Haven't read all the replies cause I'm about to go to sleep (or try), and it's been a while since I've answered this question. First, a curved blade cuts better, because it starts the cut at a single point, and also because if backleaning (true or Tartaric sabre if you will) it draws itself through the cut as a natural effect of its shape moving thru flesh; sorry, my linguistic ability is down at the moment. This automatically gives you the increased cutting power and greater ease in withdrawal of a sliding cut; this especially helps you keep holding the sword when you cut someone your horse is running past. Also, when backleaning, it has the strength of the edge bevel angle it has, but the cutting power of a finer angle (Burton explains this well). Try to flex a highly curved blade over your knee (one sharp on the convex edge, if at all; don't cut your knee or hands!
); what happens? It tries to turn to make the force distribute across the width, rather than the thickness; this makes it stronger against this kind of force, encountered primarily in parrying and in withdrawing the blade from wounds, and also tends to help turn its spine into a parry; a usually favoured method popularly known from Japan, but actually seen in Europe, PI, N Africa, etc. Also, when backleaning, the around the shield backhand thrust; this is often a neglected point; the "West" seems to have come to think of the shield as a fashion accessory or something. Give me a sheild and a machete and a smallsword is a joke. BTW, those straight things are not sabres. I know they called them that; that's military/beaurocratic organization for ya; put it in a category we already have
they're really more a type of smallsword, or to put it differently, a spear built like a sword. A real sabre is for cutting. Top of the head for youse, anyway; maybe more later when I come back and read yours. One other thing no-one's brought up now, but contradicts a popular misconception that we've discussed before, and that seems somewhat related; serated swords do cut better, and have at least one other advantage, as well. yes, I can tell you why, but I'm tired right now; search the old forum; I've explained it there. As for straight double-edged sword? It is Jack of all trades, master of none. A compromise weapon; a backcurved sword slashes and back-hand-thrusts better, a forward curved sword chops and for-hand-hrusts better, but the straight double-edger can do it all to some degree, and though it's certainly not much at the backhand thrust, it does pack a nasty backhand cut that can be used around behind the opponant's shield. Also, you get a spare sharp edge you can flip the sword to (if it hasn't a knucklebow) for those long battles where it gets dull; seriously, one reads this in old European accounts, and it makes good sense.