Sunday, September 22, 2013

Feel the power!

For my first-year seminar on "Climate & the economy," I wanted to convey the magnitude of our energy use, but in a tactile way.

So I had all of us run up three flights of stairs.

Of course, it was a little more structured than that.

First, we measured a flight of stairs, multiplied by three, and found that we would be climbing about 44.5 feet vertically.

Second, one student "won the lottery" by wearing flip-flops, so she got to stand at the top of the stairs with a stopwatch.

And third, I'd asked all the students to know their weight (more or less)--though I wouldn't be collecting that information.

The purpose of the exercise (and it was literally exercise!) was to estimate our horsepower.

According to the sages at Wikipedia, James Watt popularized the term "horsepower" as an aid to selling his new steam engines--he wanted a way of expressing the power of his machines in terms that his potential customers would have a feel for, so he estimated how hard a horse could work on a somewhat sustained basis and called it a "horsepower."

The modern definition is 550 ft-lbs per second. In other words, if you have a 550-lb weight, how hard do you have to pull in order to raise it one foot in one second. But it would be the same to lift a 225-lb weight two feet in a second, or one foot in half a second. It's all about the relationship between the weight and the speed at which it's being lifted.

So we each got our times and went back to the classroom to work out our horsepower.

Using my numbers as an example, I weigh 160 pounds and it took me 13.9 seconds. So I'd accomplished 7,720 foot-pounds of work (44.5 x 160), and I'd done it at a rate of 512.2 foot-pounds per second (7,720 foot-pounds / 13.9 seconds). And since 1 hp = 550 ft-lb / sec, my estimate of my power output was 512.2 / 550 = 0.93 hp.

I'd read that a healthy adult can produce 1 hp for a short period of time, so my number was plausible. Also, among the 14 of us who volunteered our numbers, the average was almost exactly 1 hp.

So that was the first step. Then we wanted to convert this into more familiar units--specifically units in which we pay for energy, and in which the economy's energy use is tracked.

So the next conversion was into Watts, another measure of power, but one familiar to people because of how lightbulbs are rated. The conversion factor is 1 hp = 746 W, so my power output for those 13.9 seconds had been 0.93 hp x (746 W / hp) = 694 W.

To figure out how much that was worth, we'd have to convert to Watt hours (Wh), which is the amount of energy expended if you work at a rate of 1 W for 1 hour (or 2 W for 0.5 hr, etc.). So we had to know what portion of an hour we'd been working. In my case, it was 13.9 sec / (3600 sec / hr) = 0.00386 hours (not very long).

So my 694 W of power, exerted for 0.00386 hours, was roughly equivalent to 694 W x 0.00386 hrs = 2.68 Wh. Now we're almost at being able to convert that to money.

On your electric bill, you're not charged for Wh, but for kilowatt hours, or kWh. Looking at my bill, my rate is about $0.10 / kWh (you could makea  case for $0.14, but that includes the basic service fee; if I use an additional kWh, it only costs me $0.10).

And since 1 kWh = 1000 Wh, my energy output was 2.68 Wh x (1 kWh / 1000 Wh) = 0.00268 kWh. Then to convert to money, we have $0.10 / kWh x 0.00268 kWh = $0.000268. About 1/37 of a penny!

With one penny, I could buy enough power to lift myself 3 floors, 37 times, or 111 floors. That won't get you to the top of the Burj Dubai, but it's not shabby. Of course, it's not like the electricity would just be lifting you all on its own. There'd have to be an elevator getting lifted along with you, plus a motor to use the electricity, and some losses due to friction and energy transformation.

But allowing for all those things wouldn't change the basic story.
But is that story plausible?

I've rented a Toyota Yaris and found it to be somewhat underpowered. It's top power output is 106 hp. But that's up at 6000 rpm, so let's knock it down to ... 30? ... as an estimate of what it can do on a sustained basis. I mentioned earlier that an average, healthy human adult can produce something like 1 hp, but that's only in short bursts. On a sustained basis--doing significant physical labor over an 8-hour day--a human adult can do work at a rate of about 1/8 hp. So the Yaris, pathetically powered as it is, is still 240 times more powerful than we are.

To take a look at a heavier car, the 2014 Chevy Suburban is rated at 320 hp.

Why is a pedal-powered lawn tractor not practical? Because the mechanical ones run at 10 to 20 hp.

And a Harley may produce 60 hp, which is why this guy:
can leave Lance Armstrong in the dust, even if Lance has all the ... medication he wants.

So yeah, it's plausible that the actual energy needed to lift me as high as the Empire State Building is comparable to the electricity you can buy for a penny.

We carried further with our comparisons of human power output and the quantity and cost of the energy used in our economy.

If a person can work at one-eighth hp for the course of a day, then they can produce 1 horse-power-hour per day, or 746 Wh, which is 0.746 kWh--in other words, something less than 10 cents per day. If you were to work 300 days a year (6-day weeks, 2 weeks of vacation, 15 other holidays), your energy output for the year would be 300 days x 0.746 Wh / day = 223.8 kWh /year. Depending on your electricity price, that's somewhere in the ballpark of $23 or $30 per year.

It's a good thing we don't get paid on the basis of how much physical work we do with our own bodies.

What about the the whole population of the U.S.? Or the whole adult population of the U.S.? According to the 2010 census, there were just under 200 million people in the 18-64 age group, so let's round up to that and account for people in their upper 60s.

If we can get 225 kWh / year / adult, and we have 200 million adults, we could potentially have:
200 million adults x 225 kWh / year / adult = 45,000,000,000 kWh / year.
And that's being generous. But we're almost there; we just have to bring it into line with the kind of units in which national energy consumption is measured, which are quads, short for quadrillion British thermal units (Btu). A quadrillion is a 1 followed by 15 zeroes, so that's a lot of Btu's. On the other hand, a single Btu is a pretty small amount of energy, so it's probably not that big a deal. Let's take a look.

We can learn from that there are 0.003,411,805 million Btu / kWh, so
45,000,000,000 kWh / year x 0.003,411,805 million Btu / kWh = 153,531,225 million Btu / year.
(I had to put the commas in the figure for million Btu/kWh to keep Internet Explorer from linking up with Skype and displaying the number as a telephone connection to somewhere in Spain.)

And since there are 1 billion million Btu in 1 quad, we have
(153,531,225 million  Btu / year ) / (1 billion million Btu / quad) = 0.153,531,225 quads / year.
Roughly speaking, the adult population of the U.S. could do work equivalent to about 0.15 quads per year.

Looking at it from the other end, the energy consumption of the U.S. in 2012 was 2,208.8 million tonnes of oil equivalent (Mtoe). Referring again to, there's 0.03968 quads per Mtoe, so our energy consumption was:
2,208.8 Mtoe x 0.03968 quads / Mtoe = 87.6 quads.
Compared to our potential output of 0.15 quads. That's a multiple of 570 times.

Which might have something to do with why some modern societies are so much richer than 200 years ago ...

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