Atlantic Illumination Entertainment Lighting

AIEL Instructional

STAGE LIGHTING FIXTURE
CALCULATIONS

Ways to Determine Fixture Angles, Throw
Distances, and Light Pool Diameters as
Correlate to Any Stage Lighting Fixture


THE FOLLOWING MAY NOT BE REPRODUCED
WITHOUT PERMISSION FROM THE AUTHOR ©



Topics  


Definitions       The Factors     Factor Chart

Examples        Summary         Precision

 

  DEFINITIONS

Throughout the lesson that follows the definition section,
the most important terms will be first-letter capitalised.

Beam Angle
Light emanating from a fixture that spreads outward to a perimeter which is at 50% of the highest central intensity denotes the Beam Angle. For some PAR lamps or lensed fixtures with inconsistent central brightness, the chosen intensity figure may be an average of several points. This middle number is then used to determine the Beam Angle.

Field Angle
Light emanating from a fixture that spreads outward to a perimeter which is at 10% of the highest central intensity denotes the Field Angle. For some PAR lamps or lensed fixtures with inconsistent central brightness, the chosen intensity figure may be an average of several points. This middle number is then used to determine the Field Angle.


Factor
A number provided on this webpage that is based upon a fixture's Field Angle. This number can be used to calculate a fixture's Throw Distance and the dimension(s) of its Light Pool at that distance.

Fixture
The stage lighting instrument (luminaire) itself.

Light
As used in this article, it refers to the visible radiation emitted by a stage lighting fixture.

Light Pool
The light on a surface as provided by a single fixture.

Light Pool Diameter
The dimension(s) of the area covered with light by a given fixture at a given distance.

Throw Distance
In practical usage, it is a measurement of the length of an imaginary line drawn from the center front of a fixture to the center of the Light Pool as projected onto a given surface.

   For absolute purposes, this measurement is taken from the external focal point of a fixture's lens system. With lensless fixtures, it is measured from the reflector's external focal point, or from the lamp face if the reflector design does not focus the light rays to a point.

 

  The FACTORS

    The chart displayed below gives the multiplication/division Factor
corresponding to a fixture's Field Angle. Use this number to calculate:

(1) The dimension(s) of the area covered by the light emitted
by a fixture with a given Field Angle at a given distance.

  or

(2) The Throw Distance needed to create a pool of light
of a specified dimension using the Field Angle of a given fixture.

    These Chart Factors are very accurate for fixtures that produce an even amount of light and are shining straight on to a wall, or straight down to a floor. If the fixture is tilted or panned, the light will spread out making a larger (and also dimmer) pool of light; so the results of using these Factors become less accurate as a fixture tilts or pans away from straight on. They are also less accurate for fixtures that project an uneven light.

    Even when accurate though, other criteria come into play such as ill-defined Light Pool edges, and spill coming from the fixture itself. Another is that some Light Pools will be wider than desired because the actual edges fall outside the 10% threshold used by manufacturers when determining the Field Angle specification. The latter is most often seen with the PAR lamp and fresnel fixture. The perimeter of light that falls below 10% becomes most noticeable when only one fixture is used, and it's classed as "spill" when it is unwanted.


 

Multiplication/Division Factors
for Stage Lighting Fixtures

Use Field Angles
for Calculations

  ANGLE:    5°   10°   15°   20°   25°

 FACTOR:  .09   .18   .27   .36   .45



  ANGLE:   30°   35°   40°   45°   50°

 FACTOR:  .54   .63   .72   .81   .90  



  ANGLE:   55°   60°   65°   70°   75°

 FACTOR:  .99   1.08  1.17  1.26  1.35



  ANGLE:   80°   85°   90°   95°  100°

 FACTOR:  1.44  1.53  1.62  1.71  1.80

    Directly Proportional:  Studying the chart above will show that the relationships among the Factors are in direct proportion. So if one doubles the Fixture Angle, the Factor also doubles, and vice versa. This also means that for the same Throw Distance, the Light Pool doubles in dimension(s) every time the Fixture Angle doubles. In addition, with a given Fixture Angle, doubling the Throw Distance results in a Light Pool that also doubles in dimension(s).

    Options:  So if one needs to illuminate a space with twice the dimension(s), one can either double the Throw Distance by moving the same fixture farther away, or keep the fixture's position the same, but exchange it for one rated at double the angle.

    Lower Light Levels:  Related to the above, it should be realised that when doubling the Light Pool dimension(s), the area covered will quadruple. As an example, 2 X 2 metres encompasses 4 square metres; doubling this to 4 X 4 metres will then encompass 16 square metres. Four times the area now covered means that the light intensity will be reduced to 1/4. This is because the same amount of light projected by a given fixture will be spread out to take up four times the space.


 

  EXAMPLES

    Light Pool Diameter: To find what the diameter of the light projected will be at a distance of 5 metres when shining a 25-degree ellipsoidal straight on to a surface:

5 X .45 = 2.25 metres

    The Light Pool in this instance will be 2.25 metres wide. This figure is derived by using the Factor taken from the chart for a fixture with a 25-degree angle. The Throw Distance has been multiplied by this Factor to get the Light Pool dimension.

    To find out the approximate dimensions of an oval projected by a PAR 64 `FFR' lamp at the same distance, one must use two Factors because the PAR lamp light output is not round. From the Field Angle specifications for this lamp (21 X 44 Degrees), and assuming that the barrel of the PAR fixture does not compromise the light emanating from it by cutting off part of that light:

5 X .36 = 1.80 metres
5 X .81 = 4.05 metres


    This time, the Factors taken from the chart are for the Field Angles closest to the FFR lamp's specified angles of 21 and 44 degrees. Thus, the Chart Factors associated with `20' and `45' degrees were used to get the approximate oval dimensions projected by an FFR lamp at a 5-metre Throw Distance.

    Throw Distance: At what point will a 25-degree fixture project a 2.25-metre Light Pool diameter?

2.25 ÷ .45 = 5 metres

    Here, the desired Light Pool dimension is divided by the Factor for a 25-degree fixture. This is to calculate at what Throw Distance the fixture will need to be positioned to achieve that 2.25-metre Light Pool.

    Fixture Light Angle: What happens if you know the Throw Distance and Light Pool dimensions, and want to know which fixture to employ? Using the same 2.25-metre diameter Light Pool projected from the same five-metre Distance, as in the first example, this formula will answer the question:

2.25 ÷ 5 = .45 factor

    Referring to the Chart shows that Factor `.45' corresponds to a 25-degree fixture.

 

SUMMARY

*  To determine Throw Distance, divide Pool Diameter by the Factor.

*  Doubling the Throw Distance will double the Light Pool Diameter.


*  To determine Fixture Angle, divide Pool Diameter by the Distance.

*  Doubling the Fixture Angle will double the Light Pool Diameter.


*  To determine Light Pool Diameter, multiply Distance by the Factor.

*  Doubling the Light Pool Diameter will quadruple the area covered.

*  Doubling the Light Pool Diameter will drop the light level to 1/4.


 

  PRECISION

    Now, it may be important for some to have accuracy for the fixtures in their inventories that have angles which lie between the Fixture Angle numbers shown on the chart. One can calculate the Factors for such fixtures by doing the following:

Fixture Degrees ÷ 10 X .18

    Thus, for a fixture with a manufacturer's stated
angle of 36 degrees, the Factor will be:

36 ÷ 10 X .18 = .648 factor

    Notice that this result falls between the Factors shown on the chart for 35- and 40-degree fixtures, as it should. Factors for which Field Angles are not represented could be calculated and then added, but a better method is to print out only the Factors for fixtures in one's own inventory. This could be posted wherever it might be needed. A further improvement would be to also show Light Pool diameters for each fixture at a range of Throw Distances typical for that fixture. This would eliminate the calculation step each time.


The preceding works with any stage lighting fixture regardless
of type, manufacturer or model -- as long as the field angle
of the fixture is known. Using the knowledge gained from
reading this article will save trial & error when ordering,
hanging, or designing with, any lighting instrument.




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