Why cant matters to holdover shooters (Super basic)

This will be super obvious to 99% of the people here, but I wanted to put my thoughts out there for the 1% that maybe haven't thought this all the way through.

First let's define what we are talking about with cant. Cant is where you twist the gun a little bit. Sometimes you can have scope cant, where the scope is not mounted level to the bore or other types of alignment issues. That's just setup nuts and bolts. The end result is what we are going to discuss. So let's assume we have a scope that is perpendicular to the bore.

Let's say that we have the gun and scope zeroed at 25 yards.

Now picture two long rods. Rod A is perfectly straight and we are going to stick it straight through the crosshairs of the scope and into the bullseye at 25 yards. Rod A is our point of aim, or the path of our eyeball.

Our second rod, Rod B has an arc. The shape of the arc will vary depending on the gun, but for this illustration let's say that Rod B is 50 yards long and gradually ramps up an inch and a half to about 20 yards, then ramps down from about 30 yards to 50 yards where it is about 2 inches down. Rod B is our point of impact, or the path of the pellet.

This is the important part, so I'm going to say it again. Rod A is 50 yards long and dead straight. Rod B is 50 yards long and droops at the ends, an inch and a half at the front and 2 inches at the back.

OK, so Rod A is sticking through the middle of our scope. Now we are going to stick Rod B into the barrel of the gun. Rod A and Rod B will meet exactly at the bullseye at 25 yards. This is what it means to be zeroed, every thing is lined up.

Now let's look at our 50 yard target. Rod A is still sticking into the center of the bullseye because we didn't touch anything on the scope. Rod B is now hitting the target 2 inches below the bullseye. If we want to change the elevation turrets on the scope at this point, this will cause Rod A to move down until Rod A and Rod B meet. Then we can tilt the gun up until the two rods are centered on the bullseye. So changing the scope basically re-zeroed the gun at 50 yards. So now let's twist the gun about 10 degrees. The two rods are still meeting at 50 yards on the bullseye, even though the arc of Rod B is no longer perpendicular. ( I know that this isn't 100% accurate, but we are keeping things simple here).

But we are shooting holdover, so we aren't going to change the scope elevation. What we are going to do is tilt the gun so that Rod A is 2 inches above the bullseye at 50 yards. Now Rod B is in the center of the bullseye.

Now let's give the gun that 10 degree twist (cant). We'll say we are twisting to the right, so about 12:02 on a clock face (that may not be exactly 10 degrees, but close enough for this). Because we are pivoting around Rod A (the point of aim), Rod B will now be to the left of the bullseye. The bigger the difference between point of aim and point of impact (the distance between Rod A and Rod B at the target), and the more cant (or further from perpendicular) introduced, the further left or right Rod B (the pellet) will be from the bullseye.

That's why it is important, especially for holdover shooters, to make sure that everything is perpendicular to the ground. We do that by getting the crosshairs aligned to the bore, making sure that the crosshairs are level (scope level) and using the scope level when firing a shot. Getting the scope set up correctly and using the scope level on every shot can remove left and right from the equation (until you start dealing with wind).

Like I said, very basic and not useful to 99% of the people here, but hopefully there is someone new that will get an "A ha" moment from this. The main thing I wanted to illustrate is that the dots on a mildot scope are there to help you move the crosshairs away from the bullseye, but the point of aim is still the crosshairs, not the dots. As soon as you start getting away from the zero range of your pellet, the point of impact and the point of aim are not the same and you have to make sure that they are in the same vertical plane.
 
What...EXACTLY...determines the bullet/pellets flight path ?

With the given weapon exactly straight up and down, the projectile raises X amount as it leave the barrel and takes a downward path from then on.

Now, With the weapon rotated to 10°, does the projectile have the same flight path as it did when the weapon was vertical, or with it's new position at 10° over ?

WHY ?

Someone with a high speed camera can verify this, whichever way the final fact ends up.

Mike
 
Because we are pivoting around Rod A (the point of aim)

HHmmm. IDK. To me, it would seem as though the Line Of Bore is what the system pivots around.


Line of sight is the "pivot" we can relate to. LOS is what we see and what we direct the bore with. Bore follows LOS. All changes (zero, MOA rails, etc.) simply change the relationship between LOS and bore but we see the LOS, not the bore. 
 
What...EXACTLY...determines the bullet/pellets flight path ?

With the given weapon exactly straight up and down, the projectile raises X amount as it leave the barrel and takes a downward path from then on.

Now, With the weapon rotated to 10°, does the projectile have the same flight path as it did when the weapon was vertical, or with it's new position at 10° over ?

WHY ?

Someone with a high speed camera can verify this, whichever way the final fact ends up.

Mike

Depends on how you define "flight path". The projectile will still have the same arc through space but that arc will be in a different relationship to the LOS if canted. Meaning you aim one place but now hit another.
 
Mike (MikeVV), owing to gravity & physics I don't believe that a 10 degree cant will translate to a 10 degree difference @ POI. Gravity pulls straight down, it doesn't cant with the rifle. If it did the POI would be that 10 degrees in the direction of the can't but since it DOESN'T there's a different formula at play. The formula is outside my area of expertise but I do have a grasp of physics. 
 
The amount of error is directly proportional to the drop.

The horizontal error X is [drop x sinØ]
The vertical error Y is [drop x (1-cosØ)]

Yes I realize that isn't the Greek Theta but close enough hopefully.

For the typical shallow cant angles one is likely to introduce, the error will be mostly on the horizontal. Nearly negligible vertical error. Play with Perry Babin's animated tool to get a feel for it. http://www.arld1.com/targetplottrajectory3.html
 
Mike (MikeVV), owing to gravity & physics I don't believe that a 10 degree cant will translate to a 10 degree difference @ POI. Gravity pulls straight down, it doesn't cant with the rifle. If it did the POI would be that 10 degrees in the direction of the can't but since it DOESN'T there's a different formula at play. The formula is outside my area of expertise but I do have a grasp of physics.

Well, I passed high school physics (on my third try), which is why I didn't speculate as to the amount of horizontal drift caused by a 10 degree cant. I simply said that there would be some movement horizontally, and the more cant the more movement. I think we can all agree with that without resorting to calculators. (I struggle to spell calculator. Bill Nye, I ain't.)

For my purposes of KISS, I was more interested in showing that there is horizontal movement that is related to cant, and why it's there, and why it's bad and should be avoided. 

But thanks for weighing in, I appreciate having smarter people check my work. Most of my good brain cells went away years ago, and the ones I have left don't always speak to me.
 
Here's what I'm thinking. Are we saying the same thing? 

Green line is the projectile path in canted system. The red line is true vertical. LOB aligns with vertical cross-hair of scope. The projectile follows the LOB which is the same as the vertical cross-hair until it reaches trajectory apex. In most sight in cases, this will be 1-2 Mil(MOA) above scope cross-hair's dead-center. After apex, the projectile falls with gravity and is not in line with the scope reticle. The green "triangle" should probably be more "parabolic", but for illustration purposes does this make sense?

AGN-ScopeCantExplanation.1608508092.png

 
Kind of, except when you cant the gun, the cross hairs aren't moving away from the POA. The little circle where the lines originate should be two circles about 1.5 to 2 inches apart. The green line and the red line aren't coming from the same place. If you scooted the left hand picture over so that the cross hairs are on the red line, but leave the green line alone, that would be more accurate if I'm looking at this correctly.
 
The small circle is the bore. LOB alignes withg the scope reticle.

The red line just represents true vertical and the direction of gravity. 

In either picture, the target would be behind the cross-hair or Mil hold-off.

The green line in the left image represents the projectile path when the airgun is canted. it follows LOB, which is aligned to the scope reticle until it reached the apex of the trajectory, then falls with gravity.

There is no green line in the right image, because the system is aligned to true vertical, so true vertical is the projectile path.