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The Physics of Medieval Archery

A sample:

The Speed of the Arrow

The simplest assumption we can make is that all of the potential energy eFx/2 is converted to kinetic energy of the arrow. Writing m for the mass of the arrow and v for its initial speed, we would then have

½mv2 = ½ eFx
or
v = (eFx/m)-2

In fact, this is always an overestimate of the initial speed of the arrow. The main reason for this is that, at the instant when the arrow leaves the bowstring, parts of the bow itself are moving. These parts will thus have some kinetic energy which, like the kinetic energy of the arrow, has been supplied by the potential energy stored in the bow. Exact calculations of this effect are extremely difficult, and can only really be done by computer modelling. However, we can get a rough idea when we realise that the speed of a particular part of the bow must be proportional to the speed of the arrow. We can thus write the kinetic energy of the bow as:

k ½ Mv2

where M is the mass of the bow, and k is a factor which represents the sum of the kinetic energies of all the parts of the bow. Experiments and computer models show that, for a medieval longbow, k is typically between 0.03 and 0.07, depending on the precise design of the bow. Thus, we should really write

½ mv2 + k ½ Mv2 = ½ eFx
which we can rearrange to give a formula for v:

v = ( eFx / (m + kM))-2

Clickie the link if you want to get the mathematical parameters of energy storage in the bow, range and effectiveness of the arrow and the like, as well as a discussion of the ideal materials for manufacturing both bow and arrow. Put it all together and what was the practical outcome at Agincourt?

Henry had approximately 5,000 archers at Agincourt, and a stock of about 400,000 arrows. Each archer could shoot about ten arrows a minute, so the army only had enough ammunition for about eight minutes of shooting at maximum fire power. However, this fire power would have been devastating. Fifty thousand arrows a minute - over 800 a second - would have hissed down on the French cavalry, killing hundreds of men a minute and wounding many more. The function of a company of medieval archers seems to have been equivalent to that of a machine-gunner, so in modern terms we can imagine Agincourt as a battle between old-fashioned cavalry, supported by a few snipers (crossbow-men) on the French side, against a much smaller army equipped with machine guns. Perhaps from this point of view the most remarkable fact about the battle is that the French ignored the very great military advantages of the longbow.

Actually, not so remarkable. Military history is replete with examples of armies either failing to comprehend or else ignoring (for a variety of reasons) what I suppose the war college crowd would call weapons asymmetries.

Yips! to Gail at Scribal Terror.