Abstract

Recent advances in lighting calculations, based on an integral-equation formulation for interflections, have led to the practical development of highly efficient and glare-free luminous ceilings. The exact equations, however, are formidable and even the calculated tables are somewhat clumsy for engineering use.

A slide rule is therefore devised for simplifying the design of ceiling lighting. With a single setting, the rule gives average lumens per unit area at table level, the coefficient of utilization, and the helios (brightness) ratios for walls, ceiling, and floor. The device is applicable only when standardized reflectances are employed in the room. For other values of reflectance, similar slide rules may be constructed or simple approximate formulas of an exponential type may be used.

© 1951 Optical Society of America

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References

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  1. H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); J. Opt. Soc. Am. 18, 216 (1929); Z. Yamauti, Researches, Electro. Lab., Tokyo, No. 378 (1934); Parry Moon, Scientific Basis of Illuminating Engineering (McGraw-Hill Book Company, Inc., New York, 1936), p. 321; J. Opt. Soc. Am. 30, 195 (1940).
    [Crossref]
  2. P. Moon and D. E. Spencer, J. Franklin Inst. 242, 111 (1946); J. Franklin Inst. 242, 465 (1946); Lighting Design (Addison-Wesley Press, Cambridge, Massachusetts, 1948).
    [Crossref] [PubMed]
  3. P. Moon and D. E. Spencer, J. Franklin Inst. 251 (1951).
  4. P. Moon and D. E. Spencer, Illum. Eng. 44, 465 (1949); J. Franklin Inst. 250, 151 (1950); J. Franklin Inst. 251 (1951); Parry Moon, Illum. Eng. 44, 221 (1949); H. L. Beckwith, C. M. F. Peterson, and P. Moon, Elec. Eng. 68, 577 (1949); D. E. Spencer, W. H. Buck, and A. A. Wolfson, Illum. Eng. 44, 169 (1949).
    [Crossref] [PubMed]
  5. P. Moon and D. E. Spencer, Illum. Eng. 42, 325 (1947); J. Franklin Inst. 247, 117 (1949); Illum. Eng. 45, 39 (1950).
    [Crossref] [PubMed]
  6. P. Moon and D. E. Spencer, Illum. Eng. 41, 211 (1946); D. E. Spencer and S. Malkiel, J. Franklin Inst. 245, 389 (1948).
    [Crossref] [PubMed]
  7. Parry Moon, J. Opt. Soc. Am. 33, 115 (1943); J. Opt. Soc. Am. 31, 223 (1941); J. Opt. Soc. Am. 31, 301 (1941); J. Opt. Soc. Am. 31, 374 (1941).
    [Crossref]

1951 (1)

P. Moon and D. E. Spencer, J. Franklin Inst. 251 (1951).

1949 (1)

P. Moon and D. E. Spencer, Illum. Eng. 44, 465 (1949); J. Franklin Inst. 250, 151 (1950); J. Franklin Inst. 251 (1951); Parry Moon, Illum. Eng. 44, 221 (1949); H. L. Beckwith, C. M. F. Peterson, and P. Moon, Elec. Eng. 68, 577 (1949); D. E. Spencer, W. H. Buck, and A. A. Wolfson, Illum. Eng. 44, 169 (1949).
[Crossref] [PubMed]

1947 (1)

P. Moon and D. E. Spencer, Illum. Eng. 42, 325 (1947); J. Franklin Inst. 247, 117 (1949); Illum. Eng. 45, 39 (1950).
[Crossref] [PubMed]

1946 (2)

P. Moon and D. E. Spencer, Illum. Eng. 41, 211 (1946); D. E. Spencer and S. Malkiel, J. Franklin Inst. 245, 389 (1948).
[Crossref] [PubMed]

P. Moon and D. E. Spencer, J. Franklin Inst. 242, 111 (1946); J. Franklin Inst. 242, 465 (1946); Lighting Design (Addison-Wesley Press, Cambridge, Massachusetts, 1948).
[Crossref] [PubMed]

1943 (1)

1927 (1)

H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); J. Opt. Soc. Am. 18, 216 (1929); Z. Yamauti, Researches, Electro. Lab., Tokyo, No. 378 (1934); Parry Moon, Scientific Basis of Illuminating Engineering (McGraw-Hill Book Company, Inc., New York, 1936), p. 321; J. Opt. Soc. Am. 30, 195 (1940).
[Crossref]

Buckley, H.

H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); J. Opt. Soc. Am. 18, 216 (1929); Z. Yamauti, Researches, Electro. Lab., Tokyo, No. 378 (1934); Parry Moon, Scientific Basis of Illuminating Engineering (McGraw-Hill Book Company, Inc., New York, 1936), p. 321; J. Opt. Soc. Am. 30, 195 (1940).
[Crossref]

Moon, P.

P. Moon and D. E. Spencer, J. Franklin Inst. 251 (1951).

P. Moon and D. E. Spencer, Illum. Eng. 44, 465 (1949); J. Franklin Inst. 250, 151 (1950); J. Franklin Inst. 251 (1951); Parry Moon, Illum. Eng. 44, 221 (1949); H. L. Beckwith, C. M. F. Peterson, and P. Moon, Elec. Eng. 68, 577 (1949); D. E. Spencer, W. H. Buck, and A. A. Wolfson, Illum. Eng. 44, 169 (1949).
[Crossref] [PubMed]

P. Moon and D. E. Spencer, Illum. Eng. 42, 325 (1947); J. Franklin Inst. 247, 117 (1949); Illum. Eng. 45, 39 (1950).
[Crossref] [PubMed]

P. Moon and D. E. Spencer, J. Franklin Inst. 242, 111 (1946); J. Franklin Inst. 242, 465 (1946); Lighting Design (Addison-Wesley Press, Cambridge, Massachusetts, 1948).
[Crossref] [PubMed]

P. Moon and D. E. Spencer, Illum. Eng. 41, 211 (1946); D. E. Spencer and S. Malkiel, J. Franklin Inst. 245, 389 (1948).
[Crossref] [PubMed]

Moon, Parry

Spencer, D. E.

P. Moon and D. E. Spencer, J. Franklin Inst. 251 (1951).

P. Moon and D. E. Spencer, Illum. Eng. 44, 465 (1949); J. Franklin Inst. 250, 151 (1950); J. Franklin Inst. 251 (1951); Parry Moon, Illum. Eng. 44, 221 (1949); H. L. Beckwith, C. M. F. Peterson, and P. Moon, Elec. Eng. 68, 577 (1949); D. E. Spencer, W. H. Buck, and A. A. Wolfson, Illum. Eng. 44, 169 (1949).
[Crossref] [PubMed]

P. Moon and D. E. Spencer, Illum. Eng. 42, 325 (1947); J. Franklin Inst. 247, 117 (1949); Illum. Eng. 45, 39 (1950).
[Crossref] [PubMed]

P. Moon and D. E. Spencer, J. Franklin Inst. 242, 111 (1946); J. Franklin Inst. 242, 465 (1946); Lighting Design (Addison-Wesley Press, Cambridge, Massachusetts, 1948).
[Crossref] [PubMed]

P. Moon and D. E. Spencer, Illum. Eng. 41, 211 (1946); D. E. Spencer and S. Malkiel, J. Franklin Inst. 245, 389 (1948).
[Crossref] [PubMed]

Illum. Eng. (3)

P. Moon and D. E. Spencer, Illum. Eng. 44, 465 (1949); J. Franklin Inst. 250, 151 (1950); J. Franklin Inst. 251 (1951); Parry Moon, Illum. Eng. 44, 221 (1949); H. L. Beckwith, C. M. F. Peterson, and P. Moon, Elec. Eng. 68, 577 (1949); D. E. Spencer, W. H. Buck, and A. A. Wolfson, Illum. Eng. 44, 169 (1949).
[Crossref] [PubMed]

P. Moon and D. E. Spencer, Illum. Eng. 42, 325 (1947); J. Franklin Inst. 247, 117 (1949); Illum. Eng. 45, 39 (1950).
[Crossref] [PubMed]

P. Moon and D. E. Spencer, Illum. Eng. 41, 211 (1946); D. E. Spencer and S. Malkiel, J. Franklin Inst. 245, 389 (1948).
[Crossref] [PubMed]

J. Franklin Inst. (2)

P. Moon and D. E. Spencer, J. Franklin Inst. 242, 111 (1946); J. Franklin Inst. 242, 465 (1946); Lighting Design (Addison-Wesley Press, Cambridge, Massachusetts, 1948).
[Crossref] [PubMed]

P. Moon and D. E. Spencer, J. Franklin Inst. 251 (1951).

J. Opt. Soc. Am. (1)

Phil. Mag. (1)

H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); J. Opt. Soc. Am. 18, 216 (1929); Z. Yamauti, Researches, Electro. Lab., Tokyo, No. 378 (1934); Parry Moon, Scientific Basis of Illuminating Engineering (McGraw-Hill Book Company, Inc., New York, 1936), p. 321; J. Opt. Soc. Am. 30, 195 (1940).
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

A slide rule for calculating ceiling lighting. Type IIa lighting, ρ1=0.50, ρ2=0.70, ρ3=0.30, g=0.70, ρA=0.65. (Applies also to IIb lighting with ρ1=0.50, ρ2=0.80, ρ3=0.30, g=0.84, ρA=0.65.) The body of the rule has scales for S (floor area), kr (domance), ku (coefficient of utilization, H-ratios. The slide has scales of FL (total lumens from the lamps) and DAv (average lumens per unit area on the principal surface). The rule in the above illustration is set for 150,000 total lamp lumens, a floor area of 200, and a domance of 0.70. The result is read as DAv=293 lumens per unit area.

Fig. 2
Fig. 2

Data for luminous-ceiling lighting (Type IIa). The upper curve gives the coefficient of utilization ku as a function of the domance kr. The other curves are used to check the 3:1 criterion. They give the ratios H2/HA (ceiling ratio), HA/H1 (wall ratio), and HA/H3 (floor ratio). Values are for ρ1=0.50, ρ2=0.70, ρ3=0.30, g=0.70, ρA=0.65.

Equations (18)

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k r = S 1 / 4 S ,
k r = [ h ( w + l ) ] / 2 w .
k r = h / w ,
D Av = k u F L / S ,
H A = 0.65 D Av .
H max / H A 3 ,             H A / H min 3.
luminous ceiling lighting ( Type IIa ) ; wall reflectance , ρ 1 = 0.50 ; floor reflectance , ρ 3 = 0.30 ; equivalent ceiling reflectance , ρ 2 = 0.70 ; reflectance of work , ρ A = 0.65 ; logance of ceiling , g = 0.70.
wall reflectance , ρ 1 = 0.50 ; floor reflectance , ρ 3 = 0.30 ; ceiling reflectance , ρ 2 = 0.80 ; reflectance of work , ρ A = 0.65 ; logance of luminaire , g = 0.84.
f = e - α k r / 1 - ρ 2 ρ 3 ,
α = 1.530 + 1.20 ρ 3 - 0.972 ρ 1 - 0.820 ( ρ 1 ) 2 .
H 1 M / D Av = 1 2 ρ 1 ( 1 + ρ 3 ) e β 1 k r ,
β 1 = 0.418 + 0.116 ρ 1 - 0.772 ρ 3 .
H 2 / D Av = e β 2 k r ,
β 2 = 1.608 - 1.040 ρ 1 - 0.160 ρ 3 .
H 3 / D Av = ρ 3 e - β 3 k r ,
ρ 3 = 0.544 - 0.330 ρ 1 - 0.130 ρ 3 .
k u = f g .
k u = ( f ρ 2 ) g .