6MMsteve
Gold $$ Contributor
only if you eat chicken in Tuesday's
How to explain bullet arc............ at the bar.
- Thread starter Mozella
- Start date
Hmmm.....I'm gonna go down about three fifths of scotch and I'll then come back and get you to explain this again! Maybe my head will be twisted enuff so I can follow!!
As long as we have gravity After it leaves the barrel it is only going to fall . Larry
Highpower-FClass
Gold $$ Contributor
As with many things, the frame of reference makes a difference. Both of these statements are true when firing a projectile where the barrel is angled upwards (ignoring the special case of 90 degrees for the second statement):
- In reference to the surface of the earth, the projectile will travel away from the surface (rise) until it reaches the trajectory apex after which it will travel towards the surface of the earth (fall)
- In reference to the original bore-line, the projectile will when exiting the barrel immediately start to fall and continue to fall for the remainder of its travels
Not meaning this as a criticism against any prior posts, just sharing what I use to make it easier for me to visualize discussions about trajectories.
- In reference to the surface of the earth, the projectile will travel away from the surface (rise) until it reaches the trajectory apex after which it will travel towards the surface of the earth (fall)
- In reference to the original bore-line, the projectile will when exiting the barrel immediately start to fall and continue to fall for the remainder of its travels
Not meaning this as a criticism against any prior posts, just sharing what I use to make it easier for me to visualize discussions about trajectories.
Turbulent Turtle
F-TR competitor
Hi Fredrik. This has been a fun discussion and I love poking the bear.
It seems many people here have difficulty understanding that the vast majority of the time, the barrel of the rifle is pointing upward.
Granted, it's not pointed up much, I mean we get to 1000 yards with the barrel pointed up by under one degree, closer to 35 minutes on angle or half a degree. But it is pointed upward. So when the bullet leaves the bore, it will rise above the line of sight. In our case, tt will rise up to about 8 feet at 540 yards down range and then it will start going down as the upward component of its vector finally surrenders to gravity. From that point on, it's downhill all the way with the point on. (Pardon the pun.)
It would have been much more correct to say that the bullet will never rise above the bore line, but it does rise in relation to the line of sight and in our case it will go through the line of sight twice; once on the way up at about 15 yards and the next time at 1000 yards down range.
It seems many people here have difficulty understanding that the vast majority of the time, the barrel of the rifle is pointing upward.
Granted, it's not pointed up much, I mean we get to 1000 yards with the barrel pointed up by under one degree, closer to 35 minutes on angle or half a degree. But it is pointed upward. So when the bullet leaves the bore, it will rise above the line of sight. In our case, tt will rise up to about 8 feet at 540 yards down range and then it will start going down as the upward component of its vector finally surrenders to gravity. From that point on, it's downhill all the way with the point on. (Pardon the pun.)
It would have been much more correct to say that the bullet will never rise above the bore line, but it does rise in relation to the line of sight and in our case it will go through the line of sight twice; once on the way up at about 15 yards and the next time at 1000 yards down range.
Back to the OP:
I don't think this has to be complicated. You tell the guy at the bar that if he could look down the center of the bore of the properly aimed rifle, he would see it was directed at a point 6 feet above the 600 yard bull's eye. So the drop at the target plane isn't changed, just redirected to start out at a point above the target instead of at the center of it.
As to why the high point of the arc isn't 6 ft? That's pretty straight forward. The drop is 6 feet in the time it takes the bullet to go 600 yards, NOT in the time it takes the bullet to get to the apogee of the arc, which is only about half way through the flight time. Falling is gravitational acceleration, so the speed of the fall gets faster and faster as flight time goes by, and thus the bullet falls farther in the second half of the flight time than in the first.
If you calculate it out, because acceleration is a function of time squared, you find the bullet is falling 4 times faster at the end of the second half of the flight than it was at the end of the first half. So it covers 1/4 of the falling distance in the first half of the TOF and 3/4 of the fall is in the second half. This is why a straight line from the muzzle through the apogee intercepts a 600 yard vertical at 1/4 of the total fall to the bull's eye from the point the bore was looking at when you had the rifle correctly aimed.
Why is that so confusing and counter-intuitive? A minor reason is that acceleration involves the square of time, and humans tend to think linearly, not exponentially. It's the same reason young people underestimate what compound interest would do for their savings over a lifetime or what credit card debt is actually costing them. We just aren't used to conceptualizing that way. But the main misdirection in the whole inquiry starts with measuring the height of the apogee above the line of sight instead of its drop below the bore line. It's the dropping that matters.
Yeah, yeah, I know the side and the hypotenuse of the two legs of the triangle made by the line of sight and the boreline with a line that intercepts both at 600 yards do have different lengths, but it only works out to about two ten-thousandths of an inch difference at 600 yards. The target backer isn't even that flat or that truly vertical in most instances, so let's agree just to ignore that error.
If the fellow at the bar continues to be puzzled by your 28" rise number after you've explained all the above and put the rest of the patrons to sleep, point out that in past centuries Kings gave patronage to many famous names in mathematics to figure out trajectories for artillery so they could better aim at their enemies in war. Probably almost as many as they paid to study probability to get them an edge with their gambling. But all those great minds failed to solve more than some pieces of the puzzle until the late 19th century saw the reference projectile tables and some early closed form equations that got pretty close on trajectory, and it wasn't until the 20th century that really solid solutions were known. So their confusion puts them in good, famous, and brilliant company. Offer up a toast to that.
I don't think this has to be complicated. You tell the guy at the bar that if he could look down the center of the bore of the properly aimed rifle, he would see it was directed at a point 6 feet above the 600 yard bull's eye. So the drop at the target plane isn't changed, just redirected to start out at a point above the target instead of at the center of it.
As to why the high point of the arc isn't 6 ft? That's pretty straight forward. The drop is 6 feet in the time it takes the bullet to go 600 yards, NOT in the time it takes the bullet to get to the apogee of the arc, which is only about half way through the flight time. Falling is gravitational acceleration, so the speed of the fall gets faster and faster as flight time goes by, and thus the bullet falls farther in the second half of the flight time than in the first.
If you calculate it out, because acceleration is a function of time squared, you find the bullet is falling 4 times faster at the end of the second half of the flight than it was at the end of the first half. So it covers 1/4 of the falling distance in the first half of the TOF and 3/4 of the fall is in the second half. This is why a straight line from the muzzle through the apogee intercepts a 600 yard vertical at 1/4 of the total fall to the bull's eye from the point the bore was looking at when you had the rifle correctly aimed.
Why is that so confusing and counter-intuitive? A minor reason is that acceleration involves the square of time, and humans tend to think linearly, not exponentially. It's the same reason young people underestimate what compound interest would do for their savings over a lifetime or what credit card debt is actually costing them. We just aren't used to conceptualizing that way. But the main misdirection in the whole inquiry starts with measuring the height of the apogee above the line of sight instead of its drop below the bore line. It's the dropping that matters.
Yeah, yeah, I know the side and the hypotenuse of the two legs of the triangle made by the line of sight and the boreline with a line that intercepts both at 600 yards do have different lengths, but it only works out to about two ten-thousandths of an inch difference at 600 yards. The target backer isn't even that flat or that truly vertical in most instances, so let's agree just to ignore that error.
If the fellow at the bar continues to be puzzled by your 28" rise number after you've explained all the above and put the rest of the patrons to sleep, point out that in past centuries Kings gave patronage to many famous names in mathematics to figure out trajectories for artillery so they could better aim at their enemies in war. Probably almost as many as they paid to study probability to get them an edge with their gambling. But all those great minds failed to solve more than some pieces of the puzzle until the late 19th century saw the reference projectile tables and some early closed form equations that got pretty close on trajectory, and it wasn't until the 20th century that really solid solutions were known. So their confusion puts them in good, famous, and brilliant company. Offer up a toast to that.
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