Green light produces purple - no, red! - faces

Here's something that looks like a wonderful idea - Gravia, a swish, elegant human-powered room lamp that gives four hours of light equivalent to a 40 watt light bulb. All you have to do is move a weight from the bottom of its 1.2 metre long case to the top and it gently falls, powering a dynamo that powers the high-efficiency LEDs in the base. Just like winding a grandfather clock says architect designer Clay Moulton, which can be seen as soothing, even ritualistic.

Fantastic. The report goes on about how it all works and how wonderful it all is, but it's missing one key piece of information. Let's see what that is, why they might have omitted it and what it means for you, the environmentally-aware light fan.

Now, LEDs are more efficient than incandescent light bulbs: in this case, it's safe to say that they'll be around four times more. So they'll need ten watts of energy to create the same light as that forty-watt bulb they're replacing - and ten watts of energy for four hours? Why, that'll be forty watt-hours, thank you very much.

And where does that energy come from? From the falling mass of course, dummy. And how heavy would that weight be? That's funny, the publicity doesn't say. Still, science will save us.

The maths is fairly simple, but I'll save you the calculations (well, I'll put them at the end of the article, so you can check my workings and tell me where I get it wrong), but it comes out that you need around fourteen kilos falling through 1.2 metres to make 40 watt-hours. That's about 30 pounds. Ouch. [UPDATE - I got it wrong. Absolutely, fabulously, hilariously wrong. See later for why and how]

But wait, there's more. Even good dynamos only work at around 60 percent efficiency - let's forget friction and other factors in this particular design - so we're actually looking at around 24 kilos or over fifty pounds. Getting on for twice your baggage allowance on that flight to Malaga.

Which you'll have to lift through 1.2 metres every time you want to turn the light on. You'll note the lack of winches or handles in the swish industrial design to help you in this task - at least you'll be able to see the phone to call the ambulance.

Still, nice idea. Let us know when you've changed the laws of physics to make it more standard lamp, less gym equipment.

(OK - those calculations.

The LEDs are quoted at 600-800 lumens, and good high-brightness LEDs tend to run at somewhere under 100 lumens/watt, hence the 10 watt figure. 10 watts over four hours are 40 watt-hours; one watt hour is 3600 joules, so we need to get 144 kilojoules out of the weight.

The potential energy in a mass under gravity is given by Pe = m x h x g, where m is the mass, h is the height of the mass above the ground, and g is acceleration due to gravity. Reworking that to give us the mass, we get m = Pe/(hxg), or 144000 divided by (1.2 x 9.8), which is as near to 14000 grams as makes no difference.

And 14kg divided by the 0.6 efficiency of the dynamo gives us 24 kilos or 50 pounds. Strike a light!).

[UPDATE:

It turns out that my calculations agree with those of the designer, who specifies 5 x 10lb weights. Spiffing.

Only we're both wrong. What I forgot, and I suspect he did too, was that the SI unit of mass isn't the gram, it's the kilogram. So all my calculations are out by 1000, and the weight needs to be...

TWENTY FOUR TONNES

... as pointed out by Bernde Eggen and Michael Saunby at the Met Office in Exeter.

At which point, the idea goes from the faintly silly to the utterly, utterly jaw-droppingly impossible. Even if you're Mr Incredible, the only light you'll see if you try to use one of these is that coming from the flat below where your floor and their ceiling has a nice round hole punched into it.

I should have remembered more of my schoolboy physics, most notably the rather pleasing facts that the work done by force of one newton over one metre is one joule - and on the Earth's surface, an apple exerts roughly one newton due to gravity. So if you drop an apple by a metre, you'll get a joule.

This light needs 240 kilojoules. Which is what you'd get if you dropped 240,000 apples over a metre.

So if you can imagine quarter of a million apples in the corner of your room... you can imagine this light. Cor. ]