The architecture of light: architectural lighting design concepts and techniques. A textbook of procedures and practices for the architect, interior designer and lighting designer pdfdrive com

Candela value needed = (Illuminance level desired × distance squared) ÷ cosine of the angle
The angle in question is the angle created between the aiming line of the luminaire and a line perpendicular to the surface being lighted as displayed in Figure 20.14.
or
CD = (E × D2) ÷ cosine of angle.
or, if we use the equation to solve for illuminance onto the object, we use this
E = (CD × cosine of angle) ÷ D2
An example of this situation might look like example 3
Point Calculation: Example 3:
Suppose we have an accent luminaire recessed into a 10’-0” ceiling aimed to light a collectible plate resting on a pedestal 3’-0” from the floor. To accent the plate, the luminaire is aimed at an angle. Aiming the luminaire creates an angle of 30 degrees between the aiming line of the luminaire and the line perpendicular to the plate. If we want to illuminate the plate to 100 foot-candles, what kind of center-beam candela value would we need from the luminaire?
Figure 20.14 A point calculation used to determine how to light an object when an aiming angle is involved.
We use the version of our equation that accounts for lighting at an angle
Candela value needed = (Illuminance level desired × distance squared) ÷ cosine of the angle
or
CD = (E x D2) ÷ cosine of angle
We plug in what we know:
illuminance desired
E = 100 Foot-candles
We use simple trigonometry to determine the Distance squared
D2 = 8.1 feet squared = 65 sq.ft. Cosine of angle = cosine of 30 degrees = 0.87
Our solution becomes
CD = (100 FC x 65 sq.ft) ÷ 0.87
Or
Candela value needed = 7471 Candelas.
Through this example we can see that lighting at an angle reduces the effectiveness of the light source immensely. This makes sense when we consider how the geometry affects the shape and size of the piece of light created. Rather than a defined circle or “pool” of light, the aiming angle results in a long, wide “scallop”.
It is important to recognize that this chapter presents simple calculations
that ignore any inter-reflected light. In these situations, it is assumed that all of the light being measured comes directly from the luminaires in question.
Once a designer gets the hang of the basic principles of these two types of
calculations, he/she will begin to gain an instinct for where each can be useful. As mentioned before, it is equally important to recognize where calculations will not benefit the design or help to create a good lighting solution. Calculations are merely tools to support and refine the lighting concepts that one draws up as he/she works through the more graphical and imaginative processes that we now associate with lighting design.
All of the tools we have explored through this section are geared towards
bringing us to a point where we are ready to prepare drawings that will translate our lighting concepts into a constructible project. The visualizing, the articulating, the sketching, the drawing, the describing, and the calculating are all tools to make the job of selecting the appropriate lighting easier. The next logical step is to use all of the creative and calculative input to create the drawings and details that will allow the project to be built.