## Saturday, 17 March 2012

### How much energy does scrolling a mouse-wheel produce?

I've seen this image a few times in the last couple of days, and because I'm avoiding writing a research essay on Old English literature I thought I'd work out just how much energy scrolling a mouse-wheel actually generates.

The first thing to do is to work out how many times I scroll my mouse-wheel in a given period of time. To do this, I downloaded the Mousotron 7.0 from BlackSunSoftware, which records the number of mouse scrolls you make, along with a huge amount of other mouse-related data. I then tried to replicate an average use of my computer: I read Cracked.com; checked the news; replied to some emails; and did a little bit of work on my game. I also counted the number of mouse scroll 'clicks' (you know what I mean: the little bumps the wheel makes as it rotates) that were required to make a full rotation. I did this by putting a little highlighter ink on part of the wheel, and then counting the clicks as I rotated it. For my mouse, a Razor Naga, it took 24 LED-illuminated clicks before the highlighter ink reappeared.

After almost an hour of mucking around I stopped procrastinating and looked at the counter:
After 56 minutes the scroll-count stood at 1317, which is 54.875 full rotations - about 1 a minute, or 0.102 rad/s (1rps = 2*pi rad/s). Of course, I don't know if this is a usual figure for everyone, but, as I say, it was a pretty usual hour of slacking for me.

From here on I'm going to be showing my calculations in WolframAlpha, because that gives people a good way to check my maths. So, first of all, rotational kinetic energy:
This requires us to calculate the moment of inertia and the angular velocity of the mouse-wheel. The moment of inertia is
and uses the mass of the mouse-wheel and its radius. The diameter of the wheel is is almost exactly an inch, so the radius would be 0.0125m. I'm not really in the mood to dismantle my mouse to work out exactly what the mass is, but I'm guessing around 5g: a UK 2p coin is about 7g and has approximately the same diameter. It's thinner, but is also made of copper while the mouse-wheel is made of some kind of rubbery plastic. The width of the wheel is about 1cm. Therefore the moment of inertia is about 3.9 gcm2.

Therefore the rotational kinetic energy generated by the mouse-wheel in a second is 2.0567*10-9 J, or about 2 nanojoules. If we scale this up to an hour, that's about 7.4 microjoules, or the energy a mosquito needs to fly for about 46 seconds. To put that in perspective, my mouse requires about a quarter of a Watt to function: that's 0.25J/second, which is around 36,000 times more energy than the mouse-wheel produced in an hour of web-browsing.

Another example: if 9gag.com gets 5.5 million visitors per day, and each of those visitors spends a whole hour on the site, then the scrolling each day would generate around 40J, enough to power my mouse for two minutes and 40 seconds.

In conclusion, therefore, the energy used by scrolling the mouse-wheel is at best utterly insignificant. Yes, I'm aware that I'm missing the point.

Of course, these are all rough estimates. It's also worth noting that I've assumed a perfect conversion from kinetic to electrical energy, ignoring any inefficiencies that would boundless be present in the kind of tiny generator one would have to fit into a mouse to make this work at all. As far as I remember bike dynamos are around 80% efficient at best - I have no idea what kind of efficiencies are possible on such a small scale.