Calculating Illuminance of a panel light

  1. Hello,

    I would like to build a panel light with four flourescent tubes.
    The tubes have a diameter of 26 mm and are 1200 mm long.
    They have a distance of 42 mm one to another.

    The tubes are mounted on a board, that is covered with aluminium foil as a reflector. Each tube produces a luminous flux of 2340 Lumen.

    I would like to calculate the illuminance in Lux in one meter perpendicular distance of the panel light.

    How can I do that ?

    The result does not have to be perfect – a result within 10 – 20 % of the actual value would be satisfactory.
     
  2. jcsd
  3. My attempt

    An attempt that I made, under the assumption that the light photons spread out evenly from the flouro tubes in all directions:

    1. Direct light from the tubes

    There is the area directly above the board-

    a. 0.32 x 1.3 = 0.416 m²

    then there is the surface area of the four eighth-spheres in the corners, each with a radius of 1 m:

    b. 4 x ( 0.5 x pi x 1²) = 2 x pi = 6.28 m²

    then the surface of the four quarter cylinders alongside the length and width of the board:

    c. 2 x ( 0.5pi x 1 x 1.3 ) + 2 x (0.5pi x 1 x 0.32) = pi x 1.3 + pi x 0.32 = 5.09 m²

    The sum of this surfaces is 11.19 m²

    Only half of the photons radiates directly of the tubes - the other half are reflected by the aluminum foil.

    Thus: ( 2340 Lumen x 4) :2 : 11.19m² = 4680 Lumen : 11.19m² = 418.2 Lux

    That's the direct component , 1m above the board.

    2. The reflected light That are all the photons that bounce off the aluminum foil.
    I assume a reflection rate of 85 %. Again all is evenly distributed in all directions.

    Then the reflection component of illuminance is 0.85 x 418.2 Lux = 355.5 Lux

    Thus the sum of the illuminance of the direct and reflected light one meter above the board is 418.2 Lux + 355.5 Lux = 773.67 Lux

    Do my assumptions and calculations make sense ?

    Regards, Werner
     
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