The curved blade was developed for the same reason as the scimitar and cavalry sabres -- it's easier to draw a curved blade than a straight one when in the saddle.
Browsing through the Nagoya Takashimaya Sanseido bookstore, I came across Samurai: 1550-1600, by one Anthony Bryant. Whoever this dude is, he had a crapload of impressive sounding credentials. If I were to meet this guy on the internet, I would be careful about debating him on the make and function of ancient Japanese weaponry.
There's a reason I hate to contradict Tony. But at the same time, contradicting Tony can lead to an interesting discussion if done correctly, so it can be worthwhile if one has a sufficiently thick skin.
If that was the argument used, and it might well have been, then it was a false argument. The main difference in ease between drawing a straight and a curved sword is a matter of how the scabbard is attached. If the scabbard pivots enough then there is little difference drawing one over the other until you get at the wielder's extreme reach. At that point the amount of curvature could make the difference, for example, between drawing a 43 inch curved sword vs a 40 inch straight sword, however, both swords will have the same reach, 40 inches, so the extra blade drawn is moot. The hard limit in reach, for drawing a sword, is defined by the maximum distance the user can draw his hand from the scabbard. Any increase in curvature to increase blade length drawn will not increase the sword's reach.
Weapons are all a cumulation of various factors, not any specific one. The main advantage of curved blades isn't in drawing them in a saddle, otherwise foot soldiers all over the world would not have benefited from curved blades.
The primary advantage of a curved blade hasn't changed and it's why most kitchen knives are curved today. Curved blades magnify the cutting force of a blow (pounds per square inch) based on its curvature at the point of contact, exactly the same way high-heels concentrate the weight of a woman at the point of contact between the ground and her heel so that her weight is more concentrated at the point of contact than an elephant's is over the same surface area. That is why a curved blade is a cutting
Curved swords are normally only sharpened on one side, however, early forms of the Japanese katana were sharpened on the backside for about 1/3 of it's length, presumably for the purpose of making the sword more effective for stabbing through armor and for cutting on the back swing. Since this sword type was discontinued, we can assume that, if not out of tradition, then theoretical advantages of the extra cutting surface introduced new unexpected disadvantages. Most probably because: a curved sword is more prone to breaking when making a stabbing motion as the force is concentrated on a specific point of the blade instead of distributed along it's length; double edged swords are well known for accidentally hurting the wielder or a nearby friendly; a sharp needle-like point is more prone to breakage, and subsequent, more frequent, sharpenings would create a progressively shorter sword; and because the pulling motion is naturally weaker than a pushing motion, especially one handed. That is why scythes are normally two handed weapons. Thus, the inner (scythe-like) edge of the early katana probably didn't deliver enough force to cut through armor routinely when used one handed on the back-swing. I haven't seen any records of the reason the sword was discontinued, it could be any one of these reasons, a combination of these reasons, or something else entirely.
There was actually a significant amount of disagreement as to whether American calvary should adopt a straight or a curved sabre. The main arguments used had nothing to do with drawing the sword, so far as I recall. It had more to do with reach and losing a sword because it caught in someone's body. The arguments in favor of a straight sword were greater reach for cutting kneeling infantry or stabbing prone soldiers. The greater reach argument was only valid when discussing straight and curved swords of the same length. Since, as argued above, a longer curved sword could be drawn it was a partially false argument, although the difference in material costs between different sword lengths would have been a valid argument. Swords would have been standard issue not tailor made.
Ultimately, a calvary sword had to be used primarily for cutting so a curved sword is the most natural sword to use. Stabbing and withdrawing a sword while on a moving horse is very difficult even if the user doesn't catch on a bone, and since many soldiers would try to stab more often with a straight sword than with a curved sword it is better to use a curved sword. The compromise in the American sabre is a very slight curvature.
If you want a "battle ready" katana, one that can be used in the dojo for cutting without breaking then there are many well made swords that can be had.
Here the problem is the definition of "battle ready" because that means different things for different swords, and as Mike said, you aren't going to be fighting any Battles with a sword in modern times. For example, American Calvary--when they used swords--could get by with cast swords because they were fighting unarmored people and because the swords would only be used for a relatively short period of the battle. Katana were used by Armored fighters, against armored fighters, for relatively long periods of time. The swords had to withstand a much higher amount of abuse, so a cast sword would break so often it would be unacceptable. Even properly forged swords--folded-- broke often enough because the abuse these swords underwent in battle was significant.
A Dojo practice sword is not a "battle ready" sword at all. If you're fighting a battle with a sword, plan at least 30 minutes of full contact death blow attempts. Something you shouldn't be doing with a metal sword of any kind even in armor for "practice."
Is it the use of the term "battle ready" or perhaps you really think that those who post here in a language forum give a rats ass about fighting tech or are looking here for tips on how to kill with a sword?
1, See above, 2. What do you think got many of us interested in Japan in the first place? 3. See 2.
I practice Yagyu Shinkage-ryu, another Sengoku period school. A primary teaching of that school is 助ｶ字勝ち juumonji-gachi. I let my opponent cut, and then I cut through his cut. Done right, the swords form a ? and I, cutting second, deflect the opponents sword and cut into him.
While all those techniques are good and great ways to fight under ideal conditions, say a duel. Real battles weren't that way. Real battles were fought be extremely weary soldiers, sometimes in driving rain with low visibility, and against multiple opponents with little room to maneuver. A soldier couldn't wait for the ideal moment to strike, there were too many other forces involved, the solder had make due with any opening and to create openings rather than wait for them, because the longer they wait, the more people they have to fight at the same time.
I would like to debate you that logic. let me get my research together. basic logic also tells you that a curved blade and the structure of said curved blade was to deflect/redirect energy rather than to stop it full stop. again, let me find my stuff and I will gladly frolic in the lands of sword play debate.