(Cant in a short
range handgun is not considered a problem, so this is about rifles.)
Cant is the tilting or rotation of a
rifle about its long axis. Canting the rifle differently from shot to shot
varies the point of impact of the bullet on the target. Rotating the rifle
to the right moves the impact point to the right and down; rotating the
rifle to the left moves the impact point to the left and down.
Bob Fitzgerald is one of the better and
more reliable offhand shooters in the Old Colony Sportsman’s Association,
and he holds the rifle at a substantial cant angle. Cant doesn’t bother
his shooting because he holds the rifle at the same angle for each shot.
The most important thing to know about
cant is that if the rifle is positioned the same for each shot, then there
is no change of the impact point of the bullet from shot to shot.
More precisely, cant is the rotation of
the rifle about the axis going through the sights and the center of the
target. The shooter will keep the sights aligned with the center of the
target, and canting will rotate the rifle about the line going through the
sights and to the target. As the rifle is rotated the impact point of the
bullet moves in a circle of radius = drop of the bullet and center
at the zero cant impact point - drop. Let’s say that the drop is 6”
over some range, and you have zeroed the rifle with no cant. Canting the
rifle moves the bullet through a circle of 6” radius, and the center of
the circle is 6” below the beginning, zero cant impact point.
Let R = radius and C = the cant angle
in degrees, then horizontal deflection of the impact point = R Sin C and
vertical deflection = -R-(R Cos C.)
The movement of the impact point is a
function of the bullet drop and the angle of cant.
For any cant angle up to 10 degrees or
so, the amount of vertical shift is a small fraction of the horizontal
shift, and can be ignored for most applications.
Drop is a function of muzzle velocity
and the Ballistic Coefficient (BC) of the bullet, and is easily estimated
on a personal computer using one of the ballistics programs that are
readily available.
A plain base cast bullet has a typical
BC of .4, and is fired at around 1400 feet per second (f/s.) That bullet
will drop 9.5” in 100 yards and 1449” in 1000 yards.
Canting the rifle to the right, for
example, moves the impact point to the right and down thus:
|
Cant (degrees) |
100 yd |
100 yd |
1000 yd |
1000 yd |
| |
right” |
down” |
right” |
down” |
|
1 |
.166 |
.001 |
25.3 |
.221 |
|
2 |
.332 |
.006 |
50.6 |
.883 |
|
3 |
.497 |
.013 |
75.8 |
1.986 |
|
4 |
'663 |
.023 |
101.1 |
3.530 |
A typical .30 caliber jacketed bullet
might have a BC of .5 and muzzle velocity of 2700 f/s. That bullet will
drop 2.5” at 100 yards and 414 inches at 1000 yards.
Canting the rifle to the right, for
example, moves the impact point to the right and down thus:
From the charts it is clear that the
downward or vertical shift in the impact point is a small fraction of the
horizontal shift, and that the horizontal shift varies directly with the
cant angle.
|
Cant
|
100 yd |
100 yd |
1000 yd |
1000 yd |
|
(degrees) |
right" |
down" |
right" |
down" |
|
1 |
.044 |
.000 |
7.2 |
.063 |
|
2 |
.087 |
.002 |
14.5 |
.252 |
|
3 |
.131 |
.003 |
21.7 |
.568 |
|
4 |
.174 |
.006 |
28.9 |
1.009 |
See above, 1 degree gets .044”, 2
degrees gets .087” which is twice .044”(forgetting rounding errors,) and
so on. The horizontal shift at 5 degrees is 5 times the 1 degree shift.
Then forgetting the relatively small
vertical shift, the horizontal shift resulting from canting the rifle 1
degree is simply a function of the bullet drop, thus:
|
Drop" |
1 |
2 |
4 |
8 |
16 |
32 |
64 |
128 |
256 |
512 |
1024 |
|
Hor Shift |
.017 |
.035 |
.070 |
.140 |
.279 |
.558 |
1.12 |
2.23 |
4.47 |
8.94 |
17.9 |
Estimating the horizontal shift for any
cant angle and any drop is done by interpolating and multiplying.
The horizontal shift caused by canting
a rifle 3 degrees when the drop is 432 inches is estimated so:
to interpolate: 4.47”+((432”/256”) X
4.47”) = 7.5” = 1 degree cant horizontal shift then multiply: 7.5” X 3 =
22.5” = 3 degree cant horizontal shift.
Can't we estimate Level?
I made a rig to test people’s ability
to estimate level. A 3 foot metal ruler, a screw/nut/washer, a big piece
of cardboard and some figuring gave me a calibrated measuring apparatus. I
set the rig up so that when the ruler touched the mark numbered 15, the
ruler was level. I asked people to tell me to move the ruler up and down
until they thought it was level, and then wrote the reading down. With 45
measurements the average was 14.67 and the standard deviation was .387.
What this tells us is that people can estimate level pretty well. They
were about 1/3 of a degree off on average (15-14.67), maybe because of the
design of the test rig. The standard deviation was just under 4/10 of a
degree, meaning that 68% of the time accuracy is +/- .4 degree, 95% of the
time accuracy is +/- .8 degree, and 99% of the time accuracy is +/- 1.2
degrees.
My impression is that with a more
precise and better designed apparatus, and with practice, the variation
would be reduced-people are probably able to estimate level better than
the results indicate.
Measuring cant
I set up to measure cant using two
rifles, a Maynard #16 1882 and a C. Sharps M1885, with iron sights on both
and a scope on the Sharps. A piece of plastic pipe, a nail, a bottle with
a big envelope held on with a rubber band, a bench rest and some trig and
we were off. It is setups like this that cause my wife to call one of the
kids and talk a long time.
|
Maynard, 20 tests, looking at a
blank piece of white paper. |
|
Standard Deviation
|
.73 degrees |
|
|
Max Left Deviation |
.86 degrees |
|
|
Max Right Deviation |
1.52 degrees |
|
|
Sharps 1875, 21 tests, Iron
sights, looking at gray sky. |
|
Standard
Deviation |
.41 degrees |
|
|
Max Left
Deviation |
.93 degrees |
|
|
Max Right
Deviation |
.69 degrees |
|
|
Sharps 1875, 20 tests, 30X STS,
looking at gray sky
|
|
Standard Deviation |
.30 degrees |
|
|
Max Left Deviation |
.39 degrees |
|
|
Max Right Deviation |
.61 degrees |
|
The human eyeball can repeat level
pretty well. Most of the time to within +/- one degree. And a flat or
straight surface at the front sight aids that repeatability.
Concusions
Canting the rifle doesn’t matter as
long as you do it the same for every shot.
Most of the time most people can tell
what's level and repeat holding the rifle level so that cant doesn't
matter much in the overall error equation.
For bench shooters, anti-cant devices
solve the problem(if there is one.)
Black Powder long range and silhouette
shooters love their spirit level front sights and believe that they can
eliminate cant and increase accuracy using these sights. God bless them.