Hey, sure thing. The Romans got pretty good at turning human muscle into projectile firepower. They refined the earlier Greek catapults into the ballista, a massive torsion‑powered machine that could hurl heavy stones over long distances, and the onager, a lever‑powered device that launched rocks with a nasty splash. Both used a lot of wood, leather, and tension from ropes, so the real “energy” came from the torsion in the twisted ropes. They weren’t energy manipulators in the sci‑fi sense, but they did turn a lot of human effort into focused kinetic force, which is essentially what modern explosives do. I’ve gone through a handful of ancient engineering treatises and a few battlefield reports – the math behind the tension and the angles is fascinating. If you want the details, I can pull up some diagrams or dive into the specifics of how the Romans optimized those machines for siege warfare.

I don’t have a sketch pad in front of me, but I can lay out the math in plain words. Think of a torsion ballista: a bundle of twisted ropes wound around a metal barrel. The torque that the ropes can deliver is roughly  Torque ≈ ½ k θ² where k is the torsion constant of the rope bundle and θ is the twist angle in radians. The rope bundle behaves like a spring, so the more you twist, the more torque you get, but the rope has a limit before it snaps. When the arm swings out, that torque turns into kinetic energy. The work done (and thus the energy stored in the projectile) is  E = ½ I ω² with I being the moment of inertia of the arm and ω the angular velocity at release. The arm length l, the mass m of the projectile, and the angle of release all influence ω because the arm is a lever. In practice the Romans would calculate the required force by estimating the projectile’s mass, the desired range, and the arm’s leverage. They’d then choose a rope bundle with a suitable torsion constant so that the twist would generate enough torque without exceeding the rope’s tensile strength. If you want more specifics—say, the torsion constant for a typical hemp rope or the moment of inertia for a 2‑meter arm—I can pull up the exact numbers from the Roman manuals that survived. Just let me know what level of detail you’re after.

Sure thing. Roughly, a hemp rope bundle used in a Roman ballista might have a torsion constant k of about 3 × 10⁶ N·m/rad. If you twist it by say 0.5 rad (about 30 degrees), the torque you can get is about ½ × 3 × 10⁶ × 0.5² ≈ 375 kN·m. For the arm, imagine a 2 m long, 2 kg arm. The moment of inertia for a rod pivoting at one end is I = ⅓ m l², so I ≈ ⅓ × 2 kg × (2 m)² ≈ 2.67 kg·m². If that torque is applied over, say, 0.2 s, the angular acceleration α = τ/I ≈ 375,000 N·m / 2.67 kg·m² ≈ 140,000 rad/s². After 0.2 s, the angular velocity ω ≈ α t ≈ 28,000 rad/s, but that’s absurdly high—so the real release is limited by the rope’s elasticity and the arm’s own bending stiffness. In practice, the arm might accelerate to a few thousand rad/s, giving the projectile a kinetic energy on the order of 10–15 kJ, enough to hurl a 10‑kg stone several hundred meters. Those are ballpark figures, but they show how the Romans translated human effort into a nasty punch.