First, bullets don’t travel in perfect straight lines, they travel in arcs. With that in might, most guns have adjustable sights. That means you can zero in your sights (or whatever kind of optics you have) for any desired distance. In other words, the sights are calibrated such that, at a specific known range, the point of aim of the sight and the point of impact of the bullet are the same. You can make this happen for any distance. [This image might help you visualize how it works](https://qph.fs.quoracdn.net/main-qimg-7063a9e532843a244371b562bacb0211-lq). Most optics also let you adjust left and right as well to compensate for wind and at extremely long distances, Coriolis effects.
When someone is aiming a gun (assuming iron sights) they are taking a back sight and lining it up with the front sight to create a straight line, ill call this the “sight line”. Where ever you point the sight line is, obviously, where you’re aiming.
However, the sight line and the barrel of the gun are not parallel. Typically, the barrel will be angled a bit higher than the sight line. Meaning if the sight line is parallel to the ground, then the barrel will be pointing up just a little bit.
Now before you go out and start shooting things, what you’re supposed to do is “sight” the gun at a certain range, often this range is 50 or 100 feet, though it can be much more or less, depends on the weapon and user, for now I’ll assume a 100 foot sight though. What this means is that the barrel is angled up relative to to the sightline in such a way that when you shoot at a target that is 100ft away (assuming Perfect accuracy, no wind, etc) you will hit the exact spot where you had your sights on.
However, let’s say you have your gun sighted at 100 feet but you’re shooting at something much further or closer. For example, say your target is now 500 feet away. Now when you shoot, at the target. Because the target is so much further away, the bullet will have more time to fall because of gravity, this means that you will hit the target lower than where you were aiming. The opposite effect is true as well. If your gun is sighted to 100 feet and you’re shooting at a target that’s 10 feet away, you will hit much higher than where you were aiming, because the bullet didn’t have as much time to fall before hitting the target.
Again, the reason these effects happen is because the barrel is angled up slightly with respect to the sight line, i.e. they are not parallel. When you sight the gun you’re essentially choosing how much this angle is. If you sight your gun for really distant targets, like 500 feet, then the angle between the sight line and the barrel of the gun will be a lot bigger. If you sight the gun for really close targets, like 10 feet, then you would make the angle much smaller (at 10 feet it would be pretty close to parallel).
Most modern weapons (even plenty of older ones) have multiple different sight range settings on them. This made it easy to switch how far your gun was sighted depending on the distance to your target. Is your target 500ft away? Switch to the 500ft sight. Is your target 50ft away? Switch to the 50ft sight. This made it (and still makes it) much easier to aim at targets at various distances. That said, if your gun doesn’t have a way to adjust the sights, then you need to compensate manually. If your target is really far away, then you’ll just have to aim high.
You zero.
A bullet follows an arced path because of gravity. If you shoot it parallel to the ground, it will just arc downwards. But we mount a scope 5 cm above the center line of the barrel. Then we shoot at a target say 100m away. We adjust the scope until the bullets hit at the center of the crosshairs on the scope, but what this really means is we’re aiming the gun upwards a little bit to meet that point.
So now the bullet has a different trajectory. It goes upwards (because we’re aiming a little up) until will hit exactly what the scope is aiming at, at 100m.
What about the rest of the distances? They make calculators for that. Based on the scope height, bullet velocity, size, and aerodynamics, it will tell you exactly how high or low the bullet will be at any one distance.
But overall, I sight my varmint rifle at 100m (actually yards). I know that my bullet will hit a little low at anything under that. But I never shoot closer than 50, so I’m only worried about being low by maybe 1-2 centimeters if I shoot right at the crosshairs. That’s good enough for my purposes, but I can aim a centimeter low if I want. I know my bullet will be higher from about 100-200 yards, so I know to aim down a touch if I go out that far. Now if I were shooting out to 400 yards or more, I would have to be very careful about my range and adjust accordingly because the bullet is dropping rather quickly at that point, so my range estimation being short by say 50 meters can mean the bullet will hit several centimeters below where I wanted it to and I’d probably hit the ground in front of my target.
At this point the scope height doesn’t mean much because the bullet is introducing far more of an elevation change.
But if you’re doing very careful target shooting, you know all of the bullet heights at distances above, and you adjust your scope up or down accordingly. You may even have a scope that has that bullet’s path effectively programmed into it (electronic or just the markings calibrated for that bullet), so all you have to do is set distance.
And sometimes you need sights far above the barrel because you’re shooting a slow bullet at long range, which means lots of drop, so you need to tilt the barrel way up. For very low sights, this would mean the barrel is obscuring the target. So you make [really tall sights like this](https://www.theboxotruth.com/wp-content/uploads/2014/05/e14-1.jpg). The rear sight has a sliding aperture. It goes up and down depending on the range, which means you’ll have a different tilt to the rifle to put it on target. Ranges are marked into the bar it’s sitting on based on a specific bullet used. The photo above has it set to a fairly short distance.
That kind of thing was pretty easy for military rifles because everyone was using the same issued bullet. So they just etched the markings into the sights according to the arc of that one bullet.
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