Physics of shooting a rifle

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tangolima

New member
Digging another hole.

I zeroed a rifle at 100yd. Still had several rounds left, I decided to shoot the soda can on the berm at 150yd. Expecting poi lower than POA, I held 1" above the can. To my surprise, it hit where I aimed, about 1" above the can or even a little higher.

Huh! How does it work? I haven't seen anything like that.

The rifle was an AR-15 in 5.56 NATO.

-TL

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stagpanther

New member
Can't say; though it's possible that some user error is introduced by using inherently higher mounted optic on AR's; the difference between line of bore and line of sight will tend to magnify errors. The two points at which the line of sight and trajectory intersect may also change somewhat (try shooting 9mm AR zeroed at 50 yds at longer distances with high scope mount to really boggle your mind :) )
 
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tangolima

New member
It is actually result of sight height and MV. The projectile needs flight distance before its trajectory apex reaches the line of sight.

Assuming ideal case in vacuum.

h is the sight height;
L is the distance;
V is MV;
Vv is the vertical upward component of MV;
t is TOF for the projectile reaches the apex;
g is the gravitational acceleration.

Vv^2 = 2*g*h
t = Vv/g = sqrt(2*h/g)
L=V*t=V*sqrt(2*h/g)

High MV and sight height require longer distance for zero to be on descending slope of the parabolic trajectory. Before that zero must be on ascending slope.

For AR, V=3000fps, h=2.5"

L= 340'=114yd,

so 100yd zero must be on ascending slope (funky).

For other my rem 700 in 30-06, V=2500fps, h=1.5"

L=220'=73yd

so 100yd zero has to be on descending slope (normal).

One may have noticed that AR zeroing carries way more confusion than other designs. That's related to this.

-TL

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stagpanther

New member
It really shouldn't create that much confusion--just a recognition the line of sight is slightly higher from the bore and the consequences of that. The differences in POI between high and low mounted scopes should be slight at the ranges you're talking about--though like with any trajectory the further out the bullet goes the more a slight difference can be exaggerated into a major POI offset. I find the only situation where I really need to be concerned about a high scope is if I take a quick snap shot at very close range closer than the zero distance.
 
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tangolima

New member
The major confusion indeed comes from shooting at close distance; 25yd, 10yd, or even 7yd, where certain tactical trainings are practicing. In order to hit exactly where you aim, you need to adjust the elevation UP instead of down. Then there are those endless debates on which zeroing is better; 25/400, 50/200 etc.

I get that part. But I didn't expect such mechanism still holds out 100yd. High sight height and high MV makes it happen.

At longer distance it becomes no issue. Some even claim high sight height works better for extreme long range shooting. I don't really think so. But that's another rabbit hole.

-TL

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stagpanther

New member
The bullet trajectory, muzzle velocity etc. is pretty much irrelevant--it's going to stay the same (barring significant differences in external ballistics elements) regardless of where your optic is. You should be able to easily calculate the differences due to scope height and zero distance on a ballistics calculator. Your scope height and zero are somewhat arbitrary settings the user chooses. A hunter, for example, might (I would, anyway) choose a zero distance that gives them as wide a point-blank range as possible unless they are certain of the likely shot distance (what I would do with my 44mag lever gun in the thick woods of Maine).
 
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Unclenick

Staff
What changes with sight height is not the trajectory from muzzle to target, but where the sight line height matches the trajectory height. If the sight is zeroed to strike the point of aim ("Navy" hold rather than 6:00 hold for iron sights and coincident rather than offset POA with optics), in that case the higher the sight is above the bore line, the further from the firing point the trajectory will cross the height of the line of sight (or meet it, if the target is struck right at the apogee of the trajectory).

Above, I refer to crossing the height of the sight line rather than to crossing the sight line itself it because spin drift or wind correction will see to it that the two are not exactly in the same horizontal position when the trajectory crosses on the rise prior to crossing the sight line at the target.
 
M

MarkCO

New member
Unclenick has it.

There is such a thing as a single zero and a double zero though. Some short range firearms (pistols for instance) can have sights that the zero is at one point, and before and after the trajectory is below that point. Most rifles use a double zero, where the bullet trajectory crosses the line of sight twice.
 
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tangolima

New member
Struck conversation with a hunter on range. He was zeroing his beautiful Tikka readying for a hunt. His longest shot to bag a deer was no more than 350yd. His opinion on "long range hunting"... Well let's not go there.

I asked whether he needed a level on his rifles. He never did. That made me rethink. I shoot soda can with .22lr rifle at 200yd. I always think the level helps. How much really? Here are a few figures to plug into equations.

Sight (scope) height above bore: 1.5”
Zero distance: 50yd (first crossing)
Elevation for 200yd: 32moa
Cant without level: +/-1 degree

-TL

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J

JohnKSa

Administrator
Should be interesting to contrast the result for the .22LR with the same calculation done for a much flatter shooting centerfire rifle.
 
J

Jim Watson

New member
As I was getting into BPCR, I shot a guy's .40-65. I hit 4 turkeys in a row, missed the fifth.
He said
"Took your eye off the level, didn't you?"
 
J

JohnKSa

Administrator
The cant misdirects some of the upward bore angle (required for the trajectory) to one side or the other. The more upward bore angle required (more for a 200yd .22LR shot than a 200yd .270 shot) the more effect the cant will have.

Imagine one gun that needs 50moa of upward bore angle to get the bullet to a distant target and one that needs only 10moa of upward bore angle (flatter shooting) to reach the same target. Now, let's go for maximum cant--turn them right on their side--90 degrees. One will put the bullet off to the side 50moa while the other will put it off to the side only 10moa. Same cant, different windage error. And, of course, both will go way low since when they are on their side, they don't have the upward angle necessary to arc the bullet to the target downrange.
 
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tangolima

New member
My .22lr has 1st crossing zero at 50yd. With sight height of 1.5”, assuming straight trajectory, the angle of launch is

1.5 / 0.5 = 3moa, fudging up to 4moa to account for curved trajectory.

I dialed elevation to 32moa for 200yd, the bullet drop is

2 * (4+32) = 72"

With the cant, the 72" has horizontal component of

72*sin(1)=1.3"

And vertical component of

72*cos(1)=71.99"

+/-1.3" is big deal for soda can, when there is no wind. With even light breeze, wind correction required could easily be an order of magnitude over.

Let's make up some numbers for our hunter friend, who tries to shoot a deer at 350yd with his rifle in .30-06.

Sight height: 1.5"
1st crossing zero: 25yd (for 100yd 2nd crossing zero)
Elevation for 350yd: 6moa

Launch angle for zero (no fudging up needed)

1.5/0.25=6moa

Bullet drop at 350yd

3.5*(6+6)=42"

Horizontal component

42*sin(1)=0.7"

That's why he didn't care about a level.

Some small pieces of side information.

TOF for the .22lr: 0.62s
TOF for the .30-06: 0.47s

-TL

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J

JohnKSa

Administrator
If you're asking generally why the bullet crosses the sight line twice:

The sight line is a straight line from the shooter's eye (through the scope) to the target. The bullet must follow a curved trajectory due to gravity.

The sight line is almost always above the bore in a conventional optics setup, so the bullet starts out below the sight line. So the bullet starts out its arc pointed upwards, hits its apex at some point downrange and then starts falling back down.

The most common way to sight in a rifle means that the bullet will cross the sight line on the way up, remain above it for the rest of the way to the zero range and then cross the sight line on the way back down at the zero range.

If you're asking specifically why a .30-06 bullet would cross the sight line at exactly 25 and 100 yards, I think those are just made up numbers that are in the very general ballpark. I think for a .30-06 with a 100yd zero, the first crossing of the sight line would happen closer to 50 yards than 25.
 
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