Abstract

A copper disk pyrheliometer has been designed and constructed that utilizes a new methodology to measure solar radiation. By operating the shutter of the instrument and measuring the heating and cooling rates of the sensor at the very moment when the sensor is at the same temperature, the solar radiation can be accurately determined with these rates. The method is highly accurate and is shown to be totally independent of the loss coefficient in the measurement. The pyrheliometer has been tested using a standard irradiance lamp in the laboratory. The uncertainty of the instrument is identified to be ±0.61%. Field testing was also conducted by comparing data with that of a calibrated (Eppley) Normal Incidence Pyrheliometer. This paper spells out details of the construction and testing of the instrument; the analysis underlying the methodology was also covered in detail. Because of the high accuracy, the instrument is considered to be well suited for a bench standard for measurement of solar radiation.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. L. Coulson, Y. Howell, Sun World 4(3), 87 (1980).
  2. B. D. Wood, “Solar Energy Measuring Instrument,” in Applied Solar Energy, A. B. Meinel, M. P. Meinel, Eds. (Addison-Wesley, New York, 1977), pp. 397–429.
  3. J. M. Kendall, C. M. Berdahl, Appl. Opt. 9, 1082 (1970).
    [CrossRef] [PubMed]
  4. K. Y. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1969).
  5. J. I. Yellot, The Measurement of Solar Radiation, Low Temperature Engineering Application of Solar Energy, R. C. Jordon, Ed. (ASHRAE, New York, 1967).
  6. C. G. Abbot, The Silver Disk Pyrheliometer, Smithsonian Miscellaneous Collections, 56-19 (1911).
  7. L. B. Aldrich, The Abbot Silver-Disk Pyrheliometer, Smithsonian Miscellaneous Collections, 111-14 (1949).
  8. S. Chang, X. Ge, Acta Energ. Solar. Sin. 1(2), 314 (1980).
  9. C. K. Hsieh, S. Yang (to be published).
  10. Y. S. Touloukian, C. Y. Ho, Thermophysical Properties of Matter, Vol. 1, Thermal Conductivity Metallic Elements and Alloys (IFI/Plenum, New York, 1970).
  11. E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972).
  12. R. Stair, W. E. Schneider, J. K. Jackson, Appl. Opt. 2, 1151 (1963).
    [CrossRef]
  13. W. E. Schneider, Appl. Opt. 9, 1410 (1970).
    [CrossRef] [PubMed]
  14. “Instructions for Using the NBS Tungsten-Filament Lamp Standards of Total Irradiance,” NBS Spec. Publ. 300, Vol. 7, Precision Measurement and Calibration, Radiometry and Photometry, 271-273 (U.S. GPO, Washington, D.C., 1971).
  15. “Instructions for Using the NBS 1000-Watt Quartz Iodine Lamp Standards of Spectral Irradiance,” NBS Spec. Pub. 300, Vol. 7, Precision Measurement and Calibration, Radiometry and Photometry, 278-279 (U.S. GPO, Washington, D.C., 1971).
  16. The Eppley NIP was calibrated by the National Oceanic and Atmospheric Administration against an active cavity radiometer. Financial constraints precluded us from using an active cavity radiometer for direct comparison.
  17. Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4, Specific Heat Metallic Elements and Alloys (IFI/Plenum, New York, 1970).
  18. R. E. Bolz, G. L. Tuve, CRC Handbook of Tables for Applied Engineering Science (CRC Press, Cleveland, 1980).
  19. R. C. Weast, CRC Handbook of Chemistry and Physics (CRC Press, Cleveland, 1980).
  20. D. L. Martin, Can. J. Phys. 40, 1166 (1962).
    [CrossRef]
  21. Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 5, Specific Heat Nonmetallic Solids (IFI/Plenum, New York, 1970).
  22. W. T. Ziegler, J. C. Mullins, Cryogenics 4, 39 (1964).
    [CrossRef]
  23. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).
  24. C. K. Hsieh, I. M. Yeyinmen, J. J. G. Hsia, I. Keskin, Thermophysical Properties of High Temperature Solid Materials, Y. S. Touloukian, Ed. (Macmillan, New York, 1967).

1980 (2)

K. L. Coulson, Y. Howell, Sun World 4(3), 87 (1980).

S. Chang, X. Ge, Acta Energ. Solar. Sin. 1(2), 314 (1980).

1970 (2)

1964 (1)

W. T. Ziegler, J. C. Mullins, Cryogenics 4, 39 (1964).
[CrossRef]

1963 (1)

1962 (1)

D. L. Martin, Can. J. Phys. 40, 1166 (1962).
[CrossRef]

Abbot, C. G.

C. G. Abbot, The Silver Disk Pyrheliometer, Smithsonian Miscellaneous Collections, 56-19 (1911).

Aldrich, L. B.

L. B. Aldrich, The Abbot Silver-Disk Pyrheliometer, Smithsonian Miscellaneous Collections, 111-14 (1949).

Berdahl, C. M.

Bolz, R. E.

R. E. Bolz, G. L. Tuve, CRC Handbook of Tables for Applied Engineering Science (CRC Press, Cleveland, 1980).

Buyco, E. H.

Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4, Specific Heat Metallic Elements and Alloys (IFI/Plenum, New York, 1970).

Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 5, Specific Heat Nonmetallic Solids (IFI/Plenum, New York, 1970).

Chang, S.

S. Chang, X. Ge, Acta Energ. Solar. Sin. 1(2), 314 (1980).

Coulson, K. L.

K. L. Coulson, Y. Howell, Sun World 4(3), 87 (1980).

Drake, R. M.

E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972).

Eckert, E. R. G.

E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972).

Ge, X.

S. Chang, X. Ge, Acta Energ. Solar. Sin. 1(2), 314 (1980).

Ho, C. Y.

Y. S. Touloukian, C. Y. Ho, Thermophysical Properties of Matter, Vol. 1, Thermal Conductivity Metallic Elements and Alloys (IFI/Plenum, New York, 1970).

Howell, Y.

K. L. Coulson, Y. Howell, Sun World 4(3), 87 (1980).

Hsia, J. J. G.

C. K. Hsieh, I. M. Yeyinmen, J. J. G. Hsia, I. Keskin, Thermophysical Properties of High Temperature Solid Materials, Y. S. Touloukian, Ed. (Macmillan, New York, 1967).

Hsieh, C. K.

C. K. Hsieh, I. M. Yeyinmen, J. J. G. Hsia, I. Keskin, Thermophysical Properties of High Temperature Solid Materials, Y. S. Touloukian, Ed. (Macmillan, New York, 1967).

C. K. Hsieh, S. Yang (to be published).

Jackson, J. K.

Kendall, J. M.

Keskin, I.

C. K. Hsieh, I. M. Yeyinmen, J. J. G. Hsia, I. Keskin, Thermophysical Properties of High Temperature Solid Materials, Y. S. Touloukian, Ed. (Macmillan, New York, 1967).

Kondratyev, K. Y.

K. Y. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1969).

Martin, D. L.

D. L. Martin, Can. J. Phys. 40, 1166 (1962).
[CrossRef]

Mullins, J. C.

W. T. Ziegler, J. C. Mullins, Cryogenics 4, 39 (1964).
[CrossRef]

Schneider, W. E.

Stair, R.

Touloukian, Y. S.

Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 5, Specific Heat Nonmetallic Solids (IFI/Plenum, New York, 1970).

Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4, Specific Heat Metallic Elements and Alloys (IFI/Plenum, New York, 1970).

Y. S. Touloukian, C. Y. Ho, Thermophysical Properties of Matter, Vol. 1, Thermal Conductivity Metallic Elements and Alloys (IFI/Plenum, New York, 1970).

Tuve, G. L.

R. E. Bolz, G. L. Tuve, CRC Handbook of Tables for Applied Engineering Science (CRC Press, Cleveland, 1980).

Weast, R. C.

R. C. Weast, CRC Handbook of Chemistry and Physics (CRC Press, Cleveland, 1980).

Wood, B. D.

B. D. Wood, “Solar Energy Measuring Instrument,” in Applied Solar Energy, A. B. Meinel, M. P. Meinel, Eds. (Addison-Wesley, New York, 1977), pp. 397–429.

Yang, S.

C. K. Hsieh, S. Yang (to be published).

Yellot, J. I.

J. I. Yellot, The Measurement of Solar Radiation, Low Temperature Engineering Application of Solar Energy, R. C. Jordon, Ed. (ASHRAE, New York, 1967).

Yeyinmen, I. M.

C. K. Hsieh, I. M. Yeyinmen, J. J. G. Hsia, I. Keskin, Thermophysical Properties of High Temperature Solid Materials, Y. S. Touloukian, Ed. (Macmillan, New York, 1967).

Ziegler, W. T.

W. T. Ziegler, J. C. Mullins, Cryogenics 4, 39 (1964).
[CrossRef]

Acta Energ. Solar. Sin. (1)

S. Chang, X. Ge, Acta Energ. Solar. Sin. 1(2), 314 (1980).

Appl. Opt. (3)

Can. J. Phys. (1)

D. L. Martin, Can. J. Phys. 40, 1166 (1962).
[CrossRef]

Cryogenics (1)

W. T. Ziegler, J. C. Mullins, Cryogenics 4, 39 (1964).
[CrossRef]

Sun World (1)

K. L. Coulson, Y. Howell, Sun World 4(3), 87 (1980).

Other (17)

B. D. Wood, “Solar Energy Measuring Instrument,” in Applied Solar Energy, A. B. Meinel, M. P. Meinel, Eds. (Addison-Wesley, New York, 1977), pp. 397–429.

Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 5, Specific Heat Nonmetallic Solids (IFI/Plenum, New York, 1970).

D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

C. K. Hsieh, I. M. Yeyinmen, J. J. G. Hsia, I. Keskin, Thermophysical Properties of High Temperature Solid Materials, Y. S. Touloukian, Ed. (Macmillan, New York, 1967).

“Instructions for Using the NBS Tungsten-Filament Lamp Standards of Total Irradiance,” NBS Spec. Publ. 300, Vol. 7, Precision Measurement and Calibration, Radiometry and Photometry, 271-273 (U.S. GPO, Washington, D.C., 1971).

“Instructions for Using the NBS 1000-Watt Quartz Iodine Lamp Standards of Spectral Irradiance,” NBS Spec. Pub. 300, Vol. 7, Precision Measurement and Calibration, Radiometry and Photometry, 278-279 (U.S. GPO, Washington, D.C., 1971).

The Eppley NIP was calibrated by the National Oceanic and Atmospheric Administration against an active cavity radiometer. Financial constraints precluded us from using an active cavity radiometer for direct comparison.

Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4, Specific Heat Metallic Elements and Alloys (IFI/Plenum, New York, 1970).

R. E. Bolz, G. L. Tuve, CRC Handbook of Tables for Applied Engineering Science (CRC Press, Cleveland, 1980).

R. C. Weast, CRC Handbook of Chemistry and Physics (CRC Press, Cleveland, 1980).

K. Y. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1969).

J. I. Yellot, The Measurement of Solar Radiation, Low Temperature Engineering Application of Solar Energy, R. C. Jordon, Ed. (ASHRAE, New York, 1967).

C. G. Abbot, The Silver Disk Pyrheliometer, Smithsonian Miscellaneous Collections, 56-19 (1911).

L. B. Aldrich, The Abbot Silver-Disk Pyrheliometer, Smithsonian Miscellaneous Collections, 111-14 (1949).

C. K. Hsieh, S. Yang (to be published).

Y. S. Touloukian, C. Y. Ho, Thermophysical Properties of Matter, Vol. 1, Thermal Conductivity Metallic Elements and Alloys (IFI/Plenum, New York, 1970).

E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Analog circuit for analyzing the heat exchange by the sensor.

Fig. 2
Fig. 2

Typical temperature–time history for the sensor during heating and cooling processes.

Fig. 3
Fig. 3

Master drawing showing the construction of the pyrheliometer.

Fig. 4
Fig. 4

Effect of the number of paint coatings.

Fig. 5
Fig. 5

Experimental setup for calibrating the sensor.

Fig. 6
Fig. 6

View of the field test.

Fig. 7
Fig. 7

Laboratory test data for 60-sec cycle period.

Fig. 8
Fig. 8

Laboratory test data for 30-sec cycle period.

Tables (10)

Tables Icon

Table I Empirical Equations for Specific Heats

Tables Icon

Table II Mass of Sensor Disk

Tables Icon

Table III Thermal Capacitance of Sensor Disk at 22°C

Tables Icon

Table IV Specifications of the Pyrhellometer

Tables Icon

Table V View Angle and Tracking Tolerance Comparison Among Pyrhellometers

Tables Icon

Table VI Laboratory Test Results Based on the Analysis of Temperatures for Four Cycles at a Cycle Period of 60 sec

Tables Icon

Table VII Laboratory Test Results Based on the Analysis of Temperatures for Five Levels Within a Cycle at a Cycle Period of 60 sec

Tables Icon

Table VIII Laboratory Test Results Based on the Analysis of Temperatures for Five Cycles at a Cycle Period of 30 sec

Tables Icon

Table IX Uncertainty Estimation

Tables Icon

Table X Field Test Results

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

σ T 4 B ρ A + σ T 4 B 1 A F r b = 0 ,
B = ( / ρ ) σ T 4 + F r b σ T 4 ( / ρ ) + F r b .
Q radiation / A = σ T 4 B = F r b σ ( T 2 + T 2 ) ( T + T ) ( / ρ ) + F r b ( T T ) .
Q radiation / A = h r ( T T ) .
( Q radiation + Q convection ) / A = h ( T T ) .
D ( t ) = γ s A s c s [ T s ( x , t ) T ] d x γ s A s c s [ T s ( 0 , t ) T ] ,
( m c ) e d T d t = μ H A α 2 h A ( T T ) ,
T T = H α 2 h + [ ( T i T ) H α 2 h ] × exp [ 2 h A ( m c ) e t ] , 0 t t 1 .
T T = { H α 2 h + [ ( T i T ) H α 2 h ] exp [ 2 h A ( m c ) e t 1 ] } × exp [ 2 h A ( m c ) e ( t t 1 ) ] , t 1 t t 2 .
t b = ( m c ) e 2 h A ln ( T i T ) H α 2 h { 1 exp [ 2 h A ( m c ) e t 1 ] } H α 2 h + [ ( T i T ) H α 2 h ] exp [ 2 h A ( m c ) e t a ] .
d T d t | 0 t t 1 = 2 h A ( m c ) e [ ( T i T ) H α 2 h ] exp [ 2 h A ( m c ) e t ] ,
d T d t | t 1 t t 2 = 2 h A ( m c ) e ( ( T i T ) H α 2 h { 1 exp [ 2 h A ( m c ) e t 1 ] } ) × exp [ 2 h A ( m c ) e t ] .
d T d t | 0 < t = t a < t 1 d T d t | t 1 < t = t b < t 2 = H A α ( m c ) e ,
H = ( m c ) e A α ( d T d t | 0 < t = t a < t 1 d T d t | t 1 < t = t b < t 2 ) .
T = C 1 + C 2 C 3 t .
C 1 = T + H α 2 h ;
C 2 = ( T i T ) H α 2 h ;
C 3 = exp [ 2 h A ( m c ) e ] .
C 1 = T ,
C 2 = H α 2 h + [ ( T i T ) H α 2 h ] exp [ 2 h A ( m c ) e t 1 ] ,
C 3 = exp [ 2 h A ( m c ) e ] ,
Δ A / A = ( 26.4 + 0.024 T r ) × 10 6 × ( Δ T ) ,

Metrics