Abstract

The considerable utility of ultrasensitive microwave radar in atmospheric studies can now be augmented by lidar and acoustic echo-sounding techniques. The current and potential capabilities, and limitations, of these methods of remote atmospheric probing are discussed and the techniques are compared. From this analysis the conclusion emerges that a remote sensing facility consisting of these instruments probing the same volume of the atmosphere can measure many of the meteorologically significant parameters necessary to increase our understanding of the structure and dynamics of the clear lower atmosphere, and provide the spatial and temporal density of measurements necessary for weather forecasting.

© 1970 Optical Society of America

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References

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  1. K. Ya. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1969).
  2. C. Junge, Air Chemistry and Radioactivity (Academic, New York1963).
  3. L. Elterman, Environmental Research Papers, No. 46 (Air Force Cambridge Research Laboratories, AFCRL-64-7401964).
  4. Final Report of the Panel on Remote Atmospheric Probing to the Committee on Atmospheric Sciences, Atmospheric Exploration by Remote Probes, Vol. 2 (National Academy of Sciences, Washington, D.C., 1969).
  5. K. Sakurai, H. P. Broida, J. Chem. Phys. 50, 2404 (1969).
    [CrossRef]
  6. D. Leonard, AVCO Corp., Everett, Mass. (private communication).
  7. G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 2Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, Princeton, N. J., 1960.)
  8. S. Mizushima, in Handbuch der Physik, 26–27, S. Flügge, Ed. (Springer-Verlag, Berlin, 1958).
  9. H. A. Szymanski (Ed.), Raman Spectroscopy (Plenum Press, Inc., New York, 1967).
    [CrossRef]
  10. V. I. Tatarski, Wave Propagation in a Turbulent Medium, (Dover Publ., Inc., New York, 1967).
  11. R. Bolgiano, Proc. IRE 47, 331 (1959).
  12. B. R. Bean, E. J. Dutton, Radio Meteorology (Dover Publ., Inc., New York, 1966).
  13. G. Fiocco, L. D. Smullin, Nature 199, 275 (1963).
    [CrossRef]
  14. C. K. N. Patel, Bull. Amer. Phys. Soc. 15, 505 (1970).
  15. R. S. Lawrence, J. W. Strohbehn, Proc. IEEE, to be published Sept.1970.
  16. E. W. Barrett, P. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
    [CrossRef]
  17. F. R. Krause, M. J. Fisher, Proc. ASME Symp.171, (1966).
  18. M. J. Fisher, F. R. Krause, J. Fluid Mech. 28, 705 (1967).
    [CrossRef]
  19. F. R. Krause, V. E. Derr, N. L. Abshire, R. G. Strauch, Proc. 6th Int. Symp. Remote Sensing Environ. 1, 327 (1969).
  20. J. A. Dutton, J. A. Lane et al., Radio Science 3, 1357 (1969).
    [CrossRef]
  21. J. C. Owens, Proc. IEEE 57, 530 (1969).
    [CrossRef]
  22. R. M. Huffaker, Appl. Opt. 9, 1026 (1970).
    [CrossRef] [PubMed]
  23. J. Cooney, J. Appl. Meteorol. 9, 182 (1960).
    [CrossRef]
  24. S. H. Melfi, J. D. Lawrence, M. P. McCormick, Appl. Phys. Lett. 15, 295 (1969).
    [CrossRef]
  25. J. A. Cooney, Appl. Phys. Lett. 12, 40 (1968).
    [CrossRef]
  26. K. R. Hardy, I. Katz, Proc. IEEE 57, 468 (1969).
    [CrossRef]
  27. J. H. Richter, Radio Science 4, 1261 (1969).
    [CrossRef]
  28. R. M. Lhermitte, in Proc. 8th Weather Radar Conf. (Amer. Meteorol. Soc., Boston, 1960), p. 269.
  29. D. Atlas, J. H. Richter, E. E. Gossard, Tech. Rep. No. 13, Laboratory for Atmospheric Probing, Dept. of Geophysical Sciences (University of Chicago Press, Chicago, 1969).
  30. D. Atlas, Advan. Geophys. 10, 317 (1964).
    [CrossRef]
  31. C. G. Little, Proc. IEEE 57, 571 (1969).
    [CrossRef]
  32. G. Kelton, P. Bricout, Bull. Amer. Meteorol. Soc. 45, 571 (1964).
  33. B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. 63, 106 (1950).
    [CrossRef]
  34. E. E. Gossard, D. B. Sailors, J. Geophys. Res., Space Phys. 75, 1324 (1970).
    [CrossRef]
  35. L. G. McAllister, J. R. Pollard, A. R. Mahoney, P. J. R. Shaw, Proc. IEEE 57, 579 (1969).
    [CrossRef]
  36. C. M. Harris, J. Acoust. Soc. Amer. 40, 148 (1966).
    [CrossRef]

1970 (3)

C. K. N. Patel, Bull. Amer. Phys. Soc. 15, 505 (1970).

E. E. Gossard, D. B. Sailors, J. Geophys. Res., Space Phys. 75, 1324 (1970).
[CrossRef]

R. M. Huffaker, Appl. Opt. 9, 1026 (1970).
[CrossRef] [PubMed]

1969 (9)

L. G. McAllister, J. R. Pollard, A. R. Mahoney, P. J. R. Shaw, Proc. IEEE 57, 579 (1969).
[CrossRef]

K. Sakurai, H. P. Broida, J. Chem. Phys. 50, 2404 (1969).
[CrossRef]

F. R. Krause, V. E. Derr, N. L. Abshire, R. G. Strauch, Proc. 6th Int. Symp. Remote Sensing Environ. 1, 327 (1969).

J. A. Dutton, J. A. Lane et al., Radio Science 3, 1357 (1969).
[CrossRef]

J. C. Owens, Proc. IEEE 57, 530 (1969).
[CrossRef]

S. H. Melfi, J. D. Lawrence, M. P. McCormick, Appl. Phys. Lett. 15, 295 (1969).
[CrossRef]

K. R. Hardy, I. Katz, Proc. IEEE 57, 468 (1969).
[CrossRef]

J. H. Richter, Radio Science 4, 1261 (1969).
[CrossRef]

C. G. Little, Proc. IEEE 57, 571 (1969).
[CrossRef]

1968 (1)

J. A. Cooney, Appl. Phys. Lett. 12, 40 (1968).
[CrossRef]

1967 (2)

M. J. Fisher, F. R. Krause, J. Fluid Mech. 28, 705 (1967).
[CrossRef]

E. W. Barrett, P. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

1966 (2)

F. R. Krause, M. J. Fisher, Proc. ASME Symp.171, (1966).

C. M. Harris, J. Acoust. Soc. Amer. 40, 148 (1966).
[CrossRef]

1964 (2)

G. Kelton, P. Bricout, Bull. Amer. Meteorol. Soc. 45, 571 (1964).

D. Atlas, Advan. Geophys. 10, 317 (1964).
[CrossRef]

1963 (1)

G. Fiocco, L. D. Smullin, Nature 199, 275 (1963).
[CrossRef]

1960 (1)

J. Cooney, J. Appl. Meteorol. 9, 182 (1960).
[CrossRef]

1959 (1)

R. Bolgiano, Proc. IRE 47, 331 (1959).

1950 (1)

B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. 63, 106 (1950).
[CrossRef]

Abshire, N. L.

F. R. Krause, V. E. Derr, N. L. Abshire, R. G. Strauch, Proc. 6th Int. Symp. Remote Sensing Environ. 1, 327 (1969).

Atlas, D.

D. Atlas, Advan. Geophys. 10, 317 (1964).
[CrossRef]

D. Atlas, J. H. Richter, E. E. Gossard, Tech. Rep. No. 13, Laboratory for Atmospheric Probing, Dept. of Geophysical Sciences (University of Chicago Press, Chicago, 1969).

Barrett, E. W.

E. W. Barrett, P. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

Bean, B. R.

B. R. Bean, E. J. Dutton, Radio Meteorology (Dover Publ., Inc., New York, 1966).

Ben-Dov, P.

E. W. Barrett, P. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

Bolgiano, R.

R. Bolgiano, Proc. IRE 47, 331 (1959).

Bricout, P.

G. Kelton, P. Bricout, Bull. Amer. Meteorol. Soc. 45, 571 (1964).

Briggs, B. H.

B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. 63, 106 (1950).
[CrossRef]

Broida, H. P.

K. Sakurai, H. P. Broida, J. Chem. Phys. 50, 2404 (1969).
[CrossRef]

Cooney, J.

J. Cooney, J. Appl. Meteorol. 9, 182 (1960).
[CrossRef]

Cooney, J. A.

J. A. Cooney, Appl. Phys. Lett. 12, 40 (1968).
[CrossRef]

Derr, V. E.

F. R. Krause, V. E. Derr, N. L. Abshire, R. G. Strauch, Proc. 6th Int. Symp. Remote Sensing Environ. 1, 327 (1969).

Dutton, E. J.

B. R. Bean, E. J. Dutton, Radio Meteorology (Dover Publ., Inc., New York, 1966).

Dutton, J. A.

J. A. Dutton, J. A. Lane et al., Radio Science 3, 1357 (1969).
[CrossRef]

Elterman, L.

L. Elterman, Environmental Research Papers, No. 46 (Air Force Cambridge Research Laboratories, AFCRL-64-7401964).

Fiocco, G.

G. Fiocco, L. D. Smullin, Nature 199, 275 (1963).
[CrossRef]

Fisher, M. J.

M. J. Fisher, F. R. Krause, J. Fluid Mech. 28, 705 (1967).
[CrossRef]

F. R. Krause, M. J. Fisher, Proc. ASME Symp.171, (1966).

Gossard, E. E.

E. E. Gossard, D. B. Sailors, J. Geophys. Res., Space Phys. 75, 1324 (1970).
[CrossRef]

D. Atlas, J. H. Richter, E. E. Gossard, Tech. Rep. No. 13, Laboratory for Atmospheric Probing, Dept. of Geophysical Sciences (University of Chicago Press, Chicago, 1969).

Hardy, K. R.

K. R. Hardy, I. Katz, Proc. IEEE 57, 468 (1969).
[CrossRef]

Harris, C. M.

C. M. Harris, J. Acoust. Soc. Amer. 40, 148 (1966).
[CrossRef]

Herzberg, G.

G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 2Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, Princeton, N. J., 1960.)

Huffaker, R. M.

Junge, C.

C. Junge, Air Chemistry and Radioactivity (Academic, New York1963).

Katz, I.

K. R. Hardy, I. Katz, Proc. IEEE 57, 468 (1969).
[CrossRef]

Kelton, G.

G. Kelton, P. Bricout, Bull. Amer. Meteorol. Soc. 45, 571 (1964).

Kondratyev, K. Ya.

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

Krause, F. R.

F. R. Krause, V. E. Derr, N. L. Abshire, R. G. Strauch, Proc. 6th Int. Symp. Remote Sensing Environ. 1, 327 (1969).

M. J. Fisher, F. R. Krause, J. Fluid Mech. 28, 705 (1967).
[CrossRef]

F. R. Krause, M. J. Fisher, Proc. ASME Symp.171, (1966).

Lane, J. A.

J. A. Dutton, J. A. Lane et al., Radio Science 3, 1357 (1969).
[CrossRef]

Lawrence, J. D.

S. H. Melfi, J. D. Lawrence, M. P. McCormick, Appl. Phys. Lett. 15, 295 (1969).
[CrossRef]

Lawrence, R. S.

R. S. Lawrence, J. W. Strohbehn, Proc. IEEE, to be published Sept.1970.

Leonard, D.

D. Leonard, AVCO Corp., Everett, Mass. (private communication).

Lhermitte, R. M.

R. M. Lhermitte, in Proc. 8th Weather Radar Conf. (Amer. Meteorol. Soc., Boston, 1960), p. 269.

Little, C. G.

C. G. Little, Proc. IEEE 57, 571 (1969).
[CrossRef]

Mahoney, A. R.

L. G. McAllister, J. R. Pollard, A. R. Mahoney, P. J. R. Shaw, Proc. IEEE 57, 579 (1969).
[CrossRef]

McAllister, L. G.

L. G. McAllister, J. R. Pollard, A. R. Mahoney, P. J. R. Shaw, Proc. IEEE 57, 579 (1969).
[CrossRef]

McCormick, M. P.

S. H. Melfi, J. D. Lawrence, M. P. McCormick, Appl. Phys. Lett. 15, 295 (1969).
[CrossRef]

Melfi, S. H.

S. H. Melfi, J. D. Lawrence, M. P. McCormick, Appl. Phys. Lett. 15, 295 (1969).
[CrossRef]

Mizushima, S.

S. Mizushima, in Handbuch der Physik, 26–27, S. Flügge, Ed. (Springer-Verlag, Berlin, 1958).

Owens, J. C.

J. C. Owens, Proc. IEEE 57, 530 (1969).
[CrossRef]

Patel, C. K. N.

C. K. N. Patel, Bull. Amer. Phys. Soc. 15, 505 (1970).

Phillips, G. J.

B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. 63, 106 (1950).
[CrossRef]

Pollard, J. R.

L. G. McAllister, J. R. Pollard, A. R. Mahoney, P. J. R. Shaw, Proc. IEEE 57, 579 (1969).
[CrossRef]

Richter, J. H.

J. H. Richter, Radio Science 4, 1261 (1969).
[CrossRef]

D. Atlas, J. H. Richter, E. E. Gossard, Tech. Rep. No. 13, Laboratory for Atmospheric Probing, Dept. of Geophysical Sciences (University of Chicago Press, Chicago, 1969).

Sailors, D. B.

E. E. Gossard, D. B. Sailors, J. Geophys. Res., Space Phys. 75, 1324 (1970).
[CrossRef]

Sakurai, K.

K. Sakurai, H. P. Broida, J. Chem. Phys. 50, 2404 (1969).
[CrossRef]

Shaw, P. J. R.

L. G. McAllister, J. R. Pollard, A. R. Mahoney, P. J. R. Shaw, Proc. IEEE 57, 579 (1969).
[CrossRef]

Shinn, D. H.

B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. 63, 106 (1950).
[CrossRef]

Smullin, L. D.

G. Fiocco, L. D. Smullin, Nature 199, 275 (1963).
[CrossRef]

Strauch, R. G.

F. R. Krause, V. E. Derr, N. L. Abshire, R. G. Strauch, Proc. 6th Int. Symp. Remote Sensing Environ. 1, 327 (1969).

Strohbehn, J. W.

R. S. Lawrence, J. W. Strohbehn, Proc. IEEE, to be published Sept.1970.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium, (Dover Publ., Inc., New York, 1967).

Advan. Geophys. (1)

D. Atlas, Advan. Geophys. 10, 317 (1964).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. H. Melfi, J. D. Lawrence, M. P. McCormick, Appl. Phys. Lett. 15, 295 (1969).
[CrossRef]

J. A. Cooney, Appl. Phys. Lett. 12, 40 (1968).
[CrossRef]

Bull. Amer. Meteorol. Soc. (1)

G. Kelton, P. Bricout, Bull. Amer. Meteorol. Soc. 45, 571 (1964).

Bull. Amer. Phys. Soc. (1)

C. K. N. Patel, Bull. Amer. Phys. Soc. 15, 505 (1970).

J. Acoust. Soc. Amer. (1)

C. M. Harris, J. Acoust. Soc. Amer. 40, 148 (1966).
[CrossRef]

J. Appl. Meteorol. (2)

J. Cooney, J. Appl. Meteorol. 9, 182 (1960).
[CrossRef]

E. W. Barrett, P. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

J. Chem. Phys. (1)

K. Sakurai, H. P. Broida, J. Chem. Phys. 50, 2404 (1969).
[CrossRef]

J. Fluid Mech. (1)

M. J. Fisher, F. R. Krause, J. Fluid Mech. 28, 705 (1967).
[CrossRef]

J. Geophys. Res., Space Phys. (1)

E. E. Gossard, D. B. Sailors, J. Geophys. Res., Space Phys. 75, 1324 (1970).
[CrossRef]

Nature (1)

G. Fiocco, L. D. Smullin, Nature 199, 275 (1963).
[CrossRef]

Proc. 6th Int. Symp. Remote Sensing Environ. (1)

F. R. Krause, V. E. Derr, N. L. Abshire, R. G. Strauch, Proc. 6th Int. Symp. Remote Sensing Environ. 1, 327 (1969).

Proc. ASME Symp. (1)

F. R. Krause, M. J. Fisher, Proc. ASME Symp.171, (1966).

Proc. IEEE (4)

J. C. Owens, Proc. IEEE 57, 530 (1969).
[CrossRef]

C. G. Little, Proc. IEEE 57, 571 (1969).
[CrossRef]

K. R. Hardy, I. Katz, Proc. IEEE 57, 468 (1969).
[CrossRef]

L. G. McAllister, J. R. Pollard, A. R. Mahoney, P. J. R. Shaw, Proc. IEEE 57, 579 (1969).
[CrossRef]

Proc. IRE (1)

R. Bolgiano, Proc. IRE 47, 331 (1959).

Proc. Phys. Soc. (1)

B. H. Briggs, G. J. Phillips, D. H. Shinn, Proc. Phys. Soc. 63, 106 (1950).
[CrossRef]

Radio Science (2)

J. H. Richter, Radio Science 4, 1261 (1969).
[CrossRef]

J. A. Dutton, J. A. Lane et al., Radio Science 3, 1357 (1969).
[CrossRef]

Other (13)

B. R. Bean, E. J. Dutton, Radio Meteorology (Dover Publ., Inc., New York, 1966).

R. S. Lawrence, J. W. Strohbehn, Proc. IEEE, to be published Sept.1970.

D. Leonard, AVCO Corp., Everett, Mass. (private communication).

G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 2Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, Princeton, N. J., 1960.)

S. Mizushima, in Handbuch der Physik, 26–27, S. Flügge, Ed. (Springer-Verlag, Berlin, 1958).

H. A. Szymanski (Ed.), Raman Spectroscopy (Plenum Press, Inc., New York, 1967).
[CrossRef]

V. I. Tatarski, Wave Propagation in a Turbulent Medium, (Dover Publ., Inc., New York, 1967).

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

C. Junge, Air Chemistry and Radioactivity (Academic, New York1963).

L. Elterman, Environmental Research Papers, No. 46 (Air Force Cambridge Research Laboratories, AFCRL-64-7401964).

Final Report of the Panel on Remote Atmospheric Probing to the Committee on Atmospheric Sciences, Atmospheric Exploration by Remote Probes, Vol. 2 (National Academy of Sciences, Washington, D.C., 1969).

R. M. Lhermitte, in Proc. 8th Weather Radar Conf. (Amer. Meteorol. Soc., Boston, 1960), p. 269.

D. Atlas, J. H. Richter, E. E. Gossard, Tech. Rep. No. 13, Laboratory for Atmospheric Probing, Dept. of Geophysical Sciences (University of Chicago Press, Chicago, 1969).

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Figures (7)

Fig. 1
Fig. 1

Lidar configuration.

Fig. 2
Fig. 2

Ratio of received to transmitted lidar signal as function of range, for various values of the radar backscatter coefficient β (m−1). No atmospheric attenuation.

Fig. 3
Fig. 3

Same as Fig. 2 with exponential atmospheric attenuation.

Fig. 4
Fig. 4

Crossed beam wind sensing test configuration.

Fig. 5
Fig. 5

Conically scanned wind sensing configuration.

Fig. 6
Fig. 6

Typical output of two receivers in the configuration of Fig. 2. Laser: Ar+, 2 W at 488 nm, separation between cells, 4 m, wind 0–24 km h−1.

Fig. 7
Fig. 7

Raman lidar signal vs range, and background and detector noise magnitudes. (Graph courtesy of G.T. McNice.)

Tables (3)

Tables Icon

Table I Typical Optical Scattering Cross Sections (per Particle)

Tables Icon

Table II Relative Values of C n for Acoustic, Radio, and Optical Waves a

Tables Icon

Table III Maximum Range for Wind Sensing

Equations (42)

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

S ¯ = π c ( 1 + cos 2 θ ) 16 R 2 N λ 4 ( n 2 1 ) 2 ( E ° ) 2 ,
I = 2 7 π 5 3 2 c 4 I 0 ( ν 0 | ν m n | ) 4 ρ σ | α ρ σ , m n | 2 ,
α m n = 1 h r ( μ r n μ m r ν r m ν 0 + i δ r + μ m r μ r n ν r n + ν 0 + i δ r ) .
η = 8 π 2 k 4 φ n ( 4 π / λ ) ,
D n ( r ) = | n ( x ) n ( x + r ) | 2 av = C n 2 r 2 / 3 ,
η ( λ ) = 0.38 C n 2 λ 1 3 .
N = ( 77.6 / T ) [ P + ( 4810 e / T ) ] ,
C d = 20.05 × T 1 2 msec 1 .
C m = C d ( 1 + 0.14 e / P ) msec 1 .
C = C d , m + V cos φ ,
σ r ( θ ) = 2 π k 4 sin 2 χ · φ n ( 2 k sin 1 2 θ ) ,
σ a ( θ ) = 2 π k 4 · cos 2 θ · φ n ( 2 k sin 1 2 θ ) .
σ r ( θ ) = 0.016 k 1 3 · sin 2 χ · ( sin 1 2 θ ) 11 / 3 C n 2 ,
σ a ( θ ) = 0.016 k 1 3 · cos 2 θ · ( sin 1 2 θ ) 11 / 3 [ 1.85 C υ 2 / C 2 cos 2 1 2 θ + C T 2 / 4 T 2 ] ,
N r = N t exp ( 0 S α 1 ( s ) d s ) · σ θ ( Ω ) Ω r ρ V e × exp ( 0 R α 2 ( r ) d r ) / Ω t S 2 .
N r = N t exp ( 0 S α 1 ( s ) d s ) A β θ L exp ( 0 R α 2 ( r ) d r ) / R 2 ,
N = ( η P + m τ ( η B λ A Ω r λ Δ λ ) h c + I d e G ) 1 2 ,
N = ( S / r ) 2 = ( 10 / 7 × 10 3 ) 2 = ( 1500 ) 2 .
σ I I 0 = ( 1.12 × 10 6 ) 1 2 = 1.06 × 10 3 = 0.10 % .
R max = ( η N t L A β ) 1 2 .
ρ ( z ) = 1 2 α z ln N r ( λ 1 , β , z ) N r ( λ 2 , β , z ) ,
P ( h ) = P g 0 h g ρ ( z ) d z ,
T ( h ) = [ p g g 0 h ρ ( z ) d z ] / ( ρ ( h ) R / M ) ,
I = 0 h ρ ( z ) d z
σ T 2 / T 2 = σ ρ 2 / ρ 2 ,
N r N = σ A ρ A ( R ) · · A R 2 · exp { 2 [ 0 R ρ A ( z ) K A d z ] } ,
η = 0.38 α 2 2 3 β 2 ( d n / d z ) 2 λ 1 3 ,
A ( t ) = i a i cos ( ω + ω i ) t ,
I ( t ) = i a i 2 = 2 i j a i a j cos ( ψ i j t ) ,
P r = P T σ 180 ( C τ / 2 ) ( A r / R 2 ) α T α R exp [ 2 α ( r ) d r ] ,
C n = 2.6 × 10 6 m 1 3 .
C n = C T / 2 T .
C T = 2 T C n 1.6 × 10 3 K m 1 3 .
P r = 4.25 × 10 6 σ ( θ ) .
σ ( θ ) = 0.030 k 1 3 cos 2 θ cos 2 1 2 θ ( sin 1 2 θ ) 11 3 / ( C υ / C ) 2 .
σ ( 60 ° ) = 0.090 k 1 3 ( C υ / C ) 2 .
σ ( 120 ° ) = 0.053 k 1 3 ( C υ / C ) 2 .
C υ = 6 mm sec 1 m 1 3 ( θ = 120 ° ) ,
C υ = 3.5 mm sec 1 m 1 3 ( θ = 60 ° ) .
σ a ( θ ) = 3.9 × 10 3 k 1 3 ( C T / T ) 2 .
C n 2 = ( 79 P / T · 10 6 ) 2 C T 2 / T 2 .
D r r ( r ) = [ V r ( r 1 ) V r ( r 1 + r ) ] 2 ar .

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