scope line of sight and bullet trajectory

[NCMTNHunter]

The line of sight of a scope and the bore of the barrel are straight lines. The line of sight of a barrel and a scope can either not cross (unusual), or cross only once because they are two straight imaginary lines. Scopes are mounted typically 1.5" or so above the bore and set so that the two imaginary lines intersect at some point 25, 50, 100, 200 yards from the muzzle. This is physics and does not change.

The bullet is a projectile that has an arc due to gravity. Unless is it is fired perfectly vertical then the path of a bullet is always an arc. This is physics and does not change.

The bullet is fired at a slightly upward angle from the bore to reach a target downrange. The bore of the rifle is pointed up and follows a straight line, and the bullet follows this straight line until it emerges from the muzzle. At this exact instant it begins decelerating and falling, departing from the imaginary straight line of the bore. In its trajectory, it may be gaining elevation due to the angle of the bore, however, it is always falling with respect to the imaginary line of the bore. That is it's trajectory.

Think about a football. At the instant it leaves a QBs hand it is slowing down and falling. It appears to be rising and it is in elevation, however if you drew a straight line from the tip of the football to the sky (aka the bore) the ball is falling the instant it leaves the QBs hand.

In the case of the bore of the rifle, the bullet never crosses it as it is falling.

In the case of the line of the sight of the scope, the bullet typically crosses it twice. Once near the muzzle and again on descent to the target.View attachment 1053708

This is spot on. I just considered the bullet falling away from the barrel line and the bullet literally falling to the earth (losing elevation) two different things. Because even though the bullet is falling away from the barrel line it is still gaining elevation until it reaches the top of the arch and starts losing elevation again. But yes however you describe it this is how it works.

 

[JustUs4All]

It actually accelerates downward at a constant rate. 9.8 meters per second per second. Minus any other external forces (drag, friction, resistance, blah, blah, blah)

Actually an object moving upwards is not accelerating downwards it is decelerating upwards until it reaches the apex of its upward movement then it begins to accelerate downwards until either terminal velocity or an object it can not move is reached. So since other factors besides gravity are acting to decelerate the bullet on its upward arc it is decelerating at an accelerating rate until it reaches the apex of the trajectory.

This is going to get fun in just a little while.

A tip of the hat to @KS Bow Hunter for a great post at #72 but using piturs is cheatn. LOL

 

[JustUs4All]

@BriarPatch99, please take note that the bragging board is located elsewhere.

 

[NCMTNHunter]

Actually an object moving upwards is not accelerating downwards it is decelerating upwards until it reaches the apex of its upward movement then it begins to accelerate downwards until either terminal velocity or an object it can not move is reached. So since other factors besides gravity are acting to decelerate the bullet on its upward arc it is decelerating at an accelerating rate until it reaches the apex of the trajectory.

This is going to get fun in just a little while.

A tip of the hat to @KS Bow Hunter for a great post at #72 but using piturs is cheatn. LOL

Yes. Decelerates up and accelerates down. That’s what I was saying here. Brier patch said was not accurate.



You said the bullet decelerates on the downward arc here but I believe you just made a typo. I’m pretty sure we are all on the same page here.

 

[JustUs4All]

Once fired the bullet is constantly decelerating until it comes to a rest somewhere. The only exception that I can think of would be if it were fired near vertically so that it would slow nearly to a stop at the top of the trjectory (below terminal velocity). It would then accelerate for a brief time until it reached terminal velocity on the way back down.

 

[Tight Lines]

Actually an object moving upwards is not accelerating downwards it is decelerating upwards until it reaches the apex of its upward movement then it begins to accelerate downwards until either terminal velocity or an object it can not move is reached. So since other factors besides gravity are acting to decelerate the bullet on its upward arc it is decelerating at an accelerating rate until it reaches the apex of the trajectory.

This is going to get fun in just a little while.

A tip of the hat to @KS Bow Hunter for a great post at #72 but using piturs is cheatn. LOL

Thanks...for a typical bullet arc, the force of gravity is a constant and pulling the bullet down the entire arc...that is called "acceleration due to gravity" and is a downward force from the bullet to the center of the earth.

An object will accelerate downward until it reaches terminal velocity where it will remain until it is stopped.

The bullet also has a velocity that is being affected by wind resistance and gravity. The trajectory is set by these factors...bullet weight, velocity, wind resistance, and gravity.

The bullet does not go "up" or "down" unless fired almost perfectly vertical. For discussions of hunting, the inclination or declination of the bore is a nominal impact on fast bullets at close range. At long range and slower bullets it matters more. Hence why your range finder probably has inclination and declination readouts.

The bullet again leaves the bore and begins falling toward earth at that instant, which is to say it is falling away from it's bore line of sight. It's trajectory apex is a function of the above factors. But it isn't rising and decelerating, and then falling and accelerating. It is falling and losing velocity along it's entire trajectory but to gravity and ballistic factors of bullet weight, BC, velocity, etc.

 

[NCMTNHunter]

Yes. And there is a vertical and horizontal component to the trajectory.

The vertical component is the verticle distance the bullet gains from the end of the barrel to the peak of the arch and then back to the ground. This is what is affected by gravity. The verticle component is where where the bullet decelerates up at the rate of gravity until it reaches the peak of the arch then accelerates downward at the rate of gravity until it hits the ground. This is why if you drop a bullet by hand from the peak of the arc at the same time the shot bullet passes the peak they will hit the ground at the same time.

The horizontal component is the horizontal distance from the end of the barrel to the spot on the ground where the barrel hits. This horizontal component is what is affected by drag, friction and so on. The horizontal velocity always decelerates from the instant the bullet leaves the barrel.

 

[JustUs4All]

We agree that the bullet is constantly falling away from its bore line of sight unless it is fired exactly vertically, that is along a line of radius from the center of the Earth. We do not agree that all bullets start to fall toward the earth upon leaving he barrel. So long as the path of the bullet is fired along a line that departs upward from a line that is parallel with a line that is a tangent to the Earth then the bullet will not be falling until after it reaches the highest most point along its arc of flight. Fired with enough speed it would go into orbit. (With sufficient allowances made for the irregular surface of the Earth, tall buildings, and all.)

I told ya it was gonna get fun.

 

[Dub]

I’m pretty sure we are all on the same page here.

 

[NCMTNHunter]

It been fun but I ain’t getting in to orbit here.

 

[Cmp1]

I always thought that the Wby 300mag was the flattest shooting round, appears to be the fastest round at 1500 yds,,,,saying that the 300 Win mag is flatter shooting,,,,
My Dad had a 300 Weatherby mag Mark V, always wanted to fire it,,,,

 

[Tight Lines]

Yes. And there is a vertical and horizontal component to the trajectory.

The vertical component is the verticle distance the bullet gains from the end of the barrel to the peak of the arch and then back to the ground. This is what is affected by gravity. The verticle component is where where the bullet decelerates up at the rate of gravity until it reaches the peak of the arch then accelerates downward at the rate of gravity until it hits the ground. This is why if you drop a bullet by hand from the peak of the arc at the same time the shot bullet passes the peak they will hit the ground at the same time.

The horizontal component is the horizontal distance from the end of the barrel to the spot on the ground where the barrel hits. This horizontal component is what is affected by drag, friction and so on. The horizontal velocity always decelerates from the instant the bullet leaves the barrel.

This is not actually correct. The entire trajectory of the bullet is affected by gravity, from the moment it leaves the bore until it stops. Even at rest, gravity is what keeps it there.

The bullet does not decelerate due to gravity as it is not rising, it is falling from its trajectory, always, and if you dropped a bullet at the apex it would hit the ground much faster than the bullet moving through the trajectory. The only force on the dropped bullet is the force of gravity. The force on the fired bullet is due to the propellant. The force of gravity is always a constant pulling down, and is being offset by the forces acting on the bullet by the propellant and drag. They work in concert the entire flight of the bullet. Gravity and drag.

The apex is what is messing you up. The arc of the bullet always has the downward acceleration due to gravity. There are vector quantities that change through the trajectory of the bullet.

Think of it this way. A bullet does not ever "rise" above the bore line. It is affected by downward forces of gravity the moment it leave the bore. However, due to the propellant, and rifling, and the shape of a bullet, it "resists" the effect of gravity until wind resistance (which is great at 3000 fps) starts to slow the bullet, essentially draining energy, and as this happens gravity then starts to have more of an impact hence the more rapid drop the further from the bore as per the below.

It is really simple...the bullet is affected by air resistance and gravity in concert immediately after leaving the bore, and the trajectory that is traces is based on the velocity, mass, and ballistic coefficient of that projectile. That is your trajectory.



https://www.chuckhawks.com/bullet_trajectory.htm

 

[Tight Lines]

We agree that the bullet is constantly falling away from its bore line of sight unless it is fired exactly vertically, that is along a line of radius from the center of the Earth. We do not agree that all bullets start to fall toward the earth upon leaving he barrel. So long as the path of the bullet is fired along a line that departs upward from a line that is parallel with a line that is a tangent to the Earth then the bullet will not be falling until after it reaches the highest most point along its arc of flight. Fired with enough speed it would go into orbit. (With sufficient allowances made for the irregular surface of the Earth, tall buildings, and all.)

I told ya it was gonna get fun.

All bullets are falling the moment that they leave the bore. Otherwise, they would follow the straight line of the bore until they were out of energy and then just drop, like in the cartoons. They are falling at the same time there is energy moving them along an arc. The trajectory.

 

[JustUs4All]

Please explain how a vertically fired bullet is falling before it reaches the apex of its trajectory (which theoretically could be a straight line traversed in two directions). We agree that gravity is acting on it the entire time but it only serves to decelerate the upward movement of the bullet prior to the apex.

 

[Tight Lines]

Please explain how a vertically fired bullet is falling before it reaches the apex of its trajectory (which theoretically could be a straight line traversed in two directions). We agree that gravity is acting on it the entire time but it only serves to decelerate the upward movement of the bullet prior to the apex.

If you could fire a bullet perfectly perpendicular to the gravitational forces of the earth, in a vacuum, then yes, the bullet would go straight up and straight down.

However, in the case of a bullet fired horizontally, even at a slight upward angle, the bullet is falling away from the bore line of sight and never goes above it (this is how you know it is falling due to gravity) even while it may be gaining in actual elevation. This is a function of the vector quantities and their effect on the projectile. See the diagram below. The projectile is "rising" however gravity is pulling it down immediately from the initial vector of the bore line of sight. Semantics is important.

As the wind resistance erodes the energy of the bullet, gravity then has a greater impact on the trajectory of the bullet. Hence the arc trajectory accelerating downward as the equation actually uses the square of gravity.

If you could look at the vector quantities of a bullet fired from the bore, you would see vectors pointing up (this is the force outrunning gravity) however the bullet never exceeds the line of sight of the bore.

Acceleration is a vector quantity which means it has both magnitude and direction.

Notice in this diagram the trajectory never crosses the vector of Vo?


For it to make more sense you can look at a projectile fired perfectly horizontally:

 

[NCMTNHunter]

This is not actually correct. The entire trajectory of the bullet is affected by gravity, from the moment it leaves the bore until it stops. Even at rest, gravity is what keeps it there.

The bullet does not decelerate due to gravity as it is not rising, it is falling from its trajectory, always, and if you dropped a bullet at the apex it would hit the ground much faster than the bullet moving through the trajectory. The only force on the dropped bullet is the force of gravity. The force on the fired bullet is due to the propellant. The force of gravity is always a constant pulling down, and is being offset by the forces acting on the bullet by the propellant and drag. They work in concert the entire flight of the bullet. Gravity and drag.

The apex is what is messing you up. The arc of the bullet always has the downward acceleration due to gravity. There are vector quantities that change through the trajectory of the bullet.

Think of it this way. A bullet does not ever "rise" above the bore line. It is affected by downward forces of gravity the moment it leave the bore. However, due to the propellant, and rifling, and the shape of a bullet, it "resists" the effect of gravity until wind resistance (which is great at 3000 fps) starts to slow the bullet, essentially draining energy, and as this happens gravity then starts to have more of an impact hence the more rapid drop the further from the bore as per the below.

It is really simple...the bullet is affected by air resistance and gravity in concert immediately after leaving the bore, and the trajectory that is traces is based on the velocity, mass, and ballistic coefficient of that projectile. That is your trajectory.

View attachment 1053764

https://www.chuckhawks.com/bullet_trajectory.htm

On the table you just posted, follow the zero line horizontally until you are directly under the apex. Now draw an upward pointing arrow to the apex. That 3 inch gain in elevation (not above the barrel line but above the line of sight) is where the bullet decelerates (not in the horizontal direct only in the verticle direction) due to gravity pushing straight down against the upward force from the propellant the sent it on an upward trajectory.

At the apex the upward force from the propellant has been completely overcome by gravity and gravity will continue to drive the bullet straight down causing it accelerate at the speed of gravity down towards the center of the earth.

All this is happening while the bullet is decelerating horizontally (not because of gravity but drag, resistance and so on).

Gravity only affects objects vertically and it affects them the same reguardless of whether or not they are also moving horizontally. So the bullet dropped from the apex will hit the ground at the same time as the shot bullet. Just like a bullet dropped from the end of a level barrel will hit the ground at the same time as the shot bullet.

 

[Tight Lines]

On the table you just posted, follow the zero line horizontally until you are directly under the apex. Now draw an upward pointing arrow to the apex. That 3 inch gain in elevation (not above the barrel line but above the line of sight) is where the bullet decelerates (not in the horizontal direct only in the verticle direction) due to gravity pushing straight down against the upward force from the propellant the sent it on an upward trajectory.

At the apex the upward force from the propellant has been completely overcome by gravity and gravity will continue to drive the bullet straight down causing it accelerate at the speed of gravity down towards the center of the earth.

All this is happening while the bullet is decelerating horizontally (not because of gravity but drag, resistance and so on).

Gravity only affects objects vertically and it affects them the same reguardless of whether or not they are also moving horizontally. So the bullet dropped from the apex will hit the ground at the same time as the shot bullet. Just like a bullet dropped from the end of a level barrel will hit the ground at the same time as the shot bullet.

I can follow your logic but it doesn't obey the laws of physics. Gravity does not choose when to act based on the velocity, direction, etc. of a projectile. It is always acting, that is why it is called a constant.

So let's think about an airplane. Gravity is working on the airplane all the time. So how does that projectile the size of a suburban ranch home maintain 37,000 feet exactly? It is called aerodynamic lift. The area of the wings, and their airfoil shape, create exactly enough lift to counteract the forces of gravity so long as a certain velocity is maintained. Below a certain velocity, the lift erodes, and the plane falls out of the sky.

On the graph, the fact that it is an arc, a trajectory, is how you know that gravity is working. If it was not, the bullet would follow the exact bore line of site (air resistance does not push left, right, up down) until it slowed to a complete stop, then fell straight down. That isn't what it does...think about why and there is your answer...

 

[Tight Lines]

On the table you just posted, follow the zero line horizontally until you are directly under the apex. Now draw an upward pointing arrow to the apex. That 3 inch gain in elevation (not above the barrel line but above the line of sight) is where the bullet decelerates (not in the horizontal direct only in the verticle direction) due to gravity pushing straight down against the upward force from the propellant the sent it on an upward trajectory.

At the apex the upward force from the propellant has been completely overcome by gravity and gravity will continue to drive the bullet straight down causing it accelerate at the speed of gravity down towards the center of the earth.

All this is happening while the bullet is decelerating horizontally (not because of gravity but drag, resistance and so on).

Gravity only affects objects vertically and it affects them the same reguardless of whether or not they are also moving horizontally. So the bullet dropped from the apex will hit the ground at the same time as the shot bullet. Just like a bullet dropped from the end of a level barrel will hit the ground at the same time as the shot bullet.

And go to the range and try your theory...the dropped bullet and the fired bullet have no correlation. They will not hit at the same time unless it is by coincidence. This is a myth.

 

[NCMTNHunter]

I can follow your logic but it doesn't obey the laws of physics. Gravity does not choose when to act based on the velocity, direction, etc. of a projectile. It is always acting, that is why it is called a constant.

So let's think about an airplane. Gravity is working on the airplane all the time. So how does that projectile the size of a suburban ranch home maintain 37,000 feet exactly? It is called aerodynamic lift. The area of the wings, and their airfoil shape, create exactly enough lift to counteract the forces of gravity so long as a certain velocity is maintained. Below a certain velocity, the lift erodes, and the plane falls out of the sky.

On the graph, the fact that it is an arc, a trajectory, is how you know that gravity is working. If it was not, the bullet would follow the exact bore line of site (air resistance does not push left, right, up down) until it slowed to a complete stop, then fell straight down. That isn't what it does...think about why and there is your answer...

I didn’t say gravity chooses. It does affect everything all the time in the same way but the force of gravity is only straight down, nothing else. Gravity’s effect is reguardeless of horizontal velocity. That’s why the two bullets hit the ground at the same time.

 

[NCMTNHunter]

And go to the range and try your theory...the dropped bullet and the fired bullet have no correlation. They will not hit at the same time unless it is by coincidence. This is a myth.

That’s a little tricky to do at the range.