PreGunpowder Artillery
Has anyone done a design sequence for pregunpowder artillery, such as catapult or ballista? I know WTH has the bow/crossbow design sequence, but it doesn't scale up to artillery sizes.

Now there is an interesting problem!
So which are you interested in? Stored tension like a giant crossbow or a counterbalance lever like a catapult? They will have very different design physics operating. The Catapult should scale larger. After release, ballistics are ballistics. A cannon ball, a musket ball and a stone bow do not care about how it was accelerated. Mass and velocity are all that matter. They will determine range and damage. 
Hey Robject, I told you I was a gearhead!
So using data from Vitruvius, historical recreations and FF&S I have compiled some rules for creating Roman Artillery for Traveller. Vitruvius design calculations, recreations and historic records indicate the torsion weapons hurled stones or spears at about 50 m/s to a range of about 300 meters. I have avoided historical names since they changed significantly over time, but the weapons remained fairly similar from several centuries BC through most of the middle ages. The torsion (twisted rope) engines with two arms were the most accurate and had greater range and accuracy than a TL 3 Musket, so I have focused on them. Roman Torsion Stone Throwing Artillery Creation Guidelines I. Ammunition (Iron or Stone ball) 1. Select the weight of the Ammo to be thrown (Wa) = 0.3 minimum to 163 maximum = Kilograms
II. Vitruvius Torsion Engine 3. Energy (E) = Wa x 1250 = Joules 4. Damage (D) = (E^0.5) / 15 = number of D6 5. Penetration (P): Calculate Penetration based on (E) using the table for Rifle Bullets in FF&S.
7. Required Crew = S/7 = number of men required to achieve a reload rate of "5".
III. TL 1 Composite Torsion Engine 8. Weight of Engine and Carriage (We) = [EDIT] Wa x 500 = Kilograms 9. Cost of Engine = We x 40 = Credits 10. Span of arms = Length of shaft = [EDIT] = 2 x (Wa)^0.33 = Meters
IV. Short Range 12. Muzzle Velocity (MV) = (2x E/Wa)^0.5 = m/s [typically 50 m/s] 13. Short Range (SR) = (E / Wa)^0.5 = Meters [typically 35 meters] All of the Roman Torsion Engines are designed with a velocity of 50 m/s and short range of just over 35 meters with the selected ammo, however they are all capable of firing smaller stones at greater ranges and velocities. One quarter the design weight seems to be a practical lower limit for the projectile (the forces on the weapon can damage the frame from too great an impact.) DESIGN EXAMPLE So just for fun, let's build a Vitruvian Torsion Stone Thrower ... to hurl a 10 kg ball (equal to a 22 lb cannon ball): 1. (Wa) = 10 kg
3. (E) = 10 x 1250 = 12,500 Joules 4. (D) = (12,500^0.5) / 15 = 7.45 D6 5. (P) value = 2  4  6 At Short Range: Pen = 7.45/2 = 3.76. (S) = 12,500/60 = 208 7. Crew = 208/7 = 30 men @ reload rate "5"; 15 men @ reload rate "10"; 10 men @ reload rate "15", 8 men @ reload rate of "20" and 6 men @ reload rate "25". 8. (We) = [EDIT] 10 x 500 = 5000 Kilograms 9. Cost of Engine = [EDIT] 5000 x 40 = Cr 200,000 10. Span of arms = Length of shaft = [EDIT] 2 x (10)^0.33 = 4.3 meters 11. TL 2 Steel: Cost = Cr 20,000 & Span/Length = 12.5 meters 10 KG BALL (22 pounder) (MV) = (2x 12,500/10)^0.5 = 50 m/s (SR) = (12,500 / 10)^0.5 = 35 meters Extreme Range = 8x SR = 280 meters 9 KG BALL (20 pounder) (MV) = (2x 12,500/9)^0.5 = 53 m/s (SR) = (12,500 / 9)^0.5 = 37 meters Extreme Range = 8x SR = 296 meters 8 KG BALL (18 pounder) (MV) = (2x 12,500/8)^0.5 = 56 m/s (SR) = (12,500 / 8)^0.5 = 40 meters Extreme Range = 8x SR = 320 meters 7 KG BALL (15 pounder) (MV) = (2x 12,500/7)^0.5 = 60 m/s (SR) = (12,500 / 7)^0.5 = 42 meters Extreme Range = 8x SR = 336 meters 6 KG BALL (13 pounder) (MV) = (2x 12,500/6)^0.5 = 65 m/s (SR) = (12,500 / 6)^0.5 = 46 meters Extreme Range = 8x SR = 368 meters 5 KG BALL (11 pounder) (MV) = (2x 12,500/5)^0.5 = 71 m/s (SR) = (12,500 / 5)^0.5 = 50 meters Extreme Range = 8x SR = 400 meters 4 KG BALL (9 pounder) (MV) = (2x 12,500/4)^0.5 = 79 m/s (SR) = (12,500 / 4)^0.5 = 56 meters Extreme Range = 8x SR = 448 meters 3 KG BALL (7 pounder) (MV) = (2x 12,500/3)^0.5 = 91 m/s (SR) = (12,500 / 3)^0.5 = 65 meters Extreme Range = 8x SR = 520 meters 
According to Reddit, trebuchets are superior.

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So for modeling with FF&S, the Torsion 'Ballista' seemed closer to the Heavy Crossbow and the Trebuchets seemed closer to FF&S Mortars and Howitzers. YMMV. What can you find on Trebuchets to give us some real historic data points to calibrate FF&S constants against? 
Stand off range becomes important during artillery duels.
And since for the larger artillery pieces, on land they tend to be used against non moving objects, id est walls and towers, aiming can be adjusted. https://youtu.be/rAdC2K8E4U Take Edward Longshanks' War wolf, who at one one point refused the surrender of one castle in order to demonstrate it's power. "Aye didnae hae it set up fir nuthin'." 
For steps that determine number of dice of damage you should probably indicate the rounding convention you prefer employed. Also, an armature span of 25 meters seems a bit extreme don't you think?

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What was the span for any real world "ballista" capable of firing a 10 kg projectile hundreds of meters? Find data that suggests it is wrong and I will gladly change the constants. 
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If you're open to a few revisions, what got me thinking about this was reading Osprey's Greek & Roman Artillery and trying to work out some of the math on my own, and I compared a couple numbers to what was mentioned in that book. The arm length seems very large  25 meters for a 10 kg thrower. A Greek 1talent projector had a span of slightly over 5 meters for a projectile massing 26.2 kilograms. Vitruvius gives a moderately complicated formula for the washer diameter for stone throwers  in daktyls of 19.3mm each, the washer diameter is 1.1 times the cube root of 100 times the stone's mass in minas of 436.6 grams. The arm length should be 7 times the washer diameter. Using the 10kg projector: 10 kilograms is 22.9 minas 22.9 * 100 = 2290 2290^(1/3) = 13.1809 13.1809*1.1 = 14.5 (14.49899, I'm rounding because it's so small a difference) Washer diameter = 279.85 mm, arm length = 1,958.95 mm, or 1.96 meters per arm, or 3.92 meters for total arm length, rather than 25 meters. Off the top of my head, I'm not sure how to simplify that formula to make it easier to work with. For a boltthrower, the washer diameter is bolt length divided by 9, so this machine (if refitted as a boltthrower) could fire a 2.5 meter bolt. This means the math for boltthrowers is easier, since arm length is bolt length*.78 (7/9 = .777 repeating). For weight, Douglas Campbell's work has suggested a ratio of closer to 500:1 than 100:1 for launcher:ammunition. Going off into speculation, arrowthrowers were much smaller than stonethrowers. A machine capable of firing a 4 foot long arrow was the same size as one capable of firing a 1 kilogram stone. Ammunition to machine size is closer to 200:1 instead of the stonethrower's 500:1 (possibly because of better aerodynamics on the bolt?). For Roman machines specifically, archeological finds in Rhodes, Pergamon, Tel Dor, and Carthage have turned up stones of the following masses (in kilograms): 1.3, 2.1, 3.5, 4.4, 5.2, 6.6, 7.9, 8.7, 9.6, 10.9, 13.1, 16.4, 17.5, 21.8, 26.2, 28.4, 30.6, 34.9, 39.3, 43.7, 52.4, 65.5, and 78.6. The 26.2 kilogram (1 talent) seems to have been most common in Roman service. 
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