Most manufacturers of automated lighting provide photometric data showing the throw distance, the beam, and field width as well as the illuminance in lux and foot-candles (fc). (1)
By referencing the chart below (Figure 1), the designer can quickly gauge whether or not an instrument will provide the target illuminance and field width at a given throw distance.
A chart like this will get you in the ballpark, allowing you to select lighting instruments and rough in the lighting positions, but it doesn’t provide photometric data for every situation.
For example, a Martin MAC 2000 Wash fixture with a medium Fresnel lens and the zoom at median (27 degrees) produces an illuminance of 136 fc (1461 lux) at a throw distance of 16 m or 87 fc (935 lux) at 20 m, according to their photometric data provided online. But it provides no information about the illuminance between 16 and 20 m.
You can extrapolate these in-between throw distances if you know the right formulas. Some photometric charts, however, also provide the luminous intensity of a fixture in candelas (cd), from which you can calculate the center beam illuminance any given throw distance.
Figure 1: A photometric chart showing throw distance, beam, and field width as well as illuminance in lux and foot-candles.
For example, in the same photometric chart it says the fixture produces 374,000 cd. To find the illuminance at, say, 18 m, you can use the inverse square law, which says that to find the illuminance you divide the luminous intensity by the square of the throw distance.
You can also find the throw distance to meet your target illuminance if you’re given the luminous intensity.
For example, if the fixture you plan to use for key light produces 250,000 cd and you want a minimum illumination of 1614 lux (150 fc) on stage, then using the inverse square law, you can calculate the maximum throw distance.
From the throw distance you can calculate the trim height using the formula for a right triangle, which is the Pythagorean Theorem (Figure 2).
Figure 2: Right triangle showing sides a, b, and c. The side across from the right angle (a) is called the hypotenuse.
For optimal results we want the key and fill lights to be a maximum of 45 degrees above the horizon. A steeper angle will produce harsh shadows under the eye sockets, nose, and jowls.
For a 45-degree angle of projection, the vertical distance from the subject to the light is the same as the horizontal distance from the subject to the light, as shown in Figure 3. We’ll call this distance X.
Figure 3: Illustration showing elevation, setback, and trim. For a 45-degree projection, the elevation from the target is equal to the setback.
Keep in mind that we have to add the height of the stage and the height to the center of the target to find the elevation distance from the floor to the light. This is the trim height.
Once the throw distance has been determined, we can then calculate the beam diameter at the subject given the beam angle in the photometric data. That will show if we have sufficiently covered the acting area in question.
For example, if the beam angle of a fixture is 24 degrees, then use the formula for a right triangle to calculate the beam diameter for a given throw distance. Figure 22.13 shows the beam and field angles of a fixture. If we draw a line from the fixture to the subject, that’s our throw distance (in feet or meters).
The line also bisects the beam angle and creates a right triangle where the angle closest to the fixture is half of the beam angle, the opposite angle is half of the beam width (in feet or meters), and the last remaining side of the right triangle is the hypotenuse.
Figure 4: By drawing a line from the focal point in the fixture to the subject we can create a right triangle where the near angle is half of the beam angle, the opposite side of the angle is half of the beam width, the adjacent side is the throw distance, and the remaining side is the hypotenuse.
Then we can divide the width of the stage to be covered by the width of the beam at the given throw distance to figure out how many fixtures we need to uniformly wash the stage. If the diameter of the field is too narrow then move the lighting position back.
But remember that the inverse square law says that the illuminance is proportional to the square of the throw distance; a small change in the throw distance results in a larger change in illuminance.
If the diameter of the field is too wide we can choose to leave it or move the lighting position close. If the lighting position is left as is, then the field will be wider than planned, which is okay as long as the light doesn’t spill onto areas where it shouldn’t be.