Posts Tagged ‘energy’

Earth to Humans: You’re Doing It Wrong.

April 24, 2012

Here’s my Earth Day article. You may notice it’s late. That’s because I didn’t realize it was Earth Day until a few hours after midnight when somebody said something dumb. Here it is:

The founder of a popular British festival has even said that he would consider powering the event on beer piss, should science find a way. Don’t laugh — human beings collectively produce around 6.4 trillion liters of urine a day, so an effective way of harvesting energy from this golden wonder-fuel might end our fossil fuel dependency overnight, as well as mitigating the effects of one more way we go about polluting the environment.

We do not produce 6.4 trillion liters of urine a day, even on a steady diet of coffee, alcohol, and the vague first-world boredom that leads to a bathroom break every half hour or ten games of Draw Something, whichever comes first. The 6.4 trillion figure is around 250 gallons of urine per person per day. If that were so, your urine would fill two midsize cars every week. At an average flow rate of 20 mL/sec, you’d have to pee for fourteen hours every day to get it all out.

That’s the dumb part – a silly gaffe. But there’s a stupid part, too. You can’t get more energy out of beer urine than you can get out of beer. You can’t get more energy out of beer than you can get out of beer plants. You can’t get more energy out of beer plants than you can get from the sunshine they absorbed. Processing your sunlight by way of a barley seeds, the digestive system of yeast, and a human liver is, as a thermodynamic strategy, piss poor.

Humans are not energy producers. Any energy we output came from our food and represents our bodies’ inefficiency. Only a fraction of the energy we eat can be reharvested, and the energy we eat is about one percent of the energy we use on all our gadgets and things. Measured purely by energy consumption, it’s as if every person in the US has 100 personal servants. Recapturing energy from our bodies is like realizing our 100 servants are too expensive, so we make one of them give us a percent or two of their wages back. That means we can only ever get a miniscule fraction of the power we need from any human activity – urination, generators inside exercise equipment, piezoelectric thingymabobbers in the floor, engines run on body heat, etc.

Even if you crush your enemies and drive them before you, the lamentation of their women will not provide much power.

Why bother, then? Why is there a dance club whose floor generates electricity for lighting as revelers hop around on it? Why don’t they just dance during the day?

Human-generated electrical power could make sense in special circumstances – charging your bicycle light with energy from the bicycle, for instance, but as a general plan it’s insane. The floor in that club is not about generating electricity. It’s very unlikely that the energy generated could ever recoup the cost of the installation – if you exercise for an hour, you’ll generate around a penny worth of electricity, and that’s with high efficiency. Instead, the floor is about advertising that it generates electricity.

This is what we’ve done with energy conservation – made it into a luxury item more about social signalling than ecological benefit. How many people, proud of their environmentally-conscious Prius, have any idea how much energy went into the car’s manufacture? How many of them drive it alone? (Though Prius owners may deny it, the car’s popularity is mostly about social signalling. For cars that come in gas-only or hybrid variants, the hybrids don’t sell well. If it’s not a hybrid-only brand, it’s a lot harder for people to recognize how environmentally-conscious you are.)

No one would tie a helium party balloon to a hippopotamus and say, “See? I did my part to help it fly!” Yet they feel just like that when they bring their own bags to the grocery store. On Earth Day, people turn their lights out for an hour. (Did that happen this year? Or is it some other day? Whatever.) If everyone turned all their lights out in their homes all the time, it would reduce power consumption in the US by about two percent.

The lights-out thing is symbolic, of course. It’s there to remind you of the importance of energy conservation, and to show other people you think energy conservation is important. The problem we’re facing is that everything is symbolic – our efforts at conservation are almost random, showing no systematic effort to focus on the big-ticket items, or even knowing what they are. How many cell phone chargers would you have to unplug to make up for the energy spent on one cross-country plane flight? Most people don’t know, and so most effort put into energy conservation is wasted.

Worse, if you’re conserving energy because you want the warm fuzzies associated with it, you get your warm fuzzies based on how much you inconvenience yourself and how much you show off, not on how much energy you actually save. You feel just as good about unplugging cell phone chargers as deciding to stay local on vacation. Our emotions have no sense of scale.

Even worse than that: when we talk about energy conservation and environmentalism, we’re largely bullshitting, and people pick up on that. That’s the thing with signalling to your tribe. It gets the other tribe pissed off. (And as we’ve learned, piss is not very productive.) The worst part about energy conservation and environmentalism is that they’ve been wrapped up into one issue and shipped off to the place where good debates go to die – politics.

If we could separate our conservation efforts from our warm fuzzies, we’d send out fewer of the pheromones that rile up political associations and drive out even the possibility reasonable discourse. Fewer news stories. Fewer buzz words and applause lights. More Sustainable Energy Without the Hot Air and The Azimuth Project. That is how you get a hippopotamus to fly.

We Need a Power Pyramid

May 22, 2010

You know this thing, right?

Thanks to the food pyramid, which almost all Americans recognize, we basically know what healthy eating is. You can find a lot of bickering about the details. You will even find some nutritionists who claim everything about it is wrong, but they are sensationalists.

It’s not complicated, it’s important information, and basically right. Eat lots of plants, fewer animal products (Don’t hate, vegetarians. “None” is a special case of “fewer”.), and only a little junk food. Most Americans pretty much know what healthy eating is. (Knowing what it is is quite different from doing it!)

I think we need one of these for energy consumption. We seem, as a nation, to be out of touch with the basics on this, and like the food pyramid, it’s important and it’s simple. Everyone should know the basics about energy the same way they do about healthy food.

I recently heard earnest praise of the iPad because by reading books on it, or using it as a scratchpad, it saves paper. That’s true; the iPad saves paper. But remember, homicide cuts down on traffic congestion. So I started trying to calculate which is better on environmental terms – books or iPad. I estimated that reading books sustainably winds up taking a lot more ground space than generating the energy to manufacture and use an iPad. Then I googled and found an article from the New York Times with a similar goal, but its conclusion was that once you read more than a few hundred books, the overall impact of the iPad is significantly less than buying new books. Now what do I do?

I want to use less energy, but it’s irrational to go to all ends figuring out every last thing about doing it. It doesn’t matter which choice I make because the energy involved in using an iPad or reading the books is very low when compared to more significant types of consumption.

When thinking about conserving energy, we are pretty dumb. We spend far too much attention on things that are visible, immediate, and easy to understand, rather than things that are significant. Unplugging your cell phone charger when not in use to reduce power consumption is like going to New Orleans after Hurricane Katrina and helping re-sort someone’s sock drawer.

Magazine articles that calculate the gallons of water saved if you run the faucet for 15 fewer seconds while brushing your teeth are missing the point. Why bother brushing your teeth in tiny little spurts of water from the faucet if you are about to take a hot bath? And a hot bath pales in comparison to watering your lawn. Don’t stop brushing your teeth. Stop watering your lawn.

My calculation about the iPad and similar calculations are dangerous. Even if they’re correct, they encourage us to focus in the wrong direction. There are hundreds of similar minutiae I could worry about. Metal forks or recyclable bio-forks at the cafeteria? Paper or plastic at the supermarket? How much energy do I use when downloading a porno?

To be realistic, you are only going to worry about energy consumption a certain amount. After that, you’ll have to get on with your life. Spend the worrying where it counts. In order to do this, we need to know what counts and what doesn’t.

Take a look at this graphic, for example:

Current consumption per person in cartoon Britain 2008 (left two columns), and a future consumption plan, along with a possible breakdown of fuels (right two columns). This plan requires that electricity supply be increased from 18 to 48 kWh/d per person of electricity. (MacKay's caption)

This is really good – clear and informative. MacKay’s book contains many fantastic charts, plots, and graphics visualizing energy consumption and generation.

This graphic, though, is for people who are reading an entire book about energy. That makes it for a minority. We need something simpler and more iconic, like a food pyramid for energy consumption.

It may also be useful for the graphic to show not total consumption, but how much energy can be saved by cutting back in certain areas. Cutting back in transportation energy is easy and huge potential benefit. That goes on bottom. Turning off the lights is a very small thing by comparison. That goes in a tiny little triangle on top.

One difficulty is that the power pyramid is dependent on the people it’s targeting. Here in the San Francisco Bay area, I use almost no power for heating because the weather is nice. Also, living in Berkeley, a bicycle-friendly city with good public transit, I choose to forgo a car and use very little energy for transportation. Someone living in rural Wisconsin will naturally have a very different pyramid than I will.

We’ve gotten to where most people know that we’re using too much energy, but we have a lot of work to do in consolidating the message. We need a simple, effective, clear image, like the food pyramid, that can be put where people will see it hundreds of times, and burn in the basic idea. As MacKay points out, the slogan “Every little bit helps,” is not this message, and is in fact its antithesis.

July 16, 2009

problem

In determining the damage done to you during a fast collision, probably the most important quantity to consider is the kinetic energy dissipated in your body.

For example, in a perfectly elastic collision, the hammer would have to bounce off you, the way bullets bounce harmlessly off of Superman, leaving his body totally intact.

If you make a rather stupid model of your body as a bunch of point-mass cells connected by springs, but the springs break if stretched past a certain point, then we can consider the number of springs broken to be a measure of the damage to your body. It takes a certain amount of energy to stretch the springs far enough to break, so the more energy dissipated, the more damage.

This isn’t the whole story, of course. For example, if I dissipate the energy of the sledgehammer impact over my entire body, I may not have enough energy density anywhere to break any springs, whereas if I put that same energy in one little place I could break all the springs there. So the cinder block may assuage the damage by spreading things out somewhat.

I think the most important thing the cinder block does is absorb a lot of energy. We can figure out how much by assuming all the collisions are inelastic.

Without the cinder block, all the energy of the sledgehammer is dissipated in your body (your body does not pick up any kinetic energy because the floor you’re lying on keeps it from moving). For a sledgehammer head of momentum $p$ and mass $m$, the energy dissipated is $\frac{p^2}{2m}$.

If the hammer first collides inelastically with the hammer, then the momentum of the hammer and block is the same, so the kinetic energy dissipated is now $\frac{p^2}{2(m+M)}$, with $M$ the mass of the cinder block. This is smaller than before by a fraction $\frac{m}{m+M}$, so that if the cinder block weighs nine times as much as the head of the hammer, then only one tenth as much kinetic energy gets dissipated in your body.

(I seem to have changed the target of the sledgehammer’s wrath from “the professor” to “you”, a somewhat aggressive move I swear was unintentional.)

As for the bed of nails, there’s just a lot of nails. If you can balance on tippy-toes, your contact area with the Earth is down to a few inches, but you can still manage that pressure. If the nails are an inch apart and each one has an area of $1mm^2$ at the tip, you get a few square inches of surface area out of that. By the way, it isn’t easy. It hurts.

Conservation of Energy

February 20, 2009

a continuation of conservation of momentum

note: minor edits to fix sign errors and whatnot 2/23/09

Newton’s second law:

$F = m\frac{dv}{dt}$.

$F - m\frac{dv}{dt} = 0$.

I would like to imagine a new rule about force, which is that as far as any one particle is concerned, force is a function of position alone (not time, except insofar as position changes with time, and not any of the time derivatives of position, and for good measure, not anything else your sick little mind can conceive).

$F(x) - m\frac{dv}{dt} = 0$

I would like to integrate over time to obtain a conservation law, but that would only tell me about the change in momentum. I can make things more interesting if I first multiply everything by velocity.

$F(x)v - m v \frac{dv}{dt} = F(x)v - \frac{1}{2}m \frac{d(v^2)}{dt} = 0$.

Integrating, and selectively choosing to turn one of those $v$‘s into a $dx/dt$, we get

$\int_{t_a}^{t_b}dt \left(F(x)\frac{dx}{dt} - \frac{1}{2}m\frac{d(v^2)}{dt}\right) = 0$.

And so

$-\frac{1}{2}m\left(v(t_b)^2 - v(t_a)^2\right) + \int_{x_a}^{x_b}dx F(x) = 0$

for arbitrary times $t_a, t_b$, with $x_a, x_b$ the locations of the particle at times $t_a, t_b$. The integral of force is over the path followed by the particle between the start and end times.

Defining a function

$U(x) = -\int_{x_0}^{x}dx F(x)$

called the “potential”, we have a new conserved quantity:

$-\frac{1}{2}mv^2 - U(x)$.

We generally multiply this by $-1$ to say instead that

$\frac{1}{2}mv^2 + U(x)$

is conserved. (They’re both conserved, of course. It’s pure convention.)

However, the value of $U(x)$ will vary depending on where we choose $x_0$. This will change the value of the conserved quantity, but will not change the fact that it’s conserved. The new conserved quantity is called “energy”.

Like momentum, it need not be conserved. Again, faulty measurement, problems with Newton’s laws themselves, or variable mass could all be to blame. The existence of extra particles cannot be to blame, because our derivation this time didn’t care about extra particles one way or the other. What it did need was for force to be a function of position alone.

If there are other particles around, they may exert some force on the test particle we’re interested in. That’s fine, but if the other particles start moving, the force they exert will probably change, even if the test particle itself is stationary. That’s anathema. In that case, energy will not be conserved (not for this one particle! It may or may not be conserved for all the particles put together, but that’s something else entirely. We haven’t even defined energy for multiple particles.)

Also, energy may not be conserved if force is a function of time, or of velocity. Those break the assumption that $F = F(x)$. Imagine if the gravitational constant lessened with time. Then the potential energy of the brick you’re holding above your head (you are doing that, right?) is decreasing while the velocity remains zero, and the total energy decreases. On the other hand, a friction force is velocity dependent (it senses the direction of velocity, but not its magnitude. That still counts as velocity dependence.) and does not conserve energy.

An interesting case is again the electromagnetic force. In the derivation of the energy conservation law, we integrated the term $F(x)v$ over time. A velocity-dependent force may be written as whatever force would be there for zero velocity, plus a delta to bring the force up to whatever it truly is when the velocity is present.

$F(x,v) = F_s(x) + F_v(x,v)$.

$F_s$ indicates “stationary force” and is defined by

$F_s(x) = F(x,0)$.

$F_v$ indicates “velocity-dependent force” and is defined by

$F_v(x) = F(x,v) - F(x,0)$.

Then

$Fv = F_sv + F_vv$

As it turns out, in electromagnetism, although the Lorentz force is velocity-dependent, its dot product with the velocity is zero, so

$F_vv = 0$

and

$Fv = F_s(x)v$

so the proof still holds. Energy is still conserved when considering the Lorentz force. Nonetheless, a charged particle that accelerates does not conserve energy! An accelerating particle creates an electromagnetic field that is acceleration-dependent. The particle then interacts with the field it created. So in effect, the force is acceleration-dependent. The assumption $F = F(x)$ fails, and energy is not conserved for the particle. (You might try to define energy of the field, and by doing so with sufficient cleverity retain an energy conservation law, but that’s beyond the scope of the current blog post.)

Such considerations of energy and radiation have historical importance. Before people knew about quantum mechanics, they realized that electrons orbiting a nucleus were accelerating charged particles and should not conserve energy. Instead, they should lose all their energy and collapse into the nucleus of the atom on very short time scales. The electrons gave no sign of doing that, and it was weird. End of history lesson.

We’ve seen the perils of force laws that are not purely position-dependent. Even those force laws that are solely position dependent could fail us. While it would always be true that

$\frac{1}{2}mv^2 + \int_{x_a}^{x_b}dx F(x)$

would be conserved, for many functions $F(x)$ it would be impossible to write down a sensible function

$U(x) = -\int_{x_0}^{x}dx' F(x')$.

The reason is that the value of $U(x)$ might depend on just which path we choose to go from $x_a$ to $x_b$. Maybe there is a highway and some back roads that both go between the two places. A particle takes the highway, integrates the force as it goes along, and gets the value for $U(x)$. The next day it takes the back roads, integrates the force, and gets a different value for $U(x)$, meaning that the function is not well defined.

Notice that if the function is well-defined, then the highway and back roads must have the same integral of the force. So if you go from A to B by the highway, and then go backwards from B to A on the back roads, the two integrals must cancel each other out, leaving you with zero total integral for the entire trip. This means that the function $U(x)$ will be well-defined whenever all closed path integrals of $F(x)$ come to zero. When we make those path integrals really tiny we write this as

$\nabla\times F(x) = 0$.

next time: energy of multiple particles