Maximum height of bullet trajectory?

[Alexander-M]

(This has been discussed somewhat before, but I have not seen a definitive answer. )

Numerous times I have heard conversations regarding how high our bullets fly on their way to the targets. Some shooters opined that many of the flags that are 10 to 12 feet high were useless since the bullets reach 20 to 30 feet altitude. But looking at our rifles when we shoot, even at 1000 yards, I could not imagine any bullet going 30 feet high since the rifles are essentially level. I believe the error is that they assume that the peak of the trajectory is the same as the bullet drop at the target, and I believe this is incorrect.

Using the Berger Ballistic Calculator, I used 0 as the starting range, and 1000 as the ending range, and plotted the results for 180 gr Hybrid Target bullets at 2825 fps muzzle speed. These show the peak height is at around 500 yards down range, and is closer to 89 inches, or 7-1/2 feet:



What do you think?

Thanks!
Alex

 

[butchlambert]

(This has been discussed somewhat before, but I have not seen a definitive answer. )

Numerous times I have heard conversations regarding how high our bullets fly on their way to the targets. Some shooters opined that many of the flags that are 10 to 12 feet high were useless since the bullets reach 20 to 30 feet altitude. But looking at our rifles when we shoot, even at 1000 yards, I could not imagine any bullet going 30 feet high since the rifles are essentially level. I believe the error is that they assume that the peak of the trajectory is the same as the bullet drop at the target, and I believe this is incorrect.

Using the Berger Ballistic Calculator, I used 0 as the starting range, and 1000 as the ending range, and plotted the results for 180 gr Hybrid Target bullets at 2825 fps muzzle speed. These show the peak height is at around 500 yards down range, and is closer to 89 inches, or 7-1/2 feet:

View attachment 1479967

What do you think?

Thanks!
Alex

About what? Bullets do not rise after leaving the muzzle.

 

[Ned Ludd]

The estimate of bullet arc height you showed is presumably correct. However, one must also consider that at many shooting ranges, the targets may be placed well below or well above the firing line, and that the terrain in between the firing line and target line may sometimes be substantially lower.

Thus, in an "ideal" situation one would consider the bullet height as shown in your estimate above the line of sight straight to the target center, and place the flags at that height, adding/subtracting whatever flag pole length might be necessary based on the terrain underneath. More often, it seems poles at the ranges where I shoot most often are selected based on whatever size or material might be available and/or the cost. They often are not at the same height as the top of the bullet arc, in some cases not even close to the same height.

 

[Pawnee Bill]

I believe the term you are looking for is "Mid Range Trajectory". It used to be published in some loading manuals years ago.

 

[CJ6]

The barrel/bore when fired is at an upward angle that allows the bullet to "drop" at a specific distance. Sights/Optics allows this angle to be predictable. Gravity works.....

 

[Alexander-M]

About what? Bullets do not rise after leaving the muzzle.

That is obvious - - unless we find a way to suspend gravity
Alex

 

[Alexander-M]

The estimate of bullet arc height you showed is presumably correct. However, one must also consider that at many shooting ranges, the targets may be placed well below or well above the firing line, and that the terrain in between the firing line and target line may sometimes be substantially lower.

Thus, in an "ideal" situation one would consider the bullet height as shown in your estimate above the line of sight straight to the target center, and place the flags at that height, adding/subtracting whatever flag pole length might be necessary based on the terrain underneath. More often, it seems poles at the ranges where I shoot most often are selected based on whatever size or material might be available and/or the cost. They often are not at the same height as the top of the bullet arc, in some cases not even close to the same height.

Greg, you are correct. Do realize that I am using an ideal situation just to illustrate that bullets do not reach the same height (from an ideal horizontal plane) as the drop they experience at the target.

Also, Roger, I am fully aware that the rifles have to be at a an up angle. I admit that I have not seen the shooters at the ELR matches, with targets two miles or so away. There, I would imagine the angle of the rifle could be rather noticeable.

Alex

 

[Ned Ludd]

Greg, you are correct. Do realize that I am using an ideal situation just to illustrate that bullets do not reach the same height (from an ideal horizontal plane) as the drop they experience at the target.

My point is that the flags do not have be the same height as the distance the bullets drop off at the target.

Alex

Agreed. Almost by definition the flags will never all be at exactly the same height as our bullet trajectories, if for no other reason than the different cartridges shooters are using. Nonetheless, flags that are located 5-10 feet (or more) above or below the [average] bullet trajectory may not provide as useful wind information as they could if they were placed more judiciously. Nonetheless, most shooters take whatever wind information they do provide and do the best they can.

As far as bullet arc height versus drop, they are not the same thing. Arc height is simply the uppermost point on the bullet's parabolic trajectory, and is a linear measurement. Drop is the angular measurement or scope setting required to provide the correct launch angle such that POA and POI coincide at the target center at some specified distance. By definition they are different, if for no other reason than one is a linear measurement and one is an angular measurement. However, there is more to the difference than just that. Also by definition, the angular measurement (i.e. drop) is specified at a certain distance such as 1000 yd, for example. We may wish to convert that angular measurement to an estimated linear measurement at that distance and call it "drop", but the linear measurement at the target face we refer to as "drop" is simply a surrogate for a circular arc length subtended by that specified angular measurement at the specified distance of the target face. As you noted, the maximum ordinate or arc height of the parabolic trajectory occurs some distance away from the target closer back toward the middle of the trajectory. The bottom line is that bullet arc height and drop are two totally different measurements.

 

[Rocketvapor]

Med,
Drop is actually a linear measurement, like in inches, that we convert to MOA or Mils at range so we can adjust our scopes.
We tend to ignore drop in inches, like 72 inches @ 600yds, but that's how our calculators come up with come up.

 

[Highpower-FClass]

(This has been discussed somewhat before, but I have not seen a definitive answer. )

Numerous times I have heard conversations regarding how high our bullets fly on their way to the targets. Some shooters opined that many of the flags that are 10 to 12 feet high were useless since the bullets reach 20 to 30 feet altitude. But looking at our rifles when we shoot, even at 1000 yards, I could not imagine any bullet going 30 feet high since the rifles are essentially level. I believe the error is that they assume that the peak of the trajectory is the same as the bullet drop at the target, and I believe this is incorrect.

Using the Berger Ballistic Calculator, I used 0 as the starting range, and 1000 as the ending range, and plotted the results for 180 gr Hybrid Target bullets at 2825 fps muzzle speed. These show the peak height is at around 500 yards down range, and is closer to 89 inches, or 7-1/2 feet:

View attachment 1479967

What do you think?

Thanks!
Alex

Alex, I think this is a good question and what you have posted goes towards dispelling the 'the wind is even worse than what you see at the flags because the bullet will fly even higher than the top of the flagpoles' misconception.

Assuming that the firing line and the targets are somewhat level, the highest the 7mm bullet in your example would indeed be from the ground is 7.2 feet, well below the height of most range flagpoles.

I also agree that the reason why this is a common misconception is, as you identified, the 'drop in inches at the target' that most calculators display. For example, JBM shows the bullet drop at the target as -275 inches at 1000 yards for the data you provided. I believe what a lot of people do not realize is that this is not the 'drop from the apex of the bullet trajectory' but rather 'the difference in height at which the bullet would be, from the center of the target, at the target, if gravity did not exist'.

 

[Ned Ludd]

Med,
Drop is actually a linear measurement, like in inches, that we convert to MOA or Mils at range so we can adjust our scopes.
We tend to ignore drop in inches, like 72 inches @ 600yds, but that's how our calculators come up with come up.

I know exactly what it is. Drop is interconvertible, some may choose to use angular measurement, some convert to linear measurement. Most ballistic calculators will output either, or both. The linear conversion is actually a surrogate measurement for arc length of a circle of a specific radius that is subtended by by that anugular measurement (either r1 or r2 as shown in the illustration below). We assume the circular arc segment to be essentially flat at the distances we typically shoot (i.e. a flat target face). However the arc is not flat and thus the linear conversion for a drop measurement is an estimate, not a truly accurate linear measurement. Further, the bullet never actually drops by anywhere close to that linear estimation. The estimation is the arc length subtended by that specific angle, not some "real" distance the bullet rises or falls. Nonetheless, the circular arc is close enough to being flat at the target face for the purpose, so some choose to think in those terms and and it works just fine for them. But the true measurement is angular and that is what we adjust with our scopes.



Another consideration that helps distinguish arc length or drop at the target face from bullet trajectory height is that the drop at some specified distance is always listed relative to some other zero point for the rifle setup. For example, we input a 100 yd zero into the ballistic program and it returns a drop in either an angular measurement (i.e. a scope setting change), or a linear measurement estimate at some other specified distance, such as 1000 yd. This output is the change in angular drop or the linear drop estimate/equivalent relative to the known zero point. It is not an absolute value, but a relative one. Bullet arc height is an absolute measurement above line of sight.

 

[DirtySteve]

I shot at a steel target at 1200 yards with my 45-90. My bullet was about 200 inches high at 100 yards.. Pretty sure my bullet was way above 30 feet at mid range..


Edit:
I know you are talking modern cartridges but I just wanted to throw that in there.. My bullets are 100 feet more or less above the line of sight at 600 yards.

 

[Ned Ludd]

Here is a slightly simpler illustration of the difference between bullet arc height and bullet drop. The linear representation of bullet drop is simply the difference where the bullet would have impacted the target in the absence of gravity versus where it actually impacts the target because of the influence of gravity. Theta is the increased launch angle we must use in order to account for the effect of gravity acting upon the bullet as compared to a zero reference at some lesser distance. Theta also defines the drop at some specified distance.

The fact is that the bullet never actually "drops" by the amount of the vertical linear measurement some refer to as "drop" (indicated at right). That is one reason why the angular measurement is the better descriptor [edited to add: and the primary reason for the discrepancy with respect to flag height as noted above by Alexander-M]. Also, bullet arc height will never exceed bullet drop under the influence of gravity.

 

[Highpower-FClass]

Here is a slightly simpler illustration of the difference between bullet arc height and bullet drop. The linear representation of bullet drop is simply the difference where the bullet would have impacted the target in the absence of gravity versus where it actually impacts the target because of the influence of gravity. Theta is the increased launch angle we must use in order to account for the effect of gravity acting upon the bullet as compared to a zero reference at some lesser distance. Theta also defines the drop at some specified distance. The fact is that the bullet never actually "drops" by the linear measurement some refer to as "drop". That is one reason why the angular measurement is the better descriptor. Also, bullet arc height will never exceed bullet drop under the influence of gravity.

View attachment 1480108

This visual should be included in all threads on this topic going forward Very nice!

 

[Rocketvapor]

Drop (it's real) is the result of drag, gravity, initial velocity, giving a resulting time of flight for any incremental range.
Shoot level, bullets drop, and yes, the drop is an arc. We don't want that unless shooting from a hill
Drop is the value calculated by ballistic equations. Angle (in MOA, Mils) is compensation needed to get on target. Drop for each range is first calculated, then converted to an angle for each range increment using drop and distance.

Starting from zero range ,sight above bore, or corrected for some other zero range (sight above bore plus drop) making sight angle a derived value. An output, not an input variable. You can get away without angle, but not drop. Some calculators don't like zero for a range as sight above bore gives an infinity result. Implies an instantaneous 1.5 inch drop. Some allow a zero for sight above bore and a zero starting range.

Rise above line of sight results from bringing drop up to target position at range
i.e., shooting at an upward angle to hit the target @ 1000 yards. The cosine of the upward angle also changes the effect of gravity on the trajectory. Calculations use this angle to modify the gravity constant in the calculation. This also changes flight path and time slightly for most shooting situations (less than a few degrees usually). Even when the drop is large, rockets, bombs or artillery, POI is calculated from drop, not angle.

Short answer: Drop at desired range is calculated, the compensation angle (scope setting) only requires drop and range, rise above line of sight depends on the end points of the flight path, and yes the drop is an arc.
Theta in your diagram (departure is a vector quantity) is singular for one range and velocity and calculated from drop, maybe in inches, and range, maybe in yards. Incremental points on the flight path are just that.
Incremental calculations from drop calculations as the projectile slows down. Integration of all those incremental drops gets you an X (if you adjust your scope for the drop at range).

Use drop for 1000yds, calculate angle in MOA to adjust turret, and additional drop in inches for 1005 yds.
Then you can compensate with a new angle.

Maximum rise cannot be calculated from sight angle without knowing incremental drops along the way and will be different for each situation.
Slow heavy blob of a bullet, or fast sleek bullet.
Don't get confused with circles. 60MOA drop is a whole degree.


How about maximum drift into adjacent shooting lanes shooting right for a 90 degree wind?

 

[marine52]

About what? Bullets do not rise after leaving the muzzle.

Yes they do rise, unless you are refering to the trivial classroom exercise of a launch angle equal to zero. They rise relative to the point of departure and the earth’s surface.

 

[marine52]

Here is a slightly simpler illustration of the difference between bullet arc height and bullet drop. The linear representation of bullet drop is simply the difference where the bullet would have impacted the target in the absence of gravity versus where it actually impacts the target because of the influence of gravity. Theta is the increased launch angle we must use in order to account for the effect of gravity acting upon the bullet as compared to a zero reference at some lesser distance. Theta also defines the drop at some specified distance.

The fact is that the bullet never actually "drops" by the linear measurement some refer to as "drop". That is one reason why the angular measurement is the better descriptor [edited to add: and the primary reason for the discrepancy with respect to flag height as noted above by Alexander-M]. Also, bullet arc height will never exceed bullet drop under the influence of gravity.

View attachment 1480108

Excellent description. Ned is spot on. This imaginary line (line of departure, Boreline, etc) and the “drop” associated with it has been the source of much confusion with new shooters trying to learn the basics of ballistics. That’s why I call it the fake line in the sky. If you read Robert McCoy’s book, MODERN EXTERIOR BALLISTICS, nowhere does he refer to this fake line. Why? Because it is irrelevant in determining trajectories of projectiles in motion. In McCoy’s five chapters on trajectory modeling, including vacuum, flat fire, point-mass, Siacci, and 6-DOF trajectories, he focuses on the kinematic equations that are based on a horizontal axis “tangent to the earth’s surface at the launch point and is directed from the gun toward the target.”

 

[Dave M.]

Yes they do rise, unless you are refering to the trivial classroom exercise of a launch angle equal to zero. They rise relative to the point of departure and the earth’s surface.

Pretty sure he means the bullet can never go above the straight line drawn along the barrel bore (as Ned’s picture above clearly shows).

 

[Rocketvapor]

Except for aerodynamic jump.
Yes there are some "minor" variables that impact the flight path, but for most distances I use a calculator derived MOA/Mil table for scope adjustment. Just easier at the range, knowing of course that drift and drop were calculated behind the scenes using a linear measurement.

 

[marine52]

Pretty sure he means the bullet can never go above the straight line drawn along the barrel bore (as Ned’s picture above clearly shows).

Yes. I understand that. And that is why the mass confusion exists with shooters who constantly hear “bullets always fall immediately after leaving the barrel.” In physics/engineering terms, the bullet has a positive vertical velocity vector after departure from the barrel. The laws of physics and projectile motion allow us to separate the horizontal and vertical velocity vectors and treat them separately.