[The Dark]

Not for T2K, but I worked on rules for trebuchets for TNE that would still work (though figuring Pen might be a bit problematic). To quote my work at CotI:

"One thing I noticed is that the theoretical performance GREATLY exceeds what any reproductions have done, although the large reproductions have some inefficiencies built into them, with very short counterweight arms and no distance between the arm and the weight, which causes them to suffer reduced performance. The following design sequence includes an efficiency modifier. Numbers from 0.2 to 0.5 should be fairly normal, with 0.75 being close to the upper limit for a good trebuchet builder.

Trebuchets are always considered to perform indirect fire with a Deviation Modifier of 5, a Max Hit Number of 14 and a Max Deviation Reduction of 5. They may only select targets within a range of 90-110% of their listed range.

I. Efficiency
1. Select an Efficiency (Eff) number between 0.2 and 0.75, with higher numbers being more experienced builders who have a better grasp of the science and mathematics behind trebuchets.

II. Ammunition
1. Select the mass of the projectile to be launched (Mp) in kilograms.

2. Cost of ammunition = Mp x 5 in credits

III. Counterweight
1. Select the mass of the counterweight (Mcw). Maximum is 100 times Mp.

2. Cost of counterweight = Mcw x 50 in credits

IV. Dimension of machine
1. Select the height of counterweight drop (Hcw) in meters. This is how far the counterweight falls from its maximum height to its minimum height.
2. Arm length (Al) is equal to 6.7 times Hcw. Of this length, 80% is in the long arm and 20% in the short arm.
3. Machine height (Mh) is equal to 0.67 times Al.
4. Base length (Bl) is 1.35 time Hcw. Base width (Bw) is 0.33 times Bl.
5. Empty weight (Ew) is 2.5 * Mcw + 100 * Hcw^2.
5a. If equipped with "hamster wheels" or windlasses, increase the Mcw multiplier to 3.5.
6. Loaded weight (Lw) is Ew + Mcw.
7. Cost of machine = 40 x Ew in credits.

V. Performance of machine
1. Range = 2 * Eff * Mcw * Hcw / Mp = meters
2. Velocity = (range * gravity [in m/s^2])^0.5 = meters/second
3. Kinetic Energy = 0.5 * Mp * V^2 = joules
4. Damage = (KE^0.5)/15 = D6 of damage

VI. Miscellaneous
1. Crew = Mp/3 + 2 (master artillerist and master loader).
2. Reload = Mp/2 if using windlasses or "hamster wheels." Reload = Mp*2 if using ropes and pulleys.

Example:
Let's build a light trebuchet on a low-G (0.7 g) world.
1. Efficiency is 0.5 - pretty good, but not great.
2. Mp is 10 kilograms, a light trebuchet projectile. Ammo costs 50 credits per round.
3. Mcw is 600 kilograms, 60% of the maximum. The counterweight costs 3000 credits.
4. Hcw is 5 meters, meaning the weight drops 5 meters from its maximum height to its minimum height. Arm length is 33.5 meters, machine height is 22.445 meters, base length is 6.75 meters, and base width is 2.2275 meters.
5. The trebuchet is equipped with a windlass, so empty mass is 4600 kilograms, and loaded mass with counterweight is 5200 kilograms.
6. Range is (2*0.5*600*5)/10, or 300 meters.
7. Velocity is (300*0.7)^0.5, or 45 m/s
8. KE is 0.5*10*45*45, or 10,125 joules
9. Damage is (10125^.5)/15, or 7D6 (rounded up from 6.7)
10. Total cost is (600*50)+(4600*40) = 214,000 credits plus 50 cr per shot.
11. Required crew is 5, and Reload is 5.
Without the windlass, Ew would be 4000 kilograms, cost would be 190,000 credits, and Reload would be 20.

Ew, cost, crew, and reload are all speculative, but crew and reload are loosely based on recorded performances. The sample trebuchet is very small, and examples of trebuchets firing projectiles of up to 136 kilograms are recorded (Edward I's Warwolf)."

There's also a thread over there on torsion siege engines, but since atpollard did the majority of the work on them, I don't feel comfortable with copying and pasting his work elsewhere.