Tools › Building Systems › Lighting and Electrical › Lighting and Circuit Sizing › Example
40 by 30 by 10 ft office with twenty 4,000 lm cosine down-lights: zonal-cavity CU by flux transfer against the UFC 30 fc criterion, and a 16 A continuous 120 V branch circuit on 100 ft of 12 AWG copper
| Tool | Lighting and Circuit Sizing |
| Source | U.S. Department of Defense (2016). Interior and Exterior Lighting Systems and Controls. UFC 3-530-01, Change 2, 3 March 2016, sections 3-4.4 (open offices, 30 fc at 2 ft 6 in) and B-1.5.2; National Bureau of Standards (1966). Copper Wire Tables. NBS Handbook 100, Tables 5 and 6; U.S. Department of Defense (2015). Electrical Engineering. UFC 3-501-01, section 3-2.7 (3 percent branch-circuit drop). |
| Level | Undergraduate |
Problem
An office 40 ft long, 30 ft wide and 10 ft high (reflectances 80 / 50 / 20 percent) is lit by a 5 by 4 array of recessed luminaires of 4,000 lm and 36 W with a cosine candela distribution, light loss factor 0.8, work plane at 2.5 ft. Find the cavity ratios, the effective cavity reflectances, the direct ratio of the array, the coefficient of utilization, the maintained average illuminance against the 30 fc office criterion, the luminaires needed for it, the spacing criterion, the point-by-point uniformity and the lighting power density. Then check a 16 A continuous load at 120 V single-phase, power factor 0.9, on 100 ft of 12 AWG copper at 75 C: voltage drop against the 3 percent limit, the smallest size that meets it, ampacity and breaker, conduit fill of three 0.130 in conductors in 1/2 in EMT, and the fault current at the panel and at the load from a 25 kVA, 2 percent, X/R 2 transformer.
Inputs to Enter
- Lighting: L 40 ft, W 30 ft, H 10 ft, work plane 2.5 ft, luminaires at 10 ft (recessed), reflectances 0.80 / 0.50 / 0.20, array 5 x 4, 4,000 lm and 36 W per luminaire, downward fraction 1.0, LLF 0.8, target 30 fc, distribution I(theta) = cos theta at 0 to 90 degrees in 10-degree steps
- Circuit: 16 A continuous, 120 V single-phase, pf 0.9, 12 AWG copper solid at 75 C, ambient 30 C, 100 ft one way, reactance blank (geometric estimate at 0.25 in spacing, 60 Hz), limit 3 percent, table ampacity 25 A, adjustment 1.0, OCPD cap 20 A, 3 conductors of 0.130 in in 0.622 in EMT, transformer 25 kVA, 2.0 percent, X/R 2, infinite primary, breaker AIC 10 kA
Answers
- Cavity ratios CCR 0, RCR = 5 x 7.5 x 70 / 1,200 = 2.1875, FCR 0.729; effective floor-cavity reflectance 0.194 by flux transfer (handbook sphere form 0.221); view factor ceiling plane to work plane 0.6674
- Direct ratio of the 5 x 4 array 0.687 (integrated from the cosine law); CU = 0.687 + 0.203 = 0.889 (whole-room patch radiosity in the test: within 1.5 percent)
- E maintained = 20 x 4,000 x 0.889 x 0.8 / 1,200 = 47.4 fc (510 lux) against 30 fc: 12.7 luminaires would do; spacing 8 ft / 7.5 ft, S/h = 1.07 within the cosine spacing criterion 1.284 (line) / 1.412 (square); grid 25.4 / 47.4 / 58.1 fc minimum / average / maximum; LPD 0.60 W/ft2, efficacy 111 lm/W
- Circuit: 12 AWG 6,530 cmil, R 1.588 ohm/1,000 ft at 20 C and 1.932 at 75 C (Handbook 100 Table 6: 1.59 / 1.93), geometric X 0.0476 ohm/1,000 ft; exact drop 5.655 V = 4.71 percent (approximate 5.629 V, resistive 6.181 V), over the 3 percent limit, 8 AWG is the smallest size that meets it at 75 C
- Design current 20 A, corrected ampacity 25 A, breaker 20 A within the 20 A cap; fill 13.1 percent against 40; transformer Z 0.01152 ohm, I_fl 208.3 A, panel fault 10,417 A (breaker AIC 10 kA insufficient), load-end fault 306 A (point-to-point f / M form 302 A)
Notes
The tool's default inputs are this case; press Submit (the circuit sub-tool is the second choice of the Analysis select). The case is illustrative: the office geometry and the branch circuit are the builder's, the 30 fc criterion and the drop limit are the UFC's, the wire constants the NBS handbooks'. Every number is reproduced by test_lighting_circuit_sizing.php (458 checks), which also reproduces the Handbook 100 / 109 tables, the FM 5-424 Table B-16 wire sizes for a 3 percent drop and the NAVEDTRA 14027 roadway lumen-method example, with the independent numpy radiosity and phasor checks in References/Lighting-Circuit/checks/.