The World's Four Earliest Known Cannon Depictions

[broadaxe]

Hmmm, thinking of it, you are right about the amount of powder required back then, as during the first 100 years of gunnery the blackpowder was relatively weak. The gunners were in the process of trial & error, experiencing with the percentage of ingredients. By 1420 they made a big leap by graining the powder, hence enhancing greatly its potencial.
The short-barreled bombards with the smaller-diameter burning cell look basically the same as early 1800's mortar (aside of position of the trunnions), like this one from the walls of Acre.