Abstract

An optical system consisting of a convex reflective sphere or cylinder and a collimating lens is proposed to produce a collimated beam of solar radiation whose direction of propagation varies only slightly over the course of a day. Called a passive optical solar tracking (POST) system, a spherical version of the proposed device has limited usefulness for daylighting applications due to the inverse relationship which is shown to exist between collimated beam directional stability and contained flux. A cylindrical version of the system exhibits greater promise for solar illumination of building interiors. Other applications for the device are proposed for the fields of solar research, education, and artistic design.

© 1983 Optical Society of America

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References

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  1. M. A. Duguay, R. M. Edgar, Appl. Opt. 16, 1444 (1977).
    [CrossRef] [PubMed]
  2. M. A. Duguay, Am. Sci. 65, 422 (1979).
  3. J. Parker, “Now We Have Solar Illumination,” Mech. Illus. 75, 27 (Nov.1979).
  4. A. W. Kliman, “A Design for a Modular Natural Lighting System,” in Proceedings, Solar Glazing: 1979 Topical Conference, 22, 23 June 1979, Stockton State College, Pomona, New Jersey (Mid-Atlantic Solar Energy Association, Philadelphia, 1979), pp. F-25–F-28.
  5. H. B. Edwards, “Optics for Natural Lighting,” NASA Tech. Brief PB80-974440, LAR-12333, Langley Research Center, Hampton, Va.
  6. L. A. Whitehead, R. A. Nodwell, F. L. Curzon, Appl. Opt. 21, 2755 (1982).
    [CrossRef] [PubMed]
  7. L. M. Fraas, W. R. Pyle, P. R. Ryason, Appl. Opt. 22, 578 (1983).
    [CrossRef] [PubMed]
  8. S. Selkowitz, Light. Des. Appl. 9, 6–8, 10–11, 61 (Feb.–Mar.1979).
  9. R. M. Lebens, “Determining the Optimum Design of the Solar Modulator,” in Proceedings, Third National Passive Solar Conference, 11–13 January 1979, San Jose, Calif. (American Section, International Solar Energy Society, Inc., Newark, Del., 1979), pp. 100–106.
  10. H. G. Shapira, P. A. Barnes, “RIB-Reflective Insulating Blinds,” Report of research performed at Oak Ridge National Laboratory under Contract W-7405-eng-26, U.S. Department of Energy, Energy Division, ORNL, Oak Ridge, Tenn. 37830.
  11. “Holographic Optics Concentrate Solar Rays,” Laser Focus 17, 38 (Dec.1981).
  12. K. T. K. Cheng, Photonics Spectra, 16, No. 6, 32 (1982).
  13. W. T. Welford, R. Winston, Appl. Opt. 21, 1531 (1982).
    [CrossRef] [PubMed]
  14. W. H. Bloss et al., Appl. Opt. 21, 3739 (1982).
    [CrossRef] [PubMed]
  15. R. Winston, W. T. Welford, J. Opt. Soc. Am. 72, 1564 (1982).
    [CrossRef]
  16. W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).
  17. C. J. Sletten, F. S. Holt, S. B. Herkovtiz, Appl. Opt. 19, 1439 (1980).
    [CrossRef] [PubMed]
  18. Civil Engineering/ASCE, 53, No. 6, pp. 34–37, June1983;K. Vadnais, Earth Shelter Living, No. 27, 23 (May/June1983).

1983 (1)

1982 (5)

1981 (1)

“Holographic Optics Concentrate Solar Rays,” Laser Focus 17, 38 (Dec.1981).

1980 (1)

1979 (3)

M. A. Duguay, Am. Sci. 65, 422 (1979).

J. Parker, “Now We Have Solar Illumination,” Mech. Illus. 75, 27 (Nov.1979).

S. Selkowitz, Light. Des. Appl. 9, 6–8, 10–11, 61 (Feb.–Mar.1979).

1977 (1)

Barnes, P. A.

H. G. Shapira, P. A. Barnes, “RIB-Reflective Insulating Blinds,” Report of research performed at Oak Ridge National Laboratory under Contract W-7405-eng-26, U.S. Department of Energy, Energy Division, ORNL, Oak Ridge, Tenn. 37830.

Bloss, W. H.

Cheng, K. T. K.

K. T. K. Cheng, Photonics Spectra, 16, No. 6, 32 (1982).

Curzon, F. L.

Duguay, M. A.

Edgar, R. M.

Edwards, H. B.

H. B. Edwards, “Optics for Natural Lighting,” NASA Tech. Brief PB80-974440, LAR-12333, Langley Research Center, Hampton, Va.

Fraas, L. M.

Herkovtiz, S. B.

Holt, F. S.

Kliman, A. W.

A. W. Kliman, “A Design for a Modular Natural Lighting System,” in Proceedings, Solar Glazing: 1979 Topical Conference, 22, 23 June 1979, Stockton State College, Pomona, New Jersey (Mid-Atlantic Solar Energy Association, Philadelphia, 1979), pp. F-25–F-28.

Lebens, R. M.

R. M. Lebens, “Determining the Optimum Design of the Solar Modulator,” in Proceedings, Third National Passive Solar Conference, 11–13 January 1979, San Jose, Calif. (American Section, International Solar Energy Society, Inc., Newark, Del., 1979), pp. 100–106.

Nodwell, R. A.

Parker, J.

J. Parker, “Now We Have Solar Illumination,” Mech. Illus. 75, 27 (Nov.1979).

Pyle, W. R.

Ryason, P. R.

Selkowitz, S.

S. Selkowitz, Light. Des. Appl. 9, 6–8, 10–11, 61 (Feb.–Mar.1979).

Shapira, H. G.

H. G. Shapira, P. A. Barnes, “RIB-Reflective Insulating Blinds,” Report of research performed at Oak Ridge National Laboratory under Contract W-7405-eng-26, U.S. Department of Energy, Energy Division, ORNL, Oak Ridge, Tenn. 37830.

Sletten, C. J.

Welford, W. T.

W. T. Welford, R. Winston, Appl. Opt. 21, 1531 (1982).
[CrossRef] [PubMed]

R. Winston, W. T. Welford, J. Opt. Soc. Am. 72, 1564 (1982).
[CrossRef]

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

Whitehead, L. A.

Winston, R.

R. Winston, W. T. Welford, J. Opt. Soc. Am. 72, 1564 (1982).
[CrossRef]

W. T. Welford, R. Winston, Appl. Opt. 21, 1531 (1982).
[CrossRef] [PubMed]

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

Am. Sci. (1)

M. A. Duguay, Am. Sci. 65, 422 (1979).

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

Laser Focus (1)

“Holographic Optics Concentrate Solar Rays,” Laser Focus 17, 38 (Dec.1981).

Light. Des. Appl. (1)

S. Selkowitz, Light. Des. Appl. 9, 6–8, 10–11, 61 (Feb.–Mar.1979).

Mech. Illus. (1)

J. Parker, “Now We Have Solar Illumination,” Mech. Illus. 75, 27 (Nov.1979).

Photonics Spectra (1)

K. T. K. Cheng, Photonics Spectra, 16, No. 6, 32 (1982).

Other (6)

R. M. Lebens, “Determining the Optimum Design of the Solar Modulator,” in Proceedings, Third National Passive Solar Conference, 11–13 January 1979, San Jose, Calif. (American Section, International Solar Energy Society, Inc., Newark, Del., 1979), pp. 100–106.

H. G. Shapira, P. A. Barnes, “RIB-Reflective Insulating Blinds,” Report of research performed at Oak Ridge National Laboratory under Contract W-7405-eng-26, U.S. Department of Energy, Energy Division, ORNL, Oak Ridge, Tenn. 37830.

A. W. Kliman, “A Design for a Modular Natural Lighting System,” in Proceedings, Solar Glazing: 1979 Topical Conference, 22, 23 June 1979, Stockton State College, Pomona, New Jersey (Mid-Atlantic Solar Energy Association, Philadelphia, 1979), pp. F-25–F-28.

H. B. Edwards, “Optics for Natural Lighting,” NASA Tech. Brief PB80-974440, LAR-12333, Langley Research Center, Hampton, Va.

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

Civil Engineering/ASCE, 53, No. 6, pp. 34–37, June1983;K. Vadnais, Earth Shelter Living, No. 27, 23 (May/June1983).

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Figures (9)

Fig. 1
Fig. 1

Passive Optical Solar Tracker (POST) operating principle.

Fig. 2
Fig. 2

Coordinate system used for determining image location.

Fig. 3
Fig. 3

Plot of incident rays and projections of reflected rays inside the sphere for various angles made by the sun with respect to the +y axis.

Fig. 4
Fig. 4

Plot of the x-z plane showing angle δ.

Fig. 5
Fig. 5

Drawing showing geometry of sun's image in the sphere.

Fig. 6
Fig. 6

Plot of beam instability parameter Δθz vs the ratio R/f.

Fig. 7
Fig. 7

Plot of projected flux vs angular beam motion for several values of the lens diameter D.

Fig. 8
Fig. 8

Cylindrical case coordinate system.

Fig. 9
Fig. 9

Cylindrical case geometry.

Tables (2)

Tables Icon

Table I Summer Solstice

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Table II Winter Solstice

Equations (44)

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z z 0 = m i ( y y 0 ) ,
z z 0 = m r ( y y 0 ) ,
y 0 = R sin θ , z 0 = R cos θ ,
m i = tan ( α + 2 β ) = cot ( θ β )
m r = tan ( α ) = cot ( θ + β ) .
m i = tan Ψ = tan 2 β = tan 2 ( 90 ° θ 0 )
y = R 2 cos Ψ 2 ,
z = R sin Ψ 2 .
z 2 = R 2 4 y 2 .
X 0 = R sin θ cos ϕ Y 0 = R sin θ sin ϕ Z 0 = R cos θ .
tan δ = X 0 / Z 0 = tan θ cos ϕ .
y = R 2 cos Ψ 2 ,
z = R sin Ψ 2 .
x = R sin Ψ 2 sin δ ,
y = R 2 cos Ψ 2 ,
z = R sin Ψ 2 cos δ .
cos Ψ = sin θ sin ϕ ,
α = sin 1 [ cos λ cos d cos ( 15 T ) + sin λ sin d ] ,
ϕ = 90 ° sin 1 [ sin ( 15 T ) cos d / cos α ] ,
d = tan 1 { 0.43378 sin [ 0.9863 ( D 81 ) ] }
α s = sin 1 [ 0.757 cos 15 T + ( 0.215 or 0.220 ) ] ,
ϕ s = 90 ° sin 1 [ ( sin 15 T ) 0.926 / cos α ] .
Δ z = 0.5 ° π l / 180 ° = 0.0087 l .
l = R 2 X 2 Z 2 y .
Δ z = 0.0087 y .
A = π 4 ( Δ z ) 2 = 4.7 × 10 5 y 2 .
y = y + f ,
Ω = 2 π ( 1 cos δ ) = 2 π [ 1 cos ( tan 1 D 2 f ) ] ,
Φ = T A Ω L I cos θ d ω d a .
Φ = π A T L I sin 2 δ = π 2 ρ T L s D 2 D 2 + 4 f 2 ( 0.0087 y 2 ) 2
Φ = 1.9 × 10 4 ρ T L s y 2 D 2 D 2 + 4 f 2 .
Φ = 2.0 × 10 5 L s R 2 D 2 D 2 + 4 f 2 .
Φ = 2.0 × 10 5 L s R 2 1 + 4 F 2 .
Φ = 5.1 × 10 6 L s ( R F ) 2 .
Φ 9885 ( R F ) 2 .
tan θ x = x f tan θ z = z f .
Δ θ x = tan 1 ( 1.06 R / f )
Δ θ z = tan 1 ( 0.62 R / f ) .
Φ = 8798 D 2 tan 2 ( Δ θ x ) .
cot Ψ = tan θ sin ϕ .
d 2 Φ = L I Δ z H / 2 H / 2 cos 2 θ R 2 dhdld l ,
d 2 Φ = 2 f 2 H Δ z L I [ 1 4 f 2 ( f 2 + H 2 / 4 ) + 1 2 f 3 H tan 1 ( H 2 f ) ] dld l .
Φ = 2 f 2 H Δ z L I [ 1 4 f 2 ( f 2 + H 2 / 4 ) + 1 2 f 3 H tan 1 ( H 2 f ) ] 0 L d l ,
Φ L = 2 f 2 H Δ z L I [ 1 4 f 2 ( f 2 + H 2 / 4 ) + 1 2 f 3 H tan 1 ( H 2 f ) ] .

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