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Calculation of Traction Catapult Range


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#16 Liang Jieming

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Posted 26 April 2006 - 10:00 PM

I would go higher. Have you ever seen the movie about the ringer of Notre Dame and how he puts all his weight into the rope? :P ;)

That's what I figured too. Theoretically we could use 100% body weight as the puller, like the bell ringer, could just swing on the rope to drag it down, but I hesitate to do that because of two things.

1. the leverarm + projectile isn't as massive as say, a bell (in the bell tower), so you couldn't really swing on the rope as the inertia wouldn't be great enough.

2. The put 2 men per rope. This discounts having the full weight of each man on the rope.

The estimate of 50% of the puller's weight translates to 50% x 2(pax)/rope which equals one full body weight. Maybe this can be upped a little. I'll try rerunning it with 60%.

I would rather say 60-65 kg. According to the body mass index this would equate to a body height of 170-175 cm which probably is still too high. In the 1700s there was a Prussian elite bataillon confined to soldiers over 180 cm. The king had recruitment trouble and had to import such tall soldiers from abroad.

Good point. Ok, will reduce it to 62.5kg instead of 70kg.

Does a heavier weight translate to a longer or shorter range?

Yes, a heavier projectile weight would translate to a shorter range. I chose 1kg to match Chen Gui's account.

#17 Tibet Libre

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Posted 26 April 2006 - 10:46 PM

Yes, a heavier projectile weight would translate to a shorter range. I chose 1kg to match Chen Gui's account.


But isnt that a pretty short range, considering that the numerous pulling crew would be well within the reach of counterfire by arrow-shooters, slingers and archers!

Compare with the torsion catapult which worked without dozens of pullers (and could thus certainly be better protected):

Campbell, Greek and Roman Artillery (Osprey), p.21 gives for the torsion stone thrower (13 kg projectile) an effective range (="maximum impact") of 100m (firing-angle of 5.7 degrees) respectivly of 170m (10 degrees).

Warry, Classical Warfare in the Roman World, p.78 speaks of 157m - 185m effective range (=" point-blank range") for 28 kg projectiles which was the standard heavy size of the Roman artillery.

As for primary sources, Philon (3rd century BC) gives 180m as standard range, Flavius Josephus even 300m in the Jewish War, although this has been viewed by some historians as inflated. Warry, p.179 writes, refering to the absolute range, that "Agesistratus records that the best of the catapults now had a range in excess of 800m" (in Late Roman times).

How come the torsion catapults exceeds both in effective and maximum range even traction stone-thrower with a big crew? Am I overlooking something or are we again comparing apples with oranges? Perhaps the torsion ballista was even the superior design until the counterweight was introduced in the High Middle Ages?

Edited by Tibet Libre, 26 April 2006 - 11:16 PM.


#18 Mei Houwang

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Posted 26 April 2006 - 11:20 PM

Again, the torsion ballista cannot be compared to the trebuchet. It is indeed comparing apples to oranges. I have already posted this before. Here was my quote:

"""""You can't compare a torsion with a trebuchet. You compare a torsion with a ballista. In short, torsion/ballista = giant crossbow. Trebuchet/catapult = giant sling. Comparing a crossbow and a sling simply isn't doable(a ballista-type machine obviously goes further than a catapult like machine. Usually more than twice the range). There isn't enough data to confirm anything anyways. There can also be varaibles that could make the data inaccurate(such as training/manpower for the trebuche, Rope type for the torsion, etc...)"""""

Roman catapults as well as Chinese trebuchets were constantly in danger of arrow fire. Only the ballista had enough range to escape this danger. Comparing a ballista-like machine to a catapult-like machine is just a biased comparison. Needleham states that a arcuballista would have an intial velocity of 70 yards per second while the trebuchet only have 30 yards per second. Thus, it is obvious that they can't be compared. Notice that most "torsion catapults" are misnomers because they do not work like catapults at all except that they throw stone balls. In fact, most "torsion catapults" ore basically torsion ballistas that throw stone balls of about 20 pounds. Of course, there are a few torsion catapults that are bigger than most houses, so they would obviously throw much heavier stones.

How come the torsion catapults exceeds both in effective and maximum range even traction stone-thrower with a big crew? Am I overlooking something or are we again comparing apples with oranges? Perhaps the torsion ballista was even the superior design until the counterweight was introduced in the Middle Ages?


Actually, the traction trebuchet already replaced the catapult before counterweight designed were introduced. Also remember that ranges can vary according to the weight of the projectile. Trebuchets were known to throw stones of up to 300 pounds for usual cases, while catapults had on average projectiles of 50 pounds to 200 pounds.

Edited by Anthrophobia, 26 April 2006 - 11:36 PM.


#19 Liang Jieming

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Posted 26 April 2006 - 11:25 PM

The only torsion catapult that can be compared to a lever-principled catapult would be the Mangonel (onager). You'll find that the ranges are comparable here.

The Ballista should be compared with the arcuballista instead.

Ok, here's the revised graph based on 20kg projectile, typical weight of the pullers reduced to 62.5kg but pulling contribution increased to 60%/person. All other items unchanged.

Posted Image

Something very interesting has happened here.

Ignoring the reduction and subsequent increase of the pulling force (won't make that great a difference), we are left with only one significant change, ie. the increase of projectile weight from 1kg to 20kg.

The ranges have predictably all decreased, but you'll notice that the slope of the graph has increased considerably at the upper end of the scale. This means that the 200m upper range efficiency limit no longer applies and doubling the number of pullers from 250 to 500 actually increases the range by a fairly significant 25m. The catapult can therefore, reasonably be further increased in number of pullers compared to the 1kg projectile catapult before suffering a decrease in range efficiency. Interesting. (Limited of course the the space available for hundreds of people standing underneath the catapult (or to the front if Turnbull is correct).

Edited by Liang Jieming, 26 April 2006 - 11:37 PM.


#20 Tibet Libre

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Posted 26 April 2006 - 11:49 PM

Comparing a ballista-like machine to a catapult-like machine is just a biased comparison.


Leaving the issue of the numerous variables aside, why so? I am comparing stone thrower with stone thrower. Certainly are we comparing two different mechanical systems, but who cares? We are talking about war, and those machines were employed, that a plain fact and not at all "biased".

Comparing ballista and catapult in terms of range, effective range, fire rate makes is as legitimate as comparing a gun and bow & arrow. I dont see any problem. We are talking about military history here, arent we? ;)

#21 Mei Houwang

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Posted 26 April 2006 - 11:54 PM

Leaving the issue of the numerous variables aside, why so? I am comparing stone thrower with stone thrower. Certainly are we comparing two different mechanical systems, but who cares? We are talking about war, and those machines were employed, that a plain fact and not at all "biased".

They are used in different ways, obviously. Would you compare the range of an arbalist to a self bow? Obviously not. I doubt you'd like me comparing the range of an arcuballista to a torsion catapult, or just a catapult at that. Is an arcuballista superior to the torsion catapult because an arcuballista have further range? No, b/c it's obviously comparing apples to oranges. There is more to warfare than just "how far you can throw stuff at the enemy". There are different ways to do it, for the acheivement of different results.

Comparing ballista and catapult in terms of range, effective range, fire rate makes is as legitimate as comparing a gun and bow & arrow. I dont see any problem. We are talking about military history here, arent we?



No, it is not legitimate. Because the way you are comparing it is to say "which is better". There is no "better" until the Industrial Revolution when it comes to gun and bow. They have their strengths and their weaknesses. The typical gun(musket) during European colonialism have a range that is inferior to the bow by far(thx to the fact that a bow can shoot in an arc), but that does not mean a bow is "better" as one would want to put it.

Edited by Anthrophobia, 26 April 2006 - 11:56 PM.


#22 Tibet Libre

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Posted 26 April 2006 - 11:56 PM

The only torsion catapult that can be compared to a lever-principled catapult would be the Mangonel (onager). You'll find that the ranges are comparable here.


How do you call the principle of the onager? It is torsion powered, but you wouldnt call the throwarm a lever, would you?

Do you have literature on the onager? I am pretty short on infos about that mule.

#23 Mei Houwang

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Posted 27 April 2006 - 12:00 AM

It can only shoot in an arc. When other torsion ballistas are released, it is much like a ballista, with the force being propelled from behind the projectile. An onager throws the projectile much like how you hit peas at your sister with a spoon.

#24 Tibet Libre

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Posted 27 April 2006 - 12:08 AM

Would you compare the range of an arbalist to a self bow?


Geez, I would even compare a stone throw with an intercontinental missile, if that is what two opponents each use on the battlefield. You are talking about the scientific admissiblity of such a comparison, which is completely irrelevant to my question, because I am interested in what was actually used in ancient battles or do you think a nomad horsemen rode up to a Chinese infantryman and said: Dont let us fight because I have a bow and you a sword...?! Should we stop now comparing infantry vs. cavalry, crossbow vs. recurve bow, lance vs. throwing axe? You get what I mean.

As for each thing having its the strenghtes and weaknesses you are right though, but that is exactly what I am interested in!

Edited by Tibet Libre, 27 April 2006 - 12:09 AM.


#25 Tibet Libre

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Posted 27 April 2006 - 12:13 AM

Liang,

could you make some graphs for very heavy projectiles?

Preferably sizes which were actually historically recorded .

Say, 50 kg, 75 kg, 100 kg.

#26 Mei Houwang

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Posted 27 April 2006 - 12:34 AM

Geez, I would even compare a stone throw with an intercontinental missile, if that is what two opponents each use on the battlefield.

An unfair comparison because they are of two different time zones. If you compare a ballista with a trebuche and say that the ballista is naturally "superior", than you have to compare an arcuballista with a catapult and say that the arcuballista is naturally "superior".

You are talking about the scientific admissiblity of such a comparison, which is completely irrelevant to my question, because I am interested in what was actually used in ancient battles or do you think a nomad horsemen rode up to a Chinese infantryman and said: Dont let us fight because I have a bow and you a sword...?! Should we stop now comparing infantry vs. cavalry, crossbow vs. recurve bow, lance vs. throwing axe? You get what I mean.


No, because no battlefield weapon made for different purposes is superior to another. You cannot say that infantry swords are superior to cavalry lances, or cavalry bows are superior to infantry crossbows. It is ridiculous. Do you think on the battlefield that one enemy will say "oh, they are using torsion catapults against us! That means we must counter them by using the trebuchet which totally not what it's built for!"

As for each thing having its the strenghtes and weaknesses you are right though, but that is exactly what I am interested in!


Then the subject of which is "superior" must be dropped firsthand.

#27 Liang Jieming

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Posted 27 April 2006 - 01:30 AM

Liang,

could you make some graphs for very heavy projectiles?

Preferably sizes which were actually historically recorded .

Say, 50 kg, 75 kg, 100 kg.

Did Romans throw projectiles of that size? I believe projectiles only reached that kind of size with the counterweight trebuchets.

The Onager is still a torsioned principled catapult but is single armed instead of the double "bow" armed ballista. There's a short write-up on the Mangonel (onager) in my book. It wasn't particularly accurate unlike the ballista, probably because the throwarm was not sufficiently restrained in the Z direction (Y is vertical, X is towards the target).

I'll try and see if I can find some literature giving max ranges for Onagers for comparison.

#28 Tibet Libre

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Posted 27 April 2006 - 05:45 AM

Then the subject of which is "superior" must be dropped firsthand.


Then drop the notion of superiority altogether from the human language and mind, because strictly spoken to meet the definition of superiority a thing must be at least in one aspect better and in no aspect worse, which is a extremely rare, if not outright impossible occurence in the world.

As long as one is careful to differ, explains strengthes and weaknesses in a balanced way and gives reasons as to why he judges this or that superior or inferior, I can see no wrong with that. The first rule of historical science is that everything is implicitly comparison - everything.

#29 Tibet Libre

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Posted 27 April 2006 - 05:56 AM

Did Romans throw projectiles of that size? I believe projectiles only reached that kind of size with the counterweight trebuchets.


And I was curious if projectiles of such weight had been ever thrown by pulling crews and what the more typical size was?

As for the Roman stone-thrower: Warry, p.78 says that "the lithobolos threw stones of 4,5 to 82 kg in weight" and on p.179 a onager is depicted which "shows a 80 kg" onager and, if I am not mistaken, one or two of the ancient catapult treatises mentions throwing 78 kg projectiles, but it must have been in any case a rare occurence, since a find of an arsenal of ancient artillery stone balls at Pergamum shows only two 78kg projectiles and thirty-three 52 kg projectiles among a thousand (Osprey, p.20)!

Edited by Tibet Libre, 27 April 2006 - 05:58 AM.


#30 Mei Houwang

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Posted 27 April 2006 - 07:39 AM

Then drop the notion of superiority altogether from the human language and mind, because strictly spoken to meet the definition of superiority a thing must be at least in one aspect better and in no aspect worse, which is a extremely rare, if not outright impossible occurence in the world.


As a general, the mere idea of "superiority" of one weapon designed for something completely different from another weapon would cause him to lose the battle. If you are a military historian, then the most you can do to judge which one is superior is to ask which replaced what(in this case catapult-like engines and ballista-like engines existed side by side), for just saying the ranges of a weapon won't mean much when you consider all the factors(speed, how cheap it is, how fast you can build it, the number of throwers, accuracy, resistance to weather, etc...). A crossbow cannot be superior or inferior to a bow. They are used for different purposes. One is good against lightly armored units, one is good against heavily armored knights. If you want to judge which one is "superior", then why don't you just drop the meek attitude of "realizing that they both have their respecitive strengths and weaknesses" in the first place? If you wanted to discuss which one is "superior" in the first place, then why did you bother to ask if you are "comparing apples to oranges"?

Edited by Anthrophobia, 27 April 2006 - 07:49 AM.





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