UNIVERSITY OF HONG KONG Department of Electrical & Electronic Engineering ELEC 3105 2010 Building Services Question a. A luminaire emits maximum luminous intensity, Io, of 300 cd/klm in the downward vertical direction. Its luminous intensity distribution can be represented by the following equation: I I o cos where θ is the angle between the direction concerned and the downward vertical. 2 luminaires of this type are installed 3m apart to illuminate a horizontal plane 2m below. A lamp with luminous flux output of 5000 lumen is installed in each of the luminaires. Calculate the illuminance received by a horizontal plane immediately underneath one of the two luminaires and the illuminance received by a horizontal plane midway between the two luminaires. Assume that there is no inter-reflection and no atmospheric attenuation. b. Now there is another type of luminaire which gives maximum intensity in the downward vertical direction of 900 cd/klm. Its intensity distribution is I I o cos 4 Which of these 2 luminaires is more suitable for general lighting? Explain your answer by comparing illuminance levels. Answer a) The maximum intensity in the downward vertical direction is 300 5000 1000 1500 cd Therefore, I 1500cos On a plane directly underneath one of the luminaires, the illuminance received due to one luminaire is 1500 375 lux 22 3 This horizontal plane subtends an angle of tan 1 , or 56.31o from the other 2 luminaire. The luminous intensity in this direction is K.F. Chan (Mr.) All rights reserved Page 1 of 4 Aug 2010 UNIVERSITY OF HONG KONG Department of Electrical & Electronic Engineering ELEC 3105 2010 Building Services 1500 cos 56.31o = 832.05cd Thus illuminance received by this point due to the other luminaire is 832.05 cos 3 56.31o 2 2 = 35.5lux Therefore total illuminance received by a plane directly underneath a luminaire is 375 + 355 = 410.5 lux For a horizontal plane midway between the 2 luminaires, it subtends an angle of 1.5 tan 1 , or 36.87o from either luminaire. 2 The luminous intensity in this direction is 1500 cos 36.87 o = 1200cd The illuminance received by this plane from one of the luminaires is 1200 cos 3 36.87 o 2 2 = 153.6lux The total illuminance received is thus 153.6 + 153.6 = 307.2 lux b) Let’s repeat the above calculations for this new luminaire. The maximum intensity in the downward vertical direction is 900 5000 1000 4500 cd Therefore I 4500 cos 4 On a plane directly underneath one of the luminaires, the illuminance received due to one luminaire is 4500 1125 lux 22 3 This horizontal plane subtends an angle of tan 1 , or 56.31o from the other 2 luminaire. The luminous intensity in this direction is K.F. Chan (Mr.) All rights reserved Page 2 of 4 Aug 2010 UNIVERSITY OF HONG KONG Department of Electrical & Electronic Engineering ELEC 3105 2010 Building Services 4500 cos 4 45o = 426cd Thus illuminance received by this point due to the other luminaire is 426 cos 3 56.31o 2 2 = 18.2lux Therefore total illuminance received by a plane directly underneath a luminaire is 1125 + 18.2 = 1143.2 lux For a horizontal plane midway between the 2 luminaires, it subtends an angle of 1.5 tan 1 , or 36.87o from either luminaire. 2 The luminous intensity in this direction is 4500 cos 4 36.87 o = 1843.2cd The illuminance received by this plane from one of the luminaires is 1843.2 cos 3 36.87 o 2 2 = 235.9lux The total illuminance received is thus 235.9 + 235.9 = 471.9 lux The ratio of illuminance using luminaire in (a) is 307.2 0.75 410.5 The ratio of illuminance using luminaire in (b) is 471.9 0.41 1143.2 Uniformity of illuminance is found to be better when using luminaire in (a). Therefore, the type of luminaire in (a) is more suitable for general lighting. If the spacing is wider, the uniformity given by luminaire type (b) can be found to be even worse. K.F. Chan (Mr.) All rights reserved Page 3 of 4 Aug 2010 UNIVERSITY OF HONG KONG Department of Electrical & Electronic Engineering ELEC 3105 2010 Building Services In fact, the polar curves of the 2 luminaires looks like something below: The one in (b) will be more suitable for use in accent lighting while the one in (a) more suitable for general lighting. [Example taken from ELEC 3105 2007/08 exam] K.F. Chan (Mr.) All rights reserved Page 4 of 4 Aug 2010