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 ©



Stage lighting fixture models provide different beam angles and
intensities. Knowing ahead of time which versions to rent for
your production will save trial and error testing. This article
offers information that will enable one to confidently order
the correct fixture for the required beam size at a given
distance, and to grasp the intensity/distance concept.

For those having fixtures, the instructions provided here will
determine, without the trouble of physical experimentation,
the right hang point to attain the required Light Pool size.


Topics  


The Why

Definitions       The Factors     Factor Chart

Examples        Summary         Precision

 

  The WHY

  Why take time to do the mathematics that will be presented
  here in this article? Expanding upon what was said in the
  opening statements will answer this question:

  1.   Identifying ahead of time how your lighting Fixtures will perform
    in a given situation means not having to experiment with hanging
    and rehanging Fixtures; you will already understand where to
    place them and why.

  2.   If you must buy or rent lights for your location, discerning
    which ones to order ahead of time means no disappointments
    after you actually hang those Fixtures.

  3.   When projecting patterns, the Fixtures you have chosen will
    provide exactly the desired image sizes at the selected distances
    because you did the calculations before making those choices.

  4.   By using the information gained from this discussion, coupled
    with the manufacturers' intensity specifications, you will know
    the light level that your Fixture will provide at your required
    distance.

  Remember: Hanging fixtures "on paper" will save much work
  later on. The lesson below explains how to do that.

 

  DEFINITIONS

Throughout this section and the lesson that follows, the
most important terms will be shown as first-letter capitalised.
Synonymously, first-letter capitalised terms will be defined here.

Absolute Diameter
The actual, maximum size of a Light Pool regardless of its edge intensity.

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.

   In Fixtures that allow Flat or Peak Field alignment, the Beam Angle will be affected.

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.

Field
The total area of illumination within the confines of the perimeter of the pool of light as produced by a lighting Fixture.

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.

   In Fixtures that allow Flat or Peak Field alignment, the Beam Angle will be affected.

Flat Field
Alignment of a Fixture's optics (reflector and lense[s]) that produces an even Field of light.

Fixture
The stage lighting instrument (luminaire) itself.

Keystone
As used in this article, it is the smearing of the Light Pool when a Fixture is angled other than straight at, or down to, a surface.

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

Light Pool
For the purpose of this article, the area of light on a surface as provided by a single Fixture. (Multiple fixtures can be combined to form a single, larger Pool, though.)

Light Pool Diameter
The dimension(s) of the area covered with light by a given Fixture at a given distance. It usually corresponds to the stated Field Angle of a Fixture.

Pan
To angle a Fixture horizontally.

Peak Field
Alignment of a Fixture's optics (reflector and lense[s]) that produces a bright spot within the Field of light. This spot is usually central, but may be positioned to be elsewhere in the Field for some purposes.

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 filament if the reflector design does not focus the light rays to a point.

Tilt
To angle a Fixture vertically.

 

  The FACTORS

    After the preliminary discussion below, a chart will display 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.

      That is: What size will the Light Pool be
      with this Fixture this far away?


  or to calculate:

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

      That is: How far away must this Fixture
      be to make this size Light Pool?

    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. (Further discussion is in "A Precision Caveat", father on.)


 

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 Field 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 Light Pool Diameter by the Factor.

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


*  To determine Fixture Angle, divide Light 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.

Remember that Panning or Tilting the Fixture
will affect all calculations because the Light
Pool will be Keystoned (smeared) to one side.


 

  PRECISION

    Now, it may be important for some persons 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 X .018

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

36 X .018 = .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 Fixture Field Angles not represented on the Chart 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 post Light Pool Diameters for each Fixture at a range of Throw Distances typical for that Fixture. This would eliminate the calculation step each time.

A Precision Caveat
    Realise that some Fixtures limit the edge of the Light Pool to an intensity that is higher than the actual 10% Field Angle intensity of that Fixture. Thus, that actual Field Angle intensity is not available. However, the angle stated by the manufacturer will still work for all calculations given in this article because this angle defines the maximum edge of the Light Pool.

    Conversely, those Fixtures that don't limit their light output diameter, may produce Light Pools which edge intensities are less than 10% of the central one. This could be of some concern regarding manufacturers that use the actual Field Angle specification of 10% to represent the edge diameter as opposed to stating an angle that represents its Absolute Diameter. In this case, Light Pool Diameters may be slightly larger than calculated. However, outside that calculated diameter, light intensity is usually so low and levels fall off so quickly, that it won't cause concern for most lighting purposes. If it does, choose a different Fixture for your purpose, or limit the Light Pool Diameter by using accessories such as barndoors, a snoot, or a funnel.


The methods discussed in this article work with all stage lighting
Fixtures regardless of type, manufacturer or model -- as long as
the Field Angle of the Fixture is known. Using the knowledge
gained here will eliminate trial and error when ordering,
hanging, or designing with, any lighting instrument.




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