While I do not think that many Bronze Age or Classical bows were as powerful as the longbows from the Mary Rose or the hornbows from the Tokapi Palace, I can think of one or two exceptions. Today I would like to give one which I recently stumbled over while reviewing an article by Pierre Briant. As often happens, reading this passage again revealed something which I had not remembered.
The Great Sphinx Stele tells the following story of Pharaoh Amenhotep II of the New Kingdom:
He also came to do the following … Entering his northern garden, he found erected for him four targets of Asiatic copper, of one palm in thickness, with a distance of twenty cubits between one post and the next. Then his Majesty appeared on the chariot like Mont in his might. He drew his bow while holding four arrows together in his fist. Then he rode northward shooting at them, like Mont in his panoply, each arrow coming out of the back of its target while he attacked the next post. It was a deed never yet done, never yet heard reported: shooting an arrow at a target of copper, so that it came out of it and dropped to the ground.
Andrea M. Gnirs, “Ancient Egypt,” in Kurt Raaflaub and Nathan Rosenstein eds., War and Society in the Ancient and Medieval Worlds (Cambridge MA, 1999) p. 84 citing the Great Sphinx Stele of Amenhotep II in Miriam Lichtheim, Ancient Egyptian Literature: A Book of Readings. Volume 2. Berkeley and Los Angeles: University of California Press, 1976) pp. 41, 42.