I am no Da Vinci scholar, but my feelings are that many, many of his designs are flights of fancy, or were done to satisfied patrons and gain employment. As a military weapons engineer, he was not particularly successful. Blasphemy eh?
I find it particularly interesting that the technologies developed in the Classical period were lost and bastardized / reinvented in the medieval and Renaissance periods, and were never particularly successful. Gunpowder of course was coming into its own when Da Vinci was drawing his drawings, and would doom earlier military technologies such as catapults, bows, and so on. A handgonne could be forged by a competent smith in a few hours, was very cheap, and does not need the years (lifetime) of training an archer does. A peasant or ordinary solider could be taught to load and fire a handgonne in a very short period of time, and his cost to the king about to start a campaign or war vs. a knight or bowman was very cost-effective. It also defeats the finest plate armor available. More efficient and cheaper ways to kill your enemy is what engineers were after, and that still continues.
I find it kind of funny and ironic that as you lay dying on some battlefield, your guts falling between your hands, you should blame some guy with a slide ruler for your demise.
This is a personal belief, but weapons design is mentally different than bow design, even the “war bows”. I keep in mind the sole purpose of these machines, which is efficient killing at a distance. Warfare is brutal and stark, and these machines only exist for war. A target for a bow can be a bale of hay for recreational shooting or a deer or elk, while a target for a catapult is always going to be a human being.
Bolts / arrows from these machines are quite a bit smaller than those needed for bows, as well. Maybe a giant bow needs a very small projectile, too. In that show Surviving History, they build a torsion catapult and did a good job, but they were shooting broomstick length spears, which made a lot of that work moot. The spears kind of sailed out of the machine and did interesting things trajectory-wise, if my memory serves me.
The guy Watts has been getting 350+ fps or so for his machine, which are impressive numbers, and point to what can be done with a really large machine. The big palitone stone throwing ballistas, most likely could be adapted to fire arrows, as well.
Dane