Technicalities: Something for Nothing

Parenthetically, Robert mentioned that wingtip turbines — little windmills just behind the wingtips — could capture some of the energy of the tip vortices and return it to the batteries. I soon received an e-mail from a friend who objected that this sounded like some sort of harebrained perpetual-motion scheme. After all, your battery had to supply the energy that moved the airplane and created the tip vortex in the first place; wasn’t this something like charging the battery of an electric car with a rooftop windmill driven by the car’s own motion?

Not quite. The difference is that the turbine in the tip vortex makes use of the rotational energy of the vortex, not that of the forward speed of the airplane. If the tip vortex did not rotate, a tip turbine would be useless; the energy required to drive it would inevitably be greater than the energy it returned. But the rotational energy of the tip vortex is normally lost, like the heat energy in the exhaust of an engine. Just as some exhaust heat can be recaptured by a turbocharger and put to use, some of the energy of the tip vortex can be recaptured by a turbine. Not a lot: At cruising speed, less than 10 percent of energy used ends up in the tip vortex, and only a fraction of that could be retrieved by a turbine of practicable size. So we’re talking about a few percent of cruising power — coincidentally, about what could be saved by winglets. A winglet is, in fact, a sort of one-bladed, nonrotating tip turbine.

Of course, a tip turbine would work for a conventionally powered airplane too. The power required by the electrical system is normally drawn by the alternator from the engine. Using tip turbines instead would save 1.5 cents’ worth of fuel per ampere-hour at current prices (no pun intended) and increase cruising speed by an undetectable amount. (Now you know why you’ve never seen a tip turbine.)

Recoverable energy turns up in surprising places. Sailplanes harvest the energy of the atmosphere by imposing human selection upon air movements whose sum is always zero. They linger in rising air by slowing down or circling, and they hasten through sinking air. This activity normally takes place on a grand scale, with mountain ridges and puffy clouds conveniently signaling veins of lift. But random small eddies in the atmosphere, especially near the surface, can be mined in the same way. What is required is a small, agile sailplane with a low wing loading, a high maximum lift coefficient and a rapid response — provided by an alert pilot or a microprocessor — to air movements. A few of these so-called microlift gliders exist, and they can remain aloft in conditions much too weak for normal sailplanes. Reduced to its simplest terms, the trick is just to pull the stick in rising air and push it in sinking air. In principle, given an airplane of the right characteristics, it is possible to remain aloft as long as the surrounding air continues to stir.

Dynamic soaring is similar. As an activity of radio-control modelers, it has led to some remarkable performances. YouTube videos — disappointing to watch, I’m afraid, because the airplanes are practically invisible and the tennis-match motions of the camera make you seasick — show model gliders circling in the upslope lift of ridges and attaining speeds above 400 knots. Those are extreme cases, requiring a strong wind, a well-placed slope and a determined hobbyist; but dynamic soaring occurs in nature too. The albatross, the sailplane of seabirds, may fly all the way around the world in a month and a half, flapping its wings only for takeoff and landing, and expending almost as little energy in flight as when resting on the ground. It uses two soaring techniques: slope-soaring on the flanks of ocean swells and dynamic soaring.

The albatross’s version of dynamic soaring is to fly a path that zigzags both side to side and vertically, first gliding downwind to gain groundspeed, then turning sharply into the wind and zooming upward. The increase in wind velocity farther from the surface, working against the bird’s inertia, carries it higher than it would rise in a uniform wind and gives the bird back the energy lost in the gliding descent. The albatross’s lift-to-drag ratio, between 20 and 25, is comparable to that of a low-performance sailplane; but the vast, unceasing winds of the southern oceans provide it with an inexhaustible bounty of fuel.

If it seems hard to imagine just how dynamic soaring works, think of a pendulum set up in such a way that at the peak of one end of its swing the bob enters the breeze of a continuously running fan. Each momentary boost cancels the frictional losses of the preceding swing and keeps the pendulum going indefinitely.

One of the more startling examples of reaping power from the wind goes by the initials DDFTTW, which stand for “directly downwind faster than the wind.” It has been the subject of heated debate on the Internet, demonstrating, if nothing else, that what makes things go is not always obvious.

The question is: Is it possible for a device powered by the wind alone to go downwind faster than the wind?

Suppose that you take a small cart — let’s say, for the sake of argument, that it has zero rolling friction — and you put a spinnaker or a square sail on it and point it downwind. It will accelerate until its speed is equal to that of the wind. At that point, an anemometer on the cart would register a wind speed of zero. Evidently it cannot go any faster, because if it did the sail would be blown backward and it would simply slow down again.

Now, suppose that you connect the rear wheels to the front wheels through a simple (and frictionless) transmission, such that the front wheels turn slightly faster than the rear wheels. Will the front wheels pull the cart to a slightly higher speed, once the sail has gotten it up to the speed of the wind?

If you are starting to get a headache, stop reading now.

Suppose that instead of this silly arrangement of wheels moving at different speeds — it reminds me of a boat I built as a child, which had two openings in each side, one to let water in and the other to let it out — you connect the wheels to a propeller. Get rid of the sail and just push the thing up to the speed of the wind. Now what happens?

Of 10 people who have heard of the conservation of energy, nine will reply that nothing happens, because there is no free lunch. The wind can push you only as fast as it can push you. You can’t trick it into pushing you faster.

However, if there is a sailor present, he will point out that it is a well-known fact that a fast sailboat, tacking, can outrun the wind. It will arrive at the end of a direct-downwind course sooner than a balloon. Ice yachts and other low-resistance sailcraft can do even better. They are tacking, that is, traveling at an angle to the wind, so that their sails operate like wings, not like parachutes or spinnakers.

What we may be prepared to believe about a sailboat, however, makes us incredulous when it is asserted about a four-wheel cart whose rear wheels drive a propeller. It looks like a practical joke. But once set in motion by the wind, this contraption accelerates to the wind speed and keeps accelerating past it until it arrives at an equilibrium, that is, a maximum speed. The current record — which is not claimed to represent any sort of absolute physical limit — is 2.8 times the wind speed.

As the writer of a 1,500-word column with only 150 words to go, I am now obliged to resort to the time-honored formula “It is left to the interested reader to analyze ... ”

A hint: All these examples of seemingly getting something from the wind for nothing involve differences in velocity — between ground and air, water and air, or two adjacent masses of air — that the vehicle is able to exploit. They also involve the almost miraculous ability of wings, in one form or another, to multiply force. Wings are like levers: They turn a small force — drag — in one direction into a large one — lift — in another. It’s not quite something for nothing — but it’s one of the better bargains that the natural world has to offer.