11. Lighting Calculations

Principle

Lighting design calculations ensure that sufficient illumination (measured in lux or foot-candles) is provided for a given space while optimizing fixture placement and energy usage. Two primary methods are used:

  • Lumen Method (Flux Method): Used for uniform general lighting, this method calculates the average illuminance on a horizontal plane by using the lumen output of lamps, room characteristics, and various light loss factors.
  • Point-by-Point Method: Based on the inverse square law, this method calculates illuminance at specific points from each luminaire and is useful for directional or accent lighting.

The main goal is to meet recommended lux levels for tasks—for example, an office may require 500 lux on workplanes while a corridor might require only 100 lux.

Lumen Method Calculation

The widely used formula for the lumen method is:

Eavg = (N × F × UF × MF) / A

where:

  • Eavg is the average illuminance on the working plane (lux),
  • N is the number of luminaires,
  • F is the luminous flux per luminaire (in lumens; product of the lamp's lumens and the luminaire efficiency),
  • UF (or CU) is the utilization factor—the fraction of the lamp lumens reaching the work plane,
  • MF is the maintenance factor (accounting for lamp lumen depreciation and dirt), and
  • A is the area (in m²) to be illuminated.

For example, suppose you have a room of 100 m² that requires about 500 lux. If each fixture provides 4000 lumens, with an estimated UF of 0.6 and MF of 0.8, the number of fixtures required is:

N = (500 × 100) / (4000 × 0.6 × 0.8) ≈ 26 fixtures

In practice, you might round this to 24 or 28 based on the desired grid layout. Using 28 fixtures may result in a slightly higher average lux than the target, which is typically acceptable.

Point-by-Point Calculations

For task-specific or uniformity checks, the point-by-point method calculates the contribution of each luminaire at a particular point. A common formula used is:

E = (I / d2) × cosφ

where I represents the luminous intensity (in candela), d is the distance from the luminaire, and cosφ accounts for the angle of incidence. In many modern designs, specialized software performs these detailed calculations using photometric data.

Niche Calculations

  • Daylighting Contributions: Calculation of daylight factor or daylight illuminance using window sizes, transmittance, etc., can reduce the reliance on artificial lighting.
  • Emergency Lighting: Ensures that even during power outages, the escape routes receive the minimum required lux (e.g., around 1 lux on the floor). Point-by-point calculations are often used to verify the darkest spot meets the criteria.
  • Sports Lighting: In settings like stadiums, detailed point calculations ensure uniformity and minimal glare. For example, requirements might include 800 lux horizontal and 500 lux vertical (for camera use) with a uniformity ratio above 0.7.
  • Horticultural Lighting (PAR): Similar concepts are used but focus on photosynthetically active radiation (PAR) rather than lux.
  • Colored Lighting and Luminous Efficacy: When using LED fixtures with specific spectral outputs, converting lumens to lux (weighted by human eye sensitivity) becomes important; alternate metrics may be used for plant growth applications.

Industry Relevance

Proper lighting levels are essential for safety, productivity, and comfort. Insufficient lighting can cause accidents or eye strain, while over-lighting wastes energy and can create glare. Standards such as the CIBSE Lighting Guides (UK) and the IES Lighting Handbook (US) specify recommended lux levels for various spaces. Additionally, building codes and energy regulations (like ASHRAE 90.1 or UK Part L) impose limits on lighting power density (W/m²), driving designers to optimize fixture efficiency and incorporate controls like occupancy sensors or daylight dimming.

Maintenance Factor (MF)

It is crucial to account for lamp lumen depreciation (LLD) and luminaire dirt depreciation (LDD). For example, LED lights might have an L70 rating (meaning they maintain 70% of their initial lumens after 50,000 hours). Designing for “end-of-life” illuminance might involve using an MF of 0.8 (with an initial install at MF = 1.0). Depending on the maintenance schedule and cleaning frequency, MF values can vary.

Standards

  • EN 12464-1 and EN 12464-2: Provide lighting requirements (lux levels, uniformity, glare index) for indoor workplaces and outdoor areas respectively.
  • CIBSE Codes: Offer methodologies and utilization factor tables for various standard room reflectances and luminaire types.
  • IESNA Standards: Recommend foot-candle levels and provide systems for calculating illuminance, often utilizing photometric IES files.
  • Emergency Lighting Standards: NFPA 101 (US) and BS 5266 (UK) set minimum illuminance levels for escape routes under battery backup.
  • ISO/CIE Standards: Establish global guidelines for lighting quality and emergency lighting calculations.

Software Tools

  • Dialux: A free lighting calculation tool that lets you input room geometry, surface reflectances, and luminaire photometric data to compute and optimize fixture layout, average lux, and uniformity.
  • Relux: Similar to Dialux, used for both artificial and daylighting simulations.
  • AGi32: A commercial software package for advanced lighting analysis, particularly useful for outdoor and complex indoor designs.
  • IES Visual or LitePro: Tools used predominantly in the US for lighting calculations.
  • Revit / CAD Plugins: Lighting analysis add-ons integrated within BIM models.
  • Spreadsheet Templates: For simple room calculations, Excel spreadsheets using the lumen method formula can suffice.
  • Photometric Measurement Software: For verifying actual light levels against design predictions.

Summary

Lighting calculations combine straightforward average illuminance formulas with detailed point-by-point analyses for complex environments. Adhering to relevant standards ensures that lighting levels meet safety, comfort, and energy-efficiency requirements. Modern software tools significantly streamline this process by simulating the behavior of light within a space.