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Swords, Cutting and Military History

The Asian war bow: the physics of Asian archery

The Asian war bow: the physics of  Asian archery

photo by Mai

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Serving as an introduction to the physics of historic military technology, we’ll look at a paper by Timo A. Nieminen which examines the design and physics of two of the most famous classes of bows found in Asia;  the Manchu bow (sometimes known as the Mongol bow), and the Japanese yumi — both hankyu (short bow) and daikyu (long bow) — and looks at how these various designs worked to impart maximum velocity to the arrows they launched.

This paper was originally presented, oddly enough, at a physics conference.  Why would a physicist look at bow design?  He sums this up nicely:

The development of the bow from its early beginnings into the various finely engineered forms of medieval and later times demonstrates a deep understanding—even if unarticulated—of the physics governing the bow.

The limitations imposed by real-world materials and economics necessitated compromises in the designs of bows; the requirements of the uses for which they were intended led to further design choices. Investigation of the physics of archery—the behaviour of the complex system composed of the bow, the arrow, the archer, and the target, illuminates these compromises and design choices, and can further our understanding of the role of archery in history

Mr. Nieminen starts by describing the base design of all bows:

Illustration of reflex and deflex bow curvesBows can be broadly classified by the shape of the limbs. A bow in which the tips of the limbs curve away from the archer (towards the back of the bow) is a recurve bow; if the curve is towards the belly, it is a decurve bow (a feature of some traditional bows allowing them to remain strung in an unstressed state). If the limb, as a whole, curves towards the back when unstrung, the bow is a reflex bow, and if curved towards the belly, deflex . In the absence of these types of curvature, the bow is straight.

We begin with a look at the Central Asian (Manchu / Mongol) bow — used from China to Turkey —  which is both recurve and reflex, often very much so.  Such a design allows very high draw lengths and draw weights in relatively short bows;  draw weight is often described as the maximum force in pounds/kilograms needed at the bow’s maximum draw length.

The unfortunate side effect of this is that the “belly” (center-point) of the bow is placed under huge stress as the arms of the bow are pulled back, and can result in the bow snapping.


Historic manchu archer


In order to get around the issue of weakness inherit in a single material, bowyers created composite (sometimes known as laminate) bows;  bows made up of layers of various materials which would allow the high draw weights while being flexible enough not to snap.  A common Central Asian construction would be “…a belly of horn (e.g., ox horn, buffalo horn,or antelope horn) and a back of a glue-and-sinew composite joined to a central portion of wood. Traditional adhesives that were used included hide glue and fish bladder glue.”  The final bow would have protective leather covering the composite layers

One of the problems in constructing such bows over single material designs is the technological difficulty and length of time required to build an effective bow.  The use of native adhesives meant multiple layers had to be built up, with each layer having an extended drying time.  Historical references show Turkish bowyers taking a long as a year to create a single seasoned composite bow.  An interesting

An extremely effective design, one has to wonder why its use didn’t spread across the Medieval world.  One reason suggested in this paper is simply that the organic glues used in construction of these bows were vulnerable to humidity;  a perfect design for the relatively dry Asian mainland, it may be that such bows lost power or broke under use when brought into damper or more humid environments.

The paper notes that the Japanese yumi, a composite design made of laminated bamboo, was well known for being vulnerable to humidity.  You can see the basic construction of a traditional daikyu in the video below:



The single material bow, or “self bow”, is mentioned briefly;  such bows are made from a single piece of wood, are straight when unstrung, and are uniformly long.  The length is required for a self bow to have an effective draw weight.  Examples would include the English longbow.


The physics of archery

We then move on to the actual physics of archery:

As a device for storing elastic energy, and imparting this energy to an arrow, the performance of a bow depends largely on the stored energy, and the fraction of this energy that can be transferred to the arrow. A further important element of the performance is the velocity of the arrow, which affects the range, the flatness of the trajectory, and the accuracy

Thus, drawing the bow stores energy;  releasing an arrow passes some of this energy in kinetic form to the arrow, with the majority of the rest being spent in mechanical force transferred to hand and arm of the archer (the springing and jerking of the bow in the archer’s hand).

Mr. Nieminen then expresses this in a formula, which shows that the energy available to transfer to an arrow is determined by a combination of draw weight and length;  the two are intertwined.  Normally, the maximum draw length of a bow is limited by the length of the archer’s arms;  draw weight is influenced by the archer’s technique and training.  Thus, he shows that training is a significant consideration when determining the effectiveness of archery.

He then moves on to examine how much energy can be transferred to the arrow.  He finds this highly dependent on the mass of the bow’s arms, and the mass (and therefore weight) of the arrow.  As the archer releases the arrow, the arms of the bow move forward, carrying energy;  the more the mass of the arms, the more energy.  A small fraction of this energy is transferred to the arrow.  The more the mass of the arrow, the more energy it is able to absorb.

Thus, heavier arrows carry more energy;  however, because this energy has to overcome actual inertia, the heavier arrow leaves the bow slower than a light arrow would.  Thus heavier arrows carry more energy but tend to have limited range;  this dichotomy is shown in the chart below, where mass (and therefore energy carrying efficiency) is compared to the percentage of a stated projectile’s maximum velocity.  The larger the mass, the slow it goes, and therefore has lesser effective range potential:

Mass vs Velocity

As a historic note, the paper goes on to describe how Turkish composite war bows fired arrows of between 20 to 40 grams, while the English longbow used 70 to 90 gram arrows.  He conjectures the range of arrow weights may have had less to do with individual manufacture, and more to do with selecting an arrow depending on its intended use:  heavier arrows would have been selected for closer-range armour piercing, while lighter “flight arrows” would have been used for longer-range or higher elevation targets.

It’s also noted that it was common, world-wide, for heavier arrows to be used in defensive siege warfare.  Fired from above, heavy arrows did not have to fight gravity, and indeed would not lose energy in their downward flight.  Heavier arrows had an additional advantage, in that attackers could not easily collect and use them against the defenders, as the arrows would lose energy and would not be effective when fired upwards.

In two final sections, the paper discusses firearms and archery (which we will move over)  and armour and the archer’s ability to pierce it.  In general, drawing from experiments made by other researchers, Mr. Nieminen suggests that — unless hitting the surface at a very sharp angle — most Asian war bows were able to penetrate 1mm of steel armour at close range, most of the time.  As armour on the battlefield became more common, archers had to adapt by using longer, heavier bows (thus storing more energy) and firing heavier arrows at closer range.  He notes that the designs both the Manchu bow and the yumi accomplish precisely that, and also that:

…a large bow is also a heavy-limbed bow, which limits the speed of the arrow. Consequently, little speed is lost by using very heavy arrows (this results in low-speed arrows, but the maximum possible speed is low, even for very light arrows). Manchu war arrows appear to been approximately 100g on average, and Japanese arrows often exceeded this.


Kyudo 1860sTo prove this concept e then quotes from “Armed Martial Arts of Japan: Swordsmanship and Archery”  by G Hurst I, Hurst, in which a Japanese period commentator says ““For shooting an enemy on the battlefield, one needs, moreover, to practice shooting at a distance of seven or eight ken to be able to penetrate his armor. But in toyshiya [a form of sport archery], by sending an arrow light as a hemp stalk a distance of sixty-six ken, how can one hope to pierce armor?”

The paper also notes that Miyamoto Musashi, in his Book of Five Rings, in the section: The Benefit of Weapons in Strategy , also notes that bows are useful only at close range, as per Musashi’s quote below:

“The bow is tactically strong at the commencement of battle, especially battles on a moor, as it is possible to shoot quickly from among the spearmen. However, it is unsatisfactory in sieges, or when the enemy is more than forty yards away. For this reason there are nowadays few traditional schools of archery. There is little use nowadays for this kind of skill”

As a high level of training and technique are required to make an effective bowman, the paper’s author goes on to show how primitive firearms, with their relatively low requirement for training, and high energy imparted to the projectile, made the use of bows obsolete.  He notes that, if a sufficient number of well-trained bowmen were available, there were significant advantages to the use of bowmen over firearms, and that indeed archers were used alongside of firearms in China until a very late date.

Those interested in Manchu archery may appreciate the following short video, showing the bow and implements, in which the dramatic bend of a recurve, reflex bow can be seen.





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