First thing to know about the Unterhau (blow from below with the head of your weapon) is: there is no Unterhau in the Poleaxe Plays of Hans Talhoffer – as you would do it in the Longsword Fighting with the right edge to cut your opponent.
There is a blow you do with the “false edge” of the weapon, the spike of the poleaxe like in Halfswording from the fourth stand / guard. But it is not recommended in the poleaxe part of the manuals.
There is an Unterhau from your right side which you do with the right edge with the axe or hammer. The aim of this Unterhau is the head and everything that is between this target and your starting point. But even this Unterhau is not really used in Talhoffers manuals with the poleaxe.
This is different from the works of Joachim Meyer. In Meyer’s treatise the right hand is mostly at the rear end the weapon and so he is able to do fancy things like the famous Kreuzhau.
Talhoffer uses the Unterhau from the left (which follows the crossing right Oberhau from your right side) only for bindings, or hooking, or the start of grappling. For this he changes the hands very often. If the right hand is leading, he prefers to raise the weapon in a thrust or a winding movement.
Talhoffer does not use the Unterhau from the right side in his manuals, if he is on the right side he always prefers the Oberhau (sometimes after displacing a blow), or starts thrusting or hooking or grappling.
Talhoffer changes the hands very often after the Oberhau from the right shoulder. Then he is starting something like an Unterhau, but not one that is harming directly the opponent, again it is thrusting, winding, hooking, or grappling that follows this kind of Unterhau.
The reason for this is not clear. It may have something to do with the fact, that even with the hook or spike you are not able to harm a opponent protected by a Gothic Armour by an Unterhau from the left. Every other blow is designed for building up enough impact to make the opponent stumble and reduces his capability to keep balance for at least a moment. A thrust or hook is more successful for this.
Another reason may be that if the head of the weapon is down, the rear end is up and this enables him to displace an Oberhau of his opponent and uses the impact of the recieved Oberhau to rotate to one of his own.
So if you exercise on Talhoffers Poleaxe play and do Oberhau crossing from your right shoulder down to your left side, do not raise the weapon in a blow, do never cross your arm in a way you would do it with the longsword, do thrusts to the knees, raise the weapon in a thrust, raise the weapon in winding, or let it rotate above your head. Or do a Change of Hands, which is covered in one of the next lessons.