Ballista

Guides · Long-range effects

Rifle Cant: What 2, 5 and 10 Degrees of Tilt Cost at Distance

Two degrees of tilt puts a 6.5 Creedmoor a foot right at 1,000 yards and barely moves it down. Why cant misses sideways, and why the sine rule of thumb comes up short.

Tilt a 6.5 Creedmoor 2° at 1,000 yards with the come-up dialed, and the bullet lands 12.5 inches to the side and 0.2 inches low. On a 12-inch plate that sideways miss alone puts you off the steel. The same rifle at 10° misses by 62 inches sideways and only 5.4 inches low. Cant is a sideways problem, and its size is set by how much elevation you have on the turret.

A tilted rifle points its come-up sideways

When you dial elevation, you tilt the bore up relative to the line of sight along the rifle’s own vertical axis. If the rifle is level, that axis is true vertical and all of the come-up lifts the bullet. If the rifle is rotated by an angle, the come-up still goes along the rifle’s axis, which now leans. Gravity doesn’t care about the rifle; it still pulls straight down.

A dialed come-up on a canted rifle The come-up points along the rifle's vertical axis. When the rifle is tilted, that axis leans away from true vertical, so the come-up splits into a large vertical part, cos of the cant, and a sideways part, sin of the cant. true vertical rifle's vertical axis cant come-up you dialed come-up × cos(cant) nearly all of it still works come-up × sin(cant): the sideways miss
Cant splits the come-up into a vertical part and a sideways part. The angle is drawn larger than life so the parts are visible.

The part that still works vertically is the come-up times cos(cant). The part that goes sideways is the come-up times sin(cant). For small angles these are very unequal: sin 5° is 0.087 and 1 − cos 5° is 0.004, about 23 times smaller. So the bullet moves sideways by roughly 9% of the come-up and drops by less than half a percent of it. Tilt the rifle clockwise, top to the right, and the shot goes right and low. Tilt it counterclockwise and it goes left and low.

Holding over in the reticle instead of dialing doesn’t escape this. The hold point sits on the reticle’s vertical stem, and the stem is tilted with the rifle.

What 2°, 5° and 10° cost

We solved each rifle with the exact come-up for each distance, then rotated the rifle and solved again. The difference is the cost of cant alone.

Miss from cant alone, inches right / inches low, with the exact come-up dialed. Rifle tilted clockwise; tilt it the other way and the sideways miss goes left.
Range, yd6.5: 2°6.5: 5°6.5: 10°.308: 2°.308: 5°.308: 10°
3000.8 / 0.02.1 / 0.14.1 / 0.40.9 / 0.02.3 / 0.14.7 / 0.4
5002.5 / 0.06.2 / 0.312.4 / 1.12.9 / 0.17.3 / 0.314.6 / 1.3
7005.3 / 0.113.3 / 0.626.5 / 2.36.5 / 0.116.2 / 0.732.4 / 2.8
8007.3 / 0.118.1 / 0.836.2 / 3.29.1 / 0.222.7 / 1.045.2 / 4.0
1,00012.5 / 0.231.2 / 1.462.1 / 5.416.5 / 0.341.2 / 1.882.1 / 7.2
Sideways miss from cant with the come-up dialedInches right for the 6.5 Creedmoor canted 2, 5 and 10 degrees, 300 to 1,000 yards, and the sine rule of thumb at 5 degrees. 0 20 40 60 0 200 400 600 800 1,000 Range, yd Sideways miss, in 6.5 at 10° 6.5 at 5° 5°, sin × come-up 6.5 at 2°
The sideways miss grows with the come-up, so it climbs steeply with range. The dashed line is the common rule of thumb at 5°, which runs short of the full solution at every range.

Three things stand out.

The sideways miss grows like the come-up. Cant doesn’t add its own error; it redirects part of the elevation you dialed. The 6.5 needs 2.93 mil at 500 yd and 8.85 mil at 1,000, and the 5° miss grows from 6.2 to 31.2 in.

The vertical miss is small until the angle is large. At 5° and 1,000 yd the 6.5 lands 1.4 in low, well inside the plate. Only at 10° does the vertical part reach 5.4 in.

The flatter cartridge is more forgiving, for the same reason. The .308 needs more elevation at every distance, so the same tilt costs more: 16.5 in at 2° and 1,000 yd against 12.5 for the 6.5.

Cant at your zero distance hardly matters

If you shoot a canted rifle at 100 yd with nothing dialed, the only angle that gets redirected is the small one between the bore and the scope that your zero built in. For the 6.5 that’s 1.13 mil. Hold the same 5° cant with the 100 yd zero and the bullet moves 0.9 in sideways at 300 yd and 3.4 in at 1,000, against 31.2 in once the come-up is dialed.

This is why a shooter can zero with a habitual tilt, group well at 100 yd, and only discover the problem at distance. It’s also why the same habit shows up as a “wind” miss that always goes the same way.

The sine rule of thumb, checked

The standard rule is: sideways miss = sin(cant) × come-up. Converted to inches with the come-up in mil, that’s sin(cant) × come-up × 0.036 × range in yards. It has the right physics and the wrong come-up. The rule uses the elevation you dialed above your zero, but the rifle redirects the full angle between bore and line of sight, including the part your zero already contains.

6.5 Creedmoor canted 5°. The zero angle of this rifle with its 100 yd zero is 1.13 MIL.
Range, ydCome-up, MILsin 5° × come-up, insin 5° × (come-up + zero angle), inEngine, inEngine above simple rule
3001.221.22.22.180%
4002.042.64.03.850%
5002.934.66.46.235%
6003.927.49.59.427%
7004.9911.013.413.321%
8006.1615.518.318.117%
9007.4421.024.224.114%
1,0008.8527.831.331.212%

At 1,000 yd the full solution is 12% larger than the simple rule. At 300 yd, where the dialed come-up is about the same size as the zero angle, it’s 80% larger. Add the zero angle to the come-up and the rule lands within 0.3 in of the full solution for both rifles at every distance and angle in this article. The zero angle is the tilt between bore and line of sight that your zero sets. With a normal scope height and a 100 yd zero it’s a little over 1 mil: 1.13 mil (3.9 MOA) for the 6.5 and 1.24 mil for the .308.

A version you can do in your head: each degree of cant moves the shot sideways by about 1.75% of the come-up plus the zero angle. At 700 yd the 6.5 needs 5.0 mil; add 1.1 and you have 6.1 mil, so 5° costs about 0.53 mil, or 13.5 in. The engine gives 13.3 in.

Keeping the rifle level

  1. Fit a bubble level to the scope or rail and check it against the reticle, not just against the rifle. A level that’s square to the rail but not to the reticle tells you nothing useful.
  2. Check the reticle against true vertical. Hang a plumb line at 100 yd, level the rifle on its bubble and see whether the vertical stem lies along the line.
  3. Look at the bubble after the come-up is on. Cant costs almost nothing at the zero and grows with every mil you dial, so the bubble matters most on the long shots.
  4. Treat a miss that repeats on one side as a level problem first. Wind changes; a habitual tilt doesn’t. At 2° and 600 yd the 6.5 moves 3.7 in, so small errors only start to count past mid-range.

Sources

  • Robert L. McCoy, Modern Exterior Ballistics, Schiffer Publishing, 1999. Point-mass trajectory with the sight line and bore in three dimensions.
  • Every number in this article: Ballista engine (BallistaCore point-mass solver), inputs in the box above. The exact come-up is modeled by zeroing at the target distance, which matches the dialed come-up to within 0.009 MOA. See how we compute.