A 30 ft by 40 ft classroom with 8 ft high ceilings will have an ambient lighting

Question

A 30 ft by 40 ft classroom with 8 ft high ceilings will have an ambient lighting target illuminance of 70 fc at a work plane that is 28 in. above the floor. It is anticipated that the ceiling reflectance is 0.5 and the average wall reflectance is about 0.3. The space will be illuminated with recessed lay-in 2 ft x 4 ft open troffer luminaires with four lamps. The initial output of the fluorescent lamps is 2850 lumen. The light loss factor will be assumed to be 0.7.

Use the zonal cavity method to determine the minimum number of luminaires required to provide uniform illumination in the space.

Recessed Lay-in 2 ft x 4 ft Open Parabolic Troffer Luminaire (Two Fluorescent Lamp) Reflectance Coefficient of Utilization (CU Spacing Ceiling Cavity (e 80 70 50 2 Linear Tube Criteria Wall Surfaces (pw) 70 50 30 705030 50 30 Fluorescent Lamps (CS) Cavity Ratio (CR) 10 9 41 32 2640 30 25 29 25 44 .34 28 42 34 28 33.28 .47 .36.30 46 36 30 35 29 51 40 34 .50 40343934 55 46 39 .54 45 39 42 38 50 44.4742 65 56.50 64.56.5054 48 .70 64 .57 69 63 .56 60.56 78 71 66 .76 70 6768 .65 79 82 80 78 77 75 1.41 1.21 59 . 44 .58 4 84 81 Recessed Lay-in 2 ft x 4 ft Open Parabolic Troffer Luminaire (Three Fluorescent Lamp) Reflectance Coefficient of Utilization (CU Spacing Ceiling Cavity (pec) 80 70 50 3 Linear Tube Fluorescent Criteria Wall Surfaces (p70 50 30 70 5030 50 30 Lamps (CS) Cavity Ratio (CR) 39 29 .25 38 28.2328 .23 40 32 27 40 32 27 30 26 44 .34 29 42 34 28 34 28 .47 39.33 46.38 33.36 .32 5142 36.5041 1.4L . 36 40.35 56 46 4154 46 40 45 40 59 .53 46 58.52465046 65 58.54 64.57 53 5652 .70 66 61 .68 65 .60 63.59 77 75.71 .75 .72.70 69 68 4 Recessed Lay-in 2 ft x 4 ft Open Parabolic Troffer Luminaire (Four Fluorescent Lamp Reflectance Coefficient of Utilization (CU Spacing Ceiling Cavity (p) 80 70 50 4 Linear Tube Fluorescent | Criteria | Wall Surfaces (p") | 70 | 50 | 30 | 70 50 30 50 30 Lam (CS) Cavity Ratio (CR 10 35 28 .23 34 28.2327 .23 38 29 26 36 29 .25 28 25 .40 .33 28 40 32 28 32 27 .44 .35.30 42 34 30 34 29 46 .39 .34 46.39.34.38 .34 51 42 .39 48 4238 4.38 55 47 42 .53 46 424641 .58 54 48 .57 53 485147 .58 56.56.54 68 67 65 .67 65.6463 .60 7 1.41 4 64 59.56 61 Recessed Lay-in 2 ft x 4 ft Lensed Troffer Luminaire (Four Fluorescent Lam Reflectance Coefficient of Utilization (CU Spacing Ceiling Cavity () 80 70 Linear Tube Fluorescent Criteria Wall Surfaces (p70 50 30 70 503050 30 Lam (CS)Cavity Ratio (CR) 46 35 294435 2934 .28 49 38 31 47 37 31 36 31 .52 41 34 51413440.34 .56 45 38.544438 43.37 60 49 42 58 494247 .41 65 .55 48 63 5447.52 46 54 68 60 53 5752 76 .68 61 74 .66 61 64.59 83 76.71 81 .75 .70 72 .68 .90 86 838885 82 81 .79 7 1.41 4

Explanation / Answer

1) Calculate cavity ratios as follows:

CCR = (5 X 0 X (30 + 40)) / (30 X 40)

= 0

RCR = ( 5 X 5.6667 x 70) / 1200

= 1.65

FCR = ( 5 x 2.3333 x 70 ) / 1200

= 0.6805

(2) In Table A, look up effective cavity reflectances for these ceiling and floor cavities. ?cc for the ceiling cavity is determined to be 62%, while ?fc for the floor cavity is 10%.

(3) Knowing the room cavity ratio (RCR), it is now possible to find the coefficient of utilization for the Prismawrap luminaire in a room having an RCR of 2.0 and effective reflectances as follows: ?cc = 62%; ?w = 30%; ?fc = 20%.

By interpolation between boxed numbers in the table this CU is .55. Note that this CU is for an effective reflectance of 20% while the actual effective reflectance of the floor ?fc is 10%. To correct for this, locate the appropriate multiplier in Table B for the RCR already calculated (2.0). It is .962 and is found by interpolating between the boxed number in Table B for 70% ?cc, 30% ?w, and 50% ?cc, 30% ?w at an RCR of 2.0.

Then: CU final = .55 x .962 = .53

FC INITIAL = (LUMEN OF FIXTURE X LAMPS / FIXTURE X LUMENS / LAMPS X CU) / AREA

Note that all interpolations only need to be of the approximate, “eyeball” type, giving a credible degree of accuracy to the calculation. (4) Illuminance level can now be calculated if we know the number of units to be used and the lamp lumen rating. Check spacing of luminaires.

A possible arrangement for these fixtures is three columns of six fixtures spaced ten feet on center in each direction. The Spacing Criterion is 1.4, making the maximum allowable spacing 11.2 feet.

The actual spacing is less than the maximum allowable spacing. Therefore, the illumination on the work plane should be uniform.

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