More wavy sword blade, wing, and fin theory

  In order to get a feel for the sort of  air resistance generated by a wide blade which is stalled ( keeping in mind that tubercules reduce drag even when not stalled ) one can swing a lightweight wooden staff or batten with a similar width. A flat sided batten will work best.

In doing so it's immediately apparent that the maximum speed of the cut is determined by air resistance.

In support of this we can note that air resistance goes up with square as speed increases. Also  as discussed  the drag caused by the outer part of a completely stalled wide cutting blade   is definitely very significant in proportion to the muscular energy  available to power the sword.

Once a sword is in a continuous circular arc motion  ( excluding air resistance ) it takes a lot less energy to keep it in motion than it does to accelerate it in the first place. Thus continuous arcs are not necessarily very tiring, as long as the air resistance is low. 

Air resistance is the catch. Air resistance saps energy very quickly. I've found this also with shorter weapons. For example it is less tiring to do fast whirling staff escrima drills with thin  heavy sticks than it is with  thicker lighter sticks. When such drills are done slowly the lighter thicker sticks are much easier to use, but once going fast air resistance soon limits the top speed. . .  and that's when doing very tight small radius arcs spirals figure eights and so on, it's even more the case with longer weapons.  With simple strikes where the weapon travels through a shorter arc ( e.g 90 to 180 degrees ) this isn't as apparent, the lighter stick feels faster as the limiting factor then is inertia during acceleration.

With longer weapons the most energy efficient redirections are larger arcs which maintain the speed of the weapon rather than shorter stop/start turns with greater acceleration/deceleration and consequent energy sapping inertia issues .  During larger arc redirections and turns  air resistance needs to be addressed partly because the speed is higher and partly because the blade is experiencing relativley high angles of attack even in a large arc turn.

During WWII it was discovered that the spitfire could turn more quickly than the ME109 as even though it did larger arc turns it did so with greater airspeed due to more efficient lower drag elliptical wings. Turning tightly is not always the fastest way to turn, it uses more energy.  Of course if anything gets in the way of the fast  moving blade during a turn it is going to be damaged a lot more than by a slowly moving stalled blade attempting a tight turn, and that is no doubt  a bonus when 'hedge trimming' a wall of opponents

Stall reduction via a wider range of air flow angle of attack is also useful due to the fact that pre stall and stall situations create vorteces which tend to make the wing or blade oscillate uncontrollably. . . so it's good for control as well.

One way of avoiding air resistance and stalling problems is via a narrow thicker blade tip, however with these types cutting efficiency is lost, and the pointed tips create very significant tip drag vorteces which spatulate tips largely avoid. So all things considered, for the control of 360 degrees of territory I'd design  a long wide bladed cutting blade with leading edge undulations. . . . ..   and behold such types exist !

There is another reason why undulating blades experience less drag, to do with  air flow from the strong of the blade to the weak. During cuts ( particularly the long continuous arc type )  the majority of the time the blade is presented strong first, with the weak trailing behind. This creates air flow towards the tip which makes  a big increase in the drag inducing tip vortex as the air flows off the blade at the tip. Leading edge tubercules help to prevent this flow to the tip, and spatulate  blade tips deal with it better than pointed ones.