Learning curves

My trip to the USA is almost over. I am writing this in Boston airport. The conference has just finished, and I really enjoyed it. It was very informal, as good conferences should be. The chair of one session used this:

to kick off her summary of the applications of the research in her session.

It is a spoof documentary clip from a 70s comedy movie called The Kentucky Fried Movie.

Now science really does have applications. At the conference I learned about what is called a “learning curve“, as applied to solar power.

A learning curve is a simple model for how as the technology for making something develops, more of something is made and the cost comes down. For example, in the 19th century aluminium was so rare and expensive that it was used for very expensive cutlery. Now the technology has advanced, it is made by the ton and is very cheap.

Interestingly, it appears that often the cost is a power law function of production volume; when production doubles the cost becomes a fraction from 80% to 90% of the cost before doubling.

You can see this for solar panels. The plot is about halfway down the page and note that both the x and y axes are log scales. If you plot any power law on a log-log scale graph it looks like a straight line. An example of a power law is the function y = x². You can change the 2 to anything and it is still a power law. Here it is around – 0.2.

If you extrapolate the plot into the future, you see that in a few years it should cost less than 1\$ (61 p) to make a panel that produces 1 W (Watt – the standard unit of power). With energy efficient light bulbs, £15 to £20 can then buy enough panels to light a room.