I've been researching historical weaponry, and I found that depending on the type of axe or pollaxe, the ends of the axe head are curved inward, outward, or are flat. For example:
Concave: [Halberds (only some)] (http://en.wikipedia.org/wiki/Halberd) Flat: [Voulges] (http://en.wikipedia.org/wiki/Voulge) (at least when compared to [Bardiches] (http://en.wikipedia.org/wiki/Bardiche)) Convex: [Danish Axe] (http://en.wikipedia.org/wiki/Dane_Axe)
A vast majority of axes and pollaxes seem to have outwardly curving blades. Does this design provide a military advantage, or could the different shapes result from different forging capabilities (since some of these weapons are much older than others).
Outwardly curved blades provide a much smaller surface area during a cut, transferring the force onto a smaller area, and increase the impact of a blow. This is true along the entire surface of the blade. I'm going to draw a crude picture to illustrate.
D[]
In this picture the "D" is the curved axe head hitting a target, notice how only a small portion of the head will actually make contact. If the blade was flat, it would look like this:
] [] The damage is spread over a much wider area.
It's actually a good method to tell a military axe from a lumber axe. For chopping wood, you want clean, straight, even cuts at an equal depth that will wear at the same rate. For the military polearm you need penetrating power above all else.