Design: Hybrid Cannon [4+1-1, 5+1-1, 5-1]
Taking your Theatre Commanders advice to heart, you begin work on Arstotzkas very first artillery piece.
Your design makes good use of the metal ore extracted from the mountains, but even so the device requires a new dedicated workshop for its manufacture. It's essentially a short cup-shaped tube with a water reservoir in the back. The design uses a combination of a specially-conjured PSF and water for propulsion - the PSF requires a bit of modification to be cast through the metal casing and takes a considerable amount of time to develop. The PSF instantly super-heats the water into steam, which is then forced through the tube in a single, powerful blast. Anything that happens to be inside the tube is carried along for the ride, sending it a long ways away. The ammunition must be specially crafted to fit inside the barrel, and to this end our Mathemagicians use specially-carved rocks. It takes a non-negligible amount of labor to carve these rocks into spheres smooth enough to fit within the barrel nicely, but they tend to fly straighter and more reliably than a rough-hewn boulder would. They are roughly a little larger than a mans head.
The Hybrid Cannon is very heavy, but is mounted on a wheeled, wooden frame and pulled by horses. It requires set-up before use. It requires a fresh bucket of water between each firing event as fuel, and cannot fire without an attending mage. The cannon also grows quite hot after several firings, requiring water-quenching to get down to usable temperatures. This repeated heating-cooling cycle has a tendency to cause the barrel to crack, which is preferable to firing while hot since that causes the cannon ball to jam and result in an explosion. The rock-based ammunition also has an unfortunate tendency to crack, which can jam the barrel and either cause an explosion or a lengthy repair process. The device is...reasonably accurate, reliably hitting in a radius of sixty to seventy meters at maximum range - this would make it effective against massed troops, but we won't be sniping anyone with it. Its maximum range is about the same as that of our longbowmen; mid-range. It requires several months of training before an artillery team is competent enough to use it.
Perhaps most unfortunately is the requirement that each cannon be attended to by a wizard or an apprentice for use, meaning they cannot be used elsewhere or by non-magical troops. On the bright side, the cannons take very little time to load and fire, meaning we can shoot several times a minute until we run out of the specially-crafted ammunition.
The manufacturing workshop requires a bit of investment to get up and running, but our ore bonus lets us produce them relatively cheaply. Expensive.