88 replies to this topic

[Liang Jieming]

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.

Edited by Liang Jieming, 24 April 2006 - 11:32 PM.

[shurite7]

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

[Liang Jieming]

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

Edited by Liang Jieming, 25 April 2006 - 01:43 AM.

[Liang 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.

Edited by Liang Jieming, 25 April 2006 - 06:42 AM.

[Liang Jieming]

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.

Edited by Liang Jieming, 25 April 2006 - 07:00 AM.

[Tibet Libre]

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.

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

Power of a 10 man Chinese “Hseun Fang (Whirlwind)”
Counterweight 10 men is equivalent to 600 Kg.
Upper Arm 78%
Arm Length 6 m estimate from scale model
RON number 4.5, from the Grey Company reconstruction
Calculated Range
0.5% projectile of 3 Kg range is 208 m
1% projectile of 6 Kg range is 104 m
2% projectile of 12 Kg range is 52 m
Rate of Fire was probably one shot per minute

Power of “Thessalonica Machine 597 AD”
Counterweight 20 men is equivalent to 1200 Kg.
Upper Arm 78%
Arm Length 6 m estimate from scale model
RON number 4.5, from the Grey Company reconstruction
Calculated Range
0.5% projectile of 3 Kg range is 213 m
1% projectile of 6 Kg range is 107 m
2% projectile of 12 Kg range is 53 m
Rate of Fire was probably one shot per minute

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

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)

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

Most medieval references and pictures describe pulling teams from a few men up to 50 men. However, there are some medieval documents which describe huge machines powered by 200, 400 or even 500 men. At siege of Daybul in Pakistan in 712 AD, Arabs used a Manajaniq (tension trebuchet) called “The Bride” which was claimed to be powered by 500 men.

[Tibet Libre]

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.

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

[Mei Houwang]

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

[Tibet Libre]

Hey Jieming,

wanted to show you another site which makes really fun!

http://www.punkinchu...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?)

[Mei Houwang]

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...)

Edited by Anthrophobia, 25 April 2006 - 08:06 PM.

[Liang Jieming]

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

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.

[shurite7]

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

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

[Liang Jieming]

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.

[Liang Jieming]

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

Most medieval references and pictures describe pulling teams from a few men up to 50 men. However, there are some medieval documents which describe huge machines powered by 200, 400 or even 500 men. At siege of Daybul in Pakistan in 712 AD, Arabs used a Manajaniq (tension trebuchet) called “The Bride” which was claimed to be powered by 500 men.

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.

[Tibet Libre]

2. Assumption of downward pulling force per puller expressed as 50% of the puller's weight (can actually go higher)

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?

5. Typical weight of unarmoured/weaponless Song-era soldier at 70kg

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.

4. Assumed a projectile weight of 1kg

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