Under USA federal law, air powered and black powder firearms are not firearms- so no license required.
Some local government areas may have local regulations controlling thier use though.
Did you notice the black powder bowling ball mortars- they can throw a bowling ball over 1000 metres!
Another anomaly in USA fed law,[I am pretty sure it is still valid] is that you can manufacture a machine gun, or any firearm you like- as long it is for your own personal use.
You cannot loan it, or sell it- as then you require an appropriate license, and laws regarding serial numbers and manufacturing red tape apply.
Machine guns, destructive devices like grenades, short barrelled firearms, flame throwers, artillery pieces etc are permitted by the federal govt. as long as you comply with the laws and pay the stamp duty tax thingo.
[IIRC] this involves the written approval of your local police chief, State police and Governor, and be checked out and approved by the BATFE.
[The Bureau of Alcohol, Tobacco, Firearms and Explosives]
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Is it just me or does the BATFE sound more like a destination for a fun time- than a government department?

stephen