CANT , and it's effect ?

[nervoustrig]

Thanks for the sketch. It illustrates the concept quite well I think. Just one caveat. To match the diagram better to our hypothetical scenario, the dotted lines (lines of sight) would need converge to a common point different from the actual POI. Our POI wouldn't match the 3 points of aim because we've introduced cant error by laying the gun onto its side. However since all the points of aim are the same, the amount by which we missed the target is identical for all 3 scopes...which affirms that scope height does not affect the error.

That will be the outcome any time POA matches the intended POI. That is, any time we are using mildots as aim points, or if we are dialing the turrets. Not so if using an improvised holdover technique with a simple crosshair reticle (aiming over the target so the pellet drops into the target).

 

[Michigander]

Here's another thought experiment. Consider two rifles, one with sights 1.5" above bore, and another with sights 2.5" above bore. The target (POA) is at 10 yards. We fit the bores with lasers. The aiming axis and bore axis are initially parallel. The laser dot will appear below the target by 1.5" and 2.5" respectively. We now tilt the bore up to bring the laser dot on target. The rifle with the higher aiming axis will require more angle to do so.

With the bore axis only adjusted to compensate for the difference in sight height, and the laser still in the bore, we now spin the rifles around the aiming axis and observe that the laser dot remains stuck on the target for both rifles.

Now we tilt the bore up further to compensate for the drop, say 0.5". This angular shift will be the same for both rifles. Now we spin the rifles around their aiming axes again and observe that both rifles project the dot 0.5" left at 90 degrees CCW rotation. Only the angle needed to compensate for drop contributes to the lateral error, and that portion of the total angle was the same for both rifles.

So whoever has been campaigning for no difference in cant effect related to a difference in sight height appears to be correct. Morning coffee brings clarity.

 

[nervoustrig]

I just want to say thanks to everyone who has contributed to this thread. Perhaps more so to those who challenged the position I took because it has given me reason to think of other ways to explain it, which in turn brings me greater clarity. Good stuff. 

 

[bandg]

...
Now consider an extreme cant of 90 degrees CCW. The rifle has been rotated around the aiming axis. The bore and aiming axis are now in the same horizontal plane, with no elevation compensation and the pellet will hit low by the amount of drop at the target distance....

You got that part right. The vertical equation as it relates to drop and gun cant angle:

vertical error = drop x (1-cos(cant_angle))

...But the bore is now pointed to the left of the aiming axis, and the pellet will hit left by an amount determined by the angle between aiming and bore axes. Since the magnitude of the angle is related to the amount of separation between the axes, the rifle having the greater separation of axes will hit further left.

You got that part wrong. The once vertical compensation for the drop distance is now horizontal, so it will hit left an amount that is equal to the drop. The gun does not care where the viewing angle/position is, so the sight height or angle is not part of the equation. The horizontal equation as it relates to drop and gun cant angle:

horizontal error = drop x sin(cant_angle)

For your the 90 degree example above, sin(90) = 1, and cos(90) = 0.

Your 90 degrees is a fairly extreme example but it does show the point well. The equations works equally well for any angle from vertical.

http://www.scoplevel.com/

"The once vertical compensation for the drop distance is now horizontal, so it will hit left an amount that is equal to the drop."

Wow. It absolutely amazes me that someone could state this. The first half of your sentence is correct. By laying the gun on it's side, the vertical compensation (which is by definition the convergence angle established by scope height) IS now horizontal. It is EXACTLY that convergence angle that has been moved to the horizontal, and ONLY that convergence angle function. Gravity doesn't somehow magically follow the movement of the gun and all of a sudden begin acting in the horizontal plane. Gravity always works ONLY in the vertical plane. You assume that gravity somehow "follows" the movement of the gun. It does not. It is independent of the gun. Gravity's effect works ONLY in the vertical plane. But the ANGLE established by scope height DOES follow the gun. And when the gun is laid on it's side (canted) that ANGLE is what determines how far "left" it will hit, not gravity. In that "laid on it's side" position, gravity will ONLY determine how much BELOW the now horizontal bore line it will "hit". And gravity (or "drop") will have absolutely positively NO impact on how far left it will "hit".

I believe I now understand why you cannot grasp this. You are unable to disconnect gravity (which always works only in a perfectly vertical dimension) from the "vertical compensation" (which can be vertical, horizontal, any point in between, or even upside down). IF (and only IF) one is shooting with the gun held in the VERTICAL PLANE does gravity function in DIRECT LINEAR CONNECTION with the "vertical compensation", which is by definition the ANGLE. When you lay the gun on it's side, gravity does not turn off. But NEITHER does it shift its direction of function. Gravity's function remains in the vertical plane. BUT BUT BUT when you lay the gun on it's side, THE ANGLE does change it's direction of function. By EXACTLY 90 degrees. The ANGLE was functioning in the vertical plane when upright but it has been "laid over" to function in the horizontal. Gravity doesn't somehow know to "follow" that movement. You must be able to view the two relevant factors (GRAVITY and ANGLE) independently.

Try to imagine shooting at a target with the gun in the vertical plane (NOT CANTED), with scope above bore but also inverted with scope below bore. Is the OBSERVED DROP the same? NO. NO. NO. In the first case, the "vertical correction" is working linearly with but opposed to gravity. In the second case the "vertical correction" is still present but is inverted and is still working linearly with but now synergistically with gravity. From the point of aim, the drop would be different for the two situations. GRAVITY would have the same effect in each case (it is a constant) but the ANGLE is 180 degrees different (it is a variable).

In "more normal" shooting, where a few degrees of inadvertant cant may be introduced while shooting and nothing as extreme as the above needs to be illustrated, GRAVITY remains a constant and ANGLE remains a variable. When you cant a gun some small amount, as might happen in error for any shooter, gravity has exactly the same OVERALL EFFECT (it is and always will be a constant and it is fixed in direction-the vertical plane) but the OBSERVED EFFECT (the amount AND direction of miss) is determined by that constant (gravity) modified by the variable (CANT) . GRAVITY will always effect the result by the same exact amount and in the same exact direction OVERALL because it is a constant. The FINAL OBSERVED EFFECT (impact point, cant error, or whatever we want to call it) will be determined by that CONSTANT effect (gravity) combined with the VARIABLE (angle).

Michigander has this exactly correct. You have it exactly incorrect.

 

[Scotchmo]

...
Now consider an extreme cant of 90 degrees CCW. The rifle has been rotated around the aiming axis. The bore and aiming axis are now in the same horizontal plane, with no elevation compensation and the pellet will hit low by the amount of drop at the target distance....

You got that part right. The vertical equation as it relates to drop and gun cant angle:

vertical error = drop x (1-cos(cant_angle))

...But the bore is now pointed to the left of the aiming axis, and the pellet will hit left by an amount determined by the angle between aiming and bore axes. Since the magnitude of the angle is related to the amount of separation between the axes, the rifle having the greater separation of axes will hit further left.

You got that part wrong. The once vertical compensation for the drop distance is now horizontal, so it will hit left an amount that is equal to the drop. The gun does not care where the viewing angle/position is, so the sight height or angle is not part of the equation. The horizontal equation as it relates to drop and gun cant angle:

horizontal error = drop x sin(cant_angle)

For your the 90 degree example above, sin(90) = 1, and cos(90) = 0.

Your 90 degrees is a fairly extreme example but it does show the point well. The equations works equally well for any angle from vertical.

http://www.scoplevel.com/

"The once vertical compensation for the drop distance is now horizontal, so it will hit left an amount that is equal to the drop."

Wow. It absolutely amazes me that someone could state this. The first half of your sentence is correct. By laying the gun on it's side, the vertical compensation (which is by definition the convergence angle established by scope height) IS now horizontal. It is EXACTLY that convergence angle that has been moved to the horizontal, and ONLY that convergence angle function. Gravity doesn't somehow magically follow the movement of the gun and all of a sudden begin acting in the horizontal plane. Gravity always works ONLY in the vertical plane. You assume that gravity somehow "follows" the movement of the gun. It does not. It is independent of the gun. Gravity's effect works ONLY in the vertical plane. But the ANGLE established by scope height DOES follow the gun. And when the gun is laid on it's side (canted) that ANGLE is what determines how far "left" it will hit, not gravity. In that "laid on it's side" position, gravity will ONLY determine how much BELOW the now horizontal bore line it will "hit". And gravity (or "drop") will have absolutely positively NO impact on how far left it will "hit".

I believe I now understand why you cannot grasp this. You are unable to disconnect gravity (which always works only in a perfectly vertical dimension) from the "vertical compensation" (which can be vertical, horizontal, any point in between, or even upside down). IF (and only IF) one is shooting with the gun held in the VERTICAL PLANE does gravity function in DIRECT LINEAR CONNECTION with the "vertical compensation", which is by definition the ANGLE. When you lay the gun on it's side, gravity does not turn off. But NEITHER does it shift its direction of function. Gravity's function remains in the vertical plane. BUT BUT BUT when you lay the gun on it's side, THE ANGLE does change it's direction of function. By EXACTLY 90 degrees. The ANGLE was functioning in the vertical plane when upright but it has been "laid over" to function in the horizontal. Gravity doesn't somehow know to "follow" that movement. You must be able to view the two relevant factors (GRAVITY and ANGLE) independently.

Try to imagine shooting at a target with the gun in the vertical plane (NOT CANTED), with scope above bore but also inverted with scope below bore. Is the OBSERVED DROP the same? NO. NO. NO. In the first case, the "vertical correction" is working linearly with but opposed to gravity. In the second case the "vertical correction" is still present but is inverted and is still working linearly with but now synergistically with gravity. From the point of aim, the drop would be different for the two situations. GRAVITY would have the same effect in each case (it is a constant) but the ANGLE is 180 degrees different (it is a variable).

In "more normal" shooting, where a few degrees of inadvertant cant may be introduced while shooting and nothing as extreme as the above needs to be illustrated, GRAVITY remains a constant and ANGLE remains a variable. When you cant a gun some small amount, as might happen in error for any shooter, gravity has exactly the same OVERALL EFFECT (it is and always will be a constant and it is fixed in direction-the vertical plane) but the OBSERVED EFFECT (the amount AND direction of miss) is determined by that constant (gravity) modified by the variable (CANT) . GRAVITY will always effect the result by the same exact amount and in the same exact direction OVERALL because it is a constant. The FINAL OBSERVED EFFECT (impact point, cant error, or whatever we want to call it) will be determined by that CONSTANT effect (gravity) combined with the VARIABLE (angle).

Michigander has this exactly correct. You have it exactly incorrect.

The gravity vector never changes. I know that. It's obvious. That is separate from the gun.



On a correctly held gun, there is a trajectory plane that is also vertical. The sight plane (same plane as established by the vertical reticle and the bore-line) is also in the same plane. The gravity vector lies in that plane when there is no gun cant. When you cant the gun, the gravity vector no longer lies in that plane. The gravity vector did not change, the canted gun is what changed.



When a shooter inadvertently cants the gun, their "vertical" is determined by the gun, not the gravity vector.



"...GRAVITY will always effect the result by the same exact amount and in the same exact direction OVERALL because it is a constant. The FINAL OBSERVED EFFECT (impact point, cant error, or whatever we want to call it) will be determined by that CONSTANT effect (gravity) combined with the VARIABLE (angle). ..."



What you said there is certainly true. It's drop (gravity) combined with the angle. That determines the gun cant error.

 

[bandg]

Vertical is vertical. Vertical and gravity do not change because one makes a canting error. Vertical and gravity do not know where the gun is and they don't care. Until one grasps that, one does not understand the process. 

You stated "the gravity vector never changes. I know that. It's obvious. That is separate from the gun". 

Then you state "the once vertical compensation for the drop distance is now horizontal, so it will hit left an amount equal to the drop". NO. NADA. NOPE. This is patently false and illustrates a lack of understanding of the process. The first half of that quoted sentence is plainly obvious to anyone looking with open eyes. The second half of that sentence is simply false. The DROP is caused by gravity. ONLY by gravity. GRAVITY does not realize that the gun has been moved. Gravity wouldn't care if it did realize because gravity only works in the vertical. So how can any projectile move LATERALLY in relation to GRAVITY in this scenario? It cannot. In this illustration the ONLY thing determing "how far left it hits" is the convergence angle. Gravity, which causes "drop" has nothing to do with this illustration.

Go back to Michiganders gun on it's side. 90 degree canted. A shot from that will hit left of the aim point. And it will hit low of the aim point. But the determinant of how much left it hits is the "compensation angle" that you note, which is now 100% horizontal. Used to be vertical until the shooter canted, then it became horizontal. THAT and ONLY THAT determines lateral movement. And with the gun canted 90 degrees on its side as described, the bore IS pointing off to the left as noted but it is HORIZONTAL. Gravity would not care if it were pointed north, south, east, or west. So the ONLY THING determining DROP is GRAVITY, which is still contentedly hanging around doing it's thing IN THE VERTICAL. So your statement that "it will hit left an amount equal to drop" is simply and plainly incorrect. And as long as you adher to such a view, you do not understand.

 

[Scotchmo]

... So your statement that "it will hit left an amount equal to drop" is simply and plainly incorrect. And as long as you adhered to such a view, you do not understand.

With an uncanted gun, the barrel points slightly upward to compensate for drop. When you cant the gun 90 degrees to the left, the barrel now points slightly left, so that is where the poi will now be.

This picture has the barrel pointing to the right, but same affect. Windage error = drop distance:

I think we are making progress, as scope height is no longer part of the discussion. It's now about drop (gravity) and cant angle. And that is what determines gun cant errors.

 

[bandg]

The trajectory will be the same whether the scope is mounted high or low. All agree. So again, let us oversimplify:

Sorry, we don't all agree.

 

[lbc_PSI]

Late to the party, but here's some thought on shooting system cant...


Some things we all need to agree on.

A trajectory does not curve left or right. It falls in a single plane that is determined by the start direction and launch angle of the projectile. For airguns the single plane is determined by Line Of Bore(LOB).

A trajectory is not static. It's shape is determined, in part, by the projectile launch angle.

Everything in the shooting system is relative to the trajectory of the projectile, not the Line Of Sight(LOS). The LOS is not the center of the shooting system, the trajectory is.

The LOB determines the launch angle and direction the projectile takes and what shape the trajectory will have.

A projectile begins falling with gravity immediately upon leaving the bore.

Still with me?

The LOS provided by the scope center is fixed above the LOB and can be set to intersect the trajectory in either one or two places. One point, if system is zeroed to the apex. Two points, if the system has a near and far zero. The MIL/MOA hold-offs will only be useful aim points if the vertical reticle is centered over the LOB and is perpendicular to LOB and gravity.

If the LOS is centered above LOB and the scope vertical reticle aligns with the force of gravity..IE shooting system has zero cant..then the scope can be "clicked" vertically to change the zero for distances out to the adjustment range of the scope. The MIL/MOA holdovers will also be accurate.

Good so far?

When the shooting system is canted, you've essentially changed the direction and angle the LOB is pointing relative to the LOS.

In a canted system your Point Of Impact(POI) will always be below Point OF Aim(POA).

In a canted system aiming with the center of the cross-hair and MIL/MOA hash hold under will result in the largest errors.

Using a MIL/MOA hash hold-over will result in a lesser error because the hash aim point is further down the reticle and closer to true vertical.

When the shooting system is canted, a higher scope will result in the cross-hair aiming point being tilted further from true vertical. The angle between LOB and LOS increases with height, so there has to be a spacial difference between POA and POI. Is it minimal? IDK, but there has to be a difference.

System cant errors will be more obvious at longer ranges for the same reason rifle MOA changes with distance.

When the shooting system is canted, projectiles will impact opposite the cant relative to the scope LOS up to the first zero sight-in distance. After LOS is reached, projectiles will impact in the direction of cant.

The cant induced POI relative to sight-in distance is easy to prove. Go into your garage and attach a target to something your projectile won't penetrate. Step back 3-5 yards. Cant the shooting system left 45 degrees. Center the cross-hairs on the target. Shoot. The projectile will hit low and right of center. The distance of the miss will be approximately the scope height. For any distance past the single or near zero, a miss in the direction of cant will result.

The assertion that cant does not effect POI when you're sighted in for a specific distance, is false. When you cant the system, the LOS no longer intersects the trajectory. The LOB points in the direction of cant and the LOB has a lower angle relative to the vertical sight-in LOB. In a canted system, LOS/POA is above the trajectory. This results in a POI below the POA.

So why do folks insist that they can click to a distance and system cant does not matter?

I'm going to propose a hypothesis. It could appear that system cant is not a factor because of rifle MOA and shooter MOA. How good a shooter you are and how accurate your airgun is can play a part. Think how MOA and dispersion work to form a cone. You have an airgun capable of 1MOA accuracy..your airgun is only capable of 0.5" groups at 50yds from the bench. You as a shooter have 1MOA of possible shooter induced error. At 50yds your system MOA is now 2MOA, so groups could be up to 1.0". Since your accuracy dispersion is 1", it could appear that clicking to distances and canting the system works, when actually it's just sorta close..with impacts biasing low..and within the rifle/shooter MOA error cone.

 

[Scotchmo]

...
The assertion that cant does not effect POI when you're sighted in for a specific distance, is false. ...

...

So why do folks insist that they can click to a distance and system cant does not matter?

...

"...The assertion that cant does not effect POI when you're sighted in for a specific distance, is false."

Well, scope cant does not matter if you are sighted in for a specific distance. Gun cant does matter.

"...So why do folks insist that they can click to a distance and system cant does not matter?..."

If by system cant, you are including gun cant, which "folks" insisted that? Show me the post.

 

[lbc_PSI]

Yes agreed. A scope not properly set up can be "on" at either one or two exact distances.

The gun and the sight/scope are a system. They both cant together. Even a scope that is not aligned to the LOB and gravity can be canted as part of the system.

This link.. http://www.szottesfold.co.uk/2012/03/high-scope-and-canting-end-of-ancient.html

 

[bandg]

If you have a scope that is set up "canted" while the gun is level and the shooter then "cants" while taking a shot, in the VAST majority of possible cant angles the shooter could introduce, BOTH will then be canted. If the "system" was then "canted" to level the scope, then the gun would be off level.

If you have a gun that is set up "canted" while the scope is level and the shooter then "cants" while taking a shot, int the VAST majority of possible cant angles the shooter could introduce, BOTH will then be canted. If the "system" was then "canted" to level the gun, then the scope would be off level.

 

[Scotchmo]

Yes agreed. A scope not properly set up can be "on" at either one or two exact distances.

The gun and the sight/scope are a system. They both cant together. Even a scope that is not aligned to the LOB and gravity can be canted as part of the system.

This link.. http://www.szottesfold.co.uk/2012/03/high-scope-and-canting-end-of-ancient.html

I did not read through the entire treatise, but I agree with the math to determine the gun cant errors, and the conclusions:

From the link:

The choice of variable names are different, but the equations are the same as I have posted.

Ex = horizontal_error

Ey = vertical_error

A = cant_angle

D = drop

horizontal_error = drop x sin(cant_angle)

vertical_error = drop x (1-cos(cant_angle))

 

[Michigander]

Yikes! Equations! I decided to perform a real world experiment to confirm (at least in part) the assumption that pellet impact will always be below the bore line by an amount equal to the drop at a given distance. The visual aid is imagining a laser beam projected through the bore. The pellet should always hit below that projected dot by the drop amount.

I conducted my experiment at 35 yards. For my rifle the elapsed time to cover that distance is 0.141 second, and the drop is calculated to be 3.82". I first sighted in at 35 yards. The implication is that the bore must be pointed above the target by 3.82". If I fit a laser to the bore it would project a dot 3.82" above the target. If I rotate the rifle 90 degrees around the aiming axis, the dot would be projected 3.82" left or right of the target. But no matter what the orientation, the pellet should always strike that 3.82" below the bore line or laser dot.

The prediction then is that for 90 degrees CCW rotation the pellet will strike 3.82" left and 3.82" below the target. For 90 degrees CW, the pellet should strike right and low by the same amounts. Let's see what happened.

Well not quite the 3.82" predicted, but pretty darn close. And the vertical and horizontal deviations are very similar. My take is that the actual drop is probably closer to 3.7". I believe this result to be consistent with the notion that pellet impact will always be below the bore line (laser dot) by the amount of drop at the target distance.

I am sort of busy right now, but if I can find time the next experiment will attempt to recreate the scenario of the bore line converging with the aiming axis, again at 35 yards. The expectation this time is that the pellet will strike below the target by the drop amount regardless of orientation. This is expected because rotation will have no effect on that convergence. Our laser dot will always be centered on the target, and the pellet should always land 3.82" (approximately) lower. 

 

[bandg]

"I am sort of busy right now, but if I can find time the next experiment will attempt to recreate the scenario of the bore line converging with the aiming axis, again at 35 yards."

I'm having a hard time making any sense of this. I see holes in the paper so I assume you actually did some shooting. But if "next time" you are going to attempt to recreate the scenario of the bore line converging with the aiming axis, then what exactly were you aiming with "this time" and where were you aiming it? Any sight (open, optic, or laser) would have to be "off" the bore some given distance and if "sighted in" (the term you used) it would already have a convergence angle.

 

[Michigander]

I used my Harrier with a scope offset from the bore axis by 1.76". I just replicated the typical shooting scenario, aiming at the upper circle with the vertical crosshair parallel to the vertical line on the paper, and adjusting elevation and windage until pellets hit the center of that upper circle. The upper circle was the only aimpoint used during the experiment.

Because I could estimate the drop at 35 yards from previous data, I reasoned the bore was actually pointing 3.82" above the aimpoint when zeroed at 35 yards. That is what drop is, the distance the pellet travels below the bore line at any point downrange. If the pellets are striking at the aimpoint, the bore line must be above the aimpoint by the drop distance.

The next step was to produce groups with the rifle rotated 90 degrees CCW and CW, while still aiming at the upper circle. For these groups the normally horizontal crosshair was parallel to the vertical line on the paper. The fact that these groups were displaced about 3.7" left and right is consistent with the bore line being offset from the aimpoint by the drop distance at any amount of rotation (cant). When the rifle is vertical, the bore line is above the aimpoint, when rotated 90 degrees it is left or right of the aimpoint. The fact that these groups were also 3.7" below the aimpoint is consistent with the the belief that the pellet will always strike below the bore line by the drop distance. I suppose I shouldn't have circled these groups, but they were never used as aiming points. I just circled the groups after they had been shot to help indicate the center of the groups and make measurements easier.

The point of all this is to show that once you have zeroed your vertically held rifle at any distance, the bore line has to be above the aimpoint by the drop distance. Otherwise the pellets would not be striking the aimpoint. And when you rotate the rifle around the aiming axis, the bore line is still offset from the aimpoint by the same drop distance. If you did this with a laser in the bore you would see the laser dot trace a circle with a radius equal to the drop distance around the aimpoint.

Sorry to be so longwinded, I was trying to avoid it in the previous post.

 

[bandg]

I used my Harrier with a scope offset from the bore axis by 1.76". I just replicated the typical shooting scenario, aiming at the upper circle with the vertical crosshair parallel to the vertical line on the paper, and adjusting elevation and windage until pellets hit the center of that upper circle. The upper circle was the only aimpoint used during the experiment.

Because I could estimate the drop at 35 yards from previous data, I reasoned the bore was actually pointing 3.82" above the aimpoint when zeroed at 35 yards. That is what drop is, the distance the pellet travels below the bore line at any point downrange. If the pellets are striking at the aimpoint, the bore line must be above the aimpoint by the drop distance.

The next step was to produce groups with the rifle rotated 90 degrees CCW and CW, while still aiming at the upper circle. For these groups the normally horizontal crosshair was parallel to the vertical line on the paper. The fact that these groups were displaced about 3.7" left and right is consistent with the bore line being offset from the aimpoint by the drop distance at any amount of rotation (cant). When the rifle is vertical, the bore line is above the aimpoint, when rotated 90 degrees it is left or right of the aimpoint. The fact that these groups were also 3.7" below the aimpoint is consistent with the the belief that the pellet will always strike below the bore line by the drop distance. I suppose I shouldn't have circled these groups, but they were never used as aiming points. I just circled the groups after they had been shot to help indicate the center of the groups and make measurements easier.

The point of all this is to show that once you have zeroed your vertically held rifle at any distance, the bore line has to be above the aimpoint by the drop distance. Otherwise the pellets would not be striking the aimpoint. And when you rotate the rifle around the aiming axis, the bore line is still offset from the aimpoint by the same drop distance. If you did this with a laser in the bore you would see the laser dot trace a circle with a radius equal to the drop distance around the aimpoint.

Sorry to be so longwinded, I was trying to avoid it in the previous post.

OK. YOU ALREADY HAD THE CONVERGENCE ANGLE. You said before-"the next experiment will attempt to recreate the scenario of the bore line converging with the aiming axis, again at 35 yards." You don't need to do another experiment. You already had the "convergence angle" (which is the bore line converging with the aiming axis) by sighting in at 35 yards with a Harrier and a scope height of 1.76". That setup as described SETS a convergence angle.

Also, your physical paper shows a drop of 3.82" below the TARGET. But you yourself state the bore is pointed 3.82" ABOVE THAT TARGET. The drop could not be 3.82". In what you describe, the "drop" would be 7.64". What gives?

 

[bandg]

To Scotchmo-I really want to get this resolved. So I would like to have a bit of specificity in exactly what is being stated. I will try to do the same.

The quote directly below is your response to the original Michigander post which I also put below that.

"The once vertical compensation for the drop distance is now horizontal, so it will hit left an amount that is equal to the drop.

Michigander

Accuracy: 

Member

"Way too technical a discussion for me. But with regard to rifle cant, I think it helps to have a mental picture of what is going on.

Consider a rifle with an aiming axis and a bore axis separated by some distance. If parallel, a pellet will strike below the aiming axis by an amount equal to the separation between the axes, plus the drop at the target distance. You can bring the pellet strike onto the aiming axis by tilting the bore axis up by an amount needed to compensate for the separation plus drop. The greater the separation, the larger the angle between the bore and aiming axis.

Now consider an extreme cant of 90 degrees CCW. The rifle has been rotated around the aiming axis. The bore and aiming axis are now in the same horizontal plane, with no elevation compensation and the pellet will hit low by the amount of drop at the target distance. But the bore is now pointed to the left of the aiming axis, and the pellet will hit left by an amount determined by the angle between aiming and bore axes. Since the magnitude of the angle is related to the amount of separation between the axes, the rifle having the greater separation of axes will hit further left.

Effects at intermediate amounts of rifle cant are of course intermediate."

Two questions for scotchmo-

1)MIchigander did not specify a distance for his illustration. Would you specify what distance you were considering in light of your response, please. And would you say that using 10 yards as the distance for illustration purposes (and for actual shooting for that purpose) would produce accurate results? If not 10 yards then please give a distance that would produce accurate results.

2)Would you specify what you mean by "drop". Specifically, are you referring to amount of drop from bore line or amount of drop from aiming axis (sight line or LOS)

 

[Michigander]

Maybe this will help. At no time during the experiment did the bore line converge with the aimpoint at the target. It was always offset by the drop amount of approximately 3.82". To create this scenario I simply zeroed with the rifle vertical as usual, then rotated 90 degrees while keeping the crosshairs centered on the aimpoint.

 

[bandg]

Now I believe I see what you are saying you did. Tell me if I have this correct. You first "aimed" at the very top red circle and fired a shot to see where it would hit (impact point circled and labelled "zero") and then you measured from the top red circle to the "zero" circle to quantify your "drop" which you note as 3.82". Then you drew the central circle (labelled aimpoint) around that impact point and used that point as the "aim" point to cant around. Do I have that correct?