Barrel and tank are 2.5in PVC, the right size for a tennis ball.
the valve is a modified water sprinkler valve. The modification is to remove the solonoid, and add a layer of epoxy on the edge of the rubber seal within the valve. Fill in the socket for the solonoid with epoxy. Remove the valve adjustment, and fit a ball valve in it's place.
On the tank, install a 150lb pressure gauge.
You can safely fill it to 130lbs.
Three slits in total. One big, two small.
Two holes in total, on the opposite side of the big slit.
Tie a loop of twine through the holes. Fill the ball with big hardware (big 1/2" or larger bolts). Lace up the big slit with a peice of twine through the two smaller slits to sinch the big slit closed. You could fill the ball with RTV but it would make it difficult to plunge the ball (it needs to deform to fit in the barrel). A barrel bigger than 2.5 inch will be too big for a tennis ball. The ball must be tight in the barrel.
The key: You want the hardware weight to stay in the ball. You want the ball to be able to deform as it's launched. You want a heavy ball.
Set the spool down by your feet. Plunge the ball into the barrel as far it can go. Attach the air supply and pressurize. When the pressure is 120-130lbs, lift and aim the 4 foot barrel where you want the ball to go, adjust a little for drag. Make sure the twine can dispense easily from the spool at your feet on the ground.
Fire! (open the ball valve quickly).
You want the ball to clear the branch and fall through to the other side, hopefully the ball will not be slowed by other branches or trees and will fall to the ground. With the weight secured inside the ball, it should fall to the ground.
The water valve is designed to keep the tank pressurized until the ball-valve offsets the pressure against the rubber-bladder inside the vave, springing the bladder valve open and letting all the air in the tank through to the barrel.
There's a few lbs of kick when fired, and a very loud bang. Wear ear protection.