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Outdoor Lighting and Crime - Amper

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TDU = 0.15 S + 0.5 A + 0.1 V.<br />

The total upward flux reflected from the built environment TRU is the total downwards flux<br />

multiplied by the effective reflectance of the terrain, RT:<br />

TRU = (0.85 S + 0.5 A + 0.9 V) RT.<br />

The total upward flux is<br />

TU = TDU + TRU.<br />

As an estimate of typical conditions, put A = 0.3 S <strong>and</strong> V= 0.1 S. Then the total upward flux<br />

becomes<br />

TU = (0.31 + 1.09 RT ) S.<br />

But the total flux emitted by all sources, T, is given by<br />

T = S + A + V, ie 1.4 S.<br />

Therefore the fraction of total flux that is directed upward, the Upward Fraction UF is<br />

UF = TU / T = 0.221 + 0.779 RT.<br />

As a check, UF = 1 when RT = 1. This indicates, correctly, that with a perfectly reflecting<br />

terrain, all emitted light would eventually travel in directions above the horizontal.<br />

A typical value for RT in a city is about 0.1. This results in 29.9% of the total light being<br />

radiated above the horizontal, consistent with the fraction (1/3) generally thought typical with<br />

present inefficient lighting practices. Of the Upward Fraction in this example, 0.221/0.299 or<br />

74% consists of light directly radiated above the horizontal from the light sources, ie unused<br />

light waste. The remainder is used light waste. This is consistent with the impression that the<br />

light seen in close city views from aircraft at night mostly comes directly from luminaires,<br />

unshielded lamps, undraped windows <strong>and</strong> illuminated signs rather than from illuminated areas<br />

such as paved surfaces, walls <strong>and</strong> vegetation.<br />

If all such upward unused waste light were absorbed by a hypothetical instant installation of<br />

full-cutoff shields (somewhat impracticably including all advertising signs, floodlit structures<br />

etc.), then skyglow would be reduced immediately to 26% of its former value, all else<br />

remaining unchanged. Given that skyglow is typically increasing by about 10% or more a<br />

year, it would take only about 14 years or less for the skyglow to reattain its previous value.<br />

The exponential growth would then resume its increase beyond the level it was at when<br />

interrupted by the full-cutoff transformation. This is why a permanent solution to the<br />

skyglow problem must involve m<strong>and</strong>atory caps on total outdoor light flux or energy use as<br />

well as restrictions on direct light emission above the horizontal.<br />

If the instant shielding introduction were restricted to streetlights, the immediate reduction in<br />

skyglow would be to 0.107/0.299 or to 36%. This would give less than 5 years of respite<br />

from the growth of skyglow. The time would be even shorter if the mean terrain reflectance<br />

were higher than 0.1, eg 4 years if RT = 0.15.<br />

The Upward Fraction is shown in the following table for various values of RT, along with the<br />

ratio of UF to its value for RT = 0.1. This ratio shows how increased values of RT would<br />

increase the upward flux measured by a satellite.<br />

62

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