Axes are one of the most definitive and recognised
weapons in the world, and a tool still vital in some industries. Recognised by all, these
blades have been developed by all
civilisations in one form or another, whether as weaponry or as
tools.
The chief ancestor of the
sword, the axe was developed in the stone-age; amongst the first weapons, it was indeed the first that required an edge rather than a point to inflict damage. Evolved from either or both
hammers and
daggers, the axe (and indeed its brother, the
pickaxe) still took one's
strength in addition to the weight of the
head to cause damage- making them more deadly than a
dagger- but due to the edge they beat hammers for effectivity.
Note also, in addition, it is a swung weapon: Like all swung weapons, it uses the length of the shaft as a force multiplier, in addition to that of the arm. This leverage allows an axe an even more fierce blow.
As a tool, they were indeed useful to early man- unlike a hammer, they could be used to kill animals, and unlike daggers, could be used to cut down trees. Its brother the pick-axe was also used in jobs the axe couldn't do as well (working at the earth), and in addition the pick is in fact a more deadly weapon.
Due to the cutting edge of the axe combined with its weight, a swung axe could sink deep into flesh and bone, and a well constructed axe coud easily sever a limb or break one's skull. A head-blow with an axe was normally fatal due to the shape of the head.
Whereas it eventually evolved to the superior sword, the axe was still used in warfare; it was easier to use than the sword (though barely) and much, much cheaper to make. Whereas the sword needed a long piece of metal for the blade, the axe needed only a small piece for its head, except for weapons like great-axes which needed about as much. Axes like those seen in fantasy with a blade either side of the shaft were rare, and though were a better weapon (due to the extra weight) one would be better adding another weapon to the back, such as a pick-axe.
Such combination axe-pick heads existed, using the axe-blade to cut and the pick to impale; in fact, this is where the first thoughts of a halberd probably came from. The trouble with double-headed axes is the weight would be stupid. This is a benefit for striking a target for damage, but not for actually hitting the target or indeed using the weapon quickly! Overweighting was rarely a problem with axes, as they had little chance of becoming stuck.
Used on battlefields by skirmishers, mainly, the axe was never a military masterpiece but a common weapon that only showed up in armies due to its simplicity, ease of use, and ease to find. Whereas the axe itself nor units that required them specifically inspired dread in enemy hearts, the axe still was a contender on the battlefield, the larger varieties being effective against many units; heavily-armoured targets were often as easy to fell as weak ones.
Axes themselves had a huge variety of shapes for their head, from the hatchet-like "broad-axe" (fig 1.) that looks something like a triangle of metal jammed into a bit of wood to a "hook-axe" (fig 2.) that seems like somebody just bent a sickle.
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Most axes- indeed, almost all developed- rely solely on their weight for the blow, and only require the strength to heft them in the first place. Normally fairly sharp, the edge of an axe was normally blunter than that of a sword, but an axe was often as deadly.