A brief wind power tutorial

[Bob McGovern]

Urps -- not sure how that happened. Thanks to this site's History feature, here's a recovered version.

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I've found discussions surrounding wind energy usually benefit if people have a good sense of the physics and forces involved. The science is both straightforward and subtle. If this is old hat, forgive; if it is new, hopefully a few crudely-executed sketches can give a feel for what is happening where air meets machine, and why some designs are inherently more effective than others. No math, but it helps if you are a sailor.

First, good electricity-generating turbines are not pushed by the wind so much as they are pulled. Making electricity needs medium-high RPMs at the alternator, and blades that are pushed can never go faster than the true wind speed -- usually much slower. These are called "drag turbines". Good turbines rely on aerodynamic lift to turn them: the forces involved are greater, and the blades can spin many times faster than the wind, just as a catamaran can sail faster than true wind speed.

WHOA -- sound like a perpetual motion machine? The secret is a phenomenon called "apparent wind", which is the vector sum of the true wind and the blade (or boat) speed. It looks like this:



A blade with tip-speed ratio (TSR) of 5 will spin 50mph in a 10mph wind, creating its own apparent wind of ~51 mph. The apparent direction of that wind moves closer to the blade's rotational plane the faster it spins; likewise, the blade tip sees a faster and shallower apparent wind than the blade root.

As the apparent wind contacts the leading edge, it splits. Some air goes along the convex back, some goes along the concave front. The streams adhere to the blade surface and adjacent air by boundary layer effect.



The concave side air slows down, generating a net positive air pressure; the air flowing over the convex back of the blade speeds up, creating a net (and stronger) negative air pressure. Both sets of pressures act perpendicular to the surface of the blade. The forces act in all different directions and intensities, but the net force is a flexing and forward one. The flex force is canceled by the blade's stiffness; what's left is a forward vector of surprising strength:



There's a fairly narrow window of apparent wind direction -- or attack angle -- in which a lifting airfoil will operate efficiently. The flow along its sides must be smooth, and it must remain attached to the blade surface. If it detaches, the result is lost lift, terrible drag, and turbulence -- with attendant noise and vibration. These conditions are known as stalling (attack angle too steep) and luffing (attack angle too shallow.)



The red squiggles are turbulence, eddies that form when flow detaches.

Wind turbine designers have developed numerous strategies to keep the apparent wind angle correct, which is especially hard given that different parts of the blade are moving different speeds, and to keep lift strong and constant along the full length of the foil. These strategies can be grouped in pairs: Taper and draft, twist and pitch. Near the hub of a propeller-style-turbine, the apparent wind is slower and closer in direction to the true wind; the blade root has a wide chord (breadth) and a fairly deep draft, and it faces more toward the true wind. The blade tip is traveling very fast: too much breadth or 'cup' would create crippling drag, so the blade there tends to be narrower and flatter. The tip also experiences an apparent wind nearly in line with its rotational plane, so it needs very little twist:



Finally, the best HAWTs (horizontal-axis wind turbines) are able to rotate the entire blade to vary TSR, optimize lift, and keep the alternator spinning at its prime electricity-making RPM. They use taper, draft, twist and pitch all at once. Inexpensive turbines like my Bergey XL1 may use straight blades, extruded as if from a pasta machine. They lose remarkably little in terms of efficiency in their sweet spot. But in light or very strong winds, they luff or stall (or some of each!), lose lift, and make ungodly noise.

You may see curved blades appearing on some machines: as with most such innovations, it is worth asking why, and why commercial turbines rely on a straight leading edge. Bending the tip back may keep flow attached and reduce noise somewhat, but the lifting forces pull outward rather than forward, tip spillage and drag is increased, and you are losing torque at the blade ends, right where you most want it.

Finally, it's worth a brief look at why the world's best engineers design HAWTs rather than VAWTs (vertical axis wind turbines). The very worst VAWTs are pure drag machines: paddles pushed by the wind. Their maximum apparent wind is the true wind MINUS their own rotational speed, so they can never go fast and the wind's force is gutted. And two-thirds of the time, a given blade is either contributing nothing or plowing headlong INTO the wind. These generally fall under the heading of Savonius Rotors. Their TSRs are always less than 1.0, and their efficiencies are gruesome.



Better, though not much, is a class of semi-lifting VAWTs classified as Darrius, Modified Darrius, or Gyro Rotors. These include the famous 'eggbeaters' and more modern designs. Almost half the time, their blades are on or near a "beam reach," moving perpendicular to the true wind, which sailors know is the fastest, most-efficient point of sail. But the back blade is operating in the wind shadow of the front one, its draft must somehow be inverted, the downwind blade is dragging some, and the upwind blade is a sea anchor. Darrius blades are pulling maybe 50% of the time. They aspire to TSRs of 2.5; they do spin faster than the wind, but not much.

Finally, look afresh at the humble HAWT, or propeller-style machine. Its blades are purely lifting foils, though they suffer the disadvantage of reduced speed near the hub. They have TSRs of 5-8, usually. All three blades experience the same apparent wind speed and direction all the time. All three are traveling at 90 degrees to the true wind (that ideal beam reach), pulling in the same direction all the time. A HAWT experiences great lift over a 100% power stroke. That's why GE, Mitsubishi, and Vestas build them that way.