Possibly the most powerful weapon in minecraft, and the future of the Art of Minecraft Warfare, the TNT Cannon is a game changing weapon of monstrous power. Able to fire shells super long distances or at a super close range, experienced cannoneers can place shots in virtually any seeable spot and more.
TNT Cannons work off the basic principle that when 1 TNT explodes, it will send any other TNT around it that have been ignited flying off in a direction. By building structure that direct the force of the TNT, one can direct a TNT shell using other TNT to propel it. TNT cannons have been further increased in usefulness when notch created redstone, as now redstone wires can ignite them allowing for complex ignition systems.TNT when sumberged in water will create explosive force, but not cause an explosion to destroy blocks, allowing a safe propulsion system to be utilized.
This is the basic structure of a cannon:
This is the base of the cannon, the lengthy section can be up to 7 in length, however far the water will flow.
You stick a water source at one end depending the direction you want the cannon to fire, it will fire opposite the side of the water source. Place redstone as shown. On the sides so that it will ignite the Propellant TNT
Stick a lever at the end so you can operate the cannon propellant with it.
Fill the bottom 3 spaces [NOT THE WATER SOURCE] with TNT.
Fill the top 4 spaces with TNT. The TNT at the very end is the TNT that will be fired as a shell.
Flip the switch and the 3 tnt on top merge with the 3 tnt on the bottom into the water stream forming a rocket launched propelling system. After around 2 seconds smack the shelling TNT with your fist to ignite it. The delay between explosions will send the shelling tnt flying off in the direction the cannon.
If only it was that easy... right? Unfortunately it's not. TNT, when ignited, has the strange tendency to Jump to the East [and slightly North...]. "Which way is East?" You ask? The way the sun rises from. You must learn to use the sun and clouds to orient yourself in minecraft. The Clouds always move to the North. The Sun rises in the East and sets in the West.
Because Tnt jumps to the east, Cannons facing West get a boost in power. The shelling TNT will jump into the rocket tnt allowing the rocket tnt to impart more of their explosive force onto it.
West facing cannons can be built like the one shown.
North facing cannons are can be built like the one shown.
South and East facing cannons are a bit gimmicky and need special attention:
East facing cannons lose a boost in power, and are prone to self-destruction unless a string of 3 blocks is placed above the tnt as shown in the picture below. It prevents the TNT from jumping around too much.
South facing cannons are very prone to TNT jumping off of them and self-destructing. Just invert the side on which the second tier branches from and you'll be just fine. You need to deal with both the Eastern AND the Northern jump.
The adjustments based on cannon direction are shown in the following picture:
That's about as much as I know so far about TNT Cannons. What I've learned I learned from 3 awesome minecrafters named TheBestNoobCake, Kiershar and Chebuosian. They have much more in depth information on TNT cannons than I.
A note: In my humble opinion, Cannons should NEVER, under any circumstances be used for defensive purposes. The amount of time it takes to aim a TNT cannon is far too long to hit moving targets accurately. By the time you triangulate on a position, the soldiers in it will be long gone. The use of TNT cannons is to bombard enemie structures from huge distances away, remaining unseen and safe to continue your onslaught of mass destruction.