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    Re: Nav light colors and ranges
    From: George Huxtable
    Date: 2003 Oct 17, 16:00 +0100

    Jared Sherman said-
    >The candela is the luminous intensity, in a given direction, of a source
    >that emits >monochromatic radiation of frequency 540 x 1012 hertz and that
    >has a radiant intensity in >that direction of 1/683 watt per steradian.
    Presumably, that was intended to read 540 x 10-to-the-power-12 Hertz:
    anyway, it's not very helpful to an understanding of the brightness of our
    nav. lights. If you think of a candela as being, roughly speaking, the
    brightness of 1 candle, you get a rather clearer picture, which is good
    enough for most purposes.
    Jared goes on to say-
    >The steradian of course will be instantly recognized by all list members.
    >It allows for a detection instrument which is placed xx meters away from
    >the light source with an specific area of the light source being read,
    >i.e. if a cone of light from that light source is allowed to form a
    >circular area on a sphere xx meters away from that light source, the
    >brightness of that circular area can be tightly defined and measured,
    >requiring nothing more than placing a special light meter next to the lamp
    >which is to be measured.
    Jared's definition of a steradian, here, is quite incomprehensible to me,
    though that could be my fault rather than his.
    Trevor Kenchington seemed to concur-
    >Not sure about your explanation of a steradian either. From unaided (and
    >so unreliable) memory, it is the 3-dimensional angle swept out by
    >rotating a 2-dimensional angle of one radian. A nice unit for a formal
    >definition of a candela but not, I would think, very relevant to the
    >actual measurement of the brightness of a light.
    Unusually for him, Trevor's memory has let him down here. The steradian
    isn't defined that way. If we have a sphere 1 metre in radius, and draw a
    cone from its centre that intersects its surface, and encloses an area of 1
    square-metre of that surface, then the solid-angle of that cone is 1
    steradian. It could be applied in the same way to shapes other than the
    cone, such as a pyramid. In the case of a cone, my own calculation (so it
    could well be wrong) indicates that it would require a half-angle (i.e.
    between its axis and its edge) of 32.8 degrees; very different to what
    Trevor suggested.
    Because, as we learned at school, the area of a sphere is 4 x pi x (r
    squared), there are 4 x pi, or about 12.5, steradians in a complete sphere,
    which is the biggest solid-angle that's possible. The lumen is the amount
    of light that passes through a square meter at a radius of 1 meter from a
    standard candle (candela): that is, in one steradian. Presuming that a
    candle emits, roughly speaking, the same amount of light in all directions,
    then a candle emits altogether about 12.5 lumens.
    The lumen is an example of an original unit that was tinkered-with
    ("rationalised" was the word then used) in order to avoid such factors as
    4pi being necessary in some calculations. Unfortunately, this implied that
    a factor of 1/4pi often became necessary in other calculations, and added
    much confusion, which persists to this day. It may be best to ignore lumens
    for our purpose here.
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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