what would be a good barrel length to have in order to get the longest/highest shots? ... i think it'd also be neat to fire at steep angles and watch the thing sail up and over the clouds
Keep a couple of things in mind. Mortars were not designed to be long range weapons. The idea was to lob an exploding shell over the enemy's walls and take out his troops and guns. For distance, they'd use a long barrel cannon. As CW said, much beyond 100 to 200 yards and you'll never see where a golf ball went. You can see a beer can a bit farther out but not a great deal. If you can't watch where your projectiles go, you might as well be shooting blanks.
Also, be extremely careful trying to fire at extremely high angles. It's very common for the wind a hunderd feet or more up to be coming from an entirely different direction and at a higher speed than what you feel on the ground. Guess wrong on wind speed and direction and there's a possibility that the projectile could be pushed right back at you. Not good. I'm sure that you have no desire to become a candidate for a Darwin Award. :wink:
Light projectiles, like golf balls, will be affected the most but beer cans will be too. The safest thing would be to go no higher than 60 to 65 degrees on the angle of the tube and fire with the surface wind coming from behind you if at all possible. If you want to get the best range from any shot, 45 degrees is the optimum angle.