No design can fire higher without hacks (at least that's how it was when I made it a few versions back). All you have to do is keep stacking and stacking and stacking....

I don't use the cannon to its max potential in the pictures. that's just how high you go from the standard amount per launch i've set in this specific

These are some man cannons taken from the M.A.S. Constellation
it uses TNT minecarts and rapid placement/stacking which remain dormant until activated

PROS

• Can be completely hidden in the ground, hull of a ship, or roof of a building
  
• Can add more power up to the point where it crashes your minecraft
  
• Can fire player thousands of feet upward in an instant
  
• Haven't tested the extend to which this goes but if you wear diamond armor with blast protection in survival normal mode, you can survive one or two chests full of ammo
  
• Doesn't use TNT blocks so it doesn't have to time a ton at the exact same time, they can remain dormant until activated and therefore can be stacked infinitely in a single space, and there's no worry of stray tnt flying everywhere
  
• Has levers that can reload the cannon without having to go and place a ton of ammo back into the chest/dispenser
  
• Comes with an automatic cleanup (method for automatically disposing of the leftover minecarts)
  
• For those of you who like to have those little details, it has an airlock door timed to close just before the top of the tube opens and closes just after the tube door closes, making it a complete airlock (kinda like that scene from the last Star Trek movie where they shoot out of they ship by the pull of the vacuum of space [I am not an obsessive Star Trek fan, I just saw the last 2 recent movies])
  

CONS

• I didn't make it too compact
  
• If in survival and you survive the launch (I usually do), there's no guarantee you'll survive the fall back to the ground even with featherfall boots
  
• Controls are a little inconvenient
  
• Once all the ammo chests run out, it takes a while to refill all of them but they can be stacked more if anyone wants to do so
  
• I made it in the form of a corner of a room so it might be a little annoying transferring into your own build (then again this could make it easier for you)
  

they're not completely efficient or compact but I haven't spent a ton of time on them so this is what i have so far. I'm probably not going to try to compact them more because they work with what I have right now but anyone can feel free to edit if they want (I just ask that you tell me and don't go off and change one block then call it your own design).

SCHEMATIC NOTES

1. The schematic also comes with a single cannon
   
2. you may need to restart the clocks when imported using mcedit
   
3. if it won't work, check that the dispensers, hoppers, comparators, and the dropper at the bottom above the cactus are facing the right direction. sometimes mcedit turns them in weird ways if you rotate the schematic (this seems to have been fixed in the latest version but i'm not completely sure)
   

Additional Notes

I'm aware that an end portal cannon is much more powerful, but i'm not considering it when i say that this is the most powerful since you're limiting yourself to three specific spots in the world when building it (unless you hack of course). This one can be built anywhere without hacks, cheats, or mods