Tuesday, August 12, 2014
Monday, May 26, 2014
Energy density of a spring (or a "mainspring")
My 2-year-old son loves wind-up toys, and that set me thinking... what is the energy density (the energy per unit mass) of a wound-up spring? After a bit of googling, I have come to the conclusion that this is one of the few questions to which the internet does not know the answer!
Quite a few people have already asked the question.
For example, on the xkcd forum " today I began thinking about mainsprings, the coiled springs typically used to power wind up clocks, watches, etc. While reading up on them I began to notice a trend where articles comment on how much energy they can contain (usually described as "a lot" rather than anything useful.) This led me to try to find a source for the potential energy of a mainspring, something that I've found rather difficult to find." The same question has been asked more than once on physicsforums.
And there must be plenty of experts who know the answer... for example these Birmingham researchers, and about 400 years of clock-making experts, and Trevor Bayliss who made the wind-up radio. I don't know why they are so secretive! :-)
Let's figure out a rough answer to the questionA coiled spring stores energy in the same way as a bent beam. You can read about the energy stored in a bent beam in my lecture on the musical note produced by the "beams" of a marimba or xylophone.
It's interesting stuff, but actually we don't need all that detail to get the answer. The key insights we need are
The energy per unit mass in a bit of the spring that is strained with a strain of ε is
0.5 Y ( ε2 ) / ρwhere Y is the Young's modulus, and ρ is the density.
The stress τ is (roughly) related to the strain by
τ = Y ε
- and the maximum stress you can cope with [in a spring that is to be reused many times] is called the Yield strength, which I'll denote by the symbol τmax.
|Material||Y||τmax||ρ||0.5 (τmax)2 / ( Y ρ )|
|Steel (structural ASTM A36 steel)||200||250||8000||0.005|
|Carbon fibre [.]||230||4000||1600||6.0?|
|Steel (Micro-Melt 10 Tough Treated Tool (AISI A11))||200||5000||7450||2.3|
We can compare these energy densities with those of other energy storage systems featured in my book by looking at page 199. Sadly, the wind-up spring doesn't get close to the energy density of even the worst rechargeable batteries (30 Wh/kg).
[Next steps: quality-assure the numbers in the table, and do a real-world check against the actual weight and actual energy stored in real clock mainsprings.]
Wednesday, November 7, 2012
Monday, July 16, 2012
Working as a Chief Scientific Advisor to DECC put a stop to my course (2009), but thanks to help from my research group, and a volunteer audience, we have recreated the course and put together 16 videos of lectures (plus a little bonus lecture, from a practice session).
These lectures will soon all be available on videolectures.net, and are also available from our local website.
A big thank you for Emli-Mari Nel for leading all the hard work - it is amazing how many things can go wrong with video-making, and Emli-Mari has done a fantastic job of cleaning up jittery video-signals and buzzy audio, and making things work nicely on the videolectures site.
Saturday, December 4, 2010
Monday, June 21, 2010
I'm a crusty old unix user, and I have been using nice old twm as my window-manager for ages (since about 1991). Everything worked nicely through several generations of linux, but eventually last month it was just too much hassle to get things like wireless and ethernet to work, so I gave in and switched to gnome. (Philosophically, it seems a broken arrangement that has wireless and ethernet enabled only when the X-server is working... what if the Xserver is down, and you want to connect to the outside world to install a patch?! What if you want remote users to be able to log in to the machine?)
Anyway, on this page I will note down a few of the niggles I had and how I resolved them.
Niggle 1: which is the window-manager, and why, and how are its settings being configured?
I wanted to restore behaviour to be like my twm set-up; I had a very confusing time, because it seemed along the way I had changed window manager from compiz to metacity (which meant none of the compiz settings were having any effect any more). Where was this choice determined? The answer was that I had at some point switched the Appearance setting to have "no animations", instead of "some exciting animations, oo oo ooh", or "lots of stupid 3-dimensional swishy rubbish", and this silently switches window manager! In order to get the other useful features of compiz (Eg suppressing some window titles), you have to switch back from "no animations" to one of the stupid animation levels.
Then the question is how to switch off all the animations one by one...
Niggle two: window-switching
I used to have my windows on the desktop in a cycle. Then I could use one key to rotate up the cycle, and one to rotate down it. With the default "Alt-tab" way of doing things, the windows get reordered every time you switch windows. This doesn't suit my brain's way of navigating. What's the compiz way of getting a cycle? I haven't figured this out yet.
I have a partial solution...
Under compiz settings -> window management -> application switcher, I have selected under "Bindings"
Next window = Alt-tab
Previous window = Ctrl-tab
Next window (no popup) = F10
Prev window (no popup) = F12
and under "General"
Bring to front NO (but this does not seem to work, see below)
...So Now I can rattle through the windows in one direction with F10 and in the other with F12... except, F10 doesn't leave the order of the windows unchanged. Is this a bug? So actually F10 simply exchanges two windows only.