[Darksky]Re: FCO streetlight costs vs. regulare Cobra head

[Jan Hollan]

> First, with a flat lens FCO, the angle of incidence between a ray of
> light and the lens affects the distribution and efficiency.  By trying
> to throw the peak candlepower just beneath cut off (in order to light
> the road as evenly as possible), light strikes the lens at a shallow
> angle, reducing the efficiency and therefore candlepower at the long
> angle. You can read about Brewster's angle and critical angle in any
> physics text.  This is the fundamental reason that the drop lens cobra
> outperforms the flat lens FCO and permits wider spacing.

I did not understand the remark on the Brewster's angle at all. What has
it in common with the reflection over 70 degrees (not to speak about
critical angle, as the luminaires are mostly not full of water or even
made as blocks of solid glass)? Up to that angle from nadir, there is no
large difference between flat lens and drop lens. And there is hardly a
perceptible difference below 65 degrees (a decimagnitude in astronomical
terms at most, a value which just very experienced observers are able to
discern, at low light levels common at night).

But then I realized, that the common computations of road luminance at
grazing angles are seriously flawed: the reflected component depends on
the polarisation of the light hitting the road. With no lens, there is
almost no polarisation. With both flat and drop lens, the light is mostly
polarised in such a way, that it reflects less from the road. More enters
the dielectric asphalt or stone grains and is absorbed there.

An interesting point: the standard ies or eulumdat files are not adequate
for computing the luminances, as they don't contain two values for each
direction, one for the polarisation in the plane of incidence and the
other for the perpendicular polarisation. It has never occurred me before.
The effect is not at all negligible, the differences of luminances (e.g.
between no lens and drop lens) in a logarithmic scale for the same road
illuminance are several decimagnitudes probably...

Back to glass transmittance. Below is a table of the amounts of
transmitted and reflected (unpolarised, originally) light through an
almost ordinary glass (almost: it means non-absorbing, which is not the
case). The Brewster angle, where no light of one polarisation reflects off
the glass, is at 56 degrees. (I'd be pleased to know the refraction
indices of polycarbonate and acrylic stuffs, if it's lower, also the
reflection is lower.)

 Per cent of light
 which gets through a non-absorbing layer of glass with n=1.540
 at a given angle of incidence (not considering multiple reflections;
 including them, a bit more gets through)

   angles            transmitted        reflected
 / 1 degree     electric vector         at each
outside inside   perp. along   average  surface
   0.0     0.0   91.4   91.4    91.4     4.4
   5.0     3.2   91.4   91.3    91.4     4.4
  10.0     6.5   91.7   91.0    91.3     4.4
  15.0     9.7   92.1   90.6    91.3     4.4
  20.0    12.8   92.7   89.9    91.3     4.4
  25.0    15.9   93.4   89.0    91.2     4.5
  30.0    18.9   94.4   87.9    91.1     4.5
  35.0    21.9   95.5   86.3    90.9     4.7
  40.0    24.7   96.7   84.2    90.5     4.9
  45.0    27.3   98.0   81.6    89.8     5.3
  50.0    29.8   99.1   78.1    88.6     5.9
  55.0    32.1   99.9   73.7    86.8     6.8
  60.0    34.2   99.7   68.0    83.9     8.4
  65.0    36.1   97.7   60.9    79.3    11.0
  70.0    37.6   92.2   52.0    72.1    15.1
  75.0    38.8   81.1   41.2    61.2    21.8
  80.0    39.8   62.1   28.7    45.4    32.6
  85.0    40.3   34.1   14.8    24.5    50.6

thanks to James Benya for opening an interesting field for thoughts,

jenik hollan