def _tooth_thickness(self, d_y):
        """
        Tooth thickness in transverse cross-section (chord-length)

        INPUT parameter:
        d_y : two times coordinate of tooth flank in radial direction
              (diameter of y-cylinder)

        OUTPUT:
        s_y  : chord length of tooth thickness at d_y (numeric)
        d_yc : cutting point of diameter through tooth center and chord (numeric)
        """

        # necessary due to numerical rounding errors
        if self.data.get('d') / d_y * cos(radians(self.data.get('alpha_t'))) > 1.0:
            alpha_yt = 0.0
        else:
            alpha_yt = degrees(acos(self.data.get('d') / d_y * cos(radians(self.data.get('alpha_t')))))
        s_yt = d_y * (
            (pi + 4 * self.data.get('x_E') * tan(radians(self.data.get('alpha_n')))) / 2 / self.data.get(
                'z') + inv(self.data.get('alpha_t')) - inv(alpha_yt))
        s_y = d_y * (sin(s_yt / d_y))  # tooth thickness (chord-length)
        d_yc = d_y * (cos(s_yt / d_y))  # diameter at center of tooth (cut with chord)

        return s_y, d_yc