6.1 Lighting Fundamentals: Photometric Quantities (Lumens, Lux, Foot-Candles, CRI, CCT) and Efficacy

Mastering lighting systems begins with a solid understanding of photometric quantities and the fundamental laws of light behavior. For the Certified Energy Manager (CEM) exam, you must be comfortable calculating both the quantity and quality of light, as well as the efficiency with which electrical energy is converted into visible light.

Essential Photometric Quantities

To effectively evaluate lighting systems, energy managers must distinguish between the light emitted by a source and the light that actually reaches a task surface. The four foundational photometric quantities are Luminous Flux, Luminous Intensity, Illuminance, and Luminance.

Luminous Flux (Lumens)

Luminous flux is the total quantity of light emitted by a light source in all directions per unit time. It is measured in lumens (lm). Think of lumens as the "volume" of light leaving a lamp. When comparing two lamps, the one with the higher lumen output produces more total light, regardless of how that light is directed or focused. For energy managers, lumens represent the raw material provided by a lighting system.

Luminous Intensity (Candelas)

Luminous intensity describes the amount of light emitted in a specific direction. It is measured in candelas (cd). This metric is crucial when evaluating directional light sources, such as spotlights or headlights. A light source may have a relatively low total lumen output but a very high luminous intensity in one specific direction if the light is tightly focused by a reflector or lens.

Illuminance (Foot-Candles and Lux)

Illuminance is the density of luminous flux incident upon a surface. In other words, it measures how much light actually arrives at a specific location, such as a desk or the floor.

There are two primary units for illuminance:

• Foot-candles (fc): The imperial unit, defined as one lumen per square foot ($lm/ft^2$).
• Lux (lx): The metric unit, defined as one lumen per square square meter ($lm/m^2$).

To convert between the two, use the relationship: 1 foot-candle $\approx$ 10.76 lux. For quick estimations, many professionals use a 10:1 ratio. The basic relationship between total light, area, and illuminance is given by the formula:

E = Lumens / Area

Where:

• E = Illuminance (foot-candles or lux)
• Lumens = Total luminous flux striking the surface
• Area = The surface area in square feet or square meters

Luminance (Candelas per Square Meter)

Luminance is the amount of light reflected or emitted from a surface in a given direction. It is what the human eye actually perceives as "brightness." It is measured in candelas per square meter ($cd/m^2$). While illuminance measures light arriving at a surface, luminance measures light leaving a surface towards the observer's eye.

The Inverse Square Law

One of the most important principles in lighting physics is the Inverse Square Law. This law states that the illuminance (E) on a surface is directly proportional to the luminous intensity (I) of the light source and inversely proportional to the square of the distance (d) between the source and the surface.

E = I / d²

Where:

• E = Illuminance (foot-candles)
• I = Luminous intensity in the direction of the surface (candelas)
• d = Distance from the light source to the surface (feet)

This means that if you double the distance from a light source, the illuminance drops to one-quarter of its original value. If you triple the distance, the illuminance drops to one-ninth. This geometric reality explains why high-bay lighting requires specialized optics to deliver sufficient light to the floor level.

Efficacy: The Measure of Efficiency

In the context of lighting, we rarely use the term "efficiency" to describe the conversion of electricity into light. Instead, we use Efficacy. Efficacy is the ratio of luminous flux output to the electrical power input. It is the primary metric energy managers use to compare the energy performance of different light sources.

Efficacy = Lumens / Watt

For example, if an LED lamp consumes 15 watts and produces 1,500 lumens, its efficacy is 1,500 / 15 = 100 lumens per watt (lm/W). Higher efficacy means more light for less electricity. It is crucial to note that efficacy should be calculated using the system wattage, which includes both the lamp and the ballast or driver, not just the lamp wattage alone.

Light Quality: CRI and CCT

Energy managers must ensure that energy-efficient retrofits do not compromise the quality of the visual environment. Two metrics govern light quality: Color Rendering Index (CRI) and Correlated Color Temperature (CCT).

Color Rendering Index (CRI)

The Color Rendering Index (CRI) measures a light source's ability to accurately render the colors of objects compared to an ideal or natural light source (like the sun or an incandescent bulb). CRI is scaled from 0 to 100.

• A CRI of 100 indicates perfect color rendering.
• For most commercial interior applications (offices, schools), a CRI of 80 or higher is required.
• Retail environments often demand a CRI of 90+ to accurately display merchandise.
• Low-pressure sodium lamps, historically used for street lighting, have a CRI near 0, rendering everything in shades of yellow and gray.

Correlated Color Temperature (CCT)

Correlated Color Temperature (CCT) describes the color appearance of the light emitted by a source. It is measured in degrees Kelvin (K). Counter-intuitively, lower temperatures are referred to as "warm" colors, while higher temperatures are "cool" colors.

• Warm White (2700K - 3000K): Emits a yellowish-white hue. Often used in residential, hospitality, and restaurant settings to create a cozy atmosphere.
• Neutral White (3500K - 4100K): Emits a crisp, bright white. Standard for commercial office spaces, classrooms, and retail.
• Cool White / Daylight (5000K - 6500K): Emits a bluish-white light. Typically used in industrial settings, hospitals, and outdoor area lighting.

The Lumen Method (Zonal Cavity Method)

While the Inverse Square Law is useful for point sources, most interior spaces use multiple luminaires. To calculate the average illuminance in a room, lighting designers and energy managers use the Lumen Method (also known as the Zonal Cavity Method).

This method accounts for the total lumen output of the fixtures, the geometry of the room, the reflectances of the room surfaces, and the inevitable degradation of the lighting system over time.

Foot-candles = (Lumens × CU × LLF) / Area

Where:

• Lumens = The total initial lumens of all lamps in the room (Number of fixtures × Lamps per fixture × Lumens per lamp).
• CU (Coefficient of Utilization) = A factor representing the percentage of total lumens that actually reach the work plane. It depends on the luminaire's distribution, the room's proportions (Room Cavity Ratio), and the reflectances of the ceiling, walls, and floor. CU values are typically provided by luminaire manufacturers in data sheets.
• LLF (Light Loss Factor) = A multiplier (always less than 1.0) that accounts for the depreciation of light over time due to factors such as lamp lumen depreciation (LLD) and luminaire dirt depreciation (LDD). LLF = LLD × LDD.
• Area = The total floor area of the room in square feet.

Example Lumen Method Calculation

An office space measures 40 ft by 50 ft (Area = 2,000 sq ft). It is illuminated by 30 LED fixtures. Each fixture produces 4,000 initial lumens. The Coefficient of Utilization (CU) is determined to be 0.75, and the total Light Loss Factor (LLF) is 0.85.

Step 1: Calculate Total Lumens Total Lumens = 30 fixtures × 4,000 lumens/fixture = 120,000 lumens

Step 2: Apply the Lumen Method Formula Foot-candles = (120,000 lumens × 0.75 × 0.85) / 2,000 sq ft Foot-candles = 76,500 / 2,000 = 38.25 fc

The average illuminance on the work plane in this office will be approximately 38 foot-candles. If this falls short of the recommended Illuminating Engineering Society (IES) guidelines for the specific tasks performed in the office, the energy manager would need to specify fixtures with higher lumen outputs or add more fixtures to the design.