Full size Napoleon, Parrot and wrought iron rifle carriage wheels were/are 57" in diameter; mountain howitzer wheels were/are 38" in diameter. Assuming your barrel is more or less a cannon (versus howitzer) barrel, 3.5" is to 72" as 2.77" is to 57". Or to use 3" wheels as 57" wheels, the barrel should be 3.75" long.