Create Big Cannons ballistic calculator
Aim a big cannon at a target without trial shots. Pick the shell and the load, enter where the cannon and the target are, and the calculator returns the pitch for a low direct shot and for a high lobbing arc, the yaw to turn to, and how long the shell is in the air.
Cannon mount and target (block coordinates)
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How the numbers work
Muzzle velocity is set by the charge behind the shell. Every Powder Charge adds 2 blocks per tick, and a Big Cartridge adds 2 per level of fill, up to 8 for a full one. So four charges send a shell out at 8 blocks per tick, about 160 m/s. An air gap between the charges and the shell costs you one charge's worth.
In flight a shell falls 0.05 blocks per tick per tick (the Mortar Stone half that) and loses about 1% of its speed every tick to air resistance. Because of that drag, your longest shot is not at 45°. With four charges it is around 32°, and the more charge you add, the flatter the best angle gets.
Other dimensions change the arithmetic. The Nether pulls 10% harder and its air is 10% thicker, so shells drop short. The End has 80% gravity and no air resistance at all, which makes the same load fly several times further.
A normal cannon mount can raise the barrel to 60° and lower it 30°. An angle outside that range is flagged, and you would need a steeper platform to use it. Real shots also scatter a little around this path, more with a short barrel, so keep a follow-up ready for small targets.