Tutorial:TNT cannons/Straight trajectories
Straight trajectories describe all trajectories that are not influenced further, when leaving the cannon or barrel.
Due to the way how Minecraft treats entity motion (by first calculating the Y-Axis and then the axis in that the entity has more momentum) slanted trajectories never are really straight. Also gravity induced motion can influence trajectories to be approximately parabolic. Still all those types of trajectory will be counted as "straight" because mostly the same rules would apply if they were actually straight.
Ascend (A)
An Ascending cannon can hit above itself.
If you build a front or Flank cannon you'll usually want to add Ascend modes, they are easy to implement and pretty much their only drawback is a bigger barrel.
Descend (De)
A Descending cannon can hit below itself.
For those it's pretty much the same as with Ascend modes. One difference is, that TNT hitting the block from the top will induce additional 30% drag (normal is 2%) wich is bad for efficiency. Also the entry tends to be more diagonal, since gravity tends downwards so actually hitting the enemy before the hole is finished is quite possible. For this reason Descend modes are generally less popular than Ascend ones for normal Tunnlers.

For changing the height just push the projectiles and Injectors earlier or later. The powder snow is always removed just before the Boosters explode.
Central (C)
A Central cannon can hit below as well as above itself.
As you have probably guessed by now, Central cannons are commonly found in the vertical center regions of a fighting machine. If the enemy have moving cannons those can also be found at the outer regions.
Shift (S)
Shifting describes the ability of a cannon to shoot sidewards. Flank cannons do not shift.
It is usually a good idea to give a cannon more cover and often Shifting is required to do that. Generally shifting is harder to achieve than vertical modes, with slanted shifting methods being only able to reach sideward speeds of about 2.5 blocks per tick.
Artillery (Arti)
An Artillery cannon uses the near parabolic nature of the projectiles flight path to hit the enemy from above.
Due to delay issues, when avoiding the enemies armor and shielding, an Arti is not commonly used anymore. That said, their higher efficiency compared to Downward cannons can make it devastating in the early game, if those defenses are missing.
Chunk phasing
TNT can pass unloaded chunks if it does so in a single game tick.
This is mandatory in long distance cannons, if no chunk loading can be induced.
Techniques


For the Multi platform and Rebound Shift images an example mode is traced.
Some of the most common methods of adjusting the flight path. Those generalize over the different types of trajectory.
Displacement
The often most compact and versatile way to switch between different slanted trajectories is by changing the relative position between the Boosters and the projectiles as well as Injectors.
Displacement based techniques are required in cannons without launch points supported by blocks. This technique is widely used because its ease of incorporation into cannons. The disadvantages of this technique are, that it is gets quite complicated quickly when having more than a couple of modes. It also clashes with Tunnlers since the forward momentum changes between many modes it is also hard to optimize the Tunnler shots.
Slime boost
A similar slanted shot to displacement techniques can be achieved by launching the projectile sidewards with slime.
Slime boosting is quite limited in its use because it only allows for one block per tick of initial sidewards momentum. It is also the biggest method of slanted shifting. Its most common use is in beginner level Mid-air trajectory change cannons because it has less impact on the relative position of the Injectors and Projectiles. The more common ways to achieve Mid-air trajectory changes don't face this problem though.
TNT
Having at least 2 positions, where Boosters explode and changing how many do that allows a great variety of slanted shots.
This technique usually is quite complex or big (or both). This is why it doesn't see that much use, where ever grand amounts of modes are not required. But even in this case it has one thing going for it: It can be build in a way to shoot with the same forwards momentum each mode. When build in such a way all the modes are incredibly regular for slanted shift.
Rebound
Placing blocks to stop the sidewards momentum of TNT results in shifting without a slanted entry.
This technique has poor efficiency while being very big and for that reason is mostly used in very high velocity applications such as some Factions cannons and cannons with extremely low shooting intervals since you can change fence gates to open or close each game tick.
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