Physics of shooting a rifle

[stagpanther]

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.

[tangolima]

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]

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).

[Unclenick]

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.

[tangolima]

My thoughts exactly.

-TL

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[MarkCO]

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.

[tangolima]

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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[JohnKSa]

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

[Jim Watson]

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?"

[stagpanther]

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

I'm not sure what you mean here (?).

[JohnKSa]

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.

[stagpanther]

I see, thanks for that, I didn't know this was in reference to cant.

[tangolima]

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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[stagpanther]

1st crossing zero: 25yd (for 100yd 2nd crossing zero)

Once again I'm confused --the trajectory of the 30-06 crossing/tangent the line of sight at 25 yds and 100 yds?

[JohnKSa]

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.

[stagpanther]

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.

Yes--I couldn't get my mind around the flat 30-06 trajectory hitting line of sight at those 2 distances.

[MarkCO]

Originally Posted by JohnKSa

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.

With 180grain Silvertips, my .30-06 crosses at 52 yards and 100 yards.

[tangolima]

Yeah the 25/100yd was something I made up. If 50/100yd is correct, the launch angle for zero is adjusted to from 6moa to 4moa. The bullet drop at 350yd will be less, and error caused by canting will be even less.

I picked 25yd because I have seen hunters checking zero at 25yd at indoor range. They probably did that for "battle sighting" out to 250yd.

-TL

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[tangolima]

Sorta continuation / elaboration from other thread.

I have a 40-year old Rem 700 bdl in .30-06. A Redfield wide screen 3-9x scope is on it, with duplex reticle. Clearly it is setup for hunting. I zero it at 200yd so that it shoots point-blank (battle sight) up to 250yd. I tried to use it to shoot "long range" up to say 800yd. Of course not for hunting but for being silly.

What would you do to make this setup work for distance beyond 500yd? Dialing in is not practical with the closed coin-op turrets without clicks. Hold-over? The reticle has close to none reference.

Here is a vertical dope table I made up for sake of discussion

200yd 0moa
300yd 3moa
400yd 7moa
500yd 12moa
600yd 18moa
700yd 25moa
800yd 33moa

Here is piece of information that I think is important. The reticle's center to the thick post fills the width of a letter size paper at 100yd when I set the magnification to 8x.

-TL

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[mehavey]

coin-op turrets without clicks

From your listing of integral MOA chart, you won't/don't need clicks

thick post fills the width of a letter size paper at 100yd

Notwithstanding (what you describe as) an 8-minute post to calibrate known target
size against apparent range, what you will still need is a good rangefinder.

[tangolima]

Originally Posted by mehavey

From your listing of integral MOA chart, you won't/don't need clicks



Notwithstanding (what you describe as) an 8-minute post to calibrate known target

size against apparent range, what you will still need is a good rangefinder.

Maybe I didn't describe clearly. Let me use 500yd as example.

The target is at 500yd. I already know that. No need for a range finder. Elevation is 12moa. Dialing the turret is not practical, inconvenient at the least. There is no clicks and the marks have faded. I simply don't know how much to turn the "screw head". Besides I am sure I can go back zero precisely afterwards. I just don't want to fumble with it.

Hold-over is perhaps the only option left. But how do I hold 12moa with the duplex reticle?

-TL

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[stagpanther]

But how do I hold 12moa with the duplex reticle?

You give it a bouquet of flowers and say "sorry, it just wasn't meant to be" and buy a scope that has the elevation and subtensions you need.

I guess you could also correlate the MOA distance between posts @ a known distance and then mathematically derive for the distance hold over/under.

Or just buy a scope with the elevation and subtensions you need.

[tangolima]

Buying my way out of a problem? Never. I just lectured my boy about it. I can't eat my own words .

But seriously, I did buy a scope. But the rifle has been together with that Redfield for so long. I can't put myself to separate the old couple.

It is a SFP scope. The product of post subtension and magnification is a constant =8*8=64. I just adjust the magnification to have the subtension I need for the hold.

300yd, 3moa, 9x, hold midway to the post.
400yd, 7moa, 9x, hold to the post.
500yd, 12moa, 5x, hold to the post.
600yd, 18moa, 3.5x, hold to the post.
700yd, 25moa, 5x, hold double to the post.
800yd, 32moa, 4x, hold double to the post.

Decreasing magnification for longer distance is a bit backwards. Holding double, triple, or even quadruple, is a work around. It requires some reference points in the background, rock, tree branch, etc, or you just eyeball it. For example

800yd, 32moa, 8x, hold quadruple to post.

-TL

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[stagpanther]

Just make sure you log enough time behind the trigger to confirm the reality of the math.

[tangolima]

Originally Posted by stagpanther

Just make sure you log enough time behind the trigger to confirm the reality of the math.

That could be problematic. Where I am, it is quite expensive to shoot beyond 300yd.

-TL

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