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					                                Sports
                              Lighting



Mei, Danny, Jonathan, Karen, and Mike
        MA721 Final Project
  Professor Craig Douglas, Advisor
                                Outline

• Sports Lighting Basics - Mike
• Uniformity Optimization Model - Danny
• Model Results - Jonathan
                               Basics

•   Terminology
•   Lighting Geometry Issues
•   Photometric Data
•   Aiming Diagrams
                               Definitions

• CANDELA, CD: the SI unit of luminous
  intensity. One candela is one lumen per
  steradian. Formerly, candle.
• Luminaire: A general term for a complete
  lighting unit. It includes the housing, the
  reflector, lens and lamps. (Colloquial terms
  include light, lantern, fixture, unit,
  instrument, fitting.)
                                    Definitions
• Lumen: An amount of light energy within an area.
  The lumen is the unit of 'luminous flux' and is
  defined as the amount of light which falls on one
  square metre of a surface at a constant distance of
  one metre from a source of one candela.
• LUMEN,LM: SI unit of luminous flux.
  Radiometrically, it is determined from the radiant
  power. Photometrically, it is the luminous flux
  emitted within a unit solid angle (one steradian) by
  a point source having a uniform luminous
  intensity of one candela.
                                Definitions

• LUX,LX: the SI unit of illuminance. One
  lux is one lumen per square meter (lm/m2 ).
• NADIR: when used in lighting, the point
  directly below the center of the luminaire.
• POINT METHOD: a lighting design
  procedure for predetermining the
  illuminance at various locations in lighting
  installations, by use of luminaire
  photometric data.
                                Definitions

• FOOTCANDLE, FC: the unit of
  illuminance when the foot is taken as the
  unit of length. It is the illuminance on a
  surface one square foot in area on which
  there is uniformly distributed flux of one
  lumen, or the illuminance produced on a
  surface all points of which are at a distance
  of one foot from a directionally uniform
  point source of one candela.
Beam Spread, Wasted Light, and
                        Glare
Mounting Height, Glare, and
                   Ceilings
Shadows
Beam Spread
Football
                                   Football

• Combination of aerial and ground play --
  requires „adequate‟ lighting to 50 feet above
  ground
               Acceptable Uniformity

• “…the ratio of maximum to minimum
  illumination does not exceed 3 to 1…”
• Because: Flying balls appear to accelerate
  on passing from light to dark space --
  player‟s judgement of trajectories distorted
                                                                                Photometric Data
      0   0   0   0   0    0     0     0     0      0   0   0      0        0   0        0   0        0   0        0   0

      0   0   0   0   0    0     0     0     0      0   0   0      0        0   0        0   0        0   0        0   0



80    0   0   0   0   0    0     0     0     0      0   0   0      0        0   0        0   0        0   0        0   0



      0   0   0   0   0    0     0     0     1      0   0   0      0        0   0        0   0        0   0        0   0



60    0   0   0   0   0    0     2     5     6      7   7   6      3        1   1        0   0        0   0        0   0



      0   0   0   0   0    2    21    61     96    107 101 88     33        8   3        0   0        0   0        0   0



40    0   0   0   0   0    9    90    264   380    310 249 209    76    24      8        2   0        0   0        0   0



      0   0   0   0   2   24    172   439   662    555 472 401    156   44      13       4   0        0   0        0   0



20    0   0   0   0   4   64    206   529   967    976 965 821    283   69      19       6   0        0   0        0   0



      0   0   0   0   6   120   208   552   1205   161918321496   420   90      22       6   0        0   0        0   0

      0   0   0   0   6   133   214   558   1255   183221471710   448   96      23       6   0        0   0        0   0

 0    0   0   0   0   6   120   208   552   1205   161918321496   420   90      22       6   0        0   0        0   0



      0   0   0   0   4   64    206   529   967    976 965 821    283   69      19       6   0        0   0        0   0



-20   0   0   0   0   2   24    172   439   662    555 472 401    156   44      13       4   0        0   0        0   0



      0   0   0   0   0    9    90    264   380    310 249 209    76    24      8        2   0        0   0        0   0



-40   0   0   0   0   0    2    21    61     96    107 101 88     33        8   3        0   0        0   0        0   0



      0   0   0   0   0    0     2     5     6      7   7   6      3        1   1        0   0        0   0        0   0



-60   0   0   0   0   0    0     0     0     1      0   0   0      0        0   0        0   0        0   0        0   0



      0   0   0   0   0    0     0     0     0      0   0   0      0        0   0        0   0        0   0        0   0



-80   0   0   0   0   0    0     0     0     0      0   0   0      0        0   0        0   0        0   0        0   0

      0   0   0   0   0    0     0     0     0      0   0   0      0        0   0        0   0        0   0        0   0



          -80     -60      -40         -20              0              20           40           60           80
Aiming Diagram
Aiming in the Field
View from the Top
                                  IES, 1969

• “Calculation methods make it possible to
  pre-determine the foot candle (lux)
  distribution provided by any given aiming
  pattern. However, because such calculations
  are long and tedious, it is general practice to
  base spotting or aiming diagrams … on
  scale plots of the beam spread and the area
  to be lighted, previous calculations, and
  practical experience…”
  Uniformity Optimization Model

• Mathematical Approach
• Diagrams
                                       Mathematical Approach

                                                                     2
                                                   
                                     NumLights       NumLights

   Min       I ij ( t ,t )   I kl ( t ,t ) 
1s NumLights( i , j )( k ,l )                   
      s ,s
               t 1                 t 1


                           I 0 ( ij ( ),  ij ( ))
 where I ij ( ,  )                        2
                                         Dij
 and Dij  ( xij  x0 )  ( yij  y0 )  z0      2               2   2



 where the mast is at (x0,y0,z0).
      Definition Diagram for Angles

                          light


                      


                                         
                          base of mast

where the light                             
is pointing


                                         arbitrary point
                                         on the field
Definition Diagram for Angles
              and Coordinates
          yij  y0
Let q                .
          xij  x0
If q  0 then  ij ( )    tan 1 (q).
If q  0 then  ij ( )  180  tan 1 (q)   .
               1        ( xij  x0 ) 2  ( yij  y0 ) 2   
 ij ( )  tan                                             .
                                                            
                                                           
                                       z0
                                  Results

•   Virtual Field
•   Effects of Grid Density
•   Least Squares Reduction
•   Effects of Luminare Density
Virtual Field
Virtual Field
                             Effects of Grid Density


                    Before                                        After

70                                            70

60                                            60


50                                            50


40                                            40


30                                            30

                                              20
20

                                              10
10

                                               0
 0

                                              -10
-10
                                              -20
-20                                                 0   20   40    60     80   100   120
      0   20   40     60     80   100   120
               Least Squares Reduction

2.70E+01




2.50E+01




2.30E+01




2.10E+01                                       Series1




1.90E+01




1.70E+01




1.50E+01
           0    2   4   6   8   10   12   14
Effects of Luminare Density

				
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