I'm trying to verify the figures given by Chen Gui.

"Chen Gui, author of the Shoucheng Lu or “Defense of Towns” who was an active participant and therefore a direct eyewitness of the earlier siege of De An in A.D. 1127-1132, recorded that the largest type of catapult had a pulling crew of 250 with two men to a pulling rope and had levers of 2.8 chang long (somewhat between 6 to 9 metres during the Song) while the smallest single levered catapults required a crew of 40 men pulling on 20 pulling ropes. The ranges obtained from these catapults were also recorded where he gave the ranges for Song era large and small catapults. Large first class catapults had a range of 270 bu, second class catapults 260 bu and third class catapults 250 bu, while the small single-levered catapults could hurl 1 kg stones up to a distance of 50 bu (where a bu at the time of the Song was approximately 60 centimetres)."

His maximum of 270bu only equates to 162m.

I need to clear some basic assumptions on Chinese traction catapults.

1. There were 2 pullers per traction rope.
2. What is a reasonable assumption of downward pulling force per puller expressed as a fraction of the puller's weight? (1/2? 1/3? 1/1?)
3. Throwarm ratio taken as 5:1
4. He doesn't give the projectile weights for the 1st, 2nd and 3rd class catapults although he does give a projectile weight of 1kg for small single-levered catapults. We assume a more decent projectile weight taken at 10kg?
5. Typical weight of a Song-era soldier (puller probably not wearing armour or weapons)? 65kg? 75kg?
6. Release angle for Chinese catapults are usually straight-up (ie. 180 degrees measured from throwarm)?
7. Height of catapult assumed to be 1.5 times a person's height (1.63m?), which would equal approximately 2.45m?
8. Weight of throwarm assumed at 150kg (for bamboo bundle)?
9. Length of sling taken at a reasonably long 2.45m?

Ideas anyone?

I'll load all these figures into a catapult calculator written by LTC Stephen J. Ressler, Dept of Civil and Mech Engineering, West Point, and work out the maximum ranges and post them here as a graph later.

Liang,

Have you ever gone to www.theminiaturespage.com and read about the trebuchets in the medieval forum section? There is a guy from Switzerland who has written some interesting articles regarding the trajectory, range and capabilities of trebuchets. Tomorrow, I'll try to e-mail you some pdf documents that I have on trebuchets.

Chris

Hi Chris,

Yeah I do have quite a few articles as well as formulas on catapults. I haven't been to that website but I suspect the swiss guy you're talking about is Mick? I've correspondanced with him earlier with regards to the origins of catapults.

Because there are so many factors involved in a the calculation of a catapult's range, it is not easy to find the right one that would suit the characteristics of a typical chinese catapult (which differs quite a bit from western catapults on quite a number of characteristics). I finally selected the one by LTC Ressler for a couple of reasons, he allows for the manipulation of many variables like throwarm weight, sling length etc. that many other's don't take into account in their calculations, as well as the fact that he's from the Dept of Civil and Mech Engineering from West Point where they have courses on mechanical artillery as part of their core syllabus.

This are the number of pullers I will be plotting the graph on, 40men, 110men, 180men, 250men & 500men (500 is based on an arabic account during the siege of Mecca in A.D. 692)

Cheers,
Jieming

A preliminary chart based on the following parameters:

1. 2 pullers per traction rope
2. Assumption of downward pulling force per puller expressed as 50% of the puller's weight (can actually go higher)
3. Throwarm ratio taken as 5:1 (close enough to optimal)
4. Assumed a projectile weight of 1kg
5. Typical weight of unarmoured/weaponless Song-era soldier at 70kg
6. Release angle at 180 degrees measured from throwarm
7. Height of catapult at 2.45m to the axle
8. Weight of throwarm assumed at 140kg (for bamboo bundle)
9. Length of sling taken at 2.45m
10. Effect of axle friction discounted

Maximum theoretical ranges obtained using a catapult calculator written by LTC Stephen J. Ressler, Dept of Civil and Mech Engineering, West Point.

From the graph, we could probably draw a few simple tentative conclusions:

1. 200m is the maximum optimal range. Doubling the number of pullers from 250 to 500 only gives an increment of 15m, hardly worth the added input effort.

2. The optimal range efficiency of the catapult hovers somewhere between the 2nd and 3rd point ie. between 110 and 180 pullers. This seems to match Chen Gui's figure of 250 to 270bu.

Two major factors that can affect the results but which were not taken into account are the weight of the throwarm, and the centre of gravity of the throwarm. In this simple comparison I assumed the same catapult configuration for all 5 data points as well as a uniform throwarm (ie. centre of gravity is in the centre of the throwarm) Realistically, the larger the catapult, the larger the throwarm. The throwarm can also be thickened near the axle to reduce the cantilevered weight nearer to the projectile end. This would maximise the pulling force at the pulling end. So if we were to take these two into account in the comparison, we would probably get a depressing of the righthand graph while retaining much the same values on the lefthand graph. The 500 man catapult might not actually reach the 200m range.

The same thing did strike me as well when I read Inventive Steps in Trebuchet Evolution
by Michael Farnworth!





--> doubling the crew only lets the traction catapult shoot mere 3 meters farther!







Thats what he said about the usual size of pulling teams:

Do you mean with "maximum optimal range" a flat trajectory (We know that Roman siege artillery used to shoot such direct shots)?

I don't think you can shoot flat trajectory with a catapult-like weapon.

Hey Jieming,

wanted to show you another site which makes really fun!

http://www.punkinchunkin.com/results2005.htm

Compare "adult trebuchet" and "adult torsion" and note how the top torsion catapult shoots almost as far as the top trebuchet, despite only half as much torsion catapults taking part in the competition! Yeah, torsion still rocks!

(I dont know though which catapults the category "adult catapult" features. Any ideas?)

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...)

Hehehe, what I meant by maximum optimal range is the maximum range where the catapult still gives a decent return on the input, ie. the point (or range) where the graph levels ie. where it becomes inefficient.

Yeah, Farnworth and I chatted quite a bit on thehurl.org while he was writing that article. We were comparing notes as I was also writing my Brief History of the Catapult at the time too.

I just realised that this comparison also doesn't take into account the whip secondary effect of bamboo. This additional "spring" would do two thing, depress the firing trajectory further, and help propel the projectile with greater force forward (like a whip). I doubt any catapult calculations out there take this into account. It would be freakingly difficult to calculate secondary effects on top of the initial projectile motion/trajectory.

Jieming,

Yes the gentleman's name is Mick. Since you have already been in touch with him I will not send the articles. They came from him.

Chris

Thanks all the same Chris.

Oops. My 500 men catapult account is the same siege of Daybul, not Mecca. Mick (Farnworth) and I probably got it from the same secondary source.

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?

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.




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

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%.

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

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?

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.



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.

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.



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).

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?

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.



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.

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.

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.

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!

Liang,

could you make some graphs for very heavy projectiles?

Preferably sizes which were actually historically recorded .

Say, 50 kg, 75 kg, 100 kg.

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".



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!"



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

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.

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.

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)!

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"?

Whats your problem? Do you want to cut off what has been otherwise a good discussion? Half of my posts I am obliged to attend to you trying to tell me which questions I am allowed and not allowed to pose. I am comparing stone thrower with stone thrower, if the concept of a stone is too difficult grasp, then what can I do?

So please lets keep the discussion on the topic without these endless diversions. I am well aware that torsion and traction catapults differ in a whole array of aspects, a couple of them you have mentioned, but right now I am just interested in

a. their respective effective ranges
b. typical sizes of projectiles
c. typical sizes of pulling crews

in theory and in what is recorded by the ancients.

Good day.

The weight of the stone thrown is the crucial difference between the trebuchet and the torsion catapult.

Here is the quote from Needham:

"A word or two may be added about the projective weights and ranges of these catapults. Estimates for the torsion types in ancient Greek texts vary between 160 and 600 yards for missles weighing up to 10 lb but the probable average, partly derived from experience with modern reconstructions, was really 330 to 410 yards. This span coincides with Chinese arcuballista figures (270 to 500 yards.). Ancient European sling and torsion catapults (onagers) threw stones of about 50 lb weight, occasionally up to 175 lb but never much more than 160 yards. Manned trebuchets sent larger missles, up to about 275 lb, from 80 to 190 yards, and fixed counterweight ones had a somewhat longer range. Anything as heavy as this was already dangerous for defensive masonry, whatever its character."

Range depends on the crew but the stones thrown by the trebuchet are usually twice as heavy with almost equal distance.

Comparing simply the range is meaningless, in fact stones of 100 ibs aren't going to do much against the ramed earth walls of Chinese fortifications, which are thicker and sturdier, it doesn't matter how far or fast a machine can throw the weight of their missile or how little crew they possess, if they can't even damage the fortification walls.

The need to make one side superior than the other. That's the problem. Any discussion that needs to make one country "better" than the other isn't a good discussion.

I dont know about these figures, looks to me all a bit confused and outdated.

For a start, he doesnt say which Chinese arcuballista he refers to (one bow, multi bow?) and with the trebuchet he doesnt carefully differ either. Take a look at Mick's article and you will see that even early non-pulling crew trebuchet dont surpass torsion catapults with comparable stones sizes:

Thus a "single bag counterweight beam sling on a trestle frame" from about 1100 AD has an effective range of 116m with 45 kg. Not too different from the figures I gave above for the 28 kg torsion ballista.

But anyway, I am not interested in counterweight trebuchets, but the pulling crew trebuchets (which I prefer to call traction catapults, because they were so much less powerful). Guess I have to wait for the ingenieur chinois de siege.



Last time I checked I was comparing catapults. Dont know though what you are doing.

They actually match the figures you gave quite well. The figure from your source of 28 kg is roughly 60 ibs. And 157 meter match Needham's "never much over 160 yards"

And your source 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)!85 kg is roughly 175 ibs. "

Its pretty much what Needham gave as well.

"Ancient European sling and torsion catapults (onagers) threw stones of about 50 lb weight, occasionally up to 175 lb but never much more than 160 yards."

Needham give his sources at the very bottom of the page. And his Chinese figures are taken from primary sources. There are no reconstructions for Chinese equipments of Han because there are limited sources on how they are reconstructed, and there haven't been much excavations found. But the fact that trebuchet can throw up to 275 pounds is not just the Chinese trebuchet, but manned powered trebuchet in general.




This is not about comparing the distance under the same size of stone thrown, but the Counterweight's ability to throw larger stones weighing up to a ton, which the torsion catapult cannot do.(the same goes with manned).

Second, manned trebuchet isn't inferior to the counterweight, they are just used differently. The counterweight is solely used for its destructive power, otherwise it is inferior in speed.
The small manned trebuchet can be assembled and fired at a faster rate than the counterweight. Thats why Zhu Yuan Zhang of the Ming dynasty prefered the manned trebuchet in siege over those of the counterweight.

You are now comparing ballista with onager, but, as I said, I am interested in comparing ballista with the manned traction catapult.



Yeah, that what LJ said earlier, the onager and the manned traction catapult have comparable ranges under similar load.



That why I asked LJ to feed his programm with some bigger sizes, just to show what effective ranges the manned traction catapult reaches under heavier loads than 1 or 20 kg.


LJ,

couldnt you post the link to your catapult calculator? Or feed it please with 50, 75, 100, and 150 kg.

Nope, you are comparing "torsion catapults" to trebuchets. A usual torsion catapult is not a catapult but a ballista in every way except that it throws stones instead of bolts. That is what you are doing(and other things on cultural superiority, it doesn't take much mindpower to soak up all the posts in every thread and realize that it constantly compares how the things of Europe is better than everybody else in certain things).

This is not important, the traction catapult exerts a greater force, and hence can also throw heavier stones. It has the ability to throw weights twice as heavy over roughly the same distance as well, it depends on the crew size and the design itself.

The catapult calculator is a small programme. I can e-mail that to anyone who's interested. Just drop me an e-mail.

Here's the chart different projectile weights based on a 250men puller catapult (all other catapult specifications the same).



The graph shows a nice linear relationship between range and projectile weight. I suspect this would be just as true for torsion onagers as well.

********************************

I just spoke to Mick on his comments on onagers. He actually doesn't cite any primary sources, with his main two sources being the Greek and Roman Artillery book by Marsden and an Osprey series book.



Warhead, if you don't mind, let me restate this in clearer terms.

The traction catapult doesn't exactly exert greater force, it just has a more variable ability compared to the onager. The same traction catapult frame can be made to range further, throw heavier projectiles, projectile trajectory etc. simply by manipulating the pullers on the catapult ie. playing with the number of pullers as well as varying the way the ropes are pulled/held (within a reasonable range due to constraints like standing space and throwarm strength). The onager has only two variables which can be changed, the torsional potential of the sinew/hair and the throwarm barrier. The sinew/hair has a limited range in which it can be torsioned. The relationship between the torque applied to the throwarm is not linear. Over torsioning will snap the sinew. Releasing torque on the sinew not necessarily gives an even reduction in range because you need to factor in creep in the sinew after long periods of maintaining a high torque. The torque in the sinew also needs to be maintained, again due to creep in the fibre. The better variable is the throwarm barrier which can be moved forward or backwards to change the angle where the throwarm is stopped ie. the projectile trajectory, but this is harder than it sounds because of the sling. Insuffient throwarm rotation would not fully deploy the sling. The release pin at the end of the throwarm is also needs to be readjusted to suit a new throwarm barrier angle or the sling might just shoot the projectile straight up, or worse, backwards.

Here's the graph for Projectile Weight vs. Number of Pullers (Men) with range constant at 50metres. This was probable the greatest advantage of the traction catapult, it's ability to vary it's projectile load without sacrificing range.

Very nice linear relationship. Easy for catapult commanders to calculate on the field. If 40men could fire a 25kg projectile 50m, and a 50kg projectile could be fired the same 50m by 64men, then a 75kg projectile requires 64 + (64-40) = 88men. Q.E.D.

Hmmm... all this work and no comments guys?

I want to comment but I can't think of anything. I think this goes for a lot of people in this forum. But if you keep on posting I'll keep on reading.

With this indepth material I think the only person who can respond is Mick from Switerland.

Cheers

chris

Hehehe ok then. I'll just keep posting more info then.

I been thinking and staring at the graphs for awhile now. The question that just begs to be asked is that whether a catapult design exists that would allow a traction crew to throw a decent sized projectile to the same ranges as the hinged counterweight catapults did. Surely they could since the only difference between the two was the counterweight pull force.

If I took a 350m range medieval hcw (hinged counterweight) treb, removed the hcw and replaced it with the equivalent number of pullers required to generate the same downward force, pulling at 9.18m/s acceleration downward (ignoring the contraint of space for some many people underneath the catapult), I dare say this reconverted traction catapult would perform exactly the same as the original hcw treb would.

Does anyone know what a typical weight for a medieval treb would have been? 5,000kg? 10,000kg? 20,000kg?

Jieming,

Good stuf!

Actually, the more I play around with the equations and model larger sized catapults, I'm finding that the arbitrary 200m max range limit to a traction catapult is not so much the inability of the mechanism to reach larger ranges, but simply a logistical problem of fitting sufficient people under the catapult.

The counterweighted catapult allowed greater weights to be placed within the limited area and hence, broke the "max number of pullers" limit rather than the max range limit.

Is it time f. you to write a computer-generation simulation on this particular scenario?

Hello,

I am no maths wizz, but I think you may have overlooked something:

1. The effect of inertia
2. The changing length of the beam

I am quoting in the following Donald R. Hill: Trebuchets




I do not think there are that much variables for a traction catapult.

1. I do not know what you mean with "varying the way the ropes are pulled/held". I would dispute that a large crew of dozens or even hundreds of men can make unisono subtle changes to influence the trajectory in any meaningful way. Hill for one finds that "with such large numbers, there must have been a high degree of training and discipline."

I would therefore rather say, for the motions of the pulling crew it is either all or nothing.


2. I dont see how the projectile trajectory can be influenced easier with a traction treb as it lacks a throwarm barrier and manipulating the release mechanism of a sling is as easy with an onager.


3. Playing with "the number of pullers" has also its limits. This is already obvious from the historical fact that in the initial report about Song catapults there were three different catapults: light, medium and heavy. Obviously, such a variety would not be necessary if the Song had felt they had an all-round catapult.

The physical reason seem to be inertia, which, as far as I can tell, is not part of your calculations: "In a counterweight trebuchet, for example, doubling the mass of the counterweight doubles its moment of inertia, while doubling its distance from the fulcrum quadruples its moment of inertia...exactly the same considerations can be made for the missile if it is resting on the end of the beam. In general, the same considerations also apply for the beam: increase in its mass increases its moment of inertia...an understanding of the basic concept of inertia and of the interdependence of all parts of a rotating body is essential to an understanding of the way trebuchets work."

Hill continues: "Huuri attempted to compare the power of the two machines (traction treb and CW treb) by imaginging the pulling crew loaded into the counterweight box, but rejected this line of reasoning because he felt that the weight of a man does not necessarily equal the pull he can exert. But this is the least of the reasons that make this argument absurd: the lightness of the beam due to the absence of a counterweight, the absence of inertia due to a counterweight, and the shortness of the pull are the essential factors that distinguish the traction trebuchet from the counterweight trebuchet."

And: "The three main components -counterweight, beam, and missile- are all parts of the same body. They combine to produce acceleration, and they also combine to produce the total inertia that resists acceleration. Both the traction trebuchet and the counterweight trebuchet were compound pendulums but they operated under quite different dynamic conditions."

Thus, you cant equate both trebs like you did. There is no going on with larger and larger crews for the same machine. Instead, the length of the beam varies with the weight of the missile and the counterweight respectively the pulling crew. Hill gives for large machines a ratio of 3-1 or 2-1 between long and short arm and for small machines 5-1.

Yes you can compare them. I'm comparing the same frames with only the difference being one with a counterweight, the other pulled by people. If you increase the throw arm on a counterweight treb, you can also increase the throw arm of a traction treb.

And why can't you vary the exact same things in a traction catapult as those you would in a counterweight treb?


Shifting the throwarm barrier on an onager is the same as having the pullers stop at a certain position in their pulling. Cruder perhaps but infinitely quicker than dismantling and then reassembling an onager barrier. Take a handsling. Vary your throwarm stop position as you are throwing it. Simple isn't it? Easier than keeping the same throw (ie. ignoring the ability of your hand to stop when it wants to) and having a fixed bar setup to stop your handsling at various positions.

The Song had 3 different sizes because there are limits to each type. What the traction treb gives is the ability to range from the lower limit of a catapult to it's upper limit before needing to change to the next larger frame. To illustrated, what this meant was the the Song would have catapults which could fire from ranges 1 through 3 using the light treb, 4 through 6 using the medium treb and 7 through 9 using the heavy treb. In comparison, having counterweight trebs in 3 different sizes means only 3 fixed ranges (unless you vary the weight of the counterweight which is both time consuming and rather difficult to do on the fly), ie. you can only fire ranges 2, 5 & 8.


What is inertia? Inertia is a factor of mass of the object (in motion or) at rest and the about of acceleration/force required to (stop) move it. Nothing else. Gravity is fixed. So the only thing you are varying is the mass to give a certain Force required. You can do the same with a traction catapult. This thing about interdependence of all parts applies regardless of whether it is a counterweight treb or a traction treb.


He is ignoring the fact that you can also build a heavy catapult with heavy arms and still get people to pull down on it. (Forget the loading of people into the counterweight box. That's nonsense.)

Just imagine if you can, taking a medieval European counterweight catapult (complete with all the said advantages, ie. longer throwarm, heavier beam etc.) and then removing the counterweight and replacing it with the equivalent number of people calculated to pull at exactly the same force as the counterweight would under gravity. Wouldn't the two catapults be exactly the same in performance? F = F no matter the source. You don't need maths. Common sense.