smooth bore muzzle loaders probably won't fire 200 yards. Hence why "rifles" in the civil war were the first to be used reliably outside 25 yards.
Not that I'm nitpicking. You probably do know more about the matter than I do, but I do know that 200 yards is a long distance (2 football fields) and to say the 50cal doesn't drop over distance -- IMO that just goes against gravity's laws.
I'll quote a humurous line from way back I've always liked:
"Gravity: It's not just a good idea, it's the law"
You're quote is pretty good... The rest we can work on...
Smooth bore muzzleloaders will fire (and are dangerous) much further than 200 yards. Their ineffectiveness was due to the lack of sights (most used a large bayonet lug instead of a front sight, and had no rear sight at all), and lack of stability imparted to the ball (due to the lack of rifling). Even without rifling, smooth bores with crude front and rear sights are easily capable of shooting 3 inch groups at 50 yards, and are dangerous well beyond that.
Rifles in the civil war were not the first to be used reliably beyond 25 yards. Not even close. Even those cruddy ol’ smooth bores were more effective than that. Even smooth bore pistols are that effective, if not a bit more. Rifled pistols are effective beyond 50 yards... Rifles from one hundred years
prior to the Civil War were capable out as far as 400 yards, and possibly as far as 700 yards, depending on the source of the information.
But we stray... I could go well beyond on this subject, but we can do that in another thread if you want.
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200 yards is
not a long distance when it comes to ballistics on the guns we're looking at. Heck, I use my .22-250 for shooting varmints out to 500yds.
The bullets from a .50 MG drop of course, but to nowhere near the extreme you seem to think. When it comes to the 50's I'm having trouble finding any bullet drop tables for the ranges we're discussing (they all seem to want to stretch things out to beyond 2000 yards). However, if we take a rifle I'm familiar with (which likely doesn't shoot quite as "flat" as a .50, the point still becomes clear.
Setting a convergence of 200 yards is effectively the equivalent of "sighting in" a rifle for that range. The first part of our problem is in visualizing the "correct" amount of arch in the bullets trajectory. With a .270Win, if I sight it in at 200yds (I generally sight it in a bit further, but 200 will work fine here) the bullet will start below my line of sight (which is a few
inches above the barrel; that becomes important later), crosses through my line of sight on an upward slant by about 25 yards, "climbs" to a maximum of about 1.5" above my line of sight at 100yds, and "drops" through the bulls-eye at 200yds. Carried further, the bullet will be about 6.75" low at 300yds, and 20" low at 400yds. In total, that's only about 21-22" of "drop" out to 400 yards. The .50 won't much more than that, if at all. I expect it actually flies "flatter" than that.
Here's the thing though, about how that applies to AH. Our eye doesn't sit a few inches above the barrel. It sits a few
feet above it. The line of sight in question in both cases stays the same though. It's a line from your eye, through the sight, and out to the target. In an airplane with wing mounted guns, the barrels are tilted upward much more than a hand-held (or nose mounted) barrel, in order to get the bullet to cross the line of sight at the sighted-in range. The trajectory of the round stays about the same (although, technically, it'll actually fly "flatter", further, than one fired "level", but with a more pronounced drop in the end; for example, a bullet fired straight up will have no arch at all, until it stops and reverses direction).
Look at these diagrams (sorry, I don't have zero pictures). In the side view you can see I added lines where the line of sight is in relation to the gun barrels.


An easy way to use these diagrams is to lay a ruler on it, and realize that in this case the propeller is 13'2". That will allow you to realize that the pilots line of sight is about
4.5 feet above the guns. Now, if the guns are sighted in "level" for 200 yards, the bullets will never cross the line of sight for the pilot, so will always appear to be "low". That's because from zero to 200 yards they only "climb" 1.5". In order to cross the line of sight though, they'd need to come up 4.5 feet (54 inches). That means the gun barrels need to be angled upward more...
Now, the trajectory doesn't "bend" more to allow for this. So where does that put the rounds at 400 yards? How about at 100 yards? If they shot like lasers, they'd be 2.25 feet
low at 100yds, and 4.5 feet
high at 400 yards (assuming a 200yd convergence). Taking real world trajectory into effect, they'd actually be a little less in both places (less low, followed by less high...).
This ignores that fact that the .50's probably shoot a bit "flatter" than my .270, and that the trajectory will initially "flatten" as the barrels are tipped more towards the vertical. Take this into account, and the diagram will prove my point even further...
Now, a trip to the TA with the .target will also show this to be true (I've played with it a lot...). These effects show... However, they seem to be more subtle than you'd expect, until you realize that the center or "10" ring on the .target is 20 feet across. That's one heck of a big bulls-eye, and the back of a plane can take up a deceptively small portion of it...
Keep in mind, this applies to wing mounted guns (like the A6M2's 20MM's). Nose mounted guns are a bit different (and a bit easier).