TNE Only: Pre-Gunpowder Artillery

[TheDark]

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

 

[atpollard]

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.

 

[atpollard]

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

• For Bolts: Length of Bolt = 1.169 x (Wa)^0.33 = Meters
• For Iron Balls: Diameter of Ball = (Wa/4000)^0.33 = Meters
• For Stone Balls: Diameter of Ball = (Wa/1500)^0.33 = Meters

2. Cost of ammo = Wa x 5 = Credits

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.

• At Short Range: If E<2000, then Pen = 'nil';
• If 2000<E<3000, then Pen = D
• If 3000<E, then Pen = D/2

6. Required Strength (S) = E/60
7. Required Crew = S/7 = number of men required to achieve a reload rate of "5".

• Pulleys and levers can be used to trade mechanical advantage for time so a half crew has a reload rate of "10",
• a third of a crew has a reload rate of "15",
• a quarter of a crew has a reload rate of "20"
• a fifth of a crew has a reload rate of "25".

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

• Span and Length are provided for reference only to help visualize the weapon.

11. Special Note: For a TL 2 Steel Torsion Engine, the weight (We) remains unchanged from the TL 1 version, but the Cost and Span/Length are halved.

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

• For Bolts: Length of Bolt = 1.169 x (10)^0.33 = 2.5 meters
• For Iron Balls: Diameter of Ball = (10/4000)^0.33 = 0.138 meters = 138 mm
• For Stone Balls: Diameter of Ball = (10/1500)^0.33 = 0.191 meters = 191 mm

2. Cost of ammo = 10 x 5 = Cr 50
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 = 3.7​

6. (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

 

[Condottiere]

According to Reddit, trebuchets are superior.

 

[atpollard]

According to Reddit, trebuchets are superior.

For range, I read trebuchets were FAR superior. For accuracy, I read that the two-armed torsion engines exceeded even 18th century muskets and some were used by Roman snipers to shoot commanders off enemy walls.

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?

 

[Condottiere]

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/rAdC2K8-E4U

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'."

 

[pendragonman]

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?

 

[atpollard]

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?

What is the span for a 12,500 joule Composite crossbow (per WTH)?

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.

 

[TheDark]

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.

Thanks, this is a great starting point and everything seems to make sense.

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 1-talent 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 bolt-thrower, the washer diameter is bolt length divided by 9, so this machine (if refitted as a bolt-thrower) could fire a 2.5 meter bolt. This means the math for bolt-throwers 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, arrow-throwers were much smaller than stone-throwers. 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 stone-thrower'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.

 

[TheDark]

What is the span for a 12,500 joule Composite crossbow (per WTH)?

178.5 meters. Composite is 70 joules per meter. TL 7 Composite Steel would still be 62.5 meters. WTH's numbers are either off or don't scale up at all past personal weapons.

 

[Timerover51]

Based on stockpiles of leftover trebuchet shot, they could toss up to about 400 pounds about 400 yards in the very large versions. They could also be used to toss dead horses and bodies into a town, city, or fortress in an attempt to cause plague. Sometimes they were successful. Biological warfare is not a new thing by any means.

One problem is that the knowledge of how to make very high quality twisted sinew ropes died about at about the end of the Western Roman Empire. Using sinew ropes today, it is not possible to duplicate the ballistics given by the Ancient authors.

 

[Timerover51]

What is the span for a 12,500 joule Composite crossbow (per WTH)?

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.

Hmm, Ralph Payne-Galloway wrote a whole book on how to make a crossbow, and included a small ballista in an appendix. He actually built crossbows and ballista. There is also a discussion of crossbows and ballista in Admiral Rogers books on oared naval warfare. I will see if I can look them up.

 

[atpollard]

So, scrapping the ratios in WTH as a starting point, and going back to Vitruvius to calculate arm lengths ... I get the following (after inserting conversion factors and simplifying):

Span = 1.948 x (Wa)^0.33

Which I will simplify to 2 x (Wa)^0.33

So the Design Example to throw a 10 kg stone = 2 x (10)^0.33 = 4.3 meters

 

[TheDark]

One problem is that the knowledge of how to make very high quality twisted sinew ropes died about at about the end of the Western Roman Empire. Using sinew ropes today, it is not possible to duplicate the ballistics given by the Ancient authors.

Nick Watts is probably the best experimental ballisteur right now. He's used nylon because it takes a ridiculous amount of labor to break down elk backstrap sinew, 3-ply braid it, and form large enough cables out of it. With nylon, he's basically achieved the same performance level as the ancients (which was his stated goal - do it first with modern materials to prove the inswinger design works, then back his way into doing it with materials available at the time). The last I saw, about two years ago, he was starting to work with sinew again, but only had enough for two small-scale models.

 

[atpollard]

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, arrow-throwers were much smaller than stone-throwers. 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 stone-thrower's 500:1 (possibly because of better aerodynamics on the bolt?).

I updated the span calculation. I went with 15 "holes" for the span (2 arms at 7 "holes" long and a gap between that I just guessed at 1 "hole" wide), and simplified the equation and conversion factors.

Weights were something that I had trouble finding data for. One caution I ran into frequently with people actually building them was that many texts were simply full of bad data. I found one group of historic recreationists who fired 1 kg balls from 100 kg Ballista. It was a small sample size, but all I had. I'll be happy to change the weight to Campbell's 500:1 ratio if we can find a second source to confirm his numbers.

We should research the length and weight of those bolts. It is possible that a 4' arrow weighs about 1 kg so the engines are about the same weight. I just have no idea.

I did read that the arrow throwers had better range, but damage fell off at long ranges, while the stones did not have as long of a range, bit still killed at all ranges. It made for an interesting dynamic. Perhaps a 2-4-6 Pen value for Arrows and a 2-2-2 pen value for stones.

 

[pendragonman]

What is the span for a 12,500 joule Composite crossbow (per WTH)?

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.

1) people build ballistaes (torsion arm crossbows) throw 80 Newton pumpkins 75 meters (6000 Joules) in their back yards. And their armature length is not six meters (one quarter of what you propose(1/2 squared)).

I myself have built one that threw a similar pumpkin over 150 meters. I switched from a modern-made rope to sisal. If I could have gotten a rope made of jute or hair with my windings number I am sure I could have moved that to 300 meters. Each of my separate arms were less than 1.5 meters and the base block (where the winding are stored) was less than two meters across.

The way you increase the power of a ballista is not by lengthening the arms, it is in increasing the number of rope windings and by using different rope materials and thereby increase the available spring energy.

Edit: My ballista failed for the same reason the one on mythbusters failed. I didn't forge the spindals but had them welded and the welds failed under the spring load. I got three shots before failure, all about the same range.

2) You can get a translation of Vetruvius' book in pdf for free. Pages 303-305 discuss ballistas and their manufacture. He discusses it as a spear thrower, which is what crossbows are designed for. They can also throw round ammunition with a slight modification of the launch tray. Of course there isn't a nice spreadsheet of data. but reading some historical research papers will enlighten the reader of how to interpret (approximately, of course) Vetruvius' own instructions for their construction.

EDIT #2: I just noticed that everyone else has already said the same things and the OP is adjusting his estimates. I skipped reading everyone else's posts and went to respond because I felt the OP's response to me was an attack.

 

[TheDark]

I updated the span calculation. I went with 15 "holes" for the span (2 arms at 7 "holes" long and a gap between that I just guessed at 1 "hole" wide), and simplified the equation and conversion factors.

That works. One thing people will want to keep in mind when visualizing them is that some are "in-swingers" - the springs are at the outside of the span, and the arms rotate through the inside of the piece, rather than outside (page 688 of this PDF document has a good diagram).

Weights were something that I had trouble finding data for. One caution I ran into frequently with people actually building them was that many texts were simply full of bad data. I found one group of historic recreationists who fired 1 kg balls from 100 kg Ballista. It was a small sample size, but all I had. I'll be happy to change the weight to Campbell's 500:1 ratio if we can find a second source to confirm his numbers.

This is an area where there doesn't seem to have been much research.

We should research the length and weight of those bolts. It is possible that a 4' arrow weighs about 1 kg so the engines are about the same weight. I just have no idea.

Nick Watts made Dura-Europos style bolts to three scales. The smallest was 21.5" and 276 grams, the medium one 29.5" and 340 grams, and the largest 36" and 521 grams.

I did read that the arrow throwers had better range, but damage fell off at long ranges, while the stones did not have as long of a range, bit still killed at all ranges. It made for an interesting dynamic. Perhaps a 2-4-6 Pen value for Arrows and a 2-2-2 pen value for stones.

I hadn't even really thought about Pen yet, beyond thinking about (and discarding) using the black powder artillery rules, since the energy levels aren't high enough.

 

[atpollard]

EDIT #2: I just noticed that everyone else has already said the same things and the OP is adjusting his estimates. I skipped reading everyone else's posts and went to respond because I felt the OP's response to me was an attack.

I apologize if it seemed like an attack. It was intended as a straight forward honest statement. Saying my numbers are wrong is of little help when accurate detailed data is in such short supply. I had data on one Ballista and a relationship from WTH that tracks length as linear with E as the only data to work with.

I really was just throwing down a gauntlet to get me more data if you want better numbers.

No personal attack was intended and I took your post serious enough to go look up Vitruvius' work and translate his formula into Traveller units. Vitruvius said that the WTH was wrong in its assumed relationship. It varies with the cube root of the mass of the projectile rather than linear with Energy. So the change was made in direct response to your original post.

You were right, 25 meters and my formula was wrong.

 

[jcrocker]

I love the fact that we can use a 2000-ish year old source material for Traveller.

 

[Timerover51]

You might want to download and look at the following two sources.

https://archive.org/details/Book_of_the_Crossbow_The_by_Sir_Ralph_Payne-Galloway

https://archive.org/details/cu31924102030891

Payne-Galloway actually built crossbows and projectile engines.

Edit Note: The following quote is his comment on sources for ancient projectile engines.

Of ancient Greek authors who have left us accounts of these engines. Heron (284-221 B.C.) and Philo (about 200 B.C.) are the most trustworthy.

Both these mechanicians give plans and dimensions with an accuracy that enables us to reconstruct the machines, if not with exactitude at any rate with sufficient correctness for practical application.

Though in the books of Athensus, Biton, Apollodorus, Diodorus, Procopius, Polybius and Josephus we find incomplete descriptions, these
authors, especially Josephus, frequently allude to the effects of the engines in warfare ; and scanty as is the knowledge they impart, it is useful and explanatory when read in conjunction with the writings of Heron and Philo.

Among the Roman historians and military engineers, Vitruvius and Ammianus are the best authorities. Vitruvius copied his descriptions from the Greek writers, which shows us that the Romans adopted the engines from the Greeks.