Physics of shooting a rifle - canting.

[tangolima]

Say I cant my rifle to the left (anticlockwise) by 2 degree, which is quite noticeable with a level bubble. POI is expected to shift to the left. To make calculations easier, the time of flight at different distance is as follows.

100yd, 0.114s
300yd, 0.243s
500yd, 0.476s
800yd, 0.899s
1000yd, 1.23s

How much is the expected POI shift? Is there any vertical shift?

Some professional shooters claimed that they would purposely cant their rifles in strong cross wind. Is there any point doing that?

-TL

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[Double Naught Spy]

Some professional shooters claimed that they would purposely cant their rifles in strong cross wind. Is there any point doing that?

It is a different way to compensate for the wind. It is a difficult technique to master and has the potential to introduce other errors.

[EchoFalcon23]

A 2° cant (anticlockwise) means your barrel points slightly left of vertical by that angle, so yes, your POI will shift left.
To estimate lateral shift:
Lateral shift ≈ Range × tan(2°)
For example:

At 100 yd: 100 × tan(2°) ≈ 3.5 yd (or about 10.5 ft!) left

At 500 yd: 500 × tan(2°) ≈ 17.5 yd left
So, the POI shift grows linearly with distance — quite significant!
Vertically, because you’re tipping the rifle off vertical, there will be a slight vertical shift as well, but it’s less pronounced since you’re canting around the barrel’s axis horizontally. The bullet's vertical drop will also be affected by gravity independently.

[JohnKSa]

Is there any vertical shift?

The bore of a rifle is angled upwards with respect to the sight line. That upward angle is to "fight" the effects of gravity.

Without that upward angle, the bullet would always hit below the line of the bore.

Canting the rifle takes some of that upward angle and converts it to an angle in the horizontal plane. The obvious effect is that the horizontal component will cause the bullet impact to move in the direction of the cant.

The less obvious effect is that because some of the upward angle that was supposed to fight the effect of gravity is now doing something else (moving the bullet impact to the side), the bullet will now impact lower on the target.

[tangolima]

Falcon,

I'm afraid that's too much for a 2 degree cant. Your calculation seems to treat cant angle same as windage error of 120moa. The error is a lot less than that. I listed time of flight. The error is related to that. Think of the bullet drop, a small portion of it "spills" over to the horizon left direction because of the cant.

-TL

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[tangolima]

Originally Posted by JohnKSa

The bore of a rifle is angled upwards with respect to the sight line. That upward angle is to "fight" the effects of gravity.



Without that upward angle, the bullet would always hit below the line of the bore.



Canting the rifle takes some of that upward angle and converts it to an angle in the horizontal plane. The obvious effect is that the horizontal component will cause the bullet impact to move in the direction of the cant.



The less obvious effect is that because some of the upward angle that was supposed to fight the effect of gravity is now doing something else (moving the bullet impact to the side), the bullet will now impact lower on the target.

That's right. There is minor reduction in elevation, but so small that it can be neglected in practice except for a large cant of course.

-TL

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[tangolima]

Just looked it up. For a regular bubble level with 2" vial, the angle change for the bubble to roll from end to end is no more than 0.5 degree. 2 degree is very obvious with a level. Without a level it depends. It could still be quite noticeable though.

-TL

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[JohnKSa]

There is minor reduction in elevation, but so small that it can be neglected in practice except for a large cant of course.

The sine of the cant angle gives us the horizontal component change from perfectly level and sine changes relatively quickly near zero.

The cosine of the cant angle gives us the vertical component change from perfectly level and cosine changes quite slowly near zero.

For 2 degrees of cant, the vertical component change from perfectly level is about 57 times less than the horizontal component change.

[tangolima]

Ok here is the way I estimate the error.

imaging the barrel is horizontal (zero angle of departure), the bullet drop is

d=0.5*g*t^2

g=32.34 ft/s^2 is gravitational acceleration.

With cant angle phi, d is resolved into horizontal and vertical components

x=d*sin(phi)
y=d*cos(phi)

That causes error in poi, horizontally and vertically

Ex=x-0=d*sin(phi)
Ey=y-d=d*(cos(phi)-1)

Ey is negative indicating poi is always low.

Here is the result at different distance
yd, t, d, Ex, Ex, Ey, Ey

100yd, 0.114s, 2.52", 0.09" left, 0.01moa left, 0.002" low, 0moa low

300yd, 0.243s, 11.45", 0.4" left, 0.13moa left, 0.007" low, 0.001moa low

500yd, 0.476s, 43.96", 1.53" left, 0.31moa left, 0.026" low, 0.005moa low

800yd, 0.899s, 156.8", 5.47" left, 0.68moa left, 0.096" low, 0.012moa low

1000yd, 1.23s, 293.6", 10.25" left, 1.02moa left, 0.179" low, 0.018moa low

The vertical error is really nothing. The horizontal error grows with distance as expected. It becomes a concern when it goes beyond 500yd or flight time longer than 0.5s.

-TL

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[JohnKSa]

The vertical error is really nothing.

That's true for small angles, the kind that would happen unintentionally. If the cant starts approaching 45 degrees--probably it would have to be induced intentionally for some reason since that's so much cant it would be impossible for the shooter not to notice--then the vertical displacement can become large enough that it can't be ignored.

[tangolima]

Originally Posted by JohnKSa

That's true for small angles, the kind that would happen unintentionally. If the cant starts approaching 45 degrees--probably it would have to be induced intentionally for some reason since that's so much cant it would be impossible for the shooter not to notice--then the vertical displacement can become large enough that it can't be ignored.

Quite right. I should have said it was nothing with 2 degree cant even out to 1000yd. Intentional large cant degree is different story. That's one of the reasons I am not fan of correcting cross wind by canting. It is simply unnecessary, imprecise, and with "side effects".

For instance, it is pretty crazy trying to hit target at 1000yd in 30mph cross wind. It requires about 20moa correction. Simple mildot reticle has 8moa per dot. Holding 2 dots plus 4moa on the turret will do it. No need to eyeball a large cant for it.

-TL

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[FrankenMauser]

I can't give you hard numbers.
I haven't run them myself, and I am not going to for this discussion.
But I can tell you from experience that canting is a huge deal.
The horizontal aspect is massive, even if the vertical is negligible.

We (my club) are shooting a 300 yard challenge with .22 LR tomorrow.
8", 6", 4", and 2" targets.
Any cant is a real problem.

[tangolima]

Originally Posted by FrankenMauser

I can't give you hard numbers.

I haven't run them myself, and I am not going to for this discussion.

But I can tell you from experience that canting is a huge deal.

The horizontal aspect is massive, even if the vertical is negligible.



We (my club) are shooting a 300 yard challenge with .22 LR tomorrow.

8", 6", 4", and 2" targets.

Any cant is a real problem.

For .22lr it is, because its long flight time. For 2 degree cant, anything longer than 0.5s becomes a concern, which is about 200yd for .22lr. With bubble level installed, cant angle can be cut down quite a bit.

Having said that, for long range rim fire, wind can easily be the #1 trouble, ahead of canting.

-TL

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