def trap_e_back(w, t, ratio):
    """Return distance centroid–back for trapezoid cross-sections.

    e_back_trap = (w+2W)/(w+W) * t/3
    Source: Lueger 1904

    Args:
        w: width
        t: thickness
        ratio: the ratio of back width to belly width

    Returns:
        A scalar.
    """
    sw = ratio * w
    return (sw + 2 * w) / (sw + w) * t / 3
