20.4 Illumination Engineering, Lighting Design & Photometrics

20.4 Illumination Engineering, Lighting Design & Photometrics

Illumination engineering, photometric laws, indoor/outdoor lighting design calculations, light source technologies, and energy efficiency standards represent core practical topics evaluated on the PRC Registered Electrical Engineer (REE) Licensure Examination. Electrical engineers must design lighting systems that deliver optimal visual comfort, glare control, uniform illuminance, and color rendering while adhering to energy efficiency codes (Philippine Green Building Code and PEC guidelines).

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1. Fundamentals of Photometry & Light Quantities

Photometry measures light in terms of human visual perception (standard CIE eye response curve peaking at $\lambda = 555\ \text{nm}$ in the green-yellow spectrum, where $1\ \text{Watt of monochromatic radiant power} = 683\ \text{lumens}$).

Core Photometric Definitions & Units

Solid Angle ($\Omega$): The 3D spatial angle subtended by a surface area $A$ at radius $r$: $\Omega = \frac{A}{r^2}$ steradians ($\text{sr}$). A complete sphere subtends $\Omega_{\text{sphere}} = 4 \pi \approx 12.57\ \text{sr}$. Thus, a uniform point source of $1\ \text{candela}$ emits $4\pi\ \text{lumens}$ total flux.

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2. Laws of Illumination & Point-by-Point Calculations

Inverse Square Law of Illumination

Illuminance $E$ on a surface perpendicular to light rays varies directly as luminous intensity $I$ and inversely as the square of distance $d$ from a point source:

$$E_N = \frac{I}{d^2} \quad (\text{Lux})$$

Lambert's Cosine Law of Illumination

When light strikes a flat surface at an angle $\theta$ relative to the surface normal, illuminance $E$ is proportional to the cosine of the angle of incidence:

$$E = \frac{I}{d^2} \cos \theta$$

                  POINT-BY-POINT ILLUMINATION GEOMETRY

                    Lamp Source (I candelas)
                              |
                              | \
                              |  \
           Mounting Height h  |   \ Distance d = h / cos(θ)
                              |    \
                              | θ   \
                              v      v
                     -----+-------+-------+----- Horizontal Work Plane
                          O       P
                             x (Offset)

Illuminance Formula for Horizontal Work Plane ($E_h$)

For a luminaire mounted at height $h$ above a work plane, illumination at point $P$ located at horizontal offset distance $x$ from directly below the lamp:

$$d = \sqrt{h^2 + x^2}, \quad \cos \theta = \frac{h}{d} = \frac{h}{\sqrt{h^2 + x^2}}$$ $$E_h = \frac{I}{d^2} \cos \theta = \frac{I}{\left(\sqrt{h^2 + x^2}\right)^2} \left( \frac{h}{\sqrt{h^2 + x^2}} \right) = \frac{I \cdot h}{(h^2 + x^2)^{3/2}} = \frac{I}{h^2} \cos^3 \theta$$

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3. Interior Lighting Design & The Lumen (Zonal Cavity) Method

The Lumen Method calculates the average uniform illuminance $E$ across an interior horizontal work plane ($0.75\ \text{m}$ above finished floor).

Fundamental Lumen Method Equations

$$\Phi_{\text{total, required}} = \frac{E \times A}{CU \times LLF}$$ $$N_{\text{fixtures}} = \frac{E \times A}{n \times \Phi_{\text{lamp}} \times CU \times LLF}$$

where:

• $E$ = target average illuminance (lux, $\text{lx}$).
• $A$ = total floor area ($L \times W$, $\text{m}^2$).
• $n$ = number of lamps per luminaire fixture.
• $\Phi_{\text{lamp}}$ = initial luminous flux output per lamp (lumens, $\text{lm}$).
• $CU$ = Coefficient of Utilization (fraction of lamp lumens reaching work plane, ranging from $0.30 \text{ to } 0.75$).
• $LLF$ = Light Loss Factor (Maintenance Factor $MF$) = $LLD \times LDD \times RSDD \approx 0.70 \text{ to } 0.85$.
  • $LLD$ = Lamp Lumen Depreciation
  • $LDD$ = Luminaire Dirt Depreciation

Room Cavity Ratio (RCR)

The Coefficient of Utilization ($CU$) depends on room proportions quantified by the Room Cavity Ratio (RCR):

$$\text{RCR} = \frac{5 h_{\text{rc}} (L + W)}{L \times W}$$

where $h_{\text{rc}}$ is room cavity height (vertical distance from luminaire mounting height to the work plane).

Luminaire Spacing & Layout Rules

• Maximum Spacing ($S_{\max}$): $S_{\max} \le (S/MH) \times h_{\text{rc}}$, where $S/MH$ is luminaire spacing-to-mounting-height ratio ($1.0 \text{ to } 1.5$).
• Distance from Wall ($S_{\text{wall}}$): $S_{\text{wall}} = \frac{S}{2}$ (or $\frac{S}{3}$ alongside desks).

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4. Light Sources, Color Metrics & Energy Efficiency

Comparison of Commercial Lighting Technologies

Color Quality Metrics

• Color Rendering Index (CRI / $R_a$): Measures how accurately a light source renders item colors relative to natural daylight ($0 \text{ to } 100$). Office work requires $\text{CRI} \ge 80$; inspection areas require $\text{CRI} \ge 90$.
• Correlated Color Temperature (CCT): Color appearance of emitted light in Kelvin ($2700\text{K}$ Warm White, $4000\text{K}$ Neutral White, $6500\text{K}$ Daylight).

Lighting Power Density (LPD) & Green Building Code

$$\text{LPD} = \frac{\text{Total Connected Lighting Power (Watts)}}{\text{Total Building Area } (\text{m}^2)} \quad (\text{W/m}^2)$$

• Philippine Green Building Code Limits: Office Space $\le 8.1\ \text{W/m}^2$, Educational Facilities $\le 9.4\ \text{W/m}^2$, Industrial Plant $\le 10.5\ \text{W/m}^2$.

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Solved Board Exam Examples

Example 1: Point-by-Point Illuminance Calculation

Problem: A luminaire with uniform luminous intensity $I = 3,200\ \text{cd}$ is mounted $4.0\ \text{m}$ above a horizontal floor. Calculate illuminance on the floor: (a) Directly below the luminaire ($E_0$), and (b) At a point $P$ located $3.0\ \text{m}$ horizontally away from the point directly below the luminaire.

Solution:

1. Calculate illuminance directly below the lamp ($E_0$, $\theta = 0^\circ$): $$E_0 = \frac{I}{h^2} = \frac{3200}{(4.0)^2} = \frac{3200}{16} = 200.0\ \text{Lux}$$
2. Calculate slant distance $d$ and angle $\theta$ to point $P$ ($x = 3.0\ \text{m}$): $$d = \sqrt{h^2 + x^2} = \sqrt{4.0^2 + 3.0^2} = \sqrt{16 + 9} = \sqrt{25} = 5.0\ \text{m}$$ $$\cos \theta = \frac{h}{d} = \frac{4.0}{5.0} = 0.80$$
3. Calculate horizontal illuminance at point $P$ ($E_h$): $$E_h = \frac{I}{d^2} \cos \theta = \frac{3200}{5.0^2} \times 0.80 = \frac{3200}{25} \times 0.80 = 128.0 \times 0.80 = 102.4\ \text{Lux}$$

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Example 2: Complete Office Lumen Method Lighting Design

Problem: An open-plan commercial office space measuring $15\ \text{m}$ long by $10\ \text{m}$ wide requires a target average illuminance $E = 500\ \text{Lux}$ on work planes $0.75\ \text{m}$ above the floor. Recessed LED troffer luminaires ($2 \times 20\ \text{W}$ lamps producing $2,400\ \text{lm}$ per lamp) are selected. Given $CU = 0.65$ and $LLF = 0.80$, determine: (a) Total required lumens, (b) Required number of LED luminaires $N$, (c) Proposed grid layout, and (d) Total Lighting Power Density ($\,\text{LPD}$).

Solution:

1. Calculate total floor area ($A$): $$A = 15\ \text{m} \times 10\ \text{m} = 150\ \text{m}^2$$
2. Calculate total required lumens ($\Phi_{\text{required}}$): $$\Phi_{\text{required}} = \frac{E \times A}{CU \times LLF} = \frac{500 \times 150}{0.65 \times 0.80} = \frac{75,000}{0.52} = 144,230.77\ \text{lumens}$$
3. Calculate lumen output per fixture ($2 \text{ lamps} \times 2400\ \text{lm} = 4800\ \text{lm/fixture}$): $$N = \frac{144,230.77}{4800} = 30.048 \implies 30\ \text{Luminaires}$$
4. Propose fixture grid layout ($N_{\text{length}} \times N_{\text{width}}$):
   • Along length ($15\ \text{m}$): $6$ luminaires (spacing $S_L = \frac{15}{6} = 2.5\ \text{m}$).
   • Along width ($10\ \text{m}$): $5$ luminaires (spacing $S_W = \frac{10}{5} = 2.0\ \text{m}$).
   • Total fixtures = $6 \times 5 = 30\ \text{fixtures}$.
5. Calculate connected electrical power and Lighting Power Density (LPD): $$\text{Power per fixture} = 2 \times 20\ \text{W} = 40\ \text{W}$$ $$\text{Total Connected Power} = 30 \times 40\ \text{W} = 1,200\ \text{Watts}$$ $$\text{LPD} = \frac{1200\ \text{W}}{150\ \text{m}^2} = 8.00\ \text{W/m}^2$$

   Conclusion: LPD of $8.00\ \text{W/m}^2$ strictly satisfies the Philippine Green Building Code limit of $\le 8.1\ \text{W/m}^2$.