A Sunflower Showed Solar Power Plants How to Arrange Their Mirrors

Look into the face of a sunflower on a summer afternoon and you will see more than a brown disc. The middle is packed with hundreds of tiny florets, each of which will become a seed, and they are laid out in sweeping curves that wheel out from the centre like the arms of a pinwheel. Nothing is wasted and nobody is squashed. It looks like decoration. It is actually a very good answer to a packing problem.

Engineers at the Massachusetts Institute of Technology and RWTH Aachen University in Germany had a packing problem of their own. A solar tower plant is a field of big movable mirrors, called heliostats, all turning through the day to bounce sunlight onto the top of one tall tower, where the heat is used to make electricity. Their test case was PS10, a plant near Seville in Spain, with a tower 100 metres high and more than 600 mirrors, each about the size of half a tennis court.

How the mirrors got in each other's way

At PS10 the mirrors stand in rings around the tower, staggered like seats in a cinema so that every other row lines up. It is tidy, but the researchers found it causes more shadowing and blocking than it needs to: one mirror throws shade on the one behind it, or stands in the way of light that a neighbour is trying to send to the tower. Spreading the mirrors out cures that, but it uses up a great deal of land.

So the team built a computer model that splits every mirror into small sections and works out how much light each one really delivers. Letting the computer shuffle the existing rings closer together saved 10 percent of the land with no loss in efficiency. Then they tried a pattern borrowed from nature.

The sunflower's rule

In a sunflower, the florets follow what mathematicians call a Fermat spiral, and each one is turned by the same amount from its neighbour: about 137 degrees, known as the golden angle. The engineers laid out their virtual mirrors by the same rule, as if the tower were standing in the middle of an enormous flower. The spiral field took up 20 percent less land than the real PS10 layout, and it also cut the shadowing and blocking, so the total efficiency went up rather than down. The work was published in the journal Solar Energy.

• 137° the golden angle between one floret, or one mirror, and the next
• 600+ mirrors in the PS10 field the team compared against
• 10% land saved by tightening the old ring layout
• 20% land saved by the sunflower spiral

What people often get wrong

Many people assume the link between sunflowers and solar power is that the flowers turn to follow the sun. That is not what was copied here. Every heliostat already tracks the sun with its own motors; what the flower offered was a seating plan, which says where to stand and not which way to face. It is also worth knowing that this was a result from a computer model, compared against the layout of one real plant, and not the story of a power station that was dug up and replanted.

Why it matters

A fifth less land may sound modest, but as one of the researchers pointed out, getting even a tenth of our energy from sources like this would need huge areas, so they had better be used well. There is something pleasing about where the answer came from. A plant that lives on sunlight had already found a way to fit the most into a circle, and all anybody had to do was look closely at its face and count the degrees.