevent the pump cable from flexing from side to side at its midpoint because that would disrupt the necessary forward and back motion of the pump cable. Any long cable, no matter how high its tension, can be flexed a small distance if a force is applied at the midpoint of the cable. A lower tension will increase the maximum stroke distance of the pump. The tension in the support cable determines how far the horizontal pump rope can move back and forth along its length.
 

The support cables and the pump cables are supported by 4 poles (2 guy wires per pole). Two opposite poles support the horizontal support cables, and the other two opposite poles support the horizontal pump cables. So the 4 poles are arranged in the pattern of a very large square. The poles are spaced far enough apart so that the blade cannot make contact with the poles.
 

The pump's well head is located next to one of the four poles. The pump counterweight is located on the opposite pole. The purpose of the pump counterweight is to balance the weight of the water in the delivery pipe. The blade pulls up the counterweight, and that causes the piston to descend. The blade and the pump counterweight act together to pull the pump piston up. Then the cycle repeats.
 

For very deep wells, a Spanish coil (or some equivalent device) could be used to increase the mechanical advantage. A Spanish coil consists of a larger diameter coil of rope or wire fastened to a smaller diameter coil of rope or wire, with both coils riding freely on the same shaft. Pulling the wire of the larger coil causes the smaller coil to wind in its wire. The relative size of the two coil diameters determines the mechanical advantage. Instead of rope or wire, flat belts may be used so as to insure low wear and high strength. The blade's pump cable would attach to the belt of the larger coil.  The pump’s piston rod would attach to the belt of the smaller coil. This would give the blade a mechanical advantage equivalent to using gears. But the coils are much simpler and cheaper than gears, and could be easily constructed in village workshops.
 

The radius of the blade's orbit increases until the elastic cords (such as bungee cords) can stretch no more. While the elastic cords are stretching, the blade’s rpm stays about the same. In other words, the speed of the blade and the orbit diameter of the blade increase together as the wind speed increases. That keeps the rpm reasonably constant.
 

If bungee cords are not available, conventional metal springs and wires could be used instead. If neither is available, a gang of bows (as in bow and arrow) could be used as springs. Using bamboo, these could be cheap and simple to make. Another alternative is to use cords that extend by lifting a variable weight such as a chain (the chain is initially laying on the ground, so lifting it gradually increases the weight).
 

The unbalanced centrifugal force of the blade increases because centrifugal force is proportional to the square of the blade's ground speed (and inversely proportional to the blade’s orbit radius). The force to lift the pump is the centrifugal force, minus the reduction in centrifugal force caused by the doubling of the radius. So (2 X 2)/2 = 2. During this expansion of the blade's orbit radius, the pump stroke length increases roughly linearly in proportion to the wind speed, but the windmill rpm may not increase at all.
 

Once the blade's orbit radius is at maximum, further increases in the wind speed will increase the rpm of the blade in direct proportion to the wind speed. And the centrifugal force will increase in proportion to the square of the blade's speed. So if the wind speed doubles after the blade orbit is fully extended, the pump output will increase in proportion to the cube of the wind speed. That is because the stroke length will increase by 4 times because the centrifugal force will increase by 4 times, and the pump frequency will double due to the doubled rpm of the blade. So 2 X 4 = 8, which is the same as 2 cubed. This will now be good load matching. But good load matching would seldom occur because the rpm must be kept low enough for the pump.
 

Therefore, at low wind speeds, the pump output will increase only linearly with the wind speed. At high wind speeds, when the blade is at full radius, the pump output will increase in proportion to the cube of the wind speed. Overspeed control would be used to avoid this condition.
 

If the designer wishes to increase the pump output, he may increase the size or the weight of the blade, or both. To add weight to the blade, a heavier counterweight, closer to the blade, may be used. Or, metal rods may be tied inside the leading edge of the blade.
 

The Whirlwing Windmill is most easily understood by observing a model in action. I sell small model Whirlwings, made of sheet plastic, as science-toys. The blade has a span of only 0.3 meters, but its orbit diameter can exceed 2 meters and could be made to expand much more than that. (Experimental models can be made from card stock paper, the thickness used for business cards. They can be waterproofed using 2” wide, clear packaging tape, inside and out.) Although very small, this science-toy can produce useful oscillations in strong winds due to the relatively large swept area of the blade.
 

When the windmill V blade is in the downwind pass of its very large orbit, it operates in air without much turbulence caused by the upwind pass of the blade. Therefore, the downwind pass of the blade operates almost as efficiently as the upwind pass of the blade. For most VAWT, the upwind pass converts about 80% of the wind energy. That is because the upwind pass slows the air to about half its initial speed, and the energy in the wind is proportional to the cube of the wind speed. But for the Whirlwing Windmill, the division will be closer to 50-50 for upwind and downwind energy conversion.
 

In fact, the downwind pass can produce a stronger pulling force than the upwind pass. That is because the aerodynamic lift of the blade, plus its centrifugal force, both act outwardly during the downwind pass. During the upwind pass, the blade’s pulling force equals the centrifugal force minus the aerodynamic lift of the blade. During normal operation, the centrifugal force acting on the blade is much higher than the aerodynamic forces acting on the blade. That is why the blade can maintain its upwind pass in a nearly circular arc even though it is supported only by cords.
 

The rpm of the unbalanced Whirlwing Windmill blade is low due to its large orbit diameter. The rpm is unlikely to coincide with a natural frequency of the support posts. So the support posts should be able to withstand the pulling force of the blade.
 

For eggbeater type Darrieus rotors, a fairly small outward portion of the curved blades produce  a relatively large proportion of the thrust and torque. In effect, the Whirlwing V blade retains that outer section of a curved blade, while eliminating the rest of the blade.
 

The Whirlwing V blade seldom stalls, or feathers, under normal operating conditions. That is because the pitch-control system keeps the angle of attack of the blade below the stall angle of the blade. If a gust momentarily stalls the blade, the blade’s center of pressure moves aft along the blade chord, thus increasing the aerodynamic pitching force. That increased pitching force quickly reduces the angle of attack to below the stall angle.
 

The blade's orbit diameter expands most quickly if the bottom elastic cord attached to the blade stretches more easily than the top elastic cord. That is because the top elastic cord supports the weight of the blade, but the bottom elastic cord does not. So the bottom elastic cord should stretch more easily than the top elastic cord. 
 

To prevent the elastic cords from twisting as the blade orbits, swivels are placed between the elastic cords and their attachment points to the horizontal supporting cables (located above and below the blade). For small, full scale prototypes, ball bearing fishing swivels might be used. I can recommend a design for a simple, low-tech swivel if precision swivels are not easy to obtain. Used automobile or truck bearings could be adapted for use as swivels too. Sealed bicycle bearings might work as well.
 

The elastic cords should be as thin as possible because the aerodynamic drag of a cord is equal to an airfoil that is about ten times as thick.
 

For overspeed control, I have tested the use of a friction catch that releases the V blade so as to cause it to collapse into a  <  shape in response to high centrifugal force. (A pair of strong magnets could be used instead.) The collapsed blade cannot generate thrust, so it coasts to a stop and faces into the wind. In high winds, it would oscillate randomly somewhat, but it would be protected by the elastic cords. After a storm had shut down the Whirlwing Windmill, a farmer would lower the blade and reset the friction catch, and then raise the blade to its normal operating position. A raising cord is used to raise the blade up to its operating position.
 

To achieve this type of overspeed control, the elastic cords are fastened to the ends of a vertical rod (streamlined). The rod is a little taller than the V blade. The V blade uses rings rigidly attached to the leading edge tips of the blade. The rings go around the rod and can slide up and down the rod. The top ring is held up by a friction catch made by bending a piece of wire (or by magnets). The catch releases the top ring if the pull of the ring becomes too high. The tension of the friction catch can be adjusted by bending the wire. The friction catch is tied to the top of the rod.
 

The bottom ring is loosely tied to the bottom of the rod. The ring functions as a hinge.The rod also serves to keep the V blade’s span at maximum until overspeed control commences. The rod serves to stabilize the blade when the blade is collapsed into a  <  shape.
 

Since the blade can be lowered easily, and because it is light, it could be taken home at night by a farmer if theft were a problem in his area. If the poles could be removed from their foundations, the whole windmill could be carried home at night.
 

It might seem that the upwind blade pass would be disrupted by high winds. But this does not seem to happen because the centrifugal force is much higher than the aerodynamic forces on the blade. A gust may flatten the blade’s upwind arc somewhat, but that serves to accelerate the blade (like a spinning skater pulling in her arms -- the coriolis effect) so as to resist further flattening of the orbit.
 

Due to using elastic cords, in response to a gust, the blade orbit could become more flattened on the upwind pass, and more elongated on the downwind pass. So from above, the orbit would look more like an egg shape. This type of orbit can be observed during startup when the tip-speed ratio is low. The blade accelerates quickly in response to gusts so as to re-establish a nearly circular orbit.
 

The Whirlwing Windmill does not require the owner to do any climbing to install or service the windmill. All maintenance can be performed at ground level. No cranes, cranks, or gin poles are required for installation. The parts are first assembled on the ground, and then the 4 poles are placed in their foundation holes, and their guy wires are tightened. Then the blade is hoisted into position rather like raising a flag.
 

Due to the very large swept area, it is not necessary to use very tall poles to take advantage of the wind gradient. It is easier and less expensive to use a longer blade.
 

However, lower windmills are subject to greater turbulence. Fortunately, this type of windmill is especially tolerant of turbulent conditions. Pawsey (online Ph.D. thesis) calculated that fixed, vertical blades lose about 28% efficiency in turbulent winds as compared to about a 12% loss for this type of passive, dynamic pitch-control. (Static pitch control, such as when using a cam to control blade pitch, may suffer a 33% drop in efficiency. That was the case for the Pinson Cycloturbine. The reason is that a gust or a lull causes the tip speed ratio to be too low or too high, respectively, for the fixed [static] pitch schedule of the blade. In other words, a static pitch schedule in turbulent conditions seldom operates at its correct TSR.)
 

Because the Whirlwing Windmill has so little surface area, and because it is relatively close to the ground, it is not likely to raise objections about visual pollution.
 

With respect to noise pollution however, the blade will be mildly noisy unless more advanced blade shapes or tip plates are used that suppress tip vortex shedding. VAWT using these devices are almost silent.  For rural applications, the noise should not be a problem.
  

The blade would stop producing thrust if the pump rope broke. The blade cannot function unless the centrifugal force is fairly constant. Shaking the blade's raising cord can have the same effect. Once the blade was no longer producing thrust, it would be lowered to the ground. Otherwise, the blade would experience large, random oscillations in high winds as it tried to start itself again.
 

As may be apparent by now, the main components of this windmill are just cables, ropes, and cords, plus one simple blade, 4 guyed poles, 3 or 5 pulley blocks, and 2 swivels. So the cost should be extremely low. The total weight of the windmill should be less than 50 kilograms, not including the foundations for the 4 poles.
 

The precise efficiency (Cp) of this windmill will be very difficult to determine because it will vary widely. VAWT typically use a fixed solidity ratio (blade area divided by rotor swept area). But this windmill uses a variable solidity ratio. The Cp will be much lower than for most VAWT. On the other hand, the swept area will be far larger than for other VAWT with the same blade area. However, that does not mean that the power will increase in proportion to the swept area because the solidity ratio is far below normal. On the other hand, the downwind pass of the blade will convert much more wind energy than is the case for a conventional VAWT (perhaps 50% vs. 20%). So compared to a conventional VAWT, the blade will produce the equivalent of 80% (for the upwind pass) plus 80% (for the downwind pass) equals 160% of the energy conversion that would normally be produced if the downwind pass of the blade were operating in turbulent air slowed by the upwind pass of the blade.
 

The blade’s pitch schedule (a curve showing the degrees of pitch of the blade at each phase angle for a given TSR) of the Whirlwing blade will be different from that of a blade used on a more conventional 3-bladed VAWT with the same form of pitch control. The pitch schedule for the upwind pass of the blade would be similar, but different for the downwind pass. The downwind pass of the blade on a conventional VAWT does not require much blade pitch because the air has been slowed and made turbulent by the upwind pass, so the local TSR of the blade is high, and that by itself decreases the angle of attack of the blade. But for the Whirlwing Windmill, the downwind pass experiences air that is faster and less turbulent, so the blade will pitch about as much as during the upwind pass.
 

The dynamics of this windmill are very difficult to analyze even though the windmill is easy to construct. It may turn out that the aero and mechanical dynamics are so complex in their interactions that the only way to obtain realistic data will be to build and test a series of prototypes.
 

If someone wishes to do computer modeling, there are subtle variables to consider. For example, when the blade is heading directly upwind and producing no thrust, the high aerodynamic drag on the blade (due to the TSR plus the wind speed) may serve to assist pitch reversal because the blade is already rocking aft. (I say “may” because that effect would occur if the blade were part of a conventional VAWT, but that effect may not occur when the blade is not attached to the end of a horizontal support arm that is part of a conventional VAWT. Another example is that the tip speed ratio of the blade is lowered slightly as the blade swings aft, and increased considerably as the blade “flips” forward. Also, the blade spends more time swinging aft than swinging forward. And, as the blade pitches, the rotor radius becomes smaller.
 

This windmill should produce high power relative to the total weight of the windmill. So it should have a high power to weight ratio. Weight correlates fairly closely with cost. So it should have a high power to cost ratio. In other words, it should be especially inexpensive for the amount of wind energy it converts.
 

The windmill and pump could be manufactured in village workshops. Well boring costs are now low when using newly developed, manual drilling techniques. So the total cost could be very low. If this low cost can be realized, it should be a cost breakthrough for windpumping. Such a low cost would permit the windpump to be used in areas where the average windspeed is too low for conventional windpumps. Even the poorest farmers earning a dollar a day could afford this windmill. It might be sold as a kit. Then the farmer would supply his own poles, foundations, and the borehole. The kit could include everything else. The farmer would also purchase a training class.
 

This windmill could be so light that all of the parts might be delivered to the site by bicycle or canoe, or perhaps by two people walking. This is an important consideration for remote locations. A small airplane, small boat, or ox-cart could transport many Whirlwing Windmills.
 

Since this windmill connects to the pump via an oscillating cable or rope, the windmill need not be located right next to the well pump. It is possible to transmit energy up to 400 meters using an oscillating wire. The wire is suspended from short strings suspended from the tops of short posts
arranged in a row. Tension in the wire minimizes sag. The same posts could support two or more wires.
 

Another option is to connect this windmill to existing treadle pumps or hand pumps that are either permanently installed or portable (such as the treadle pumps designed by Kickstart). The pump cable would be made to pull down on one of the treadles. And the counterweight cable would be made to pull down on the other treadle. No pump counterweight would be needed.
 

Treadle pumps have had a dramatic impact on raising the incomes of millions of poor farmers. However, Umei Scheuermeier of Viltec (based in Switzerland) mentions on his website that treadle pumps tend to be abandoned as soon as a farmer can afford a diesel or electric pump. After all, no one wants to treadle for 2 to 5 hours each day.
 

Those diesel and electric pumps cause the release of large quantities of CO2 and particulates into the atmosphere. Mr. Scheuermeier has found that solar voltaic pumps can be used if there is a supportive infrastructure such as provided by Sunlabob in Laos. I believe this single-blade windpump is a much cheaper solution (where there is enough wind) because it can make use of existing treadle pumps. It should cost far less than solar voltaic pumps, and wind is infinitely cheaper than diesel fuel, especially now that fossil fuel prices are steadily rising. Furthermore, this wind technology can be sustained using local manufacturing, thus creating many jobs in rural areas. That is not true for diesel and solar pumps, most of which need to be imported.
 

Windpumps usually require a water storage tank because the wind is so unpredictable. But if the Whirlwind Windmill is coupled to a treadle pump or hand pump, human power can be used on windless days, so little on no water storage would be necessary. 
 

If the Whirlwing Windmill proves to be successful as a windpump, its might be adapted to many other tasks. These include compressing and storing air to produce electricity on demand, heating cooking oil by agitation heating (100% efficient if very well insulated), vacuum evaporation cooling, water desalinization or purification, vacuum sewage collection (as on ships), pressure irrigation pumping, pumping water over long distances by using a string of reservoirs, etc. Compressed air could be stored in large banks of used, plastic soda bottles. They can withstand 10 bar. An explosion of one of the bottles would do little damage.
 

It is possible to make a Whirlwing Windmill using nothing but a flat board or a piece of corrugated metal (with the corrugations horizontal). The power will be far lower because the TSR will not exceed about 1.0. But the basic centrifugal pendulum system will work with almost any sort of vertical blade that is balanced like a centrifugal pendulum. The blade does not have to be a true airfoil.  My experiments with models indicate that cloth sails operate at a TSR of about 2 to 2.5.
 

Blade construction for the Whirlwing Windmill is simple. The upper and lower halves of the V blade can be made separately and then taped together to create a hinge. At the hinge, the ends of the blade halves are pressed flat before taping. The counterweight arm is tied to the outside of the hinge.
 

Each blade half is constructed by bending a sheet material around a tube that is tied or pop riveted to the inside of the leading edge. Then the trailing edges are joined using tape or pop rivets. The blade skin is under tension and holds its shape well.
 

The blade skin can be further stiffened and shaped by tying short lengths of thin plastic tubing between the blade skins at the thickest part of the blade. Just a few pieces of tubing along the blade span will stiffen the skins considerably. Small holes are punched in the blade skins. A string is pushed through one of the holes, through the short length of tubing, and out the other hole in the other blade skin. Then the string is tied at the leading edge of the blade. The tight string is then gently slid until the knot goes inside of the blade so that the knot doesn’t create aerodynamic drag. The leading edge tube could be tied in place similarly.
 

If the blade skin material is plastic, it should be painted, preferably with aluminum paint, to protect it from UV radiation.
 

The blade profile can be controlled to some extent by the way the sheet metal is fastened to the leading edge tube. The resulting blade profile typically has its maximum thickness at near mid chord. So the blade functions like a laminar flow blade, or like a NACA633018 blade.
  

Laminar flow blades tend to stall easier than a more conventional NACA018 blade that is thickest at about ¼ chord. But because the blade of the Whirlwing Windmill pitches, the blade doesn’t stall, so most symmetrical blade profiles can be used. Laminar flow shapes may be best because they have a high lift to drag ratio as long as they do not stall. They cannot operate at a high angle of attack, but they would not need to do so if used with a passive, dynamic pitch-control system.
 

If the counterweight arm of the Whirlwing blade is made from a flexible rod, it can serve as an overspeed control device. If the counterweight arm flexes in response to excessive centrifugal force, that will unbalance the blade and cause it to begin to toe-in excessively, thus causing too little pitch during the upwind pass and too much pitch during the downwind pass. The blade will stall during the upwind pass, and produce poor thrust during the downwind pass.
 

For applications where the rpm or cycle rate does not need to be kept low for a deep-well water pump, an alternate tower arrangement could be used.  The guyed tower would have an “F” shape. The elastic cords of the Whirlwing attach to the outward tips of the F. The tower oscillates as the Whirlwing blade orbits. The long arms of the F tower then serve as levers to amplify the force of the oscillation. Thus high forces could be produced by a relatively small blade. The Whirlwing “F” Windmill could be used for compressing air, friction heating, or low-lift water pumping.
 

The blade will stop orbiting if the F tower is allowed to oscillate without a load. The F tower would be connected to the load using two ends of an oscillating cord. The cord would simply wrap around the vertical shaft of the F tower a few times. The vertical shaft would function like an oscillating pulley wheel to alternately pull the two ends of the cord.
 

It may be possible to operate an F tower Whirlwing in river water to pump irrigation water. The blade would need to be filled with sand or metal to create enough centrifugal force since water is roughly 800 times as dense as air. The pumping rate for low lift pumping can be much higher, so the orbit diameter of the blade would not need to be very large.  The blade itself could be relatively small. The double acting pump could be located on land and operated by oscillating ropes from the F tower. How to best mount an F tower in a river has not yet been determined.

 

 

          

           Copyright 1/30/2008

           Peter Allen Sharp        sharpencil@sbcglobal.net              

 

This is still an experimental concept and only preliminary, proof-of-concept models have been constructed, and then tested only in wind. This information is intended for experimenters who are looking for cheaper ways to extract energy from wind and water. The Fluttermill is very easy and cheap to build, and that is why it may prove to be useful. It could be used for pumping water or for compressing air, either of which could then be converted into electricity. The Fluttermill is not patented and anyone may use or sell Fluttermills for mechanical applications.

A Fluttermill consists of flexible blades on strings that strongly flutter in the wind or water current. The flutter of a blade contracts the string longitudinally to produce a pulling force rather like the flexed bowstring on an archery bow contracts the ends of the bow. Two or more such blades may be used together to control each other’s flutter, and to produce a rapidly oscillating force. The blades flutter 90 degrees out of phase and produce pulses at twice the flutter rate of the blades. The pulses could be used to oscillate a piston.
 

In March of 2007, Dr. Jonathan Hare, a physicist with The Creative Science Centre at the University of Sussex, UK, built the first Fluttermill wind generator. (I built the first experimental Fluttermills around 1975, and built the first 2-bladed, 90 degrees out of phase, windmill around 1995.) His wind generator combines my Fluttermill concept with Dr. Hare’s “shake-a-gen” (a magnet oscillating inside of a plastic photo film container, with electrical wire wrapped around the film container, and the ends of the wire connected to an LED; similar to a shake-type flashlight). It lit an LED, although it required a strong wind because it was not optimized. His work was done under a NESTA Fellowship. Dr. Hare is also part of the group of scientists who participate in the educational television program “Rough Science”. Photos can be seen at: http://www.creative–science.org.uk:80/sharp_flutter.html   Or, search Google for “Peter Allen Sharp Fluttermill”.

The model was constructed using nothing but my verbal description to Dr. Hare, so the overly massive bell cranks were due to my ambiguous description.

In January of 2008, I contacted Shawn Frayne about the Fluttermill. Mr. Frayne is an inventor with a degree in physics from MIT. He invented the Windbelt wind generator (patents pending; still under development; working prototypes). His company’s name is Humdinger Wind Energy, LLC, with headquarters in Hawaii.

I learned that a few years ago Mr. Frayne began by experimenting with devices similar to a Fluttermill but found that the oscillations were not fast enough, or steady enough, to generate reliable electricity. That is why he switched to the Windbelt, which is a flat strip (belt) of flexible material that vibrates in the wind somewhat like an Aolian Harp. Small magnets are mounted near one end of the belt and they vibrate between two coils of wire at about 100 cycles per second. His current models are about 1 meter in length and are intended to provide micro power to small electronic devices, plus function as low cost sensors in ventilation ducts. He believes the concept can also be scaled up to produce significant amounts of power.  He encouraged me to explore the Fluttermill concept for mechanical applications. His patents cover the use of fluttering blades for the production of electricity.

Sailors know that a sail aligned with the wind will luff. A Fluttermill, in effect, retains only that portion of a sail that luffs. It should be possible, for example, to build a sailboat that can use the same blades, when non-fluttering, to sail across the wind, and then use the same blades to sail directly upwind by letting the sails flutter (luff) to power an oscillating-fin propeller. When someone claims that it is not possible to use a sail to sail directly upwind, that is no longer entirely true (since windmill boats can sail directly upwind; however, the two functions, sail and windmill, are distinct).

There are different kinds of flutter that can be used to produce useful energy. A particularly beautiful slow-flutter windmill was invented and developed by Dr. Simon Farthing (www.econologica.com). The single, tall, elegant blade sways back and forth rather like a windshield wiper in slow motion, or as if it were waiving hello from a great distance. It is simple, inexpensive, and sturdy. It requires only a stub tower. It can produce a very powerful pumping force for use with deep or shallow wells, or pond aeration. It uses a heavy counterweight below the blade’s axis of oscillation.

The pumping stroke begins only when the blade and its heavy counterweight are moving rapidly past the midpoint of their oscillation. A Spanish coil is used to increase the mechanical advantage. (It consists of two drums of different diameters that are fixed to each other, and both turn freely on their common axle. The windmill pulls and unwinds the belt on the large drum, and that action winds in the belt of the small drum in order to pull up the pump piston.)

A tail vane orients the blade to the wind. The windmill has good protection in high winds. It can be located on land or water. It has also been used to compress air. I believe that one of his windmills has been in use in Cuba for a few years.

Another type of slow-flutter blade is used by the kinetic sculptor Theo Jansen to power his many-legged beach robots called “animaris” (www.strandbeest.com). The multiple spines of the horizontal blades are each connected to a crank shaft so that they sway in the wind in sequence. The resulting movement is like the wing of a manta ray, or a slowly swimming eel. He uses them to compress air which he stores in used plastic soda bottle (at up to 10 bar). The compressed air is used to operate long pistons made from plastic tubing so as to cause the legs of his robots to walk along the beach. They are large, typically have dozens of legs, and are fascinating to watch.

It is possible to combine a large number of Fluttermill blades so as to achieve more power. The blades may be limited by a scale effect, so they might not work in large sizes. However, in flowing water, even small blades could produce useful power.

The blades of Fluttermills may be flexible strips of flat plastic, or card-stock-paper covered with clear, wide, package-wrapping-tape to make them waterproof. A cord is taped to the leading edge of the vertical blade and extends well beyond the ends of the blade. The top of the string is fixed to a supporting frame. The bottom of the string is attached to an L-shaped bell crank. The aspect ratio of the blades (span of the blade divided by the chord of the blade) is roughly 6 to 1, but this is not critical. The length of the blade chord (from the front of the blade to the back of the blade) will mostly determine the blade’s flutter frequency. (The other factors are the amount of slack in the string, the blade mass, and the flexibility of the blade.) The original blades of my 1995 proof-of-concept model were 11’ (28 cm) span (length) and 2” (5 cm) chord (width). The two blades oscillated a seesaw rod.
 So far, I have not found that symmetrical airfoils work any better than flat strips for the blades, and they do not seem to work as well. That may be because flat strips have less inertia and so can flutter faster. Also, since the blades rapidly increase their angle of attack while fluttering, that may delay blade stall. If so, then that is the Kramer Effect. (The purpose of curved blades or wings is to delay blade stall. But a rapidly increasing angle of attack can also delay blade stall and produce a momentary large increase in lift; that is the Kramer Effect.)

When exposed to a moving fluid such as wind, the Fluttermill blades flutter violently from side to side. The Fluttermill concept was inspired by the wind induced flutter that destroyed the very large Tacoma Narrows suspension bridge in the state of Washington, USA on Nov. 7, 1940. Films of its collapse are available on the Web. Wing flutter is something that airplane designers are very careful to avoid because it can reduce lift, increase drag, and can even cause the wings of an airplane to snap off due to metal fatigue. The Fluttermill is based on the idea of turning a serious problem into a solution. To see videos on that subject, search the Internet for “aeroelastic flutter”.

When a Fluttermill blade moves all the way to one side, it functions like a bowstring of an archery bow to contract the vertical distance between the two ends of its string. Two (or more) blades are linked to each other using two (or more) L shaped bell cranks that connect to a piston rod. The bell cranks oscillate the piston rod. The oscillating piston rod may be used to pump water or to compress air using a double acting pump.

The two Fluttermill blades (or opposite sets of blades when more than two blades are used) flutter 90 degrees out of phase with each other. When one blade is curved and all the way to one side, the other blade is straight up and down, and in the middle of its side-to-side oscillation, with its string pulled tight by the curved blade. Thus each blade controls the oscillations of the other blade so that they oscillate at the same frequency. That enables them to take turns pulling the pump piston back and forth. The length of the blade strings is chosen by trial and error to produce the most powerful flutter. No formal analysis or testing has been done to determine the optimum proportions, so the current proportions are just best guesses based on informally testing flutter-blades. They are unlikely to be optimum.

For each complete cycle of blade oscillation, the blade string contracts twice. For each complete blade-cycle (center, left, center, right, center), the blade causes its bell crank to oscillate twice. In other words, the oscillation frequency of the bell cranks is twice the oscillation frequency of the blades. In effect, the system has a built in 1 to 2 step up ratio even though there is no “transmission”.
 

The mechanical advantage of the Fluttermill can be modified by using bell cranks with one arm longer than the other.

Any number of blades may be ganged together in order to achieve the desired amount of power. Their bell cranks may be joined to each other using cords. The ganged unit would look like a very wide picture frame with many vertical blades. For use in water, the bell cranks and pump would be mounted on the top of the frame and above the water.

The bearings for the bell cranks only need to oscillate. Therefore, each bearing can be made from a short length of tight cord or cable that twists back and forth a few degrees. A tube or rod is mounted on the cord, and the bell crank is attached perpendicular to the middle of that tube or rod. The tube or rod is not as long as the cord. Consequently, short lengths of cord at each end of the tube are free to twist back and forth while under tension. These bearings should have very low friction and they should require no lubrication.

All of the parts should be kept as light as possible so as to not absorb much of the Fluttermill’s energy. The bell cranks should be as small as possible, and the pump piston should be as light as possible.

A Fluttermill is safe to touch while the blades are oscillating rapidly since they are flexible, have very little mass, and have no sharp edges. If used in rivers or tidal flows, Fluttermills should not harm fish or swimmers.

The strings extending above and below the blades can twist without affecting the oscillation of the blades. So the blades can automatically orient to the current flow (such as a tidal flow) through 360 degrees of rotation. No separate yaw mechanism is required. In effect, the yaw mechanism is built-in. If the strings become twisted due to changing flow directions, the blades strings will unwind when the current (tidal flow or wave oscillations) stops to reverse.

The blades of experimental Fluttermills cost only a few cents, and each blade can be made in a few minutes using a wide variety of materials. They could be replaced periodically. All of the parts are easy to fabricate using hand tools. There is no need to make a water turbine especially durable if it can be maintained and repaired as cheaply and as easily as a Fluttermill, and if it will be used close to where people live.
 

Fluttermills are ideal for teaching students about converting wind and water energy into electrical and mechanical energy because all of the parts can be assembled by students, and because the completed device is safe. Testing does not require adult supervision.

Fluttermills could pump irrigation water from slow moving rivers if connected to small, double acting pumps.
 

For wave energy conversion, the rectangular frame could be mounted horizontally at the end of cords hanging down from a float. The frame would be weighted with ballast. As the waves lifted the float and the frame up and down, the blades would oscillate to compress air, and the compressed air could be sent to a small air turbine on shore.  Where the water was deep enough, compressed air could be stored in plastic bags anchored at a depth of perhaps 100 to 200 feet below the surface.
 

A difficult problem for island communities is how to obtain and store enough cheap energy. Since islands and atolls have tides, here is a concept for those with large areas of shallow water. Create a tidal lagoon divided into two parts using rocks, sand and perhaps biorock. The main part of the lagoon fills and empties with the tides by water flowing through a water turbine placed in the opening to the lagoon. Part of the inward flow of water is used to pump water (perhaps using Fluttermills) into the other section which has higher walls. Its water level is kept above the high tide level. At high tide, and at low tide, this higher water is released through the turbine to maintain a steady power output from the lagoon. About 2/3 of the energy used to pump the water can be recovered.

The tidal lagoon could serve additional purposes if nets (with a large mesh) were mounted across the opening to the lagoon. Small fish would be free to come and go, but when they grew large, they would not be able to get out. This would be similar to the ancient Hawaiian fish ponds used to feed the king and his large entourage when they came to visit. They used holes in the stone walls only large enough for small fish.

Part of the available power could be used to grow biorock coral reefs within and outside of the tidal lagoon to increase fish stocks, to create a dive industry for tourism, and to reinforce the walls of the lagoon.

Another type of Fluttermill could be constructed by using very long, narrow-width blades that flutter somewhat randomly. The blades form nodes and standing waves, so the frequency remains high. Long blades still contract only a short distance, but the contraction force is much stronger.
 

My proof of concept model (around 1975) used only one blade that was 5 feet (1.52 meters) long with a 1inch (2.54 cm) chord. I held the upper end of the string and the bottom end of the string rapidly oscillated a heavy horseshoe magnet (restrained by a spring) next to the 110 volt coils from a fish tank air pump. A skeptical neighbor sparked the ends of the bare wires together and was painfully shocked (literally) to discover the power of a blade made from a single sheet of paper, string, and tape. Many such long strip-blades might be arranged in a rectangular frame and connected to bell cranks as before.

I am not certain that more than one very long blade per side will work properly, but I believe that it would. I have not yet tested this option. Any initial random oscillation of the rod initiates a positive feedback in all of the blades so that they would fall into synchrony to oscillate the seesaw rod. If this works, then this type of Fluttermill could be more powerful and less expensive. See drawing “Proposed Fluttermill; Semi-Random Flutter”.

Another experimental option is to mount many flutter blades parallel, and close together, in a rectangular frame, and then synchronize all of the blades by tying a common string to the midpoints of their leading edges. The common string must not prevent the blades from freely twisting to flutter. To create a freely twisting bearing, just cut a small notch in the leading edge of the blade such that the normal string along the leading edge of the blade bridges that notch. That bridging string will then serve as a nearly frictionless bearing. The synchronizing string attaches to the middle of those bridging strings.

All of the blades oscillate in phase, and the entire frame oscillates with the blades. The frequency is much lower. The frame may be attached directly to a water pump or some other oscillating device. But the frame must be oriented toward the moving fluid. The frame can be made to oscillate up and down or from side to side. Since a lower frequency of oscillation is desirable for water pumping, larger blades may be used. The frame should be allowed to oscillate at close to its natural frequency.

My proof of concept model windmill (around 1975) was about 18” square. The wooden frame was suspended between three, tight, horizontal strings that met above the frame, and three, tight, horizontal strings that met below the frame.  These horizontal suspension strings were supported by three poles arranged in an equilateral triangle, with the frame located in the center of the triangle. The normal flex of these strings provided the frame with a nearly frictionless linear bearing, allowing it to bob up and down a few inches as if on springs. The weight of the frame contributed to the force of the down stroke.

It might be possible to oscillate all the blades together by using a synchronizing rod instead of a string. The rod could then be attached directly to a double acting pump. The frame would not need to oscillate and it could be held in a fixed position.

 

Fluttermills are ripe for experimentation. They may prove to be exceptionally simple, powerful, and inexpensive water turbines. I plan to explore them further in order to sell them as part of my line of science-toys that demonstrate new principles.