If I go on a (EU internal) flight with my bow, do I have to register my uncommon luggage somehow? Is just handled as sporting equipment like a ball?
Of course we're not talking about the "hand-luggage".
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In general, you can find information about what items are permitted on the flight on both the website of the airline (they will have a restricted items page) and on the website of the relevant athourity who would control things for the country you are flying from.
As you don't give that here, I'm going to take the information from the British Airways restricted items list, which under the category "Sporting Goods" says:
Bows and crossbows | Hand luggage: No. | Checked Luggage: Yes.
with no additional restrictions. So you will probably be OK. If I were you however, I'd enquire about the legality of possessing and transporting these items in your destination country - archery is a fairly common hobby, so I doubt they are illegal anywhere, but some places may restrict how they are transported and where they can be removed from containers.