r'''Calculates drag coefficient of a smooth sphere using the method in
    [1]_.

    .. math::
        C_D = 8\times 10^{-6}\left[(Re/6530)^2 + \tanh(Re) - 8\ln(Re)/\ln(10)\right]
        - 0.4119\exp(-2.08\times10^{43}/[Re + Re^2]^4)
        -2.1344\exp(-\{[\ln(Re^2 + 10.7563)/\ln(10)]^2 + 9.9867\}/Re)
        +0.1357\exp(-[(Re/1620)^2 + 10370]/Re)
        - 8.5\times 10^{-3}\{2\ln[\tanh(\tanh(Re))]/\ln(10) - 2825.7162\}/Re
        + 2.4795

    Parameters
    ----------
    Re : float
        Reynolds number of the sphere, [-]

    Returns
    -------
    Cd : float
        Drag coefficient [-]

    Notes
    -----
    Range is Re <= 1E6
    This model is the wider-range model the authors developed.
    At sufficiently low diameters or Re values, drag is no longer a phenomena.

    Examples
    --------
    Maching example in [1]_, in a table of calculated values.

    >>> Barati_high(200.)
    0.7730544082789523

    References
    ----------
    .. [1] Barati, Reza, Seyed Ali Akbar Salehi Neyshabouri, and Goodarz
       Ahmadi. "Development of Empirical Models with High Accuracy for
       Estimation of Drag Coefficient of Flow around a Smooth Sphere: An
       Evolutionary Approach." Powder Technology 257 (May 2014): 11-19.
       doi:10.1016/j.powtec.2014.02.045.

def Barati_high(Re):
    r'''Calculates drag coefficient of a smooth sphere using the method in
    [1]_.

    .. math::
        C_D = 8\times 10^{-6}\left[(Re/6530)^2 + \tanh(Re) - 8\ln(Re)/\ln(10)\right]
        - 0.4119\exp(-2.08\times10^{43}/[Re + Re^2]^4)
        -2.1344\exp(-\{[\ln(Re^2 + 10.7563)/\ln(10)]^2 + 9.9867\}/Re)
        +0.1357\exp(-[(Re/1620)^2 + 10370]/Re)
        - 8.5\times 10^{-3}\{2\ln[\tanh(\tanh(Re))]/\ln(10) - 2825.7162\}/Re
        + 2.4795

    Parameters
    ----------
    Re : float
        Reynolds number of the sphere, [-]

    Returns
    -------
    Cd : float
        Drag coefficient [-]

    Notes
    -----
    Range is Re <= 1E6
    This model is the wider-range model the authors developed.
    At sufficiently low diameters or Re values, drag is no longer a phenomena.

    Examples
    --------
    Maching example in [1]_, in a table of calculated values.

    >>> Barati_high(200.)
    0.7730544082789523

    References
    ----------
    .. [1] Barati, Reza, Seyed Ali Akbar Salehi Neyshabouri, and Goodarz
       Ahmadi. "Development of Empirical Models with High Accuracy for
       Estimation of Drag Coefficient of Flow around a Smooth Sphere: An
       Evolutionary Approach." Powder Technology 257 (May 2014): 11-19.
       doi:10.1016/j.powtec.2014.02.045.
    '''
    Cd = (8E-6*((Re/6530.)**2 + tanh(Re) - 8*log(Re)/log(10.))
    - 0.4119*exp(-2.08E43/(Re+Re**2)**4)
    - 2.1344*exp(-((log(Re**2 + 10.7563)/log(10))**2 + 9.9867)/Re)
    + 0.1357*exp(-((Re/1620.)**2 + 10370.)/Re)
    - 8.5E-3*(2*log(tanh(tanh(Re)))/log(10) - 2825.7162)/Re + 2.4795)
    return Cd