JamesCronen.com

Wind turbines sit quietly on mountaintops, silently spinning away. Stealing a little bit of the wind’s kinetic energy, these turbines convert the energy the wind imparts to electrical energy. As power generation goes, wind is one of the most environmentally-safe sources we have. There is essentially zero carbon emission, other than that required to make the turbines in the first place.

Last week, a windstorm in Aarhus, Denmark caused the braking mechanism for one particular turbine to fail.

This was the result:

In this particular accident, it’s theorized that one of the rotor blades struck the tower as the turbine whirled out of control. In turn, the entire system was knocked out of balance and the remaining blades disintegrated immediately thereafter. Danish site Jyllands-Posten has an article on the collapse (in English).

Wind turbines that spin too fast are a very bad thing. In order to reduce the rotational kinetic energy, most turbine systems use a braking mechanism to slow the rotors down to a manageable speed. Often, the heat generated as a result of braking is used to heat the tower itself.

To find the rotational kinetic energy of a wind turbine, assume that it’s made up of three slender rods coming out of a central hub. According to windturbines.ca, the mass of a Nordtank 600 kW turbine’s rotor blade is 2,000 kg and the rotor diameter is 43.0 m. We’ll assume that the length of one of the blades is half that, or 21.5 m. Its rated rotational speed is 27 revolutions per minute (though we’ll convert to 2.83 radians/second).

The variable I is known as the rotational inertia; basically, the resistance to rotational acceleration. The variable ω (Greek letter omega) is the angular velocity. We have to calculate the rotational inertia of each blade. We’ll use the formula I = (1/3)mL², where I is the rotational inertia, m is the mass of the rotor blade and L is its length. This makes I = (1/3)(2000 kg)(21.5 m)² = 308,200 kg · m². But there are three blades, each with an enormous 308,200 kg · m² of inertia. The total is 924,500 kg · m²! For reference, the rotational inertia of a bicycle’s tires is about 1 kg · m².

Now that we have the rotational inertia, the kinetic energy is easy. The kinetic energy is one-half of the rotational inertia, times the angular velocity squared (or, speaking math, KE = ½Iω²). Plug in all the numbers above, and we find that the kinetic energy is a whopping 3.7 million joules at rated speed. For reference, this is about the energy of two mid-size cars colliding head-on at 110 miles per hour!

But what about the speed at which the turbine was actually turning at the time of failure? Watching the video, I’ve been trying to count the number of turns per second and it’s really hard. The best I can do is count to 25 as blades pass by the vertical. Since there are three blades, seeing 25 blades means 8 1/3 rotations. I timed it three times and got 3.60 s, 3.53 s, and 3.50 s. Close enough. Take the average of these three (3.54 s) we find that the speed of rotation is about 2.4 revolutions per second, or 14.8 radians per second.

Notice that the energy varies as the square of the speed at which it rotates. If you were to double its rotational speed, this particular turbine would have four times the kinetic energy. In our case, since we quintupled its rotational speed, this turbine’s energy will be twenty-five times its previous value.

The rotational kinetic energy is 101 million joules! This is the same as the energy of a collision in which two cars collide head-on, each one traveling 580 miles per hour. That’s about three-quarters the speed of sound!

I’m glad I wasn’t standing under the thing.

I turned thirty-two a couple of weeks ago. Seeing as this was a major milestone (I’ve turned 0x20!), I figured it was time to get into better shape. I’ve had some chronic back pain the last few months, and when I was undergoing physical therapy the therapists recommended that walking and running would be a very good way to strengthen my back muscles.

The past few days I’ve really gotten into my running. I go to a local park at which during the day music from a local radio station is played over the loudspeaker. Since I’m probably one of the few people in the country remaining that does not have an iPod or other MP3 player for exercising, the music is at least something to take my mind off of the almost-pleasant torture that is running in a circle for a half-hour.

In particular, this radio station prides itself on providing a “safe” listening environment for mothers and their children. There’s nothing wrong with that. The result is that most of the ads are intended towards women. Three times I’ve heard an ad now for a local shopping center chain, Hannaford. The ad describes Hannaford’s efforts to remain environmentally-friendly as they do business.

I don’t have a problem with this. Most companies don’t make much of an effort to be green because there’s no financial incentive. If Hannaford wants to make this a selling point, good for them. As people increasingly see a company’s environmental policy as a reason to go there, there will be an economic incentive for companies to think about the environment as they do business.

Two things struck me as odd, though. First, as the chipper woman in the ad is proud to mention, “Hannaford recycles over one hundred million pounds of waste per year! That’s fifty thousand tons, more than the Titanic!” Fair enough, that’s all correct. I applaud Hannaford’s efforts, but wouldn’t it be more valuable for Hannaford to not waste anything at all? The old adage goes that reuse is better than recycling. It seems a little silly to me to be advertising that you waste a cruise-ship-size mass of junk every year, but whatever. Then again, I also don’t have anything to which to compare that number. Other local chains don’t readily publish their waste amounts, so for all I know the others waste ten times that amount.

The second thing was just plain weird. “By using environmentally friendly lighting, Hannaford saves 24,000,000 kilowatt-hours per year. Those 24,000,000 kilo-… umm, jiggers, *confused pause*, …is enough energy to power two thousand homes for a year!”

I would have loved to be in the ad company meeting where this script was pitched. What good does it do anyone to have the actor fake stupidity, especially when the real information has already been stated?

In the words of H. L. Mencken, “No one ever went broke underestimating the stupidity of the American public.” This may be true, and perhaps it is this guiding principle that Hannaford’s advertising firm lives by.

At best, this ad passively laughs at the science-illiteracy which pervades the public consciousness. At worst, the ad tells its listeners that science is just something for “those eggheads” to do. These small and arguably meaningless words in its monologue tells these stay-at-home parents, mostly moms, that they have no hope of understanding energy or environmental concerns. The messages then being sent from parent to child are that “science is too hard; you won’t understand!” Science is hard, but by making kids disqualify themselves from science from the beginning, they don’t have a fighting chance.

Rather than use this as a teaching moment, the ad company (and Hannaford by extension) continues to propagate the idea that science is for smart men, not everyone. Certainly, science as a career is usually pursued by smart men and women, but science literacy is important for every single citizen of the world.

I applaud Hannaford’s efforts at environmental progress, but certainly they could use some help in educating their listeners. Maybe I’m splitting hairs too much and looking too deeply into meaningless ad banter. Then again, that’s what we old fogies are supposed to do.

Poor Steorn. Their machine wasn’t able to handle the spotlight. Literally.

Sean McCarthy CEO stated that “technical problems arose during the installation of the demonstration unit in the display case on Wednesday evening. These problems were primarily due to excessive heat from the lighting in the main display area. Attempts to replace those parts affected by the heat led to further failures and as a result we have to postpone the public demonstration until a future date.” (link to press release)

While I’m completely skeptical about how this “free energy” is supposably obtained, I still really want to see the demonstration. I’m curious to see what kind of contraption they’ve concocted, and what exactly is so special and ground-breaking about it. Nutty ideas sometimes do lead to legitimate and inventive applications, even though the applications may have absolutely nothing to do with the original idea.

Thought is never a bad thing.

The old adage goes that “there’s no such thing as a free lunch.” This isn’t a bitter statement from world-weary businesspeople, or crusty old government officials. The idea that it’s possible to get something out of money is present in economics, government, mathematics, and especially physics.

In physics, energy is measured in units called joules. Take an apple and raise it from the floor to about belt-level. You’ve now given the apple one joule of potential energy. If you drop it, immediately before the apple hits the ground, it should have exactly one joule of kinetic energy. We know this because of the principle of conservation of energy — the total amount of energy in an isolated system is always the same.

But, I guarantee you — if you measure the velocity of the apple immediately before it hits the floor, and do the calculation to find the kinetic energy of the apple at that point, it will be close to one joule, but slightly less. Where did the extra energy go?

In the case of the falling apple, some of the tiny bit of missing energy has gone into friction. Friction affects everything. In this case, the friction of the air whizzing by the skin of the apple causes the air to heat up a tiny bit. That heat is actually represented as kinetic energy of the air molecules and the apple’s molecules — meaning they, in turn, are moving faster!

Sometimes, the language we use in physics is misleading. Physicists often say that this energy is “lost”. We don’t really mean it’s lost in the sense of “disappeared forever”, just that it’s not exactly where it’s supposed to be. Total energy is still conserved, it’s just that some of the mechanical energy of the apple has been converted to thermal energy in the air.

Some machines are very good at keeping their mechanical energy. Lubricants and low-friction materials can be used to limit the amount of heat produced as parts rub together. However, friction is a fact of life. There are not any two surfaces or fluids in nature that do not produce at least some friction when they rub against each other. Fluids even exert friction against themselves as they flow! This is called viscosity.

Today, a company called Steorn was supposed to demo a perpetual motion machine. So what happened? From their website:

We are experiencing some technical difficulties with the demo unit in London. Our initial assessment indicates that this is probably due to the intense heat from the camera lighting. We have commenced a technical assessment and will provide an update later today. As a consequence, [the demo] will not be open to the public today (5th July). We apologise for this delay and appreciate your patience.

Let’s even give Steorn the benefit of the doubt: if they can produce a perpetual motion machine, then pretty much everything we know about physics, in particular the sub-fields of mechanics and thermodynamics, will have to be thrown out the window.

I doubt it. The idea of the perpetual motion machine goes against just about every observation we’ve made in all of recorded history.

People are still convinced that it is possible to get something for nothing. That is probably one of the defining characteristics of humanity, and unfortunately it’s not about to change anytime soon.

More on the Steorn demo when it actually happens, hopefully very soon.