Analysis of Variance of Firing Angles and Hit Percentages on the Battlefield

Marching wrote:

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?

NY wrote:

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.

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.

Double canister at 100 yards ends all this discussion.

Or,

2 snipers from 400 yards, each one locked on a target !!



Chamberlain

True B,

Then maybe we need 4 snipers, 2 for each one...1 to aim high, and 1 to aim low !



Chamberlain

Marching wrote:

Hancock The Superb wrote:

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.

If I am upsetting people, I must apologize. I am just trying to point out that my way works.

In addition, if I may be so bold to say, you and Barrow may have committed an error in assuming that the time of the bullet in flight is 0.316 seconds, or 91.4m divided by the muzzel velocity of 290m/s. In the physics I have learned, the muzzel velocity at an angle does not translate into horizontal velocity. According to my calculations below, it should actually be the 290m/s * cos(THETA).

As you can see, the messy vertical displacement equation has a plethora of THETAs (due to the coorelation between the vertical initial velocity and the horizontal initial velocity to determine the time and speed), so I plugged it into my TI-84+ SE calculator and determined the THETA values of the intersection between the curve and the 0 meter vertical displacement line as well as the 1.78m vertical displacement line.

As you can see from the table on the right, the difference between the angles exactly follows my prediction of earlier (as seen by the chart on the first page): off only by the third significant figure on a couple of them.

Hopefully this moves us further towards the goal of coming up with an excellent equation simulating the ability of Civil War soldiers to hit a target.

I do appreciate all the constructive criticism I have recieved, it has definitely caused me to focus all aspects of physics involved as well as hopefully improving my communication skills.

As a side note, I find the calculated top angle for 50, 100, and 160 yards rather odd. However, I triple checked my work and my calculator inputs, and have decided that somewhere between 100 and 160 yards gravity plays a role such that the angle must increase in compensation to hit the top of the target.

>As you can see from the table on the right, the difference between the angles
>exactly follows my prediction of earlier (as seen by the chart on the first
>page): off only by the third significant figure on a couple of them.

If I'm reading your table correctly, in all these calculations your target is
at a different elevation from your shooter, and your "distance" is the hypotenuse.
In your original post it seemed like your distance was the horizontal separation
between shooter and target, and they were both at the same elevation.

Barrow wrote:

>As you can see from the table on the right, the difference between the angles
>exactly follows my prediction of earlier (as seen by the chart on the first
>page): off only by the third significant figure on a couple of them.

If I'm reading your table correctly, in all these calculations your target is
at a different elevation from your shooter, and your "distance" is the hypotenuse.
In your original post it seemed like your distance was the horizontal separation
between shooter and target, and they were both at the same elevation.

I guess I don't quite understand what you mean. In all of my work, I have been firing at two points, the top of a person and the bottom, which are 1.78m apart vertically. You may have missed that in the flurry of posts.

The gun is being shot from an elevation on 1.78M not 0 as you have drawn in your last post. There is no vertical component to the muzzle velocity. As I said before you are needless complicating the issue by trying to solve for 2 triangles. One is sufficient. Repeat your calculations using the method that I showed you. It is the correct way to solve the problem.

I know nothing about physics that I didn't learn in highschool, but it seems to me you are solving two different problems, which is why you can't agree.

One is trying to determine that whatever angle hits the target, be it 30 degrees or 300, what range of angles up or down from that would hit the target of X height and Y range.

The other is trying to determine what angle would actually hit, which is why you keep talking about hitting the ground and other irrelevant facts.

Regardless, "march through georgia", even if you are correct you come across as arrogant and preachy. Go back and read how many times you condescendingly wrote "I am right you are wrong". That's the real lesson to learn in this thread.

And you, Mayonaise, come across as misspelled, white and fluffy, and quite tasty on a turkey and cheese sandwich.

Honestly, to someone who has lead troops for many years this whole discussion is a kinda silly. Humans are not mathematical solutions and attempting to apply a detailed mathematical standard to their behavior in the most varied conditions ever faced is sheer folly.
Try this, take 1000 men, run them through two or three years of fighting and I can assure you that the surviving men will hit and kill someone at well beyond what you think they can, more often, and they will do it very methodically, coldy, efficiently, and blow your calculations away. Marching Through Georgia mentioned how people flinch and pull up and do all sorts of things when firing. Yep, very true for beginners. Not so for that steely killer who has done it a thousand times.
BTW, calculate that the target and firer are constantly changing lateral position. Additionally, the target is likely changing height constantly or is your world flat and people slide along or just stand still? Add on top of that in high humidity and still air visibility goes to ZERO immediately after firing and stays that way. Might skew some numbers.
If you want a ballistically correct game, great, not sure what that brings, but okay, go for it. I'd rather time be spent on ensuring the battlefield framework, comprehensive scenario editor, battlescript for co-op games, better orders, placeable breastworks, and such be worked on.
The funny part is Hancock, you were the guy that told me that detailed studies were not necessary and got all over me for asking questions.

@Olszowy - Well now, where have you been hiding, it's good to see you back in-action!

davinci

30th wrote:

NY wrote:

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.

They were actually told to aim low because many men unused to handling firearms had an over-exaggerated concept of bullet drop and thus aimed far too high. "Aim low" meant "Aim lower than you think you need to" and not "Aim at their knees".

Check out some civil war photos taken of battlefields soon after the combat was over and notice how many trees are stripped of their leaves.

Perhaps I missed the post, and I concede to not possessing a background in mathematics, BUT. Has anyone considered that the ability of an individual to hit a specific target at range may be of lesser importance than the ability to simply put a round downrange in the vicinity of the enemy unit? An infantry unit with ~100 men is likely engaging a unit of similar size. Missing one individual (target) doesn't exclude the possibility or likelihood of hitting someone nearby. Given that, is it reasonable to treat the entire unit as an homogenous whole for the sake of approximating accuracy and casualties? I noticed on Wikipedia that some of the rifles of the day were capable of throwing out rounds to nearly 1500' with no degree of accuracy of course. Today we train to hit targets at that range, and can do so quite reliably with only iron sights. (A man sized target appears to be about the size of a pencil lead at that range.) Does the engine actually track the trajectory of EVERY projectile in the game? Just a thought.

Does the engine actually track the trajectory of EVERY projectile in the game? Just a thought.

No.

Nor does the game try to calculate accuracy as if a soldier is shooting at a single target.

But nor does the game make you more likely to hit when you shoot at targets with more men in the same area (as far as we know).

(This thread isn't really relevant to the game -- it was just a discussion.)