As the populations of big cities increase, pressure for space is resulting in buildings being built higher and higher, and for streets to get narrower. This combination means that less sunlight can filter down to street level, leaving some streets as shady as a politician’s expenses form.

Having a good supply of sunlight is not just important for tourists keen to top up their tans – being deprived of sunlight can lead to both physiological and psychological health problems.

So a team of researchers from Egypt have developed a special panel to help redirect light from the top of tall buildings into the dark streets below – using a simple mathematical function that most secondary school kids would know.

So, what’s the point?

Is sunlight really that important? Well first of all, the body needs sunlight in order to manufacture vitamin D – and vitamin D deficiency can lead to rickets. Sunlight is also thought to play a role in the body’s natural sleep cycle (circadian rhythm) and a lack of it is thought to lead to seasonal-depression.

So finding a way to direct more light onto shady streets and through windows could help to remedy these problems. In addition, if a good level of sunlight can be redirected late in the day, artificial lights don’t need to come on until later in the evening – saving energy.

What did they do?

The researchers designed a plastic panel based on a simple mathematical function known as a sine wave. They suggest that it can be placed on the edge of rooftops where its special shape can direct light that would normally shine onto the wall of the opposite building down into the street below.

The panel can be specifically designed to suit an individual street, with the exact height (amplitude) and width (wavelength) of each ‘bump’ in the sine wave changed to cause the light to fan out by a different amount. The tilt angle of the panel is also important in capturing as much light as possible.

The researchers used a computer simulation to help design a panel that would maximise the amount of light redirected from the sun from a variety of angles – taking into account the position of the sun in the sky at different times of day and throughout the year.

They then built a 1:10 scale model of a narrow street and fixed their prototype panel to the roof of one of the ‘buildings’. They used a tungsten lightbulb to provide light and measured how much was redirected by the panel into the ‘street’ below.

Did they prove anything?

The scientists claim that the panel could redirect between 40 and 90% of the light that shines on it, depending on the position of the ‘sun’ in the sky. It manages to redirect the light so that rather than shining on the opposite building, it fans out into the street below.

The computer simulations found that it would be most effective at times of the year when the sun is lowest in the sky: in Autumn, they predict the panel will provide the street with more than twice the amount of sunlight it would normally get, and in Winter it would receive more than four times as much light.

So, what does it mean?

The researchers have shown that their panel could work well – in theory. In practice, these panels are likely to be less efficient than in the simulations due to ‘real world’ problems: less light will come through if the panels are covered in dirt or if birds perch on them for instance.

However, it is a simple and, perhaps more importantly, a cheap solution that could be implemented fairly easily. From an engineering point of view, using maths to figure out the best way to capture and redirect the light is quite a neat approach and they have arrived at an elegant solution.

It is a good example of how maths can be used in real life – how it can be used in design and engineering. And maybe in the future it can bring more sunshine to people’s lives.

Original article in Optics Express Apr 2014

All images are open-source/Creative Commons licence.

Credit: DreferComm (First); S I El-Hanawy et al. (Second, Third and Fourth- From original paper); P VanDerWerf (Fifth)

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