Abstract

An examination has been carried out of the difficulties a horizontally placed parabola would encounter in concentrating the sun's rays when the angle of incidence between the axis of the parabola and parallel incident rays grows from 0° to 50°. The results obtained with two catenary curves formed by hypothetical reflecting adjustable sheets were compared with the parabola, showing that the concentration can be held at interesting levels as regards technical application.

© 1978 Optical Society of America

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References

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  1. R. H. Mc Fee, Appl. Opt. 14, 1493 (1975).
    [CrossRef]
  2. G. Francia, Sol. Energy 12 (1), 51 (1968).
    [CrossRef]
  3. F. Trombe, A. Le Chat Vinh, Sol. Energy 15 (1), 57 (1973).
    [CrossRef]
  4. W. G. Steward, F. Kreith, Appl. Opt. 14, 1509 (1975).
    [CrossRef] [PubMed]
  5. W. W. Shaner, H. S. Wilson, Sol. Energy 17 (6), 351 (1975).
    [CrossRef]
  6. M. Kovarik, Sol. Energy 17 (2), 91 (1975).
    [CrossRef]
  7. K. Hassan, M. F. El-Rafaie, Sol. Energy 15, 219 (1973).
    [CrossRef]
  8. F. James, M. Roos, MINUIT—A system for minimizing a function of n parameters and computing the parameter errors and correlations, CERN Computer Centre (Language:Fortran).

1975 (4)

W. G. Steward, F. Kreith, Appl. Opt. 14, 1509 (1975).
[CrossRef] [PubMed]

W. W. Shaner, H. S. Wilson, Sol. Energy 17 (6), 351 (1975).
[CrossRef]

M. Kovarik, Sol. Energy 17 (2), 91 (1975).
[CrossRef]

R. H. Mc Fee, Appl. Opt. 14, 1493 (1975).
[CrossRef]

1973 (2)

F. Trombe, A. Le Chat Vinh, Sol. Energy 15 (1), 57 (1973).
[CrossRef]

K. Hassan, M. F. El-Rafaie, Sol. Energy 15, 219 (1973).
[CrossRef]

1968 (1)

G. Francia, Sol. Energy 12 (1), 51 (1968).
[CrossRef]

El-Rafaie, M. F.

K. Hassan, M. F. El-Rafaie, Sol. Energy 15, 219 (1973).
[CrossRef]

Francia, G.

G. Francia, Sol. Energy 12 (1), 51 (1968).
[CrossRef]

Hassan, K.

K. Hassan, M. F. El-Rafaie, Sol. Energy 15, 219 (1973).
[CrossRef]

James, F.

F. James, M. Roos, MINUIT—A system for minimizing a function of n parameters and computing the parameter errors and correlations, CERN Computer Centre (Language:Fortran).

Kovarik, M.

M. Kovarik, Sol. Energy 17 (2), 91 (1975).
[CrossRef]

Kreith, F.

Le Chat Vinh, A.

F. Trombe, A. Le Chat Vinh, Sol. Energy 15 (1), 57 (1973).
[CrossRef]

Mc Fee, R. H.

Roos, M.

F. James, M. Roos, MINUIT—A system for minimizing a function of n parameters and computing the parameter errors and correlations, CERN Computer Centre (Language:Fortran).

Shaner, W. W.

W. W. Shaner, H. S. Wilson, Sol. Energy 17 (6), 351 (1975).
[CrossRef]

Steward, W. G.

Trombe, F.

F. Trombe, A. Le Chat Vinh, Sol. Energy 15 (1), 57 (1973).
[CrossRef]

Wilson, H. S.

W. W. Shaner, H. S. Wilson, Sol. Energy 17 (6), 351 (1975).
[CrossRef]

Appl. Opt. (2)

Sol. Energy (5)

G. Francia, Sol. Energy 12 (1), 51 (1968).
[CrossRef]

F. Trombe, A. Le Chat Vinh, Sol. Energy 15 (1), 57 (1973).
[CrossRef]

W. W. Shaner, H. S. Wilson, Sol. Energy 17 (6), 351 (1975).
[CrossRef]

M. Kovarik, Sol. Energy 17 (2), 91 (1975).
[CrossRef]

K. Hassan, M. F. El-Rafaie, Sol. Energy 15, 219 (1973).
[CrossRef]

Other (1)

F. James, M. Roos, MINUIT—A system for minimizing a function of n parameters and computing the parameter errors and correlations, CERN Computer Centre (Language:Fortran).

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Figures (18)

Fig. 1
Fig. 1

Profile of the sheet held in point A and C.

Fig. 2
Fig. 2

Profile of the sheet held in point A, C, and B.

Fig. 3
Fig. 3

Parabola with 2-m deep concavity—angle of incident radiation 90°.

Fig. 4
Fig. 4

Parabola with 2-m deep concavity—angle of incident radiation 60°.

Fig. 5
Fig. 5

Parabola with 2-m deep concavity—angle of incident radiation 45°.

Fig. 6
Fig. 6

Parabola with 3-m deep concavity—angle of incident radiation 90°.

Fig. 7
Fig. 7

Parabola with 3-m deep concavity—angle of incident radiation 60°.

Fig. 8
Fig. 8

Parabola with 3-m deep concavity—angle of incident radiation 45°.

Fig. 9
Fig. 9

Catenaries with 3-m deep concavity—angle of incident radiation 90°.

Fig. 10
Fig. 10

Catenaries with 3-m deep concavity—angle of incident radiation 60°.

Fig. 11
Fig. 11

Catenaries with 3-m deep concavity—angle of incident radiation 45°.

Fig. 12
Fig. 12

Position of point B vs the best focalization—3-m concavity.

Fig. 13
Fig. 13

Dispersion comparison between parabolic concentrator and catenary curves.

Fig. 14
Fig. 14

Catenaries with 2-m deep concavity—angle of incident radiation 90°.

Fig. 15
Fig. 15

Catenaries with 2-m deep concavity—angle of incident radiation 60°.

Fig. 16
Fig. 16

Catenaries with 2-m deep concavity—angle of incident radiation 45°.

Fig. 17
Fig. 17

Position of point B vs the best focalization—2-m concavity.

Fig. 18
Fig. 18

Dispersion comparision between parabolic concentrator and catenary curves.

Tables (1)

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Table I Concentrator with 2-m Deep Concavity—Coefficient K

Equations (5)

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y = B cosh { [ ( x x υ ) / B ] } C
y 1 = B 1 cosh ( x x υ 1 B 1 ) C 1 , y 2 = B 2 cosh ( x x υ 2 B 2 ) C 2 .
L A B = B 1 [ sinh ( x 0 x υ 1 B 1 ) sinh ( x 1 x υ 1 B 1 ) ] Y x = x 1 = B 1 cosh ( x 1 x υ 1 B 1 ) C 1 = F Y x = x 0 = B 1 cosh ( x 0 x υ 1 B 1 ) C 1 = H } ,
B 1 [ cosh ( x 1 x υ 1 B 1 ) cosh ( x 0 x υ 1 B 1 ) ] = F H .
cosh ( x 1 x 0 B 1 ) = ( F H ) 2 + L A B 2 2 B 1 2 + 1 .

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