Level 1 on the blueprint, Level 3 on the gear, and that gap is the whole story of this craft. Everything else is wood and frags a fresh group already has, and the research costs half the scrap of a ballista. But crafting a gear waits for a Level 3 bench, so in practice the tower gets built the day someone brings a gear home from a road run.
The calculator also leaves out the door. The tower locks with your own, and a sheet metal door holds up far better than a wooden one when the defenders are awake. Add its frags to the bill and craft both in one sitting, so the tower never rolls out with an empty doorway.
Tip
Bring a battering ram only if the high quality metal is there for it. On its own the tower already buys your team cover and height for the price of one gear.