You can engineer it all you want or you can make a cannon. The engineering has been done already, so no need to reinvent the wheel
First I suggest you visit our sticky at the top of of the forum called Safe loads and cannon plans. The is a link the to N-SSA Rules. Read their safety rules for cannons and you will find all the information you need to construct a safe gun.
First beer can cannons. Why bother. At best a cement can mortar round is entertaining. It is pretty neat to see the big can fly through the air, tumbling and flipping then the big whack when it hits. But where it hits is not consistent. One of the first things I did was get a round ball mold for my beer can mortar and cast up some zinc round ball...I know pretty close to where the the round ball will land, a lot closer than the beer can.
A cannon for a beer can will need to be at minimum, 7.95 inches at the breech. That's pretty big for a 24 long inch bbl. You could go smaller by making a howitzer. But it still would have be pretty big. Then you have the issue of bore, smooth bore and long beer can projectile don't go hand in hand. The long projectile will have the tendency to tumble and fly all over the place---satisfaction level will drop real fast.
Besides if you are going build a gun that big why not build the real deal
What I suggest you do is get a set of plans from
Antique OrdnancePublisher and build a gun for a known round object.
If you have the skills you could also find the post here on the board about building a rifling machine and build a rifled barrel. You can shoot long bolt like projectiles then.
If you still have the engineer in you burning to build, then I suggest an even better challenge. Get a copy of John Muller's
"A Treatise of Artillery 1780" Muller discuss the design of a late 18th century artillery and expresses all dimensions as part of the caliber. For example, Muller says this:
General dimensions of brass guns
The caliber of the gun is divided into 16 equal parts.
The thickness of the of the metal at the base ring from the bore is 16 parts.
At the end of first reinforce ring 14.5 parts
At the same place, for the beginning of the second reincorce 13.5 parts
At the end of the second reinforce 12.5 parts
At the same place for the beginning of the chase 11.5 parts
At the end of the chase or muzzle, the moulding excluded 8 parts..
Lots of of discussion on barrel length, but Mullers preferred length was 21 calibers.
The length is divided in 7 parts.
The length of the first reinforce is 2 parts.
the second reinforce is 1 part.
The chase is 4 parts
Using Muller your beer can bore gun would have to 55.65 inches long and 7.95 inches in diameter at the first reinforce or breech. Muzzle diameter would be 3.975 inches. The first reinforce would be 15.9 long, second reinforce 7.95 inches, and chase is 31.8 inches long.
I have plans to build a gun to Muller's design in the future.. His treatise also use the ratio system to build carriages for the gun.