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Modelling SkyGlow

Street lighting standards

Streetlights are laid out on roads to give maximum uniformity of illumination. There are many commercial layout design programs to optimise this. Each light source unit (luminaire, as they are called), houses a bulb and optical arrangement with weather protection, in principle to direct the light where it is needed. Computer ray-tracing, is used extensively in the design. There is no requirement to light roads, but it if not done, then the council responsible could be liable in the event of an accident. There are standards to be met voluntarily, in the event of illumination being done. Accidents are reduced by street illumination but nowhere near as much as has been reported in the past by the lighting industry, and it very much depends on local traffic density and road layout and circumstances.

Luminaire designs and concerns about sky glow

In recent years there has been a switch from deep orange low pressure sodium (SOX) tube which have very little optical control and no colour rendition, to high pressure sodium (SON) with its broader spectrum pink light, which has a much smaller bulb unit and so can be better optically controlled. Most recently, white light luminaires have been introduced, and the future is in clusters of LEDs . Reflectors are much better in restricting the light beam, than refractors.
Luminaires are often used with polycarbonate shallow bowls for protection. Some designs have flat glass instead which when mounted horizontally provides full cut-off at the horizontal. The assemblies are slightly tilted to the horizontal to prevent rainwater accumulating. Traditionally, lighting manufacturers have promoted shallow bowls, because in principle they offer more uniformity on the road. The lighting industry had been advocating the use of shallow bowl luminaires and their supposed benefits, without rigorous physics justification.
Flat glass has a narrower beam angle as light at extreme angles is reflected off the glass back into the unit rather than transmitted through it. In principle one would need more of these per kilometre for the same uniformity on the road than using shallow bowls, with higher power and maintenance cost. But in practice road junctions and local layout requirements and improved optical design mean there is very little difference.
There is a tendency now to switch off lights where possible late at night in areas of low traffic density to reduce electricity cost. Dimmable luminaires under remote control are starting to be used.
If a light can be seen, it's not doing its job properly. The illuminated area should be seen and not the light itself.

Why model the relationship between skyglow and luminaires

I wrote this mathematical model over eight years, in my own time, in order to understand the physics behind sky glow. I wanted the ability to predict how different luminaire designs could make a significant difference to the night sky and to put physics around the argument of flat glass versus shallow bowls. I also wanted to understand the impact on the night sky of changing from low pressure sodium to white light sources. There are plenty of sky glow models but they are not normally attached to specific luminaire designs.
The conclusions were written in an advisory note for the lighting industry which also influenced the thinking of the Highways Agency, and American lighting industriesl. They had previously not understood light propagation and scattering through the atmosphere, which is important to minimise sky glow. The physics is not too complex, light scattering propagation can be demonstrated simply with a green laser pointer. The scatter is dominantly forwards and backwards at small angles on either side of the beam and never at right angles.

The Skyglow Model

Industry-standard photometry curves for any given selection of luminaire's are read in from a database. RayTracing is performed from the luminaire in all directions that there is photometry data. The data includes all angles from the vertical to the horizontal, all azimuth directions and upwards at all angles.
Reflection off surfaces depends on the roughness, so every surface was considered as a fractional mixture of a reflector with one mirror reflection angle, and a perfect scatterer. The scattered light varies as the cosine of the angle from the normal of the surface, i.e. a projection of the surface area in that direction. The scatter and the reflector have opposite properties and lead to 2 illumination patches on the road from a given luminaire . One patch is the mirror reflection at some angle away from the luminaire (called the mirror point) , and the second patch is the area underneath the luminaire which should be maximally illuminated. Any direct illumination above the horizontal is dependant on the fraction scattered off the ground. Asphalt surfaces are generally only a few percent reflective, while grass and other vegetation is far more reflective and strongly biased towards the green.
The Skyglow model assumes atmospheric conditions for clear nights. For each section of observers viewpath to the sky, the illumination is determined from the direct component from the luminaire and the surface scattered component. For each incident angle the scattering in the view path can be determined from the components of air molecules and aerosols. This is passed through the atmospheric scattering algorithms along the view path, adding all other components to see how much comes back down again for any particular location and view angle to the sky. The amount of scatter seen from the sky is highly dependent on the scattering angle which varies along the view path length from nearest to the light source to well in front of the source (see the sectioned view path length in Model Results). Scattering at shallow angles in the lower atmosphere is mostly by aerosols, water droplets and dust; this is predominantly in the forward direction and slightly in the reverse direction, but never at right angles. It is also not wavelength dependent. The scattering in the upper atmosphere is mostly molecular scattering, this is mostly forwards and backwards and less sideways. This scatter is very strongly biased towards the blue and gives us our blue skies.

Modelling Results

Results can be plotted for a particular distance from the luminaire for all angles always upwards and backwards or for a given angle over a range of distances from the luminaire. These are discussed further below against the diagrams .
The results show that there is a big difference to the effect of Skyglow between luminaire designs. Any direct light to the sky creates much more light pollution than that which is sent down to the road. Only a small proportion of the light which hits the ground is reflected back up to the sky. The light which shines just above or below the horizontal causes the most scattering in the atmosphere and travels the furthest distance. This is discussed further down in the first diagram.
The light which is reflected off vegetation and grass verges also goes to the sky. In this case the amount of light from white light is much higher, as the vegetation reflects green light and absorbs red light.

New standards of luminaire design

The results from this model have caused proposals for new benchmarks in luminaire design. Initially allowing good designs to pass the criterion and the rest fail. This will encourage the lighting industry to design better luminaires with better cut-off angle; and then the criterion bar would be raised. Eventually we would end up with much better designed luminaires with far less light pollution to the sky. I calculated by using full cut-off flat glass, highly directional luminaires for the same level of illumination on the ground we could reduce the light of the sky by a factor of 10, and even more when viewing int the opposite direction to the source of light where back scattering is important.
This would allow the beauty of the Milky Way to be visible in suburban areas. Currently the Milky Way is only visible on the very edges of town and in rural areas and even there, rarely do we see a fully dark sky, as the horizontal propagation from our street lights extends from one town to another.

The stars are far brighter
Than gems without measure,
The moon is far whiter
Than silver in treasure.
-J.R.R. Tolkien (The Hobbit)