What If

I had this thought. Everyone¹ wears these fitness wristband things² now. In the Dresden Files books, Harry Dresden the wizard has a set of magical finger rings which store a little bit of kinetic energy every time he moves his arms. So it’s a tiny bit harder to move them, but not enough that you’d notice, and then he (because he’s a wizard) can release all that energy in one go and use it to do impressive things like punch a car over onto its roof. So, what if you invented a fitness wristband thing which worked like that³ and then you made everyone wear one. Could you use the energy thus accumulated to power the whole of humanity?

We shall leave aside such tedious and boring questions as where all the extra food is coming from to produce this extra energy⁴, how one collects all the energy thus produced and feeds it into the National Grid⁵, and whether the wristband company would bother producing Ubuntu drivers. Treat it as a maths problem.

A trick I picked up from the What If xkcd column is Fermi estimation, which Randall correctly uses to mean that you estimate stuff to the nearest order of magnitude to give yourself a rough estimate of an answer, and I am going to misuse to mean making up a bunch of the numbers because maths is a bit annoying. This means that either I’ll be somewhere roughly within the same area⁶ as the answer (10% chance), or I’ve screwed up some calculation like the number of grams in a kilogram and I’m miles out (90% chance, and feel free to moan at me on twitter if so).

So, basic physics. Raising a 1kg weight 1m requires 10 joules of energy. Let’s imagine that he magic wristband makes moving your arms ten percent harder than it actually is, so when you pick up a 1kg weight and move it 1m it takes you 11J of energy and the extra joule goes into powering humanity so we can stop digging up oil. How much energy do you use moving your arms every day? Well, how much does an arm weigh? An average person weighs about 65kg (it’s around 83kg for men and 70kg for women, but people in the UK are better fed than the world average⁷, and children weigh less⁸). The Rule of Nines⁹ says that each arm weighs about 9% of body weight, as does your head, and legs are 2×9=18%. So an arm weighs about 6kg. I reckon that I move my arm a foot once every 10 seconds or so¹⁰, at a guess (this Fermi thing is great, isn’t it?). So that’s 6kg × 0.3m × 6 × 60 ≅ 650J/hour. There are seven billion people in the world, and everyone stays awake for, let’s say, twelve hours a day¹¹, which means that our energy wristbands would collect somewhere around:

7.125 billion people × 650 J/person/hour ≅ 5×1012 J/h 
                                         ≅ 5×1016 J/year

That’s not actually that bad! 50 petajoules/year of energy just from magic wristbands! Is that enough?

No. World energy consumption figures get disputed a lot, but we are apparently using over 500 exajoules per year. That’s 5×10²⁰ joules, or four orders of magnitude out. That’s not four times as much, that’s ten thousand times as much. That’s the difference between¹² shaking Simon Cowell’s hand and hitting him in the face as hard as you can with a croquet mallet. Dammit. I shall not solve the energy crisis today. Back to the drawing board, I suppose.

1. by which I mean Dan Newns↩
2. I don’t, but Dan is wearing enough for both of us, and a netball team besides ↩
3. how? I don’t know, it’s magic. Imagine that the extra energy is because of friction against the luminiferous aether ↩
4. from Philpotts the sandwich shop, if there’s any justice ↩
5. transmission through the luminiferous aether, clearly; Star Trek did this, they just called it “subspace” ↩
6. by a pretty loose definition of “area” ↩
7. because we have Philpotts ↩
8. because they don’t eat enough sandwiches ↩
9. which I think I picked up from an old Dragon Magazine↩
10. spare me the jokes ↩
11. if they’re lazy, which statistically a few of them must be ↩
12. although not the most serious consequence of ↩