A pair of designers based in London has raised $200,000 towards developing their design for a gravity powered lamp – GravityLight. The idea is that these can be used in communities where access to electricity is restricted.
As you may remember from our lessons spent running up flights of stairs, gravitational potential energy (Joule) = weight lifted (Newton) × vertical height (metre). So lifting a canvas sack filled with sand or rocks could offer an energy source for a machine.
The Law of Conservation of Energy – “Energy cannot be created or destroyed but it can be changed from one form to another.”
The classic example of a gravity-powered machine is a grandfather clock that uses weights within the cabinet to drive the mechanism (the pendulum just measures out the seconds). This is the promotional video from their website.
.
It looks impressive doesn’t it?
Let’s do a “back of an envelope” calculation. For the purposes of this sum I am going to assume that their machine is 100% efficient. In other words, that it converts all the available energy into light. This is impossible in practice as energy is always lost as sound energy and heat energy due to friction.
How high up will this lamp be hung? I will assume 2 metres. This gives us
the largest fall that the weight can achieve.
How heavy will the weight be? Let’s suggest 10kg. That is reasonably heavy without needing an exceptionally strong structure from which to hang it. It’s about equivalent to 100 standard sized apples.
What is the weight in Newton? Weight is mass (kg) times gravity (approximately 10N/kg on Earth).
10kg × 10N/kg = 100N
How much energy is available to the GravityLight?
100N × 2m = 200J
This is the total energy available to the machine.
How much power does this represent?
Power is the energy released over time and is measured in Watt (W). The manufacturers suggest that one lifting of the weight could provide 30 minutes of light. The standard unit of time is seconds so we must convert 30 minutes into seconds.
30 minute × 60 second/minute = 1800 seconds
I am going to make a big rounding-off here to make the sums easy again and call it 2000 seconds. (This actually represents 33⅓ minutes, so rather more than the manufacturers suggest but this is only an estimate.)
Power (W) = 200J ÷ 2000s = 0.1W
Now that we know the power available, let’s find a light to use with it! Filament lamps are no good because they waste most of their energy as heat and have a tendency to blow after a long period of use. The obvious choice is an LED of some sort (light emitting diode) as they use silicon to convert electricity directly into light. I have found some 0.1W ones on the Internet – but they are tiny.
The next important thing to consider is how much light our LED is going to produce. I have consulted some tables that compare different sources. LEDs are similar in efficacy to fluorescent tubes and produce between 58 – 93 lumens per Watt. (The lumen (lm) is the standard unit of light.) I am going to assume that the manufacturers of the GravityLight have access to state of the art LEDs capable of 100lm/W (to keep the sums easy!)
What is the light output?
100lm/W × 0.1W = 10lm
We can compare different light sources by using a unit called the lux (lx). 1 lux is equivalent to 1 lumen per square metre. What this means is that if the GravityLight is used to illuminate exactly 1m2 then there will be 10lx of useable light. Wikipedia has a table of common lux levels; for example, a full moon on a clear night can be as much as 1 lux. Office lighting needs to be between 350 to 500 lux. 10 lux is slightly less than you would probably expect from a small candle. This is not a useless amount of light but I would have thought less than the light shown in the video.
For me, the most important detail is that all of these calculations require a system that is 100% efficient. In the video the inventors hope to use the money they have raised to “double the efficiency”. This means that the efficiency at the moment must be less than 50% so you can at least halve my final answer to less than 5 lux.
I appreciate that I have hugely over-simplified this problem, but it is often useful in science to make an estimate to help to predict a possible outcome. Perhaps another way to think about it would be to decide what light output you need, work out the wattage needed to produce this and then calculate the current and voltage that the gravity device will need to produce.
What do you think?
Am I missing something?
Comments