It seems that the principle is timeless. That is, the head-covering (hair) for women is a timeless principle in all ages and in all places, since angels have co-existed with man since man was created.
God's glory is his authority. Man (or the male) reflects that glory as the authority of God in creation. His head is therefore not to be covered. Although woman is "one flesh" with man, her glory on the other hand is her beauty, and therefore her head is covered with hair (or a wig, to which I believe is what Paul was actually referring in 1 Cor 11). She is not the glory of God (authority), but the glory of man (beauty). Otherwise a woman without hair is shamed. If a woman insists on bucking the creative order (and she happens to have long hair), then she might as well as shave her head, because bucking the creative order is shameful. Likewise a male with long hair is shameful (to which Paul invokes "nature" as testimony in 1 Cor 11:14).
In other words, the angels have recognized the creative order between God and man and then woman since creation, and therefore this biblical principle is not restricted to any cultural or era of time... but is timeless "because of the angels," who also recognize God's creative order between man and the woman in creation. Man and woman are "one flesh," but the one who reflects the authority of God is man, and the one who reflects the glory of man is the woman (and not vice-versa).
This principle is as timeless as the angels.