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Chapter 4
Geese And Ducks

What Technology Says About Aerodynamic Lift

Now that some space has been devoted to discussion of the two concepts of (a) airflow deflection and (b) the mass of air, lending some insights to them, which give them added importance as they relate to the theories of the aerodynamic lift principle and the technological derring-do that goes by the name of wind energy, it is possible to move on to a detailed view of modern beliefs about how lift itself works. This is easy stuff and fun. Why do some birds such as geese and ducks fly in "V" formations? What does everyone think about this? Below are some comments excerpted from a small newsletter of the type many neighborhood organizations produce, material deeply rooted in centrist culture and serving as a good source of popular beliefs:

Thanks to Merrick Community Services, 715 Edgerton Street, St. Paul, MN 55101 for the above
material excerpted fair use from the Fall 2000 issue of their "Making Communities Strong" newsletter.

Is this good science or is it just good organizational doctrine? The parallels to people working together to achieve a common purpose are clear. Although not stated in these terms, the impression given is that the lead bird does a lot of work pushing the air out in front of it and the forward motion thus given to the air, as added to by others, helps the flock as a whole move faster and with less effort.

Emerald City In The Land Of Oz

The wonder of and fascination with flight has hit a responsive chord within the human race although birds are far more familiar with this specialty of theirs, having seen it for a much longer period of time. What happens with an advancement like this can be likened to peoples everywhere entering the Emerald City in the land of Oz. Everyone accepts it all even with little or no satisfactory explanation. But behind it, explanations, if even mundane ones, exist that are hidden from view behind the curtains that hide all the levers and persons pretty much like themselves following ordinary procedures operating them.

The wings of birds create lift. There is little need to question this. Look at the way their wings are designed. Do this the same for aircraft. It works. What else need be said. To look for more precise explanations and newer designs is not welcomed. This is Oz and the phenomenon that surrounds this circumstance can be called "Ozmania".

This book is about an "Ozmania" that surrounds the field of wind energy. Aircraft emulate the avian world and now wind generator blades emulate aircraft. Going this one step further, the going begins to show evidence of some roughness around the edges. It is not something that yet creates much of a stir because all is going well. But some of us are more attuned to some of the nuances of how the processes work and want to say a few words about what we see and so this is our story. But before getting into some of the whys and wherefores, it serves a purpose to look at what this Emerald City looks like, what it is that everyone the world over believes when they see the windmill blades turning. For this is the wisdom, the groupthink that holds the industry in its thrall, not to mention providing the votes that draw even the movers and shakers in government into involvement.

The Stylus And Wedge Theory Of Wind Generator Blades And Sailboat Sails

Take a stylus or a pencil. Force its point straight down against a wedge with frictionless surfaces. Watch the wedge move sideways under the force. That's how most of the world conceives of the big wind generator blades at work - and this is the same way, of course, as the way the sails of sailboats work. The process depends on a small angle being there between the blade or the sail and the direction of motion and some ability of the device to slide forward from this what is mostly a lateral force such as that from the point of a stylus.

But it is possible to be even smarter than this and use the principle of lift, something distinctly different. For lift, the aerodynamic shape doesn't even need an angle of attack. The sailboat with such a special airfoil-shaped rigid sail need only luff the sail "out" of the wind and the boat continues to move forward! This can be even tried as another advancement in the state of the art of sailing, for the lift principle does not depend on there being an angle such as that which sailboat sails normally present to the wind. A variation on this idea, sometimes seen in magazines that cover popular technology, is the powering of large ocean liners with sails that are in the shape of tall metallic rotating cylinders where their smoke stacks would otherwise be and interact with the wind with what is called the "Magnus Effect". Who has not seen this? This is something that also comes from the magic of the lift principle and holds future promise. All of this has its parallel in wind generator blade technology. The talk is all the same - blade pitch to zero angle of attack and even of the "Magnus Effect". The wind generator blade (wedge) moves even without requiring force (stylus point) from the passing wind.

Take A Ride On A Small Packet Of Air

Let's get back to our feathered friends. Does anyone doubt that a principle called "lift" exists? The wings of birds are somewhat curved, convex above and concave below, but otherwise flat and encounter the air with a zero angle of attack and yet the bird's weight is more than amply supported by them. How can this, such a simple, everyday happenstance, be disbelieved? Once accepted, then, the rest must follow as well. Let's begin with a ride, a short trip aboard a packet of air moving along under the motion of the wind toward a wind generator blade that is at work producing energy. As we ride we can see just exactly how this packet of air encounters the blade and what it does to it, maybe even see the principle of lift at work, if we are lucky.

First, let it be said that this is about the lift principle as opposed to the drag principle. The blade is propelled to move at speeds greater than, and even much greater than, the speed of the wind that drives it. (Drag presupposes that the device driven never achieves a speed greater than that of the wind.) So as we start our ride, no blade is to be seen. We move in the direction of where the blade's intersecting path is supposed to be and see it coming from afar off to our right, moving with great velocity toward us. Watch out! We are on a collision course! As the blade arrives, traveling some three to ten times our own speed in a direction at or close to perpendicular to ours, we notice for the first time that it has a pitch angle.

Blade Pitch Angles

At this point some minor differences of opinion surface. Some hold that this pitch angle is best set to be such that as we encounter the surface of the blade, it moves past without interrupting our motion or there being any collision at all. We just skim the surface with a light touch. Lift arises on the side opposite of that on which we touch its surface and pointing to a direction off at right angles to it. Since this direction is partly aligned with the direction of travel of the blade, then forward motion is created in it which drives the machine to produce energy. We hardly touched the blade at all! We continue on past the blade entirely unaffected by our brush with it as if it didn't even happen! What a wonder this concept of lift is!

Now suppose the pitch were to be adjusted to be something else. If it were made to be a larger angle to the direction of motion, then it would have less lift although the direction of the lift force would be more aligned with the direction of motion of the blade, a bad and a good thing, respectively. If it were made to be a smaller angle to the direction of motion, then it would have a greater angle of attack and therefore greater lift but the direction of the lift would be aligned less with the direction of motion of the blade, also a mixed result, this time a good and a bad thing, respectively. Changing the pitch angle, then, is not a particularly strong factor in changing the power output of the blade, except that as we approach a zero degree pitch angle, all driving force forward ceases because the lift force is no longer aligned in a direction that helps create any forward motion. It seems that somewhere between zero degree pitch and some large pitch angle, a maximum occurs and this is the best angle for operation. Again, some say that this angle is the place where the wind brushes by entirely unaffected by its interaction with the blade, the point of zero angle of attack.

Blade Pitch Twist

This is not entirely agreed to by everyone. Some papers have been written, as referred to earlier, saying that a larger angle of attack is needed for wind generator blades than those that bird wings and aircraft wings see. It is also plain that some wind generators operate with blades almost flat against the wind, something that hardly looks right at all. But the proof is in the pudding. If they work, then nothing more need be said. For the rest of the industry, however, a standard has been adopted of providing some optimum angle for the blades to be pitched to, however this optimum is decided upon, and, since the angle must vary with the tangential velocity of the point along the blade length arising from the blade's rotation, then the pitch angle must vary along the length of the blade, giving rise to what is termed "pitch twist". The reader is invited to look at the blades of large operating wind generators and see this. Typically, and even traditionally now, the pitch twist of many wind generators is set to be about 15 degrees from root to tip, being the greatest at the root. Some say that this pitch variation should increase with blade length but others disagree, saying that the longer blades on the higher rated machines often run at somewhat slower rates of rotation thus obviating this requirement.

Where did the driving force come from? The answer is that it comes from the same place the lift force comes from for aircraft wings and, further back, the wings of birds. The air sees a difference in the surface curvature of the top of the wing as opposed to its bottom and, according to the Bernoulli equation and the Magnus Effect (in which a "circulation" is set up in the air rushing past), lift is created. Some say that this circulation sees its manifestation in small vortices that trail off after the interaction with the airfoil shape, which also "tallies" or agrees with conservation of mass when the airspeed is theorized as being greater on the top surface than the bottom. So as we conclude our ride on our small packet of air, we would expect to see, after our near brush with a collision with the blade that turned out to be nothing more than touching it lightly, some disturbances in or near the small piece of the wind we are riding on in the form of little swirls. It is also interesting that if the blade pitch angle is different from a zero angle of attack, it makes no difference; our ride is unaffected as well. We move on past our interaction with the blade having never experienced anything other than some force against it (like the stylus) or lack thereof but the number of these small, what are more properly called, vortices produced is different.

This is approximately the way that current theories explain how wind generator blades work and how the industry responds to these theories with blade design.

The "Futuristic" Verticals

It doesn't take much of a look at the vertical axis wind generators under this concept of things to be highly discouraged by what is to be seen there. For one thing, the blade attack angles are constantly changing as the blades move around their circuits. (Remember that, however, the pitch angle, or angle between the blade and its direction of motion, remains the same, usually something at, or close to, zero degrees.) This is like a sailboat that is trying to not only run a circular course but also do so with sails set the same the whole way! What is presupposed by practically everyone in this circumstance is that the blade works in only two places in its whole round trip, once while moving directly across the wind in the front half of its path and the other time is while moving directly across the wind in the back half. Everywhere else the aerodynamics aren't right and the stylus is pushing on a wedge from a direction other than perpendicular to its motion with results far from ideal, something like running a sailboat too close to the wind while tacking or running downwind without letting the sail out. The procedure of tacking is well known by the boating crowd and is called upon frequently to be performed, bearing in mind that (a) one never runs for any length of time straight into the wind and (b) it takes a lot more effort. In the final analysis, efficiency kills the verticals. The blades, as expensive or inexpensive as they may be, are working only a small part of the time even in the best of circumstances. The rest of the time they are moving but not of use and may even be counterproductive between these brief moments of energy production.

Sandia Laboratory's 34 meter Darrieus Vertical in Bushland, Texas.
Our thanks for this photo taken fair use from a Sandia Laboratory,
Albuquerque, New Mexico brochure "Vertical Axis Wind Turbines,
The History of the DOE Program" published by the U.S. DOE,
Sandia Labs, and the American Wind Energy Association

But wait. Did we say that the blades are pitched to something close to a zero degree pitch angle? How can this be. According to what was stated in no uncertain terms above, a zero degree pitch angle does not work, the lift angle being perpendicular to the direction of motion of the blade by definition and therefore of little use in propelling the blade forward. So in stricter terms, vertical axis machines don't even work at the only two points on their paths for which we earlier gave them any credit. (Further, if they are given some pitch angle, the effect alternates between positive and negative in each half of the circuit, canceling each other out.) It must be said here that current dogma has never fully explained to any degree of satisfaction how vertical axis works and itself remains mystified by the apparent anomaly of the production figures that have been obtained by these machines in actual practice. But stranger things have happened and, as for the case mentioned above of blades on horizontal axis machines that work well while pitched flat or nearly flat against the wind, the proof is in the pudding. What works works. Nothing more need be said, the stylus point pushing straight down on a wedge that is no wedge at all but a flat stick with no taper and yet the stick deciding on its own to move anyway. No argument!

Upon reflecting upon what was just written, it must be said that no harshness is intended and things are not all that left to chance. The industry has spent a good deal of time and many manhours on all aspects of these machines, the verticals included. What has come out of it as far as the theory is concerned as best as can be put into words herein is that the verticals present a more complicated problem to solve in the field of aerodynamics and solutions to the equations involved are more difficult to arrive at. One always hears at every gathering at which these subjects are discussed the mandatory references to the three dimensional fluid flow theoretical equations termed "Navier-Stokes" and "Euler", the latter being a simplified case of the former, and how these equations have not been solved for the verticals yet. The implication seems to be that some day they will be but everyone must wait. Patience is necessary. This material accepts this. Maybe a youngster in school reading this somewhere and wondering if all the world's scientific challenges are fully funded and under investigation to a level of effort commensurate with their national importance and popularity with the will of the people will be persuaded to believe by it that they are not, that something remains to be looked at, at least in the particular case being discussed here. Being even fairer, it must also be said that computers have been programmed with the results of largely correlative (empirically-obtained) relations, sometimes from far afield but nonetheless having been found to apply, that make looking for purely theoretical relations almost of no practical use and, especially where some difficulty is involved, nearly irrelevant to the progress of the technology.

Conclusion

Ducks and geese fly in "V" formations, something that has a touch of the unexplained about it. Maybe it is better to leave this little bit of mystery to remain. To remove it would only take something away from what is to be enjoyed otherwise as a beautiful experience in the natural world among those we have more frequent opportunities to observe. The same cannot be said, however, of the technology of wind energy. In the next chapter, the politeness and the evensay fuzzy mystique of this renewable energy enterprise, as now put before us, are taken up as targets, wherever and however, to be attacked viciously and with no mercy, none given and none taken. Ozmania is the Emerald City of Dorothy, you know, before she discovers the Wizard of Oz hiding behind the curtain.