def equation_of_time_spencer71(dayofyear):
day_angle = _calculate_simple_day_angle(dayofyear)<EOL>eot = (<NUM_LIT> / <NUM_LIT:2> / np.pi) * (<EOL><NUM_LIT> +<EOL><NUM_LIT> * np.cos(day_angle) - <NUM_LIT> * np.sin(day_angle) -<EOL><NUM_LIT> * np.cos(<NUM_LIT> * day_angle) - <NUM_LIT> * np.sin(<NUM_LIT> * day_angle)<EOL>)<EOL>return eot<EOL>
Equation of time from Duffie & Beckman and attributed to Spencer
(1971) and Iqbal (1983).

The coefficients correspond to the online copy of the `Fourier
paper`_ [1]_ in the Sundial Mailing list that was posted in 1998 by
Mac Oglesby from his correspondence with Macquarie University Prof.
John Pickard who added the following note.

    In the early 1970s, I contacted Dr Spencer about this method because I
    was trying to use a hand calculator for calculating solar positions,
    etc. He was extremely helpful and gave me a reprint of this paper. He
    also pointed out an error in the original: in the series for E, the
    constant was printed as 0.000075 rather than 0.0000075. I have
    corrected the error in this version.

There appears to be another error in formula as printed in both
Duffie & Beckman's [2]_ and Frank Vignola's [3]_ books in which the
coefficient 0.04089 is printed instead of 0.040849, corresponding to
the value used in the Bird Clear Sky model implemented by Daryl
Myers [4]_ and printed in both the Fourier paper from the Sundial
Mailing List and R. Hulstrom's [5]_ book.

.. _Fourier paper: http://www.mail-archive.com/sundial@uni-koeln.de/msg01050.html

Parameters
----------
dayofyear : numeric

Returns
-------
equation_of_time : numeric
    Difference in time between solar time and mean solar time in minutes.

References
----------
.. [1] J. W. Spencer, "Fourier series representation of the position of the
   sun" in Search 2 (5), p. 172 (1971)

.. [2] J. A. Duffie and W. A. Beckman,  "Solar Engineering of Thermal
   Processes, 3rd Edition" pp. 9-11, J. Wiley and Sons, New York (2006)

.. [3] Frank Vignola et al., "Solar And Infrared Radiation Measurements",
   p. 13, CRC Press (2012)

.. [5] Daryl R. Myers, "Solar Radiation: Practical Modeling for Renewable
   Energy Applications", p. 5 CRC Press (2013)

.. [4] Roland Hulstrom, "Solar Resources" p. 66, MIT Press (1989)

See Also
--------
equation_of_time_pvcdrom