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5. Calculate Lighting Fixture’s Beam Angle and Lumen

CALCULATE LIGHTING FIXTURE’S BEAM ANGLE AND LUMEN

EXAMPLE 1: CALCULATE LIGHTING FIXTURE’S LUMEN AND DIAMETER OF ILLUMINATION AT SURFACE HAVING FOLLOWING DETAILS.

  • Required illumination at surface is 1390 Lux * The distance from Lighting Fixture to illumination surface is 3 Meter. * The Fixture Beam Angle is 10 Degree.

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CALCULATION:

  • Required Lux at Surface (E2) =1390 Lux. * Distance between Lighting Fixture and Surface (D) = 3 Meter. * Fixture Beam Angle (ϕ)= 10° * Irradiance at 1.0 meter (E1)= DxDxE2 * Irradiance at 1.0 meter (E1)=1390x3x3 =12510 Lumen / M2 * Irradiance at 1.0 meter (E1)= 12510 Lumen / M2 * Solid Angle of The Lamp (Ω) =2xπx(1-COS(ϕ/2)) * Solid Angle of The Lamp (Ω) =2×3.14x(1-COS(10/2)) =6.28x(1-0.996) * Solid Angle of the Lamp (Ω) =0.0239 Steradian. * Required Lumen of Lighting Fixtures= E1x Ω * Required Lumen of Lighting Fixtures=12510×0.0239 * Required Lumen of Lighting Fixtures=299 Lumen. * Illumination Diameter at surface =0.018xDx ϕ * Illumination Diameter at surface =0.018x3x10 * Illumination Diameter at surface =0.54 Meter.

EXAMPLE 2: CALCULATE LIGHTING FIXTURE’S BEAM ANGLE AND ILLUMINATION DIAMETER AT SURFACE HAVING FOLLOWING DETAILS.

  • Required illumination at surface is 22 Lux * Lighting Fixture Lumen is 1547 Lumen. * The distance from Lighting Fixture to illumination surface is 4 Meter.

CALCULATION:

  • Required Lux at Surface (E2) =22 Lux. * Distance between Lighting Fixture and Surface (D) = 4 Meter. * Irradiance at 1.0 meter (E1)= DxDxE2 * Irradiance at 1.0 meter (E1)=4x4x22 =352 Lumen / M2 * Irradiance at 1.0 meter (E1)= 352 Lumen / M2 * Solid Angle of The Lamp (Ω) = Lumen of Lighting Fixtures / E1 * Solid Angle of the Lamp (Ω) =1547 / 352 * Solid Angle of the Lamp (Ω) =4.394 Steradian. * Solid Angle of The Lamp (Ω) =2xπx(1-COS(ϕ/2)) * 39 =2×3.14x(1-COS(ϕ/2)) * Fixture Beam Angle (ϕ)=145° * Illumination Diameter at surface =0.018xDx ϕ * Illumination Diameter at surface =0.018x4x145 * Illumination Diameter at surface =10.44 Meter.

EXAMPLE 3: CALCULATE LUX LEVEL AND ILLUMINATION DIAMETER AT SURFACE HAVING FOLLOWING DETAILS.

  • Lighting Fixture Lumen is 299 Lumen. * The distance from Lighting Fixture to illumination surface is 3 Meter. * The Fixture Beam Angle is 10 Degree.

CALCULATION:

  • Required Lux at Surface (E2) =1390 Lux. * Distance between Lighting Fixture and Surface (D) = 3 Meter. * Fixture Beam Angle (ϕ)= 10° * Solid Angle of The Lamp (Ω) =2xπx(1-COS(ϕ/2)) * Solid Angle of The Lamp (Ω) =2×3.14x(1-COS(10/2)) =6.28x(1-0.996) * Solid Angle of the Lamp (Ω) =0.0239 Steradian. * Lumen of Lighting Fixtures= E1x Ω * 299= E1x0.0239 * Irradiance at 1.0 meter (E1)= Lumen of Lighting Fixtures / Ω * Irradiance at 1.0 meter (E1)=299 / 0.0239 * Irradiance at 1.0 meter (E1)= 12506 Lumen / M2 * Lux at Surface (E2) = E1 / (DxD) * Lux at Surface (E2) =12506 / (3×3) * Lux at Surface (E2) =1389.5 Lux * Illumination Diameter at surface =0.018xDx ϕ * Illumination Diameter at surface =0.018x3x10 * Illumination Diameter at surface =0.54 Meter.