[Request] Odysseus shoots an arrow that punctures 12 solid bronze axeheads. How fast must the arrow be going?
When Odysseus shoots an arrow through twelve axeheads, it's usually envisaged that the arrow passes through twelve openings in the axeheads, as demonstrated [in this video](https://www.youtube.com/watch?v=2mUKauErjfM) and a few other places.
But that's because what the *Odyssey* actually describes is too implausible to take seriously.
The idea of the contest, the setting, and the genre all encourage the idea that Odysseus is performing a superhuman feat beyond the reach of any living mortal, and that his feat is a feat of strength, not aim. The scholar Walter Burkert favoured an interpretation where the arrow penetrates the metal of the axeheads -- similar to depictions of some Egyptian pharaohs, and the Indian hero Arjuna, shooting arrows through sheets of metal. [I wrote up an account of some competing alternatives here](http://kiwihellenist.blogspot.com/2019/09/mythbusters-odysseus-axes.html) a few years back.
So let's assume the following figures:
* The arrow is perfect (won't shatter on impact or be deflected from its course), and has a circular arrowhead 9.5 mm across (to give a round figure for the cross-section, 0.0003 m^(2)); and it's a relatively heavy arrow of over 600 grains, let's say 0.04 kg.
* Each axehead is made of bronze and has a thickness of 1.3 cm, similar to [one of these Bronze Age axeheads](https://ancienttouch.com/bronze_age%20axes,%20adzes.htm).
* Bronze is ductile and has an average shear strength of 297 MPa, [as per MatWeb](https://www.matweb.com/search/DataSheet.aspx?MatGUID=66575ff2cd5249c49d76df15b47dbca4&ckck=1), and other physical properties listed there as needed.
The arrow penetrates 12 such axeheads, either puncturing them or shattering them (whichever you consider more likely), and ends up lodging in a wooden door behind them. I assume the distances involved in the scenario and the time taken by the arrow will be negligible by comparison with the speed needed to get through 12 axeheads.
(For bonus marks, is it possible to calculate the required draw strength of the bow?)
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**Edit:** I belatedly checked the *Odyssey* and realised that it specifies that the axeheads are made of iron (Odyssey 21.114, 21.126-127, and 21.328). My bad. Let's go with bronze for now anyway.