Scourge of War Boards

Hancock The Superb wrote:

the angle added due to gravity (as the projectile takes an parabola instead of a line) is cancelled on both sides of the equation.

And therein lies your problem. There is nothing on the other side of the equation to cancel. The target is motionless, it is not growing into the ground while the bullet is in flight. From the perspective of the bullet, the target is actually accelerating upward. At 100 yd. if you aim between the target's knees and feet, you will miss.

Ah. But the angle at which you fire it does not matter in my study. The only thing that matters is the range of angles that will hit a target. The target could be below the ground, above the ground...it really doesn't matter. As far as my study is concerned, the Civil War could have taken place on the moon. The range of ANGLES = Upper angle - lower angle. I just removed the step of actually calculuting what that upper and lower angle are at specific distances.

Adding the lower angle to both sides gives you Lower angle + range of ANGLES = Upper angle...if we break the lower and upper angles into their velocity/acceleration components, you get 1/2at^2 on both sides, and since the t is roughly the same...they can be cancelled. This leaves me with the fantastically simple law of cosines that works for a target anywhere. The target just has to be 5'10" tall, but as far as the math is concerned, it may as well be sinking into the soil at 9.81m/s^2. To shift the angles up, I just add a factor to the top and bottom that accounts for gravity, but like I suggested earlier, there is no need when I only care about the difference between the two.

So realistic projectile motion, no. But I was never trying to accomplish that. It is safe to assume that the mean soldier will aim his weapon at the correct angle to hit the target, with his peers aiming in a normal fashion a little too high or a little too low. I am trying to find out how many of his peers will aim their rifles at about the correct angle based on 3 standard deviations (99% confidence interval).

If this does not successfully convince you that my fashion works, I guess I'll have to do the work with projectile motions and show that both ways produce the same result...a conclusion my math above indicates.

>the Civil War could have taken place on the moon.


I think there's another effect of gravity that you are not taking into account.
You've already discussed the case in which gravity is turned off. In that case
you should aim directly at the target. Now, turn gravity on and keep the target
at the same distance. In this case you need to fire your projectile at an angle
relative to the horizontal. Because of this, the projectile will approach the target
at the same angle you fired it, which makes the target (effectively) smaller
due to a sine-theta effect. If you double the strength of gravity and keep the
target at the same distance, the firing angle relative to the horizontal will increase, the
sine-theta will decrease, and the range of angles will decrease as well.
If you need to fire your projectile at a 45 degree angle, the range of
angles should be ~30% smaller (just a quick estimate) than your case in
which gravity is turned off.

So I don't think gravity drops out of your calculations, and I think you are
overestimating your angle ranges.

Does any of this help the South win at Gettysburg?

If these numbers are correct why were they always told to low? Doesn't the bullet fall enough already.

They were told to aim low because a standard .58 Calibre Minie Ball moves in an arc when fired. Modern weapons do the same thing. Thus they were told to aim low because at the short distances they were fighting from, the bullet would still be moving in an upward arc.

Hancock The Superb wrote:

Ah. But the angle at which you fire it does not matter in my study. The only thing that matters is the range of angles that will hit a target. The target could be below the ground, above the ground...it really doesn't matter. As far as my study is concerned, the Civil War could have taken place on the moon. The range of ANGLES = Upper angle - lower angle. I just removed the step of actually calculuting what that upper and lower angle are at specific distances.

Adding the lower angle to both sides gives you Lower angle + range of ANGLES = Upper angle...if we break the lower and upper angles into their velocity/acceleration components, you get 1/2at^2 on both sides, and since the t is roughly the same...they can be cancelled. This leaves me with the fantastically simple law of cosines that works for a target anywhere. The target just has to be 5'10" tall, but as far as the math is concerned, it may as well be sinking into the soil at 9.81m/s^2. To shift the angles up, I just add a factor to the top and bottom that accounts for gravity, but like I suggested earlier, there is no need when I only care about the difference between the two.

That makes absolutely no sense whatsoever. Since you are unwilling to do the calculation properly, I shall do it for you.

Without gravity:
d = Dist. to target: 100yd. (91.44M)
h = Height of target: 70.2in (1.78M)
angle = atan(h/d) = 1.12 degrees

With gravity:
speed of bullet: 950ft/sec (290M/S)
g = 9.8M/S**2
time of flight of bullet = t = 91.44/290 = 0.316 sec
drop of bullet during flight = hg = 1/2gt**2 = 0.49M
hr = real height of target = h - hg = 1.29M
angle = atan(hr/d) = 0.81 degrees

Gravity reduces the acceptance angle by 28% (good estimate Barrow)

If you have any desire to go into a field where quantitative measurements and calculations are required, I urge you, for your own sake, to listen to the criticism you receive and perform the measurement as they suggest. Only then can you determine its accuracy. No one gets particularly upset if you make a mistake in your assumptions or measurements. Science is a self correcting endeavor. However, people get very upset when you refuse to entertain the possibility of error.

I know nothing about physics but I do know there are two kinds: theoretical and experimental (hey, I watch PBS). So my question is: Isn't there some empirical evidence to back this stuff up somewhere?

Or better yet, maybe we have MTG and HTS stand 100 yards apart with muskets and see who hits whom based on their calculations.



B

George M wrote:

So my question is: Isn't there some empirical evidence to back this stuff up somewhere?

Yes, it is called adjustable sights. That's why rifles have them, to compensate for the gravitational drop of the bullet.

I know nothing about physics but I do know there are two kinds: theoretical and experimental (hey, I watch PBS). So my question is: Isn't there some empirical evidence to back this stuff up somewhere?

Or better yet, maybe we have MTG and HTS stand 100 yards apart with muskets and see who hits whom based on their calculations.



B

Hey, the 100 yard thing might be quite entertaining, but with two Yanks going at it, it might last all day.

That's funny!



B

Double canister at 100 yards ends all this discussion. :laugh: