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NOT SO SCARY LIGHTING MATH Light – the Foot-Candle

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NOT SO SCARY LIGHTING MATH Light – the Foot-Candle Lighting Math NOT SO SCARY LIGHTING MATH Light – The Foot-candle 1 fc 1 foot The direct illumination from one candle placed at a distance of one foot from a surface is defined as…. 1 foot-candle (abbreviation = fc) Foot-candle is also known as a unit of light or light level. Light – The Lumen Light – The Candela 180 deg 270 deg 90 deg 1 lm Candela 0 deg The energy of light from a candle falling on a one foot square area is Distribution Curve Polar Chart One Lumen (abbreviation = lm) Distribution Curve represents the total light pattern produced by a The total amount of light coming out of the candle is approximately 13 lumens source The total amount of light coming out of 100-watt A-lamp is approximately 1650 lumens NOT DEFINED BY DISTANCE Candela is the intensity of light at any given direction. 1 Lighting Math Lumens versus Candelas Light Measurement • Lumen is an amount of ENERGY Measures the candlepower distribution of a particular • Candela is an amount of INTESITY lamp or luminaire. • Lamp output can be measured in Lumens and Information is generated in a -- Photometric report Candelas. • Fixtures alter Lumen and Candela output (Their values can only be found in Photometry Reports) Integrating SphereGonio-Photometer The Spectro-Radiometer Methods to Calculate Light Direction of Light Point-by-Point – Direct Illumination from a Fixture or Lamp • Goal of a luminaire is to put light where the user needs it • You need…. • Convenient way to classify luminaires is by the direction of light – Photometry emitted from the luminaire – Distances from Fixture or Lamp • Commission Internationale de l’Eclairage (CIE) sets up these classifications Lumen Method – Average Light Level in a Room from a Fixture • You need…. – Photometry – Room Dimensions and Surface Reflectance's 2 Lighting Math CIE Luminaire Types / Distributions Candlepower Distribution Curve Candlepower 90 deg distribution curves 80 300 provides intuitive 70 information on how a 60 luminaire will perform 600 Direct Semi-Direct General Diffuse 50 Candela values are used 900 in calculations to predict light levels 1200 40 Candle PowerCandle Distribution 1500 0 deg 10 20 30 (IES) Direct-Indirect Semi-Indirect Indirect Distribution angles Asymmetrical Distribution Curve Photometry Reports Rectangular Tubular Plot of candlepower values Fluourescent fixture Summary of candlepower 90 deg Perpendicular values in different planes Fixture Efficiency Perpendicular – Lumen Summary 90 degrees Candlepower Distribution 0 deg Parallel Luminance summary Rectangular Tubular Spacing criteria (SC) or Fluourescent fixture Spacing/Mounting Height (S/MH) for uniformity Coefficient of Utilization Table Guides – allel Par s gree 0 de Candlepower Distribution 3 Lighting Math Photometry Reports Photometry Reports • Lensed Downlight • Indirect Pendant Candle Power Candle Power Point-by-Point Foot-candle = 2 Point-by-Point Foot-candle = 2 Distance Foot-candle = Distance 2 • Ceiling Fixture Example FC = 2651candelas / 9ft2 Ceiling height = 9ft FC = 2651 / 81 FC = 32.7 foot-candles Elevation Section Light Level at Floor 4 Lighting Math Candle Power Candle Power Foot-candle = 2 Foot-candle = Point-by-Point Distance Point-by-Point Distance 2 To solve for D, you can: Ceiling height = 9ft Ceiling height = 9ft 1. Scale the Drawing, or 2. Use Trigonometry Light Level at the D Light Level at the D Wall Wall D X Top Head = 6ft Top Head = 6ft 3ft Y6Y ft X2 + Y2 = Z2 32 + 62 = D2 D = (9 + 36) 2 9 + 36 = D D = 6.7 Room Width = 12ft Room Width = 12ft Candle Power Candle Power Foot-candle = Foot-candle = Point-by-Point Distance 2 Point-by-Point Distance 2 2 To solve for Angle, you can: FC = 169 candelas / 6.7ft Ceiling height = 9ft Ceiling height = 9ft 1. Scale the Drawing, or FC = 169 / 44.89 2. Use Trigonometry FC = 3.76 foot-candles D Light Level at the 6.7ft Light Level at the Wall 26deg Wall ? X Top Head = 6ft 3ft Top Head = 6ft Y6Y ft Tan (Angle) = X / Y Angle = Tan-1 (X / Y) Angle = Tan-1 (3 / 6) Room Width = 12ft Angle = 26 degrees Room Width = 12ft 5 Lighting Math Point-by-Point Factors Point-by-Point Factors • Calculated Levels are Facing the Light Fixture • You need to factor an adjustment if you want levels at other angles (IE Horizontal, – With the exception of directly below Vertical Angles) – COSINE Adjusted!! Vertical Vertical Horizontal COSINE Adjustments Point-by-Point… with COSINE Adjustment Candle Power 2 Foot-candle = 2 X COS(Angle of Incidence) FC = CP/D x COS(angle) Distance Ceiling height = 9ft Light Level at the 6.7ft 2 Vertical to the 26deg FC = 169 / 6.7ft x COS(64deg) Light Source Wall 64deg FC = 169 / 44.89 x 0.43 FC = 1.6 foot-candles Incidence Reflectance θ θ Room Width = 12ft 6 Lighting Math Point-by-Point Factors MF = Maintenance Factors • Calculated Levels are Initial. • You need to factor an adjustment for Light Loss – Light Loss Factors to Consider •Dirt • Lamp Depreciation Non-Recoverable • Environment Recoverable Candle Power Foot-candle = x COS(Angle) x MF Distance2 Non-Recoverable Light Loss Factors Recoverable Light Loss Factors •Ballast Factor (Fluourescent approx 90%) •Lamp Burnouts (approx 80%) •Ambient Fixture Temperature •Lamp Lumen Depreciation (Fluourescent approx 70%) •Supply Voltage Variation (Low Voltage approx 4%) •Fixture (Luminaire) Dirt Depreciation •Indirect Lighting (approx 65%) •Industrial Environments (ranges from approx 50% to 80%) •Open Fixtures – Lamp exposed (approx 85%) 7 Lighting Math Review of Formulas Multiply one factor against another and you get the……….. • To find Dimensions or Angles of a Triangle MF = LIGHT LOSS FACTOR! To solve for any item, you can: 1. Scale the Drawing, or Use Trigonometry Formulas: Candle Power Foot-candle = x COS(Angle) x MF X2 + Y2 = Distance 2 Distance2 Angle Distance Tan (Angle) = X / Y Y Angle = Tan-1 (X / Y) X Review of Formulas Methods to Calculate Light • Point by Point Point-by-Point – Direct Illumination from a Fixture or Lamp To calculate direct light levels: • You need…. 1. You need a fixtures Candle Power Distribution – Photometry – Distances from Fixture or Lamp Formulas: Lumen Method Light Light Fixture Fixture Candle Power – Average Light Level in a Room from a Fixture FC = 2 • You need…. Angle Distance – Photometry Distance Distance Multiply by Cos(Angle) – Room Dimensions and Surface Reflectance's for horizontal light level FC FC 8 Lighting Math Calculations using Lumens Photometry Reports Plot of candlepower values • Lumen is an amount of ENERGY • Candela is an amount of INTESITY Summary of candlepower • Lumen Method Calculation values in different planes – Calculates the Average Illumination for a room. Fixture Efficiency – Takes into account the room surface reflectance's – but assumes the surfaces are diffuse (not shiny!). Lumen Summary – Assumes an empty room (without furniture). Luminance summary – Can also be used to determine the required Quantity of Fixtures needed for a target light level. Spacing Criteria (SC) or – Does not determine light fixture layout or location – you must following mnfrs spacing criteria. Spacing/Mounting Height (S/MH) for uniformity Coefficient of Utilization Table Guides Coefficient of Utilization Lumen Method Steps • Also known as CU 1. You need Room Dimensions and the Fixture Mounting Height. • Defines the percentage of light 2. You need to select a Light fixture output that is expected from a fixture 3. Determine the rooms Room Cavity Ratio (RCR). • The value is determined by a CU 4. Look-up the fixtures Coefficient of Utilization for the RCR. table 5. Calculate! • For commercial Reflectance of 80/50/20, the actual CU value is this. 9 Lighting Math Room Reflectance Room Reflectance • Room comprised of Walls, • Surfaces with less reflectance will Ceiling, and Floor. bounce less light • Walls typically have Doors • Typical Reflectance Values: – 75%-90% White, Off White, Grey, and Windows Light tints of Blue or Brown • All surfaces have a – 30%-60% Medium Green, Yellow, reflectance value to bounce Brown, or Grey light. – 10%-20% Dark Grey, Medium Blue – 5%-10% Dark Blue, Brown. Dark • Light from Light Fixture Green, and many wood finishes bounces off of all surfaces. 5xMHx(L+W) RCR = Room Reflectance Room Cavity Ratio Room Area • Room Cavity Ratio (aka RCR) is the volume • Typical Commercial Values: between the Fixture and Height of Calculation – 80% Ceiling • Workplane height is – 50% Wall typically 30-inches above – 20% Floor the floor • A rooms RCR will always • Typical Industrial Values: be between 1 and 10 – 50% Ceiling – 30% Wall – 20% Floor 10 Lighting Math 5xMHx(L+W) 5xMHx(L+W) RCR = RCR = Room Cavity Ratio Room Area Room Cavity Ratio Room Area • The RCR can vary • The RCR can vary depending on the height depending on the height you want to of the fixture….as calculate…as shown shown here with Wall here with the Brackets or Sconces. calculation height at the floor. 5xMHx(L+W) 5xMHx(L+W) RCR = RCR = Room Cavity Ratio Room Area Room Cavity Ratio Room Area • The RCR can vary Example: depending on the height of Ceiling 10ft Room Width: 12ft the fixture….as shown Room Length: 15ft here with Pendants. Ceiling Height: 10ft 8ft RCR = 5(5.5)(12+15) (12x15) RCR = 742.5 180 RCR = 4.1 Table 2.5ft 11 Lighting Math Lumen Method Formula Lumen Method Example 1 To Calculate Foot-candle level: FC = Qty of Fixtures x Number of Lamps per Fixture x Lumens per Lamp x CU Area of the Room To Calculate number of Fixtures: FC = Total Lumens in the Room x CU Area of the Room What is the resulting Foot-candle Level at table height from four downlights? Qty of Fixtures = FC x Area of the Room Number of Lamps per Fixture x Lumens per Lamp x CU Qty of Fixtures = FC x Area of the Room Total Lumens in the Room x CU Coefficient of Utilization Lumen Method Example 2 • Also known as CU • Defines the percentage of light output that is expected from a fixture • The value is determined by a CU table • For our example: • RCR_ ______… • the CU is ______ • For commercial Reflectance of 80/50/20, the actual CU value is this.
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