|From the ARMA website.|
First off, two quick things about axe combat that are pretty self-explanatory but I want to put down here anyways.
1 - your hands do not remain static on the haft but slide closer together or farther apart as needed. When performing a queue parry you can slide your low hand back up the haft to give yourself more room. Likewise with performing a blow with the head, sliding your hand down the haft gives more oomph to the blow.
2 - the length of haft will determine how the axe is used. A longer axe (x>5 feet) is used as a spear with benefits, as seen in Le Jeu de la Hache and the Anonimo Bolognese. A shorter axe (x<5 feet) is used as a longsword with benefits, as seen (IMO) in Armizare. Some techniques work better with a long axe (like stabbing them in the foot) and some work better with a short axe (using the haft to do a ligadura mezzana).
So keeping those two things in mind - my theory is that by gripping the axe just underneath the head you give yourself just as much queue space as on a longer axe, thus allowing you to still play like in Le Jeu or the Anonimo. To figure out if this was true I had my wife mark the outside edge of my bottom (left) hand as I gripped each of my three axes, doing my best to keep the space between my hands the same. Below are the results.
Total length: 70.5" (About my height)
Queue length: 23"
Total length: 65.75" (Tip comes up to the point of my nose)
Queue length: 22"
Total length: 39.25" (Tip comes even with my shoulder)
Queue length: 22.25"
What my massively scientific (HA!) study proved is that it is possible to get the same amount of haft below your hands, for parrying and striking, with a short axe as it is with a long axe. I will be continuing to play with my shorter hafted axes (although I will most likely be buying some of the new heads from PHA to try out), specifically playing with them against longer axes.
Now, as to why that picture sparked me on this mission, well the answer is simple - in matters of pollaxe haft length, my preference is towards shorter. That's really all. But, other than what appear to be shorter axes in the Getty MS, the above illustration is the only place I've seen that short of axes used.
P.S. I am also going to try and make (or purchase) a Polish nadziak, or war hammer, that was used by the Hussars from the 16th to 18th centuries alongside their sabres. They look very similar to Western European hammers except that they average about 33" in total length. They were used not only as weapons of war but as walking sticks for gentlemen. The nadziak was so nasty that it was outlawed in Poland. New toy!