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Incorrect. The bullet begins to move in and arc as viewed by anyone attached to the accelerating reference frame since the bullet becomes unattached as soon as it leaves the gun. The bullet's arc is the primary reason that engagement ranges were ~110 yards.The earth is an accelerating reference frame (according to Einstein’s Theory of General Relativity), thus the projectile can be assumed to travel in a straight line instead of an arc influenced by gravity.
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Marching Thru Georgia wrote: Hancock The Superb wrote:
Incorrect. The bullet begins to move in and arc as viewed by anyone attached to the accelerating reference frame since the bullet becomes unattached as soon as it leaves the gun. The bullet's arc is the primary reason that engagement ranges were ~110 yards.The earth is an accelerating reference frame (according to Einstein’s Theory of General Relativity), thus the projectile can be assumed to travel in a straight line instead of an arc influenced by gravity.
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Incorrect again. Your homework for today is to calculate the drop of a bullet traveling 950 ft/sec over the distances of 50, 100 and 150 yd neglecting air friction. Then calculate dTheta from this result. Tomorrow we will add air friction back in. Note, you can save yourself some work by reorienting your frame of reference so you only have to solve for one triangle.The idea is that I do not need to account for the fall of the bullet aimed at the top of the head or the bottom of the feet because the bullet will fall the same distance over a specific time regardless, which does not change the angle of error. Of course, at longer ranges the bullet will need to travel slightly farther, but those distances would need to be significant in relation to the earth, not being merely several hundred yards.
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Now I need Hancock to show his work so I can see he did not copy off your paper.If the rifle is held at the horizontal the bullets will fall 4.79 in. in 50 yards, 19.17 in. in 100 yards, and 43.13 in. in 150 yards.
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NY Cavalry wrote: Again, with the rifle at the horizontal, [...] If these numbers are correct why were they always told to [aim] low? Doesn't the bullet fall enough already.
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It was due to a person jerking the gun back and up just before firing. It's a very common reaction to the anticipated recoil of the gun. I use to shoot blackpowder competitively and also teach it to interested people. I would usually allow the newbie to fire a couple of rounds and then substitute a cap that I had removed the fulminate from. You could watch what happened to the end of the gun when the trigger was pulled. If they were new to shooting, the barrel inevitably came up. It was a good teaching device.If these numbers are correct why were they always told to low? Doesn't the bullet fall enough already.
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NY Cavalry wrote: If these numbers are correct why were they always told to low? Doesn't the bullet fall enough already.
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born2see wrote: This is the equation that Norb uses:
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Marching Thru Georgia wrote: Incorrect again. Your homework for today is to calculate the drop of a bullet traveling 950 ft/sec over the distances of 50, 100 and 150 yd neglecting air friction. Then calculate dTheta from this result. Tomorrow we will add air friction back in. Note, you can save yourself some work by reorienting your frame of reference so you only have to solve for one triangle.
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Garnier wrote:
born2see wrote: This is the equation that Norb uses:
Obviously the game doesn't calculate ballistics, because if it did, shots would be able to fly past the target and hit someone 500 meters away.
Better to keep it simple and just have a factor for different ranges. But we would love to know what that factor is, since it seems to have an extremely small effect. Troops firing at 200 yards kill almost as many as at 20 yards.
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As an actual physicist, I can tell you that what you have been writing is shear nonsense. Gravity does not act linearly as you are trying to assume, but as the square of the time the projectile has been in flight. It cannot be omitted. Until you grasp this fact, you are simply digging the hole you are in deeper. I must say that trying to invoke general relativity, incorrectly, was original but nonetheless wrong.First off, I would appreciate it if you would kindly refrain yourself from belittling my credibility; I understand that you may have significant experience in the area of projectile motion, but that does not give you permission to "teach".
Second, I checked my work with one of my physics professors, and as I expected, my physics were sound; it is perfectly reasonable to omit gravity as long as we assume that each bullet will fall approximately the same distance (which I will proceed to show why this works). Remember, I am trying to estimate the angle of error needed to just hit the target, not find any exact angle. The statistical analysis can be compared to that of an Analysis of Variance Test (ANOVA).
Since each of the three hypothetical bullets will travel roughly the same distance; at 10 yards the distances are different by 4 orders of magnitude, which will not influence my work with 3 significant figures. Thus, since the distances, velocities and times can be considered the same, gravity will affect each bullet the same (in terms of vertical displacement). Taking advantage of the accelerating reference frame of the bullet, each bullet can be assumed to travel in a straight line. Remember, I am not trying to find specific angles. The amount I add due to gravity to the lowest angle, I would have to add to the upper angle. So when I "subtract" the two angles (I actually bypassed the step using triangles and the law of cosines), the angle difference due to gravity is cancelled out, further indicating that using the accelerating reference frame of the bullet is a reasonable approach, considering I am merely exact to 3 significant figures.
Hopefully this will sway readers as to why my approach can be considered accurate.
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Marching Thru Georgia wrote: As an actual physicist, I can tell you that what you have been writing is shear nonsense. Gravity does not act linearly as you are trying to assume, but as the square of the time the projectile has been in flight. It cannot be omitted. Until you grasp this fact, you are simply digging the hole you are in deeper. I must say that trying to invoke general relativity, incorrectly, was original but nonetheless wrong.
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Since when HAVE you EVER communicated in a coherent fashion?!Hancock the Superb wrote: I am probably not communicating ..... in a coherent fashion.
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So in that case the best option is to aim directly at the target
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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.the angle added due to gravity (as the projectile takes an parabola instead of a line) is cancelled on both sides of the equation.
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Garnier wrote:
So in that case the best option is to aim directly at the target
Only if your gun is level with the tree limb relative to the earth's surface.
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