Han Dynasty Crossbow II

[FONT=&quot]The following is a rehash of Han Dynasty Crossbow. The reason is because the pictures of the last thread are gone now, and also because of new information.


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The prevalence and praise of the crossbow in ancient Chinese texts is so widespread (The excavated Donghai accounting records show the existence of up to half a million crossbows in its stockpile) that I find this single weapon notable enough to write an entire article centered on it. No doubt, from its inception during the 6th century BC the crossbow revolutionized Chinese warfare. Projectiles fired from a crossbow are much more powerful than those fired from bows, and only a little time is needed for one to become proficient with it. Bolts can be fired with enough force to penetrate shields and armor at a distance. No longer can heavily armored, skilled nobility outmatch the everyday peasant. This essay only deals with ancient crossbows of the Han dynasty, although it was one of the primary weapons in Chinese history for a much longer time than the dynasty itself.


[/FONT] [FONT=&quot]Just how powerful a crossbow could be is glimpsed in the excavated Chu-yen slips, from which records of crossbow maintenance was kept. From the slips already excavated, we have available a set of records showing six crossbows shooting 168 to 280+ meters. Each of these crossbows had only draw weights of 3-5 stone, as compared to typical Han era crossbows of 6 stone. Without knowing the weight of the quarrel, the range in itself doesn't speak for the effectiveness of these crossbows. However, two slips record tests for their penetration ability. Both show that the crossbows tested punctured a wooden wall (most likely a plank or fence) at 252 meters.

[/FONT] [FONT=&quot]Slip 14.026: [/FONT][FONT=&quot]一今力五石廿九斤射百八十步辟木郭[/FONT][FONT=&quot]
Translation: Present strength 5 stone 29 jin (341 lbs) and will penetrate a wooden wall at 180 paces (252 meters).
Slip 515.46: [/FONT][FONT=&quot]三石具弩射百廿步[/FONT][FONT=&quot]
Translation: 3 stone (193.5 lbs) crossbow, fully assembled, shoots 120 paces (168 meters)
Slip 36.10: [/FONT][FONT=&quot]官第一六石具弩一今力四石【四十】二斤射白八十五步完（[/FONT][FONT=&quot]The words in [/FONT][FONT=&quot]【】[/FONT][FONT=&quot] is used to display what the word on the slip means, but the actual word cannot be typed by computer as the word is no longer in use)[/FONT][FONT=&quot]
Translation: Number one 6 stone crossbow, fully assembled, present strength is 4 stone 42 chin (285 lbs), and it will shoot to the end of 185 paces (259 meters).
Slip 510.026: [/FONT][FONT=&quot]五石具弩射百廿步[/FONT][FONT=&quot]
Translation: Five stone crossbow fully assembled, shoots 120 paces (168 meters)
Slip 341.3: [/FONT][FONT=&quot]具弩一今力四石射二百[/FONT][FONT=&quot]…[/FONT][FONT=&quot](too smeared to make out)[/FONT][FONT=&quot]…[/FONT][FONT=&quot]
Translation: Fully assembled crossbow, present strength 4 stone (258 lbs), shoots two hundred and …[text too smeared to make out] (280-418.6 meters).
Slip 14.62A: [/FONT][FONT=&quot]一今力三石廿九斤射百八十步辟木郭[/FONT][FONT=&quot]
Translation: Present strength 3 stone 29 jin (212.2 lbs) and penetrates wooden wall at 252 meters.

[/FONT] [FONT=&quot]In general Chu-yen slips categorize crossbow draw weight by 1, 3, 4, 5, 6, 7, 8, and 10+ stone, with each stone unit being the modern equivalent of ~64.5 pounds. The majority of crossbows have a draw weight of 6 stone. From the above tests, one can extrapolate that typical Han crossbows of 6 stone would have an average range of over 300 meters, assuming that the bolt fired was no different from those fired from weaker crossbows. The following is a calculation on the percentage of crossbows for each categorical draw weight, but it is currently not verified by me as I did not count them personally(However, historian Yang Hong also states that the majority of crossbows were categorized with draw weights of 6 stone):

[/FONT] [FONT=&quot]1 stone: 1.37%[/FONT][FONT=&quot]
[/FONT][FONT=&quot]2 stone: 1.37%[/FONT][FONT=&quot]
[/FONT][FONT=&quot]3 stone: 21.92%[/FONT][FONT=&quot]
[/FONT][FONT=&quot]4 stone: 2.74%[/FONT][FONT=&quot]
[/FONT][FONT=&quot]5 dan: 17.81%[/FONT][FONT=&quot]
[/FONT][FONT=&quot]6 dan: 43.84%[/FONT][FONT=&quot]
[/FONT][FONT=&quot]7 dan: 2.74%[/FONT][FONT=&quot]
[/FONT][FONT=&quot]8 stone: 2.74%[/FONT][FONT=&quot]
[/FONT][FONT=&quot]10 stone and above (Great Yellow Crossbow): 5.48%[/FONT]


[FONT=&quot]What must be noted is that crossbows were typically weaker than bows pound for pound due to their shorter powerstroke. Powerstroke is the length required for a string at rest to be drawn back to the trigger. This means crossbows must have heavier draw weights than bows in order to shoot the same projectile at the same velocity. Crossbow-maker Andreas Bichler also confirmed that with crossbow prods of the same draw weight, the one with the lower powerstroke would have more mass, which slows down the prod's shooting speed. Due to this reason, typical crossbows of Medieval Europe generally need to have three to eight times the draw weight of a bow in order to give a similarly powerful shot. but made up for this by utilizing winches to maximize the draw weight.[/FONT]
[FONT=&quot]However, ancient Chinese crossbows thanks to their trigger design allow the nut of the trigger to be placed near the back of the stock. This results in relatively long power strokes rivaling that of a bow, which greatly reduces the crossbow’s usual weakness of energy transference inefficiency. Han dynasty crossbows would have a draw length of 24 inches, implying a powerstroke of 18-20 inches, or rivaling that of a bow.[/FONT]
[FONT=&quot]Generally speaking, the power of a bow or crossbow measured in inch lbs = 0.5 x powerstroke length x draw weight. The most commonly mentioned crossbow in excavated accounting records were of the 6 stone (387 lb) type. In comparison most bows would only have draw weights of 40 to 100 lbs. Against armored men, Song dynasty archers could use bows with draw weights of up to 160 lbs, still less than half the draw weight of typical Han crossbows. Furthermore, thanks to the long powerstroke and composite prod, the Han crossbow would have very high efficiencies for a crossbow. Andreas Bichler noted how longer powerstrokes give higher dynamic efficiencies, so even composite prods would have low efficiency insofar that their powerstroke remains short. From this, we have the following result for shooting power

Potential Energy
Heaviest standard 8 stone Han crossbow power = 516 lbs draw weight * ~19 inches powerstroke/2 = 4902 inch lbs
Andreas Bichler's 1200 lb composite crossbow = 1200 lbs draw weight * 7.48 inches/2 = 4488 inch lbs
Tod Todeschini's 1250 lb steel crossbow = 1250 lbs draw weight * 6.5 inches powerstroke/2 = 4062.5 inch lbs
Typical 6 stone strength Han crossbow's power = 387 lbs draw weight * ~19 inches powerstroke/2 = 3676.5 inch pounds
Heavy Song dynasty bow made to pierce armor = 160 lbs draw weight * ~23 inches powerstroke/2 = 1840 inch pounds

The above only shows each weapon's potential energy, but does not compare the actual energy transferred into the projectile. Take note that the pontential energy shown is only an estimation of the area under the force draw curve, but not the actual area of the force draw curve. The estimation is missing the part highlighted in yellow:

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If we measure actual area, then the potential energy would be higher across the board, with composite prods benefiting much more than steel prods because composite prods have a more prominent "bulge" above the linear line. Because we only have the estimated area under the linear line, dynamic efficiency would be calculated upwards to compensate. So for the information below, just note that actual dynamic efficiency would be lower, but actual potential energy would be higher. The resulting joules should be the same.

Projectile Energy
Heaviest standard 8 stone Han crossbow power = 4902 inch lbs * 60% efficiency = 2941 inch lbs = 332 Joules[/FONT][FONT=&quot]
[/FONT][FONT=&quot]Typical 6 stone strength Han crossbow's power = 3676.5 inch pounds * 60% efficiency = 249 Joules
Andreas Bichler's 1200 lb composite crossbow = 4488 inch lbs * 39.04% efficiency = 1752.3 inch lbs = 198 Joules
Heavy Song dynasty bow made to pierce armor = 1840 inch lbs * 75% efficiency = 1380 inch lbs = 156 Joules
Tod Todeschini's 1250 lb steel crossbow = 4062.5 inch lbs * 30.5% efficiency = 1239 inch lbs = 140 Joules

Dynamic efficiency of Han crossbows is adjusted to 60% because that is mid-way between the efficiencies of composite bows and composite prods with short powerstroke. I adjusted upwards because Han powerstrokes are closer to that of bows than that of Medieval European crossbows. Crossbow maker Andreas Bichler confirmed long powerstrokes help with efficiency and gave that as the reason why his own Medieval composite crossbows had such low efficiency compared to composite bows. He also noted how composite crossbows tend to have higher potential energy than steel crossbows of the same draw weight (Composite bows have a greater amount of the yellow area shown in the graph above).


[/FONT] [FONT=&quot]Most bronze weaponry died out during early Han, but throughout the dynasty most crossbow arrowheads were made of bronze with a metallic tang, inserted into a wooden shaft. Some crossbow bolts were not entirely bronze. Rather, the arrowhead was of bronze while the tang (which sockets the bolt into the shaft) was iron. The reason for this is answered by Donald Wagner, who points to the superior casting properties of bronze. Han bronze arrowheads were remarkable for its attention to detail. Their intricate wings placed along the bolt tip were so small yet finely cast that it would be beyond the casting ability of iron for more than a thousand years afterwards.
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Such precise casting techniques allow a more aerodynamic bolt. Because this aerodynamic design only focused on the bolt tip, having the tang of the bolt be made out of iron would not affect its flight. Therefore, with iron being the cheaper metal, it was only natural for Han metallurgists to design crossbow bolts with a bronze head and an iron tang. Regarding weight, it is standard for crossbow projectiles to weigh 2 liang per stone. This meant that a Han quarrel for its most common crossbow of six stone would weigh 93.75 grams.[/FONT]


[FONT=&quot]Yet how were one able to draw these powerful crossbows? Weaker Han crossbows were categorized as “arm-drawn”, in that the bow was drawn in a standing position with the two feet grounded on the prod while the arms pulled the string up towards the trigger. More powerful Han crossbows were “foot-drawn”, in that the string was drawn in a sitting position using both the legs and the arms. This allows a much heavier draw weight as the muscles from the legs are much more powerful than those in the arms. Distance shooter Harry Drake used a 300 lb foot bow, drawn similarly to that of foot-drawn Han crossbows, in order to participate in his archery competitions.[/FONT]
[FONT=&quot]The heaviest crossbows would be drawn with a winch. These would no longer be handheld but must be used with at least a prop. Immobile crossbows fixed inside military forts on on top of walls are called "Revolving Shooters". Each revolving shooter would have a very thick wooden plank in front of it for protection against enemy fire.

[/FONT][FONT=&quot]"Yellow Crossbows" was the name given for more mobile devices. The strongest Heavy Yellow Crossbow could have draw weights of 90 stone, implying that its size would probably be akin to that of a ballista.

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The primary strength of the crossbow is without doubt its strong armor penetration capability. With a median draw weight of 387 lbs, and a powerstroke rivaling that of a bow, Han crossbows could shoot a projectile further and faster than that of a bow. According to the Han era government official Chao Cuo, one of the biggest advantages of Han armies over the Xiongnu was that the crossbow could penetrate the leather armor and wooden shields that the nomads possesed.
Furthermore, a crossbow has the option to shoot shorter projectiles. For a bow, the length of an arrowshaft must be greater than the bow's draw length, or else the bow would not be able to shoot the arrow at full draw. A Han crossbow may very well shoot quarrels with a length rivaling that of an arrow, or it could shoot significantly shorter bolts. This is possible because the quarrel would be launched from the groove of the stock, so a crossbow could even shoot quarrels small enough to be called darts should the occasion warrant it. By shooting shorter quarrels, spent projectiles cannot be picked up by enemy archers to be shot back against the crossbowman. Needham speculates that the East Asian arrow-tube guide (called pyun-chun to the Koreans), was developed by nomadic peoples in order to counter precisely this advantage.
Another advantage is that the crossbow is much easier to aim and shoot than a bow. A bowman must take aim while his arms resist the tension of the string at full draw. Even the strongest bowman could only aim within a limited time frame before his bow arm gives in. A crossbowman can take aim indefinitely, as the tension is held by the trigger. When used in a chariot or ship, the stability that the crossbow provides while aiming no doubt also alleviates the rocking motion of the vehicle involved.
A crossbowman can also draw the string before battle starts, to make sure he is able to take the first shot within a moment’s notice. Examples of this can be found such as when Xiangyu tried to kill the first Han emperor by hiding a pre-cocked pistol crossbow within his clothing. When emperor Wen inspected the military camp of general Zhou Yafu, the sentries were described in the Shiji as “in armour and bearing their swords and other weapons, their crossbows cocked and full of arrows”. The advantage to having a crossbow loaded indefinitely becomes particularly useful in sieges, as crossbowmen could use this advantage to take very quick pot-shots when enemies peek their heads from pavises, battlements, or any other protection.

The Han crossbow does come with shortcomings. Han crossbow prods were composite, including sinew and horn materials. Compared to metal prods of winched crossbows in Medieval Europe, composite prods needs more maintenance and are more susceptible to bad weather conditions. The long powerstroke also requires a very long prod. Andreas Bichler noted how his 617 lb composite crossbow performed very badly because its 75 cm prod was too short for its powerstroke. The Han crossbow design requires a very long prod, otherwise the string would be pulling the bow limbs apart rather than storing energy (a case known as stacking). Thus each crossbowman requires more horizontal space for shooting, which forces crossbowmen to either use open skirmishing formation, or adopt special formations to compensate (such as the countermarch, which will be described below).
The high draw weight of the crossbow also makes stringing difficult, particularly when the bow is recurved like those of Han crossbow prods. By the Qin dynasty, this problem was probably alleviated by having a bastard string in addition to the main string, so that the prod could be left partially unstrung to make stringing easier for future use. When shooting at a particularly elevated angle, the stock of the crossbow would block the user's line of sight, nullifying the crossbow's advantage in superior range when it comes to precision shooting. The biggest offset for the crossbow was its reloading speed. Even when pulled by hand as opposed to mechanical means, a crossbowman would still be outpaced by an archer in rate of fire. [/FONT]


[FONT=&quot]The standard deployment for crossbows would be to have the crossbowmen placed at the flanks of the army, screened by cavalry. In this way they could shoot at the flanks of the enemy. The Han also adopted tactics to offset the disadvantages of their weaponry. [/FONT]
[FONT=&quot]To nullify the disadvantage of the long reload time and the requirement for space, Han era soldiers came up with a drill similar to the countermarch:

“The drill of crossbowmen alternatively advancing [to shoot] and retiring [to load]; this is something the Xiongnu cannot face” –Chao Cuo of Western Han, Shiji[/FONT]

[FONT=&quot]The requirement for horizontal space meant that for a given line of 100 meters, a single volley from the front row would consist of only around 70 quarrels, whereas crossbows with shorter prods could squeeze more crossbows into the front row and hence shoot double that many quarrels in a single volley. The countermarch offsets this by allowing the people at the back rows to participate through the practice of shooting in rotation. The number of quarrels per volley would still be the same, but the Han countermarch formation allows for more volleys within a given span of time. Furthermore, the countermarch gives crossbowmen more time to rest in between shots, and offsets their slow fire rate.
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[FONT=&quot]By the late Han new tactics were developed that, when viewed from the front, would look very similar to the square formation of the flintlock era.[/FONT]

[FONT=&quot]When the enemy comes to the deer-barricades, the soldiers must hold their position behind them and thrust with spear and halberds. They must not stand as rising would hinder the shooting of the crossbowmen.-Military Commands (Late Han-3kingdoms period)[/FONT]
[FONT=&quot]Unlike the crossbows shooting at the back, the couched spearmen at the front could adopt as dense a formation as they wanted.

With this formation, the open-order formation of the crossbowmen would not be susceptible to melee, as the barricades and crouching infantry in front of them acts like a protective wall. The spearmen and halbadiers in front, not being armed with crossbows, could be packed as densely as they wanted to be, and hence be efficient in prolonged melee. This is especially so when they have crossbowmen shooting over their heads and into the ranks of the enemy.


[/FONT] [FONT=&quot]The aiming of the crossbow was refined by both technology and technique. The Han trigger mechanism is a perfect manifestation of this. The trigger itself is designed to operate like a modern trigger in which stored horizontal energy is transferred into a vertical one. This sophisticated design is perhaps the first of its kind that fully allows both hands to stabilize a ranged weapon when discharging a shot. [/FONT]
[FONT=&quot]The trigger also comes with graduated sighting blade and grid sight in order to adjust for target distance, which allows the crossbowman to aim with better accuracy. Liu Chong of the Han dynasty, himself very adept as a crossbowman, described how to use it: [/FONT]
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“of all the things in the whole wide world, there is none so extraordinary as the principle of sighting. There are three minute points and three small points. The three minute points and three small points are upon the warp and the three small points are upon the weft [analogy to silk looms]. They unite upon the catch of the crossbow. “-translation from atarn

[/FONT] [FONT=&quot]Nearly 1000 years later, Shen Gua of the Song dynasty unearthed a trigger mechanism with a sighting blade. Using Liu Chong’s method for shooting, he managed to score 7-8 hits out of 10. Shen Gua claimed he could have scored even better with a graduated sight.

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[FONT=&quot]A handheld weapon that could penetrate armor at a distance would be a technology that the Han military would no doubt want to hold a monopoly over. There are plenty of records which show the government attempting to limit such weapons over a certain grade from being brought outside its borders. But the biggest impediment to the empire’s enemies from mass-replicating Han crossbows would be the manner in which the Han crossbow trigger was made. Ancient Chinese bronze-making technology was unique, in that it derived as an offshoot from its advances in ceramic technology. Whereas the rest of the world used the lost-wax process to create bronzework, the ancient Chinese used the piece-mold process. Both bronze making processes entail pouring bronze into a clay mold, which determines the shape of the bronzeware. What’s special about the piece mold process, is that the clay mold could be re-used to make cloned copies of the bronzeware, whereas the clay mold of the lost-wax process would require the clay mold to be destroyed in order to extract the finished product. [/FONT]

[FONT=&quot]The Han crossbow trigger is very intricate, and if any part is off by even a little then the entire mechanism could fail to function properly. The piece mold process allows each individual part of the crossbow trigger to be reproduced again and again in a systematic fashion, with each copy being a virtual clone of the other. In this way trigger parts could be made interchangeable as long as they come from the same cast. Whereas with the lost-wax process, the work and care required to make just one more identical copy of a single trigger mechanism would skyrocket.


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The Chinese were the first to grade the stiffness of their bows by draw weight. This practice is done by seeing how much weight is added to the string until the string is pulled back to the distance of full draw.[/FONT]
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[/FONT]谓若干胜一石，加角而胜二石，被筋而胜三石，引之中三尺。假令弓力胜三石，引之中三尺，弛其弦 ，以绳缓擐之 ，每加物一石，则张一尺[FONT=&quot]
Translation: For a bare bow-stave with draw weight of one stone (64.5 lbs), adding sinew will increase draw weight to two stone, and adding horn on top of that will increase it to three stone. The draw length is 3 chi (1 chi is about 9 inches). If the present draw weight of 3 stone (193.5 lbs) with draw length of 3 chi (27 inches), then if strung with a relaxed string on both sides of the bow, each additional stone added will cause it to be drawn by one chi. [/FONT][FONT=&quot]-From Zheng Xuan Zhu

[/FONT] [FONT=&quot]The Book of Later Han listed some of the most popular works read during the Han dynasty. Two of the lost books are named “The Strong Crossbow General Wang Wei’s Way of Shooting” and “The Way of Shooting from Afar with the Interconnected Crossbow [a ballista]”. There are other book titles that mention styles of shooting such as “General Li’s Way of Shooting”, which may include the art of shooting crossbows. It is unfortunate that all but the title of the books are lost.


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The difference in power was not lost on the late Ming. When they dug up their old crossbows they noticed how they were more powerful than contemporary ones, despite being of lighter draw weight.[/FONT]
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"近于陕西省城见有城楼旧题神臂弩数百张，相传者百余年矣。乃知先朝亦尝制此。虽皆损坏，而制度 犹存，但箭则 无矣。臣谨从宜遵效造成。其制以阔厚坚劲大弓，其力一百五十斤上下、及一百二十斤上下、及九十 斤上下，为三 等，虑人力有强弱也。其长均为四尺五寸，矢取其利最远，而端可及三百步内外者。为矢，其长均七 寸五分，其重 则六钱上下，亦三等，俾与弩称。复效汉耿恭之法，箭簇开四尖，又辅以荷兰嵩县等处射虎箭药，俾 入马中无不三 洞。尤虏所畏。其箭簇后小铁管心，仅长分许，入箭杆处内用漆胶外用竹丝以夹缚之，俾虏不能取以 反射。盖虏之 射艺极精，矢无虚发，惟此足以胜之。”
"recently at a city in Shanxi province there were several hundred old shenbi crossbows in the tower which has been passed down for over one hundred years. It was created by the previous regime. Even though they are all broken, the instruction system survived but there are no arrows. I followed the instructions and successfully created them. It was made from thick and strong bows and it have a draw weight of around 150 jin, 120 jin, and 90 jin, three total...it can shoot a range of around 300 paces."

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我中国之御夷虏，专以长兵取胜。故前代弓矢不足，加以弩箭。汉制：官有强弩将军、射声校尉，器有神臂弩、大黄弩、连弩、药弩。匈奴呼药箭为汉家神箭。自有火器，弩制遂废 -神器谱
When defending against Yi and Hu barbarians, our country traditionally relied on ranged troops for victory. In ancient times the bow and arrow was not enough, so crossbows and quarrels were introduced. By the Han, the officials have strong crossbow generals and captains who shoot by sound. The machines include Divine Arm crossbows, Great Yellow crossbows, Interconnected Crossbows, and Medicine Crossbows. The Xiongnu called the Medicine quarrels as the Han’s divine quarrels. Ever since gunpowder weapons, crossbows became abandoned.

Yet even with the advent of gunpowder weapons, the effect of the crossbow was not totally lost. Notice how the following looks similar to the countermarch and deer-barricade formations described above?:


[FONT=&quot] Sources used:[/FONT][FONT=&quot]
[/FONT][FONT=&quot]Records of the Grand Historian, by Simaqian
The Book of Later Han, by Fan Ye
Chu-yen slips
The Military Storehouse of YongShi’s 4th year Equipment Account Book
Handbook of Oriental Studies, by Donald Wagner
Asian Traditional Archery Research Network, by Stephen Selby
Science and Civilization in Ancient China, by Needham
Journal of the Society of Archer-Antiquaries, Volumes 12-22
Andreas Bichler's Comments
Tod Todeschini
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It's my own built up over the years with information that I acquired. Everything's in my own words excluding some of the translations. Obviously I used tons of sources. If it's just a copy/paste of other people's work I imagine the grammar would be better. I myself never cared much for it.

You can see my original here: http://historum.com/asian-history/69030-han-dynasty-crossbow.html

Haakbus said:

It's pretty impressive, to be honest.

I've done some similar research into premodern Korean firearms and ships but I've never gotten around to putting it all together in a coherent form like this.

Click to expand...

Thanks Haakbus.

Anyway, I detect some might get confused between actual and linear draw force curves. From my discussion with Andreas Bichler, he said:

50% could be possible but only with a very heavy bolt and at the cost of speed. So a speed between 50 and 60m/s is the best choice between power and large range but the efficiency will be between 30 and 40%. My old crossbows wasn't exact close to originals so the 280kg bow had a to long powerstroke - a reason for a broken horn core.... A composite crossbow is able to store more cinetic energy like a steelbow - for example my 550kg composite bow is able to store aprproximately 590J. The 500kg steelbow from Ingo Lison (a very excelent german crossbow maker) stores only 390J and his 1000kg steelbow stores 599J. So you can see one of the great advanteges: A horn bow with a similar draw weight of a steel bow is more capable in storing energy and thus transferring more energy to the bolt, which results in greater shooting distances and more penetration power. For futher informations you can contact me per mail.

Unlike Bichler, my equations used the linear draw curve, which gives lower potential energy than that of the actual, and this also results in higher dynamic efficiency. The two differences would even each other out, so the resulting projectile energy would be more or less the same if I did it Bichler's way (in fact they have to even out because for most of them, because I calculated backwards).

Bichler used the actual draw curve, but most crossbows don't have this information so I resorted to the simpler equation above. He also confirmed what I said here:


If you don't mind me asking, do you know why these composite crossbows have such a low efficiency (~40-45%) compared to composite bows (~75%)? Right now my guess is prod mass. Whereas a bow only needs to achieve its full draw weight with the string pulled back ~23 inches, a crossbow must achieve its full draw weight when its string is pulled back to 6 inches (or in this case 15 inches). This requires a relatively stiffer prod.

Bichler's answer: You are absolutely right - the Austrian crossbow expert Egon Harmuth wrote in his book "Die Armbrust" that a composite crossbow has an efficiency of 60% . All my experiments showed an efficiency between 30 and 40%

Again, keep in mind he is speaking in terms of calculating using the actual potential energy, which includes the yellowed area in the graph above. If speaking in terms of calculating using the linear curve to estimate potential energy like what I did with my equations (and this is what most people do because few bother to measure the actual draw force curve), then dynamic efficiency would be roughly 20% higher, and this is evened out by lowering potential energy down by about 20% because we are excluding the yellowed area. Multiply by 1.2 and then divide by 1.2 means you end up having the same number.

Now as shown in the OP above, crossbows by the late Ming became much weaker as powerstroke shortened in favor of ergonomics. But the following passage from the Ming showed that they knew this to be the reason:

The powerstroke is an expression of anger. With the crossbow, the force applied can easily be multiplied several times (than that of a Bow). A crossbow used in a normal fashion with a poundage of approximately 150 to 160 catties (~200 lbs, each catty is about 1.32 lbs), it can shoot an arrow weighing not more than 2 maces (7.4 grams). Within 50 steps, (the arrows) can be fired accurately and powerfully. If shot from too far a distance, it is difficult to hit (the enemy). Moreover, (the arrow fired) will be weak and unsteady. It is being said historically: "A strong crossbow cannot pierce even a plain white silk at the end (of its effective shooting range".
Using a bow is exhausting. The archer has to use his strength to draw the bow and may end up exhausted. If the bow has a poundage of 40-catties, everyone can use (draw) it. And shoot arrows that are 5 maces (18.9 grams) in weight. Why is that?
Loaded on the bowstring, the distance from the undrawn bowstring to the bow-frame is 5 cun (6.5 inches). Deducting away that 5 cun (6.5 inches), there is a remainder of 1 chi 8 cun (23.4 inch powerstroke). Fully-pulled to the maximum power. Adding on to that, the archer's skillful release. Therefore, the arrow can kill the enemy even at a distance of 100-steps. When crossbow's bowstring is drawn, the powerstroke is only 5 cun (6.5 inches). The arrow is shot with only the power (powerstroke) of 5 cun. Arrows on the crossbow cannot be loaded as deeply as the bow (Meaning: Crossbows has shorter powerstroke). Furthermore, the user cannot put his own archery skills to use (as the Crossbow is rigidly fired as a gun).
The Crossbow may be powerful, but the arrows are light, and cannot be shot far. The Bow may have less power, but its arrows are heavy, and have an effective range of more than 100-steps. The power of the Crossbow's fury, cannot reach up to the Bow's fine skills. Although Archery practioners can be found everywhere in the world, in the midst of hundreds of thousands, there may not necessarily be a skillful one. Archery techniques are difficult.
Hence, Ruan-Zi says "Most are good with the Crossbow, but clumsy with the Bow."
The Bow itself is not accurate, and relies on the Archer's skills. The Crossbow itself is accurate, hence it's easier to shoot. Thus, based on this situation, the Foot-drawn crossbow is constructed. With moderate amount of strength, one is able to draw the crossbow. Average people can practice and use it too. As documented later, the loading methods and shooting methods can be learnt in the morning, and completed at sunset (Meaning: the training can be completed in a short amount of time.). Though it is smaller and inferior to the Bow, the Crossbow has better accuracy. No worries of moisture ruining it, the cost (of a Crossbow is economical). -Martial Arts Practiced After Farming by Master Cheng Zong You

The "foot crossbow" he mentions looks like this:



^The three crossbows above are adjusted to scale with each other.

Cheng Zong You later tried to replicate ancient designs and came up with a crossbow with a longer powerstroke and using an ancient trigger mechanism:

I (author Cheng Zong You) obtained an old copper mechanism and made a Waist-Drawn Crossbow. Drawing the bowstring to the mechanism, it has about 800 catties (1052 lbs) of force. It can only be drawn by someone highly capable. The Foot-Drawn Crossbow allows people to draw more quickly. However, to shoot arrows far and powerfully, one must use the Waist-Drawn Crossbow. As it has the ability to pierce rocks and destroy walls. Those who are weaker shall use the Foot-Drawn crossbow, while those who are stronger shall use the Waist-Drawn Crossbow. With my method of using the Waist-Drawn Crossbow, one can draw and load it alone. If more power is desired, then the Waist-Drawn Crossbow can only be draw with the assistance of other people. Compared to the Foot-Drawn Crossbow the difference is in its shooting range.
Naming the Waist Drawn Crossbow:
Arm's strength is insufficient, thus the waist shall contribute. Devastating and resolute, shooting far and swift, though it takes the strength of 2 or more men to draw, it may be used by only 1 man.



Notice that the cheek rest is gone, so that the draw length is lengthened to about 14.3 inches. Its ~12 inch powerstroke is still only ~2/3 that of the powerstroke of ancient Han design, because the stock length is still very short at 20 inches and the prod is not placed at the very front of the stock. It appears all Chen did was use the same stock length of the crossbows of his time, but merely replaced the cheek rest as the new trigger location. Nevertheless, the increased draw weight of 800 catties made up for it.

Note: The translation is by Jack Chen from chineselongsword.com, but I think he mixed draw length with powerstroke, so I corrected it (The author deducted a brace height from the draw, so the remaining distance should be the powerstroke). The passage clearly describes that the brace height for bows is 5 cun, and 2 cun for crossbows.
Note2: The late Ming passage is going to be confusing when read with the OP. With the introduction of the crossbow stirrup, the arm-drawn crossbow is called the foot-drawn crossbow, and what was previously called the foot-drawn crossbow, is now the waist drawn crossbow.

Late Ming author Cheng Zong You (the guy quoted above) also speaks of how crossbowmen were also armed with spears and giant two handed swords. When engaging the enemy, the swordsmen are in front, shooting first. These are followed by the spearmen, practicing rotating fire. When they are about to engage in melee, the spearmen engages first, while the swordsmen "cover the left and right sides of the spearmen". After the spears engage in close combat, swordsmen "roll out to cut and kill. The Long (Spear) and Short (Sword) shall mutually support each other, covering each other's weaknesses."

There is also a lot of emphasis on how to carry the crossbow, in order to conveniently grab melee weapons in quick order. This heavily implies one reason why Ming crossbows shortened the stock length (and in effect shortened the powerstroke). As gunpowder weapons became prevalent, crossbows stopped being primary weapons but became a sidearm, and sidearms needed to be small. This way soldiers won't be too slow to retrieve their spears/swords once melee engagement occurs. You can see how Chen viewed crossbows as a sidearm because even in his chapters concerning crossbows he still talked about what type of sword design is best. This is despite how he has his own chapter on swords too.

^Thanks!

More from late Ming author Cheng Zong You:

Ancient warriors went to war, armed with a Spear, a Crossbow, a Quiver, Poison Bottle, and Arrow Shaving Knife. These items are secured to a leather belt, or carried in a shoulder-bag. Hang the Crossbow and other items at the right-waist. Hold the Spear in formation. Use the Crossbow if the enemy is far. Use the Spear if the enemy is close This is the best way.
After consideration, when shooting with the Crossbow, my (author Cheng Zong You) opinion is that one should discard and place the Spear on the ground. When needed, one can pick up the spear and use the Spear again. If the enemy is close and it is crowded, there will be no impediment. Or, for Spears with a pointed rear-end, it can be thrust into the ground for it to stand straight up, while one is shooting the Crossbow. Then, there won't be any inconvenience of having to bend down and pick up the Spear.
However, we wouldn't know if Spears will always have a pointed butt-end and thus this method of erecting the Spear cannot always be used. Moreover, the Spear is long. If the enemies suddenly rush forward and crowd in one can only thrust where the Spearhead is pointed at. Both left and right sides will be difficult for the Spearmen to thrust.
However, when facing the enemy, there is nothing more advantageous than a long Spear. My opinion is that the Long-Saber will be able to tactically cover the left and right sides of a Spearman. So that both short and long weapons can work together and complement each other. This is the best way to deploy the Spear in battle.
The long Saber is 3 zhang 7 cun long, and it is sashed in the belt at the left side of the waist.
When engaging the enemy with the Long-Saber take one end of the crossbow's prod, and insert it diagonally into the belt at the back. Then draw out the long saber to face the enemy. One can turn and cut at all directions with maximum convenience.........

One can see from the above passage that late Ming crossbowmen were expected to fight in melee while still having the crossbow strapped onto his own person. This is made possible by the small size of the late Ming crossbow. Whereas, the Tang crossbowmen in the Tongdian were expected to engage the enemy in melee by dropping their crossbows onto the ground and picking up his polearms. So pre-Ming crossbows seem too big to both carry it on one's own person AND fight with a polearm, but this also meant the crossbow was much more powerful because the increased size allowed a longer powerstroke.

[FONT=&quot]A division consists of an army of 20,000 people. 14,000 of them are used for battle, making up 180 dui………The crossbowmen fire at the bandits when they are within 150 paces (225 meters), the bowmen fire at the bandits when they are within 60 paces (90 meters). If the bandits come within 20 paces (30 meters), the crossbowmen and bowmen drop their bows and crossbows, to be picked up by people from the back. These bowmen first grab the sword staffs and ferociously attacks with the Zhanfeng dui.[/FONT]-Tongdian


The Donghai Commandery military inventory slips also heavily implies that Han dynasty crossbowmen used a similar tactic, because its two most common weapons by far is the crossbow and the Pi. The Pi is just a spear, except the spearhead is incredibly, incredibly long (so basically a sword with its handle long enough to be a staff, which is more or less how ancient Chinese records describe the Pi). No other weapon quantity comes even close to the quantity listed for crossbows/Pi within the inventory.



So it seems that wheareas Han/Tang crossbowmen used a single melee weapon that is a blend between the spear and the sword, late Ming author Cheng Zong You advocated that crossbowmen use a mix of the spear and the sword.


Han DongHai inventory slip:

Bows&Crossbow:
--------Crossbow: 537,707 (imperial owned: 11,181)
--------Bows: 77,521
--------Subtotal: 615,228
Projectiles:
--------Crossbow bolts: 11,458,424 (imperial owned: 34,265)
--------Imperial owned arrows: 1,199,316 (imperial owned: 511)
--------Subtotal: 12,657,740
Armor:
--------Jia Armor: 142,701 (imperial owned: 34,265)
--------Iron thigh clothing: 255, 1 pair of unique ones
--------Kai armor: 63,324
--------Armored thigh clothing: …ten thousand 563
--------Iron lamellar armor: 587,299,
--------Leather armor is 14 jin [7.5 lbs]
Helmets:
--------Helmets: 98,226
--------Horse helmet: 5,330
Shields:
--------Shields: 102,551
Polearms:
--------Bronze Ge: 632 (imperial owned: 563)
--------Spear: 52,555 (imperial owned: 2377)
--------Imperial owned sheng: 943
--------Pi sword-staff: 451,222 (imperial owned: 1421)
--------Ji halberd: 6,634
--------YoFang: 78,393
--------Duan: 24,167
--------Subtotal: 614,546
Blades:
--------Sword: 99,905 (imperial owned: 4)
--------JingLu Dagger: 24,804
--------Saw…sabre: 30,098
--------Sabre: 156,135
--------Great Sabre: 127 (232)
--------Subtotal: 311,069
Axes:
--------Iron axe: 1132 (136)
Battle Carts:
--------ChengYuZheng chariots, drum chariots,
--------WuGang chariots:18
--------Soldier’s ChengYu chariots: 24
--------Interconnected Crossbow Carriage: 564
--------Charging chariot: 37
--------Drum Chariot: 4
--------Battle Chariot: 1
--------…chariot: 564
--------…chariot: 1
--------WuGang strong crossbow chariot: 10
--------ZuiBi chariot: 1
--------Battle chariot: 502
--------3 wheeled soldier’s chariot: 1 (168)
--------Tracking: 9
--------High…chariot: 11
--------….chariot: 7
--------….chariot…chariot: 2133
--------Su…heavy chariot: 1993
--------Soldier’s…chariot: 677
--------He chariot: 2
--------FeiLow temporary chariot: 2
--------Subtotal: 7174 (imperial owned 42 + 7132)


The metallic parts of Han dynasty Pi:

Ichon said:

On that inventory slip what is the point of repeating Imperial Owned, and if it wasn't Imperial Owned where did it belong?

Click to expand...

Heavenlykaghan thinks that imperial owned means the weapons were sent from the capital.

We talked about it here: http://historum.com/asian-history/45323-han-dynasty-donghai-military-inventory.html

Anyway, late Ming crossbows, due to their low powerstroke, seem to deal with armored opponents by the use of poison and aiming for the unarmored parts:

If one were to meet enemies who are wearing heavy body armour, then one must examine for unprotected gaps at the face, armpits or flank areas, and aim these spots to kill. -Chen Zong Yang

Earlier crossbows with longer powerstrokes seem to 'pure force' the problem by simply penetrating the armor.

《皇宋中兴两朝圣政》卷53:
步司诸军弓箭手，带甲六十步射，一石二斗力，箭十二，六箭中垛为本等。弩手，带甲百步射，四石 力，箭十二， 五箭中垛为本等

"For military archers, against those wearing armor shoot at 60 paces (90 meters), with draw strength of 1 shih 2 dou (71.04 kg), have 12 arrows with 6 being normal arrows. For crossbowmen, against those wearing armor shoot at 100 paces (150 meters), with draw strength of 4 shih (236.8 kg), have 12 arrows, 5 being normal arrows." -Edict of Song emperor's revival of Two dynasties, scroll 53

From the Han era comparison of Han and Xiongnu military advantages over each other, made by the official Chao Cuo:

Now both the country and the tactics of the Xiongnu are different from those of the Chinese. Their lands are nothing but mountain-slopes with ways going up and down and winding through gorges in and out; in such regions our Chinese horses cannot compete with theirs. Along the tracks at the edges of precipices still they ride and shoot; our Chinese horse archers can hardly do the like. Rain and storm, exhaustion and fatigue, hunger and thirst, nothing do they fear; our Chinese soldiers can in these things hardly compare with them. These are the merits of the Xiongnu.

On the other hand, on plains light chariots can be used and cavalry charges made; in such conditions the Xiongnu are readily thrown into confusion. The strong crossbow (劲&#24361 and the ballista shooting javelins have a long range; something which the bows of the Xiongnu can in no way equal. The use of sharp weapons with long and short handles by disciplined companies of armoured soldiers in various combinations, including the drill of crossbowmen alternatively advancing [to shoot] and retiring [to load]; this is something that even the Xiongnu cannot face. The troops with crossbows ride forward and shoot off all their bolts in one direction; this is something which the leather armour and wooden shields of the Xiongnu cannot resist. Then the [Chinese horse-archers] dismount and fight forward on foot with sword and halberd; this is something that the Xiongnu do not know how to do. Such are the merits of the Chinese. -Records of the Grand Historian, Simaqian

I forgot to mention quotes from the Revolving Shooting Machines. The earliest mention of these are in the Mozi, so here it is.

As for the power of these revolving shooting machines, none was passed down to modern day. We know that handheld crossbows could go up to 8 stone, or 516 lbs in draw weight. The lightest "Great Yellow Crossbow" would have draw weights of 10 stone, or 645 lbs. Assuming these are just big enough to necessitate a prop except when wielded by particularly strong men, revolving shooters (which certainly weren't handheld) should be somewhat stronger, at perhaps 12 stone, or 774 lbs. Of course, these are based off of assumptions. At the very least revolving shooters would have draw weights over 516 lbs, or else there would be no point in creating them as 516 lbs could be the draw weight of handheld crossbows.

Now there is no way for us to interpret the units of measurement used in the Mozi, but based on the information given by Mozi on door height, people height, etc.... I was able to make a rough guess and create this:



So these would be the rough dimensions of defensive trebuchets and revolving shooters during the time of the Warring States period.



^Ratchet system of the Warring States era. Needham thinks that it's for winched ballistas (such as revolving shooters) so that when you take you hand off the windlass, the string won't slip back to its original position. Personally this could also be used for other things, such as a windlass for taking buckets out of a well.

The efficiency of torsion weapon replicas seem to be pretty bad, at around roughly 25%, but these are using modern ropes instead of sinew. Authentic ones would probably be better. If the manuballista was drawn in any way like the gastraphetes (which is how most manuballista replicas are made), then its draw weight would be around 90 lbs. This is because its draw weight is limited by the body weight of the user (and not all of the body weight could be used to draw the string back). After a certain point it would be akin to trying to fly by grabbing ahold of only yourself and pulling upwards..



For efficiency, the only replica I know of that's not a random claim on the internet:

Two shots were made before the light faded. The stats on the first shot are: bolt weight 6991 grains, draw length 38″, draw weight 4500 lbs., velocity 333.1 fps, energy 1722 foot lbs. Specs on the second shot with the same bolt, are: draw length 40″, draw weight 4700 lbs., velocity 337.9 fps, energy 1772 foot lbs. -http://wattsunique.com/blog/1772-foot-lbs/

Note that the above is talking about a giant sized torsion field artillery, definitely too big to be handheld. Since it's an outswinger (unlike the manuballista), brace height is zero.

Potential energy: 4,500 lbs * 38 inches * 0.5/8.85 = 9,661 joules
Projectile energy = 453 grams * 103 m/s * 103 m/s * 0.5 = 2,402 joules
Efficiency = 2402 joules/9661 joules = 24.87%



Again, this weapon is more than big enough to be field artillery. If he made one suitable to be handheld, with the likewise toning down of draw weight and draw length, I wouldn't be surprised if efficiency would get better. Big versions suffers from a lot of friction and limb weight that the machine have to deal with. Of course, handheld versions would also be way less powerful by magnitudes upon magnitudes, despite the increase in efficiency.

In comparison, CCTV did make a giant sized multi-prod ballista too, but unfortunately the draw weight was made waaayyyy too low at a measly 390 lbs. This is the draw weight of the average Han handheld crossbow. More authentic draw weight should multiply that number by around 10, not to mention the prod would be composite which makes the energy transfer more efficient than that of the replica. The replica's powerstroke is at an impressive 61 inches though. The quarrel is big enough to be a long, thick spear. This means it's way too big for the draw weight. They didn't say how heavy it is, but it looks to be at least 2 kg in weight. The velocity is a measly 28 m/s but would be way higher if not for the draw weight.



Retrieving the projectile after it was shot into a cliffside.

Yes, I think your translation makes sense. I asked heavenlykaghan for his input.