Clockwork & Fusrodah
Clockwork Clockwork
Fusrodah Fusrodah
Clockwork Clockwork
Hey Fusrodah, I've been tinkering with a new trebuchet mechanism that might just bring a new level of precision to the battlefield—care to test its limits together?
Fusrodah Fusrodah
I appreciate the initiative, but first show me the full design and calculations, we must keep everything in line with proper siegecraft, and only then shall we test its limits.
Clockwork Clockwork
Here’s the plan in plain terms, step by step. **1. Frame and Materials** - 3 m long wooden beam, spruce, cross‑section 0.3 m × 0.3 m, will be the main spar. - Reinforced with iron straps at 0.3 m intervals, 6 mm thick, to keep bending stress under 20 MPa. - The counterweight block is cast iron, 200 kg, mounted on a short iron arm, 0.6 m from the pivot. **2. Release mechanism** - A simple lever‑pull release using a 2 m long iron bar attached to the pivot. - The bar is locked by a brass cam that snaps into a notch on the pivot arm. - When the lever is pulled, the cam slides out, the spar swings free. **3. Projectile and launch geometry** - Projectile: 25 kg stone, weight gives about 225 N of gravity. - The launch angle is set at 30°, giving the optimal range for a 30 m trajectory. - The spar rotates about a pivot 0.5 m from the base. **4. Calculations** **a. Torque from counterweight** - T = m × g × r = 200 kg × 9.81 m/s² × 0.6 m = 1,177 N·m. **b. Torque needed to raise the spar** - Assume spar mass 50 kg, center of mass at 1.5 m. - T_raising = 50 kg × 9.81 m/s² × 1.5 m = 736 N·m. **c. Net torque available for acceleration** - 1,177 N·m – 736 N·m = 441 N·m. **d. Angular acceleration** - Moment of inertia of spar: I ≈ (1/3) m × L² = (1/3) × 50 kg × (3 m)² = 150 kg·m². - α = τ / I = 441 N·m / 150 kg·m² = 2.94 rad/s². **e. Angular velocity at release** - Starting from rest, θ = 90°, so θ = π/2 rad. - Using v² = 2αθ, v = sqrt(2 × 2.94 rad/s² × 1.57 rad) = sqrt(9.24) ≈ 3.04 rad/s. **f. Linear velocity of projectile** - v_linear = v × r_projectile. - r_projectile = 0.5 m (distance from pivot to point of contact). - v_linear = 3.04 rad/s × 0.5 m = 1.52 m/s. **g. Range estimation** - Using R = v² sin 2θ / g, with θ = 30°, sin 60° ≈ 0.866. - R = (1.52 m/s)² × 0.866 / 9.81 = 2.31 m / 9.81 ≈ 0.24 m. The calculation shows a very short range, so we need to adjust. **Adjustments** - Increase counterweight to 300 kg: T = 300 × 9.81 × 0.6 = 1,764 N·m, net torque 1,764 – 736 = 1,028 N·m. - New α = 1,028 / 150 = 6.85 rad/s². - New v = sqrt(2 × 6.85 × 1.57) = sqrt(21.5) ≈ 4.64 rad/s. - v_linear = 4.64 × 0.5 = 2.32 m/s. - R = (2.32)² × 0.866 / 9.81 = 5.39 m / 9.81 ≈ 0.55 m. Still low. **Solution**: raise the release point to 1 m, so r_projectile = 1 m, v_linear doubles to 4.64 m/s. R = (4.64)² × 0.866 / 9.81 = 21.5 m / 9.81 ≈ 2.19 m. **Final tweak**: use a 45° launch angle for maximum range: sin 90° = 1. R = (4.64)² × 1 / 9.81 = 21.5 / 9.81 ≈ 2.19 m. So with 300 kg counterweight, 1 m release arm, 45° angle, we get about 2.2 m range. **5. Safety and checks** - Verify all joints are tightened to a torque of 50 Nm. - Ensure the counterweight has a rail guide to avoid swinging sideways. - Test with a lightweight dummy first to confirm motion. That’s the full schematic and math in plain English. Let me know what you think, and we can tweak the numbers or materials until it meets the siegecraft standards you’re after.
Fusrodah Fusrodah
The plan is solid in spirit, but the numbers do not line up with historical siege practice. Your torque calculations are correct, but the angular velocity at release is underestimated because you used a 90° swing; in reality the spar starts higher, and you lose energy on the return arc. Also, converting angular to linear speed requires the correct arm length at the moment of release—if you move the release point to 1 m, the projectile velocity will be twice as high, but the energy transfer becomes less efficient if the spar flexes. For a 45° launch you need a projectile speed of about 18–20 m/s to hit 200 m, not the 4–5 m/s you’re getting. That means you either need a counterweight of around 4 t or a much longer arm. If you keep the 300 kg weight, try raising the spar to 4–5 m, give it a 60° launch, and use a rigid iron bar for the arm; that will raise the range to the 150–200 m range that counts on the field. Also double‑check the tension on the straps—20 MPa is generous, but the dynamic load will exceed that during launch. Test with a lighter stone first; record the actual velocity with a simple photogate or high‑speed video. That data will let us tweak the counterweight and arm length precisely. In the meantime, tighten all joints to at least 60 Nm, ensure the rail guide is perfectly straight, and never compromise on the pivot seal; a single slippage could ruin the whole effort. Let’s proceed methodically, and we will see a trebuchet that honors the great engineers before us.
Clockwork Clockwork
Sounds good, Fusrodah. I’ll raise the spar to about 4.5 m, set the launch angle at 60°, and replace the arm with a 1.2 m iron bar. I’ll also increase the counterweight to roughly 3.5 t to hit that 18–20 m/s goal. I’ll tighten every joint to 65 Nm, run the rail guide through a straight‑edge test, and seal the pivot with a hardened steel gasket. I’ll lay down a photogate in front of the sling and film a few test shots with a small stone—got the sensors ready. Once I’ve got the speed data, we’ll tweak the weight or arm length until the range locks in at 150–200 m. Let’s make sure each component sings in harmony and no part slackens under the load. We'll honor those great engineers with a machine that’s as elegant as it is lethal.