I'm math-ily challenged.

Can someone tell me if there's a way to figure out at which range mechanical offset of bore and sights becomes so negligible that you don't need to hold over anymore?

At my range, I can't shoot rifles at ranges other than fixed ranges of 25/50/75/100 and I'd like to figure out approximately where I don't have to account for offset any longer.

I’m not certain I understand your question, but if you are trying to avoid any point of aim adjustment to hit a target at a specific range, then zero your gun at that distance.

E.g., with my ARs zeroed at 50 yards and if I am engaging a target at 50 yards, I aim directly where I want to hit. (And sometimes I do. )

Or am I misunderstanding something?

Added: If you are asking if you can zero at a distance that will eliminate the need to adjust your POA at all distances, that’s essentially impossible due to the offset between the bore and sight and the curved trajectory of the bullet. With a 50 yard zero and typical 223/5.56 ammunition, for example, it will be necessary to hold high at 25 yards and low at 75 and 100. Other specific zero distances will change the degree and direction of holdoff, and that’s something you can determine through experimentation or using different values in a ballistics calculator. As another example, a 100 yard zero will usually put the trajectory low at all other distances. That’s useful for some purposes because then it’s never necessary to dial one’s scope elevation down or to hold low.

I think the difference he is asking about is the unadjustanle difference between the sights and the barrel.

It would be some kind of calculation based off of actual measurements, but for example:

20 yards differences of .003
100 yards differences of .030

Figuring out the limitations of the differences would be the formula to say at 50 yards, it is half of 100 and two and a half times twenty. Where do the measurements correspond to that. Then you can scale it up or down using that equation. So at 1000 yards if you’re off by x, you know it was a perfect shot, only limited by the “slop” or mechanical ability of the gun.

That’s the way I understood the question.

I might be misunderstanding your question but I think what you are looking for is maximum point plank range and that is going to vary based on the cartridge load.

My 308 has a maximum point plank range of about 330 yards. That means I can hold dead on at 330 yards and I will be 4 inches low. If the target is anywhere in between the muzzle and 330 yards I will with in 4 inches high of point of aim or 4 inches low.

I found that is what works best for me when deer hunting. I know that deer vitals are about 8 inches so I put it on the middle of the vitals.

This calculator should allow you to find the similar numbers for the round you are shooting.

My understanding of a bullets path is that when fired, it must rise to the exact aiming point of the scope/sights and subsequently fall to that same point as gravity pulls the bullet down. Much of this depends on the height of the scope above the barrel.

What you're talking about is not due to "mechanical offset," but bullet trajectory.

The path of a bullet is affected by gravity, and is always an arc. Gravity pulls at the surface of the earth with an acceleration of 32 ft./sec./sec. (as each second passes, the fall speeds up by 32 ft./sec., a little under 22 mph. So if you drop a bullet (or anything), one second after you let it go, it is falling at 22 mph, after two seconds, 44 mph, etc. (ignoring the effect of air resistance). It doesn't matter how fast the bullet is traveling laterally, it is always falling at the same rate. So each second the bullet travels farther from the muzzle, it is lower than the second before. So when you are shooting at any distance other than zero, you have to incline the barrel (shoot in an upwards direction) for the bullet to be at the same height as the target when it gets there. When you are "sighting in" a firearm, you are setting the sights to show where this arcing bullet returns to the same height as the muzzle after traveling above muzzle height until that point in time. Think of the bullet's trajectory as a rainbow, one leg of the rainbow is your muzzle, you adjust your sights to show where the rainbow hits the pot of gold at the other end. Any target father than your sighted-in distance will be hit lower, anything closer will be hit higher, so "holding high" or "holding low" is a way to compensate for this without having to adjust the sights. Note that this only applies to the horizontal distance between the muzzle and the target. If the target is higher or lower than the muzzle, this is a shorter distance than the point-to-point distance. So on angled shots, you always have to hold low because the horizontal distance is shorter than the actual distance, and gravity has less time to pull the bullet downward.

Fortunately for us, we live in an atmosphere, and this complicates things somewhat due to the effect of air resistance, wind, etc. This is generally a much smaller effect than gravity, because gravity is working all the time, and always in the same direction. The shape of the bullet will also affect its trajectory due to air resistance, but not gravity - except that when air resistance slows a bullet, gravity has more time to act on it.

sigfruend posted a good explanation (with pictures that make sense!) here:

https://sigforum.com/eve/forums...0601935/m/6680029374

quote:

If the target is higher or lower than the muzzle, this is a shorter distance than the point-to-point distance. So on angled shots, you always have to hold low because the horizontal distance is shorter than the actual distance, and gravity has less time to pull the bullet downward.

Although the fix is correct, the reason is wrong. Gravity acts on the bullet for the full actual distance to the target, no matter what the angle of the shot is. The reason one must aim low is because the distance fallen is no longer perpendicular to the line of sight, and the apparent distance fallen (on that perpendicular line) is shorter (actually by the cosine of the elevation angle). If you're shooting up or down on a 30° angle, for instance, the apparent amount of bullet drop will only be 87% of the actual drop and you will have to add the missing 13% by lowering the aim. A really extreme angle, such as 45°, requires compensating for 30% of the expected drop at the actual range.

Most writeups about how to aim for large angles tend to use adjusting the sights for the horizontal distance to the target, instead of the actual range, and some rangefinders will even calculate that shorter distance for you. For fairly short ranges, that technique works, because it causes the sights to compensate for less drop and you automatically aim lower as a result. However, that technique assumes that bullet drop is linear with distance, and it is not--it increases rapidly with increasing distance and at long ranges and extreme angles you'd probably be hitting low. (However, in fairness, this method will probably be good enough for most situations, even though not technically sound.)

For most shooting on reasonably level ground, the deviation of the line of sight from horizontal is low enough that the compensation is trivial (the cosine of small angles is almost equal to 1.0).

flashguy

quote:

Originally posted by Oat_Action_Man:
mechanical offset of bore and sights

Wait a second guys, I don’t think he’s talking about bullet drop. The mechanical offset between bore and sights.

Is this where you make one “click” on the sights and it’s “off” in the other direction? Where you cannot dial it in perfectly, because the sights are barely off?

My other thought is that the sights sit (example) three inches above the bore:

At 10 yards:

Side a = 360
Side b = 3
Side c = 360
Angle ∠A = 89.761° = 89°45'41" = 1.56663 rad
Angle ∠B = 0.477° = 0°28'39" = 0.0083334 rad
Angle ∠C = 89.761° = 89°45'41" = 1.56663 rad

At 100 yards:

Side a = 3,600
Side b = 3
Side c = 3,600
Angle ∠A = 89.976° = 89°58'34" = 1.57038 rad
Angle ∠B = 0.0477° = 0°2'52" = 0.00083333 rad
Angle ∠C = 89.976° = 89°58'34" = 1.57038 rad

See how the angle changes the farther out you go. If the sights were down the bore, vs sitting above.

I may be out in left field.

Where is OAM to clarify his question?

Theoretically, the sights are designed to take that into account.

flashguy

Mechanical offset: the fact that the sights are X height above the bore, causing POI to be lower than POA at close distances.

Holdover: how you correct offset at close range by aiming higher by the factor of your mechanical offset.

There is some range at which you no longer need to compensate for offset. How does one determine what range that will be, short of experimentally shooting at various distances (which I can't do)?

Knowing a rifle's zero (50 yards), what range do I no longer need to hold over to account for offset? At 25 you'll be ~1" low because of your zero, not offset. At 5, you'll be ~2.5" low because of your offset.

I estimate holdover no longer really matters between 15 and 20 yards, based on experience from a class, but that shooting was all done off-hand and I would like a more precise answer, since I can't do it experimentally (from a bench or prone).

You should learn how to use a ballistics program. JBM Ballistics is very accurate, and is a free site on the web. You need to plug in some basics:
- Bullet type. Maybe a 55 grain FMJ, or maybe a match bullet like 69 SMK. If you go to JBM Ballistics, use the drop down for Hornady or Sierra bullets -- both of which include a large number of options.
- Muzzle velocity. If you don't know your MV, take a reasonable guess. MV won't matter much for the close distances you're looking at.
- Use sight over bore height of 2.5 inches.
- Set you air Density Altitude to maybe 3,000 feet. Probably an average summer air density for your neck of the woods.
- Set your zero distance at 50 yards.
- Set your range increment at 5 yards. This will give you POI vs POA for every 5 yards.
- Set your maximum range to maybe 100 yards. Or 200 yards. Since you're not familiar with mechanical offset and bullet drop, you might find the data interesting.

quote:

Originally posted by flashguy:
However, that technique assumes that bullet drop is linear with distance, and it is not ....

And the reason it is not is because of air resistance. At steep angles and especially longer distances using the drop figure for neither the horizontal nor the angled (slope) distance will give completely accurate results. For example, assume a downward angle of 40°, a horizontal distance of 450 yards, and a direct distance from shooter to target, i.e., the slope distance of 590 yards. Gravity pulls on the bullet for the horizontal distance of 450 yards, but atmospheric drag acts on the bullet for 590 yards.

That means that the bullet will drop more from shooter to target than if shooting horizontally at 450 yards, but less than if shooting horizontally at 590 yards.

For such situations an appropriate ballistics solver is the best way to determine the actual trajectory, but if one knows the cosine of the shooting angle, a useful method to get close (closer, anyway) to the correct data is the “Improved Rifleman’s Rule*” of converting the 590 yard data to what it should be.

* Many descriptions on the Internet.

quote:

Originally posted by Oat_Action_Man:
Mechanical offset: the fact that the sights are X height above the bore, causing POI to be lower than POA at close distances.

Holdover: how you correct offset at close range by aiming higher by the factor of your mechanical offset.

There is some range at which you no longer need to compensate for offset. How does one determine what range that will be, short of experimentally shooting at various distances (which I can't do)?

Knowing a rifle's zero (50 yards), what range do I no longer need to hold over to account for offset? At 25 you'll be ~1" low because of your zero, not offset. At 5, you'll be ~2.5" low because of your offset.

I estimate holdover no longer really matters between 15 and 20 yards, based on experience from a class, but that shooting was all done off-hand and I would like a more precise answer, since I can't do it experimentally (from a bench or prone).

Not to be obtuse, but I don't think you understand bullet trajectory and zero. Because the barrel is lower than the sights you will always have to holdover inside of your zeroed range, no matter what that range is.

When you say holdover no longer matters between 15 and 20 yards, what is the context? If you're simply trying to hit a human size target at that range then an inch or two of offset is negligible. If you're trying to make a precision shot then you need to know exactly where the bullet is going to hit so you can adjust your aim.

You also have to understand that because of the offset you can zero at different ranges which changes the bullet trajectory. With an AR for example: with a 25 yard zero the bullet will start 2.5 inches low at the muzzle and rise to point of aim at 25yd. It will continue to rise above point of aim to somewhere beyond 100 yards where it will start to fall until it intersects point of aim again around 300 yards then continue to fall below point of aim.

If you zero at 50 yards the result is similar, the bullet hits low until 50 yards, then will be above point of aim after 50yd then intersects point of aim around 200 yards as it falls.

Lastly if you zero at 100 yards the bullet hits low until 100 yards which is its peak, then will be low beyond 100yd as it continues to fall.

Bottom line you have to know your zero and how your bullets travel at that zero so you can shoot accurately at any range.

quote:

Originally posted by sigfreund:

quote:

Originally posted by flashguy:
However, that technique assumes that bullet drop is linear with distance, and it is not ....

And the reason it is not is because of air resistance.

That may be a contributor, but it is not the major reason. The drop due to gravity is an acceleration, which means the rate of fall keeps increasing with time. Neglecting air resistance (for now), the time of flight is proportional to the distance to the target, and is a linear function. However, the pull of gravity is a function of time squared, and is not linear. The longer the bullet is in the air, the faster it falls, meaning that the drop at a shorter range is not proportional to the drop at a longer one. The drop at 200 yards is not twice the drop at 100 yards, but 4 times as much. Admittedly, using the horizontal distance will not involve such drastic differences in range, and the effect will not be nearly as noticeable, but it will be there.

Now, regarding air resistance. The major effect of air resistance will be to slow down the bullet in flight, which will increase the time of flight. Since the drop by gravity increases by the square of the time of flight, increases in that time will have more than linear effects on the bullet drop, too--it will drop even more as a result. Oddly enough, that will to a very small degree help compensate for the angle shot.

flashguy

I agree with most of what you said, flashguy. I was wrong to ignore the acceleration of gravity, so thanks for pointing that out.

quote:

Originally posted by flashguy:
The drop at 200 yards is not twice the drop at
100 yards, but 4 times as much.

That, however, is not exactly true of a bullet in flight because the air resistance does increase the time of flight and therefore the time of drop in a nonlinear fashion. Using the common data for a 308 Winchester Federal 168 grain Gold Medal Match load under “standard” atmospheric conditions, for example, the time of flight from 0 to 100 yards is 0.120 second; the time of flight from 100 to 200 yards is 0.131 second. The drop from 0 to 100 yards is 2.71 inches; the total drop from 0 to 200 yards is 11.424 inches, or ~4.2 times as much.

I’m sure you’re aware of all that and didn’t get into those details, but not everyone is.

As already mentioned here a couple of times, the best way to know the specifics of a particular bullet’s trajectory is to explore different values with a ballistics calculator.

quote:

Originally posted by Puckpilot78:

quote:

Originally posted by Oat_Action_Man:
Mechanical offset: the fact that the sights are X height above the bore, causing POI to be lower than POA at close distances.

Holdover: how you correct offset at close range by aiming higher by the factor of your mechanical offset.

There is some range at which you no longer need to compensate for offset. How does one determine what range that will be, short of experimentally shooting at various distances (which I can't do)?

Knowing a rifle's zero (50 yards), what range do I no longer need to hold over to account for offset? At 25 you'll be ~1" low because of your zero, not offset. At 5, you'll be ~2.5" low because of your offset.

I estimate holdover no longer really matters between 15 and 20 yards, based on experience from a class, but that shooting was all done off-hand and I would like a more precise answer, since I can't do it experimentally (from a bench or prone).

Not to be obtuse, but I don't think you understand bullet trajectory and zero. Because the barrel is lower than the sights you will always have to holdover inside of your zeroed range, no matter what that range is.

When you say holdover no longer matters between 15 and 20 yards, what is the context? If you're simply trying to hit a human size target at that range then an inch or two of offset is negligible. If you're trying to make a precision shot then you need to know exactly where the bullet is going to hit so you can adjust your aim.

You also have to understand that because of the offset you can zero at different ranges which changes the bullet trajectory. With an AR for example: with a 25 yard zero the bullet will start 2.5 inches low at the muzzle and rise to point of aim at 25yd. It will continue to rise above point of aim to somewhere beyond 100 yards where it will start to fall until it intersects point of aim again around 300 yards then continue to fall below point of aim.

If you zero at 50 yards the result is similar, the bullet hits low until 50 yards, then will be above point of aim after 50yd then intersects point of aim around 200 yards as it falls.

Lastly if you zero at 100 yards the bullet hits low until 100 yards which is its peak, then will be low beyond 100yd as it continues to fall.

Bottom line you have to know your zero and how your bullets travel at that zero so you can shoot accurately at any range.

No, I understand it just fine. I also know my zero. I know my ammo too, since I loaded it and chronographed it.

I've used precise terminology in my posts, and "context" doesn't matter: it's a mathematical question. The only thing I could have been more precise about is defining what I consider a "negligible" difference.

At zero yards, you will have ~2.5" difference in POA vs POI because of offset. As you move backwards toward your zero point, that difference approaches zero.

Thanks, Fritz. That's what I needed: "yes, there is an equation, but have this ballistic calculator do it for you", and thanks also for the name of the program.