In addition, I would like to see scotchmo address what you post here and whether he agrees with it.
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CANT , and it's effect ?
- Thread starter harrymoreland
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I agree. Not with your view on the subject but with what I gathered trying to understand Michiganders description of his PROCESS was incorrect. I believe I grasped his process description a bit later and I asked some very simple questions of both Michigander and scotchmo, questions to which I'm still awaiting the responses . You are still incorrect, as are the rest of the szottesfeld afficionados. I'll certainly address this EXACT issue once those responses are given.
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I'm a nice guy and I like to be inclusive, so I'm going to invite you to the party as well. Feel free to answer the simple question I addressed to scotchmo. Reread Michiganders last post containing his picture and diagram and state whether you do or do not fully agree with his conclusion. Simple yes or no will do.
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Yes, Michigander's results are what would be expected.
When the gun is rotated through a 360 degree cant circle (shown in blue), it will paint a circle of radius D(drop) about the aim point. A POI circle (shown in red) of the same radius will hit below the cant circle by an amount equal to drop.
Michigander only tested two cant angles (+90 and -90 degrees) and both had the expected POI errors. The drop was determined to be in the 3.6" to 3.8" range and that was the radius of the circles. I'll call it 3.65". I also showed where the POI would be if the gun was held with a 45 degree cant angle, and a 180 degree cant angle.
The calculated values for the 90 degree POI errors would be:
At +90, horizontal_error = 3.65" x sin(90) = 3.65", and vertical_error = 3.65" x (1-cos(90)) = 3.65"
At -90, horizontal_error = 3.65" x sin(-90) = -3.65", and vertical_error = 3.65" x (1-cos(-90)) = 3.65"
And that is about what he got.
For a -45 degree cant, it would be:
horizontal_error = 3.65" x sin(45) = -2.58", and vertical_error = 3.65" x (1-cos(45)) = 1.07"
For a 180 degree cant, it would be:
horizontal_error = 3.65" x sin(180) = 0", and vertical_error = 3.65" x (1-cos(180)) = 7.3"
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"The once vertical compensation (A1) for the drop distance is now horizontal (A2), so it will hit left (B2)an amount that is equal to the drop (3.65").
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No that is not what I did. When I started the experiment, the only things on the paper were the twin circles I call the aimpoint, and the vertical line below the aimpoint to use as an aid in establishing cant angles. I started by sighting in in the normal manner. The first shot went high and right, so I adjusted elevation and windage until I was satisfied that I was sighted in on the aimpoint. Then I laid the rifle on its left side, centered the crosshairs on the aimpoint and fired the left group. Next I laid the rifle on its right side, centered the crosshairs on the aimpoint and fired the right group. After firing all three groups, I circled the left and right groups and made measurements of how far left or right, and below they were with respect to the aimpoint.
The depiction of the bore line locations and path was a later addition. As you can see I had to tape an extra piece of cardboard to the top of my target to draw them in. None of this was present when I shot the groups. All groups were shot with the crosshairs centered on the aimpoint.
How did I know where to draw the bore line locations? I simply knew they had to be the drop distance above each group.
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One more contribution to help visualize the relationships between sight line, bore line, aimpoint and drop. This illustration is the exact situation with my rifle sighted in at 35 yards.
The yardage axis is compressed, but the vertical axis is to scale on 1/4" grid graph paper. As in real life, the pellet starts out 1.76" below the sight line, rises to a high of 0.30" at 25 yards, then intercepts the aimpoint at 35 yards. Along the entire length of the pellet trajectory the pellet drops steadily further and further below the bore line, until at 35 yards it lies 3.7" below the bore line.
Things to note:
The yardage axis is compressed, but the vertical axis is to scale on 1/4" grid graph paper. As in real life, the pellet starts out 1.76" below the sight line, rises to a high of 0.30" at 25 yards, then intercepts the aimpoint at 35 yards. Along the entire length of the pellet trajectory the pellet drops steadily further and further below the bore line, until at 35 yards it lies 3.7" below the bore line.
Things to note:
- The relationship (angle) between the bore line and sight line is mechanically fixed and does not change with cant angle. That is what makes it easy to predict the bore line location at any cant angle.
- At any distance, the bore line will always lie above the POI by an amount equal to the drop at that distance.
- At any distance, the POI will always lie below the bore line by an amount equal to the drop at that distance.
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Finally, there is the troubling question of why sight height is not needed to correctly predict cant behavior. We know that sight height definitely affects how much sight adjustment is needed to sight in at any distance. The higher the sight line the more barrel elevation will be needed to bring the POI onto the aimpoint.
The trick to understanding how this works is to break the sighting in process into two steps. The first step is to bring the bore line in line with the aimpoint. This first step is absolutely dependent on sight height. The higher the sights, the more barrel elevation will be required to bring the bore line onto the aimpoint. This is just a matter of simple geometry.
But, with the bore line aligned with the aimpoint, the pellets will be hitting below the bore line by the amount of drop at the target distance. So more correction is needed. In all cases, the barrel must be elevated to compensate for the drop. In my experiment, that additional elevation amounted to about 11.6 MOA. This additional elevation that fixes the location of the bore line above the aimpoint will always be the same, and is not dependent in the sight height.
The trick to understanding how this works is to break the sighting in process into two steps. The first step is to bring the bore line in line with the aimpoint. This first step is absolutely dependent on sight height. The higher the sights, the more barrel elevation will be required to bring the bore line onto the aimpoint. This is just a matter of simple geometry.
But, with the bore line aligned with the aimpoint, the pellets will be hitting below the bore line by the amount of drop at the target distance. So more correction is needed. In all cases, the barrel must be elevated to compensate for the drop. In my experiment, that additional elevation amounted to about 11.6 MOA. This additional elevation that fixes the location of the bore line above the aimpoint will always be the same, and is not dependent in the sight height.
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One more contribution to help visualize the relationships between sight line, bore line, aimpoint and drop. This illustration is the exact situation with my rifle sighted in at 35 yards.
The yardage axis is compressed, but the vertical axis is to scale on 1/4" grid graph paper. As in real life, the pellet starts out 1.76" below the sight axis, rises to a high of 0.30" at 25 yards, then intercepts the aimpoint at 35 yards. Along the entire length of the pellet trajectory the pellet drops steadily further and further below the bore line, until at 35 yards it lies 3.7" below the bore line.
Things to note:
- The relationship (angle) between the bore line and sight line is mechanically fixed and does not change with cant angle. That is what makes it easy to predict the bore line location at any cant angle.
- At any distance, the bore line will always lie above the POI by an amount equal to the drop at that distance.
- At any distance, the POI will always lie below the bore line by an amount equal to the drop at that distance.
"...As in real life, the pellet starts out 1.76" below the sight axis..."
You showed a level sight axis. For a level shot, the pellet starts at the muzzle which is level with the target. The sight axis is 1.76" above the level line and angles slightly downward toward the target. Unless the scope is really high in relation to the target distance (i.e., really close target and really high scope), it won't really matter, just more confusing in my opinion.
My shooting bench does not get lower when I add higher scope mounts. The scope just gets higher above the gun, and it's included angle gets greater.
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"...Now consider an extreme cant of 90 degrees CCW. The rifle has been rotated around the aiming axis. ..."
Is the aiming axis really the same as the gun cant axis? You can look at it that way but here is another way that I find easier to understand:
Canting the gun should not significantly change the gun/muzzle position. For these exercises we are considering the same level/horizontal shot. Only the gun cant angle changes. The cant axis remains horizontal and the gun cant plane remains parallel to the target plane. Don't try to imagine the gun being rotated about the scope axis, it might mess you up. If you do that, you will then need to reposition the gun in order to keep the muzzle level with the target. Imagine this - the muzzle stays in the same place when you cant the gun. So imagine that the cant axis is the vector running from the muzzle to the target. And if there is a scope, the scope tips slightly off to the right or left side depending on which direction that you are canting. Whether you are holding the gun or resting it on a bench, any cant will tip the scope about the gun cant axis. The sight-axis converges with the aim point at the target whether the gun is canted or not. No significant difference, just more real to life and easier to understand.
Keep the end of the muzzle level with the target and cant the gun.
"...MIchigander did not specify a distance for his illustration. Would you specify what distance you were considering in light of your response, please...."
35yds I believe is what he used.
"...Would you specify what you mean by "drop". Specifically, are you referring to amount of drop from bore line..."
Yes, from the bore-line.
"...or amount of drop from aiming axis (sight line or LOS)..."
That's not the drop, that would be the POI with respect to the zero. Drop has nothing to do with the LOS. Drop is determined by time of flight, and gravity.
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"That's not the drop, that would be the POI with respect to the zero. Drop has nothing to do with the LOS. Drop is determined by time of flight, and gravity."
In large part I view your quote above as mostly semantics and I bet a large percentage of people that shoot also view it that way. Which seems to sum up the entire issue. Some have a view based on one method of shooting and others have a view based on a different way of shooting. As another poster noted to me recently, there will probably be no agreement. Both methods can hit the target but they seem to be utilized predominant for generally different undertakings and maybe that is all that can be said.
I'll say the same thing that I've said before. I'll never agree with the generalized statement-"Scope height has no effect on cant error". Never. Because just one instance where such isn't the case negates such a generalized statement. I'm sure in your method (and that of those who agree with you) it is correct. But there are other methods where it isn't correct. And even Szottesfeld conceded such, although he stated that there was only the one specific method where such is true, the method that nervoustrigger also referred to recently (I can't remember the exact term he used but something like artificial holdover).
One final scenario for you to address. Consider a single rifle. A higher velocity accurate air rifle shooting a good BC pellet. Consider two different scopes mounted correctly on that rifle. The first a 2" scope zeroed for 20 yards. The second a 4" scope, also zeroed for 20 yards. When held vertically, both will hit center when aimed "correctly", meaning no "artificial holdover" and no mil-dot holdover. Just crosshairs on the center. Then cant both the same number of degrees relative to vertical. Can the higher mounted scope produce more horizontal lateral "miss"?
In large part I view your quote above as mostly semantics and I bet a large percentage of people that shoot also view it that way. Which seems to sum up the entire issue. Some have a view based on one method of shooting and others have a view based on a different way of shooting. As another poster noted to me recently, there will probably be no agreement. Both methods can hit the target but they seem to be utilized predominant for generally different undertakings and maybe that is all that can be said.
I'll say the same thing that I've said before. I'll never agree with the generalized statement-"Scope height has no effect on cant error". Never. Because just one instance where such isn't the case negates such a generalized statement. I'm sure in your method (and that of those who agree with you) it is correct. But there are other methods where it isn't correct. And even Szottesfeld conceded such, although he stated that there was only the one specific method where such is true, the method that nervoustrigger also referred to recently (I can't remember the exact term he used but something like artificial holdover).
One final scenario for you to address. Consider a single rifle. A higher velocity accurate air rifle shooting a good BC pellet. Consider two different scopes mounted correctly on that rifle. The first a 2" scope zeroed for 20 yards. The second a 4" scope, also zeroed for 20 yards. When held vertically, both will hit center when aimed "correctly", meaning no "artificial holdover" and no mil-dot holdover. Just crosshairs on the center. Then cant both the same number of degrees relative to vertical. Can the higher mounted scope produce more horizontal lateral "miss"?
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Scotchmo’s excellent description of the fact that scope high does NOT matter when it comes to gun cant. Scope high matters when it comes to first and second zero, but that is not what this thread is about.
The subject is; Does scope high effect gun cant? And bandg and nervoustrig - the answer is? (A simple yes or no will do)
The subject is; Does scope high effect gun cant? And bandg and nervoustrig - the answer is? (A simple yes or no will do)
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"scope high does NOT matter when it comes to gun cant. Scope high matters when it comes to first and second zero, but that is not what this thread is about."
Who decided it's "NOT what this thread about", and why? I'll wait for scotchmo to explain EXACTLY what would occur in THIS SPECIFIC shooting setup.
Who decided it's "NOT what this thread about", and why? I'll wait for scotchmo to explain EXACTLY what would occur in THIS SPECIFIC shooting setup.
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"...In large part I view your quote above as mostly semantics..."
When talking about external ballistics, "drop" is the common term for the affects of gravity on a projectile.
You can call it whatever you want, it won't change the result.
Can the higher mounted scope produce more horizontal lateral "miss"?
Short answer - No.
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"...In large part I view your quote above as mostly semantics..."
When talking about external ballistics, "drop" is the common term for the affects of gravity on a projectile.
You can call it whatever you want, it won't change the result.
Can the higher mounted scope produce more horizontal lateral "miss"?
Short answer - No.
I still say semantics, and yes I can call it what I want. As can each shooter who reads this. And above, you didn't say "drop from bore" or "drop from sight" you just said "for affects of gravity on a projectile". Drop from bore will ALWAYS be different than drop from LOS.
I like the deflection on the second part. "Short answer". I will wait for the long answer. I'll write the question again. With 2 different height scopes on the same rifle, zeroed at 20 yards (2 zero method) for each, will the higher mounted scope produce more horizontal cant error at it's far zero than the lower mounted scope will at it's far zero given the same amount of cant in degrees?
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When you sight in a shooting system at zero cant, the sight settings and the trajectory shape depends on the LOB being pointed with an upward elevation angle and the LOS intersecting the LOB and the trajectory. When you set up a system in this fashion, you can click vertically and LOS remains on the trajectory path. Shooting system means sight mounted in a fixed position to a gun, bow, etc.
The ability to click to any distance on a trajectory is only possible when LOS is aligned with LOB and the scope vertical reticle aligns to gravity and the LOB. In this scenario, LOB is pointed with an upward elevation angle and the LOS pointing downward intersecting the LOB. Up and down.
The LOS and LOB directional relationship is not altered with cant. Up and down becomes right and left or left and right.
When you cant the system, the LOB points in the direction of cant AND the LOS points in the opposite direction AND the LOB upward elevation angle decreases relative to LOS. When you cant from 0 to 90 degrees, the LOB goes from it's upward elevation angle down to 0 degrees. When you cant the system and change the LOB elevation angle, you create a new trajectory that is different from the zero cant trajectory. The more you cant, the closer the upward elevation angle gets to zero degrees.
When you cant the system, the projectile will always impact low in the direction of cant beginning at the sight zero distance and it will always hit low and opposite the direction of cant at distances less than the sight zero distance. If your system has a near and far zero, the sight zero distance for left and right deviation is the near zero. The amount of deviation before the sight zero depends a great deal sight height above LOB.
As soon as you change the trajectory shape by changing LOB elevation angle, the sight reference points..the center cross-hair, the MIL/MOA hash marks, your distance click table...are all invalid.
The "laid on it's side" 90 degree cant has an a LOB with a 0 degree upward elevation angle. In this position, the LOS will never be able intersect the trajectory. A 0 degree LOB has a trajectory that only drops. When you cant the system the LOS and LOB will still intersect, but the LOS will not intersect the trajectory. You cannot cant the shooting system and click to a known distance and be exactly "on". It is a mathematical impossibility.
The error in thinking "scope height does not matter" comes from the faulty logic used in the Szottesfeld writing. A different scope height creates a different LOS to LOB geometry. It assumes a scope height of 0.5" or 1.5" or 2.5" yield the same results because the example that is always used is a SINGLE common sight in distance..IE all different heights sighted to zero at say 40 yards. Of course scopes of different heights can be sighted in to hit exactly "on" at the same distance. That does not mean that different height scopes will have the same aim points for other distances.
Using a 875fps 18gr .22, I used ChairGun to model holdovers. I changed the scope height to see where the MIL/MOA hash marks lined up yardage-wise. With a 40 yard far zero, reticle center was the only distance the reticle hash marks agreed on yardages. 2.0" Scope Height(SH) yields 40 yards at reticle center, 1 MIL=58yds 2 MIL=73yds, 3 MIL=85yds, 4 MIL=97yds, 40-97=39clicks. 2.5" SH yields 40 yards at reticle center, 1 MIL=60yds 2 MIL=75, 3 MIL=88, 4 MIL=99, 40-99=39clicks. So a lower scope height yields MIL marks that are more compressed..which, in my simple mind tells, me a lower scope height is more forgiving when using MIL/MOA hold-overs and minimizes errors when you shoot estimated/un-ranged distances...like when hunting without a rangefinder. I mean heck..I've never left my rangefinder at home when going shooting. LOL.
If a different scope height yields different sight reference points for a shooting system with 0 cant, then a shooting system with a higher scope will yield greater POI changes when the system is canted.
The Szottesfeld document goes against everything I've personally experienced shooting airguns and competitive archery. I tried to read it with an open mind..but between the hard to follow diagrams, wording, and logic I ended up with migraine. Anytime something makes a claim of "debunking an ancient myth", I tend to view it with just a tiny bit of skepticism.
That said, FT shooters claim system cant and scope height does not affect their shooting. IDK. Maybe at the distances shot and the way they setup their choice of zero there is some error canceling going on.
The ability to click to any distance on a trajectory is only possible when LOS is aligned with LOB and the scope vertical reticle aligns to gravity and the LOB. In this scenario, LOB is pointed with an upward elevation angle and the LOS pointing downward intersecting the LOB. Up and down.
The LOS and LOB directional relationship is not altered with cant. Up and down becomes right and left or left and right.
When you cant the system, the LOB points in the direction of cant AND the LOS points in the opposite direction AND the LOB upward elevation angle decreases relative to LOS. When you cant from 0 to 90 degrees, the LOB goes from it's upward elevation angle down to 0 degrees. When you cant the system and change the LOB elevation angle, you create a new trajectory that is different from the zero cant trajectory. The more you cant, the closer the upward elevation angle gets to zero degrees.
When you cant the system, the projectile will always impact low in the direction of cant beginning at the sight zero distance and it will always hit low and opposite the direction of cant at distances less than the sight zero distance. If your system has a near and far zero, the sight zero distance for left and right deviation is the near zero. The amount of deviation before the sight zero depends a great deal sight height above LOB.
As soon as you change the trajectory shape by changing LOB elevation angle, the sight reference points..the center cross-hair, the MIL/MOA hash marks, your distance click table...are all invalid.
The "laid on it's side" 90 degree cant has an a LOB with a 0 degree upward elevation angle. In this position, the LOS will never be able intersect the trajectory. A 0 degree LOB has a trajectory that only drops. When you cant the system the LOS and LOB will still intersect, but the LOS will not intersect the trajectory. You cannot cant the shooting system and click to a known distance and be exactly "on". It is a mathematical impossibility.
The error in thinking "scope height does not matter" comes from the faulty logic used in the Szottesfeld writing. A different scope height creates a different LOS to LOB geometry. It assumes a scope height of 0.5" or 1.5" or 2.5" yield the same results because the example that is always used is a SINGLE common sight in distance..IE all different heights sighted to zero at say 40 yards. Of course scopes of different heights can be sighted in to hit exactly "on" at the same distance. That does not mean that different height scopes will have the same aim points for other distances.
Using a 875fps 18gr .22, I used ChairGun to model holdovers. I changed the scope height to see where the MIL/MOA hash marks lined up yardage-wise. With a 40 yard far zero, reticle center was the only distance the reticle hash marks agreed on yardages. 2.0" Scope Height(SH) yields 40 yards at reticle center, 1 MIL=58yds 2 MIL=73yds, 3 MIL=85yds, 4 MIL=97yds, 40-97=39clicks. 2.5" SH yields 40 yards at reticle center, 1 MIL=60yds 2 MIL=75, 3 MIL=88, 4 MIL=99, 40-99=39clicks. So a lower scope height yields MIL marks that are more compressed..which, in my simple mind tells, me a lower scope height is more forgiving when using MIL/MOA hold-overs and minimizes errors when you shoot estimated/un-ranged distances...like when hunting without a rangefinder. I mean heck..I've never left my rangefinder at home when going shooting. LOL.
If a different scope height yields different sight reference points for a shooting system with 0 cant, then a shooting system with a higher scope will yield greater POI changes when the system is canted.
The Szottesfeld document goes against everything I've personally experienced shooting airguns and competitive archery. I tried to read it with an open mind..but between the hard to follow diagrams, wording, and logic I ended up with migraine. Anytime something makes a claim of "debunking an ancient myth", I tend to view it with just a tiny bit of skepticism.
That said, FT shooters claim system cant and scope height does not affect their shooting. IDK. Maybe at the distances shot and the way they setup their choice of zero there is some error canceling going on.
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When you sight in a shooting system at zero cant, the sight settings and the trajectory shape depends on the LOB being pointed with an upward elevation angle and the LOS intersecting the LOB and the trajectory. When you set up a system in this fashion, you can click vertically and LOS remains on the trajectory path. Shooting system means sight mounted in a fixed position to a gun, bow, etc.
The ability to click to any distance on a trajectory is only possible when LOS is aligned with LOB and the scope vertical reticle aligns to gravity and the LOB. In this scenario, LOB is pointed with an upward elevation angle and the LOS pointing downward intersecting the LOB. Up and down.
The LOS and LOB directional relationship is not altered with cant. Up and down becomes right and left or left and right.
When you cant the system, the LOB points in the direction of cant AND the LOS points in the opposite direction AND the LOB upward elevation angle decreases relative to LOS. When you cant from 0 to 90 degrees, the LOB goes from it's upward elevation angle down to 0 degrees. When you cant the system and change the LOB elevation angle, you create a new trajectory that is different from the zero cant trajectory. The more you cant, the closer the upward elevation angle gets to zero degrees.
When you cant the system, the projectile will always impact low in the direction of cant beginning at the sight zero distance and it will always hit low and opposite the direction of cant at distances less than the sight zero distance. If your system has a near and far zero, the sight zero distance for left and right deviation is the near zero. The amount of deviation before the sight zero depends a great deal sight height above LOB.
As soon as you change the trajectory shape by changing LOB elevation angle, the sight reference points..the center cross-hair, the MIL/MOA hash marks, your distance click table...are all invalid.
The "laid on it's side" 90 degree cant has an a LOB with a 0 degree upward elevation angle. In this position, the LOS will never be able intersect the trajectory. A 0 degree LOB has a trajectory that only drops. When you cant the system the LOS and LOB will still intersect, but the LOS will not intersect the trajectory. You cannot cant the shooting system and click to a known distance and be exactly "on". It is a mathematical impossibility.
The error in thinking "scope height does not matter" comes from the faulty logic used in the Szottesfeld writing. A different scope height creates a different LOS to LOB geometry. It assumes a scope height of 0.5" or 1.5" or 2.5" yield the same results because the example that is always used is a SINGLE common sight in distance..IE all different heights sighted to zero at say 40 yards. Of course scopes of different heights can be sighted in to hit exactly "on" at the same distance. That does not mean that different height scopes will have the same aim points for other distances.
Using a 875fps 18gr .22, I used ChairGun to model holdovers. I changed the scope height to see where the MIL/MOA hash marks lined up yardage-wise. With a 40 yard far zero, reticle center was the only distance the reticle hash marks agreed on yardages. 2.0" Scope Height(SH) yields 40 yards at reticle center, 1 MIL=58yds 2 MIL=73yds, 3 MIL=85yds, 4 MIL=97yds, 40-97=39clicks. 2.5" SH yields 40 yards at reticle center, 1 MIL=60yds 2 MIL=75, 3 MIL=88, 4 MIL=99, 40-99=39clicks. So a lower scope height yields MIL marks that are more compressed..which, in my simple mind tells, me a lower scope height is more forgiving when using MIL/MOA hold-overs and minimizes errors when you shoot estimated/un-ranged distances...like when hunting without a rangefinder. I mean heck..I've never left my rangefinder at home when going shooting. LOL.
If a different scope height yields different sight reference points for a shooting system with 0 cant, then a shooting system with a higher scope will yield greater POI changes when the system is canted.
The Szottesfeld document goes against everything I've personally experienced shooting airguns and competitive archery. I tried to read it with an open mind..but between the hard to follow diagrams, wording, and logic I ended up with migraine. Anytime something makes a claim of "debunking an ancient myth", I tend to view it with just a tiny bit of skepticism.
That said, FT shooters claim system cant and scope height does not affect their shooting. IDK. Maybe at the distances shot and the way they setup their choice of zero there is some error canceling going on.
Couldn't have said it any better myself. Actually, I couldn't say it that well. I'm sure the FT guys mean well and believe what they are saying but the view they hold seems to be dominated by the single distance and click-to-zero blinders they always wear. Not everyone shoots exactly the same way.
Anyone who says "scope height above bore does not affect cant error" is simply wrong. It certainly fits in the FT world and probably in other ways of shooting but not in some others. An overgeneralization is an error and makes the statement false. Even if it is true in many situations, a single situation where it isn't invalidates the overgeneralized statement. Even Szottesfeld admitted this after pushback by long range firearms shooters but was "still standing by everything written above". Incorrect is incorrect and overgeneralized (not taking into considerations the exceptions) is incorrect.
I posed a question to scotchmo that illustrates a SECOND exception to Szottesfeld's conclusion. Not only does holding over with the crosshairs create an exception (admitted to but called an "aiming error") but so does shooting at the distant zero of the two zero method. Yes, they are at two separate distances for the distant zero with low and high scope height. But AT EACH RESPECTIVE DISTANCE, one is aiming dead center with the crosshair to hit that spot. But any common cant angle for the two "systems" will produce more cant error with the higher of the two scopes. It isn't an "aiming error" because you are "aiming" dead on WITH THE CROSSHAIR. It isn't a "ranging error because you are shooting at a specific distance tied to that scope height. It is simply AN EXCEPTION. A second exception (in addition to the one that Szottesfeld DID identify) that further disproves the overgeneralized statement "scope height above bore does not effect cant error". It absolutely does, in some situations. And it absolutely does not, in some others.
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OK - a longer answer:
"...Consider a single rifle. A higher velocity accurate air rifle shooting a good BC pellet. ..."
Then lets just say that the velocity is so high that gravity has no significant affect. In other words, there will be no cant error from gravity. We can model the trajectory as a straight line. That simplifies the explanation. Now we can look solely at your assertion that the different LOS from different scopes heights causes a difference in cant errors.
The images show a gun with two scopes, one at 2" above the bore-line and another at 4" above. One or two, it does not matter as their is no difference in the end result. we can use 3D geometry to model the problem and get an accurate representation of what will happen. All dimensions and angles are correct except for the 20yds to target as that too far to include, so distance was shortened drastically.
The first image (A0-A90) I decided to show how I visualize it. With the cant about the muzzle. I know that you like to visualize it with the cant about the LOS, so that is shown in the second image (B0-B90). With your method, the gun position changes some when compared to my method, but the LOS and cant axis all still intersect at the target.
A0-A90: Gun is canted about the muzzle. That would be the same as canting about a scope height of 0.00". Muzzle stays in same position XY. It stays pointed at the target. POI is still the same as POA, so no error.
B0-B90: Gun is canted about the 4" high scope. Muzzle shifts out of position of XY. It moves horizontally and vertically with respect to the target. So you might think that it will miss the target. But since the muzzle rotates with the scope about the scope's LOS axis, the muzzle's new direction still intersects at the target. POI is still the same as POA, so no error.
If we were to assume a low velocity projectile that is affected by gravity, when canted, the actual POI would not be the same as the POA, so there is a cant error. With high and low scopes sighted in for the same distance of 20yds, both LOS intersect the intended POI at the target. If we then canted the gun 90 degrees, both LOS would still intersect the intended POI. The actual POI will have X shifted equal to the drop compensation which is now sideways, and then Y = actual drop distance downward.
I can show an actual trajectory (rather than the straight line) in the example above, and it will then show the cant errors, but I can tell you ahead of time that the errors will be the same whether rotated about either scope axis or muzzle.
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"...FT shooters claim system cant and scope height does not affect their shooting..."
I know a few successful/knowledgeable FT shooters. Cant can affect our shooting. Most of us use a bubble level to avoid gun cant. Scope height can amplify or reduce errors from miss-ranging (aiming errors) and produce additional reticle/clicking cant errors if the gun is canted. But if there is no ranging error, then the scope height won't affect the magnitude of gun cant errors. We use scope height to move the Point Blank Range into the range that we prefer, not to reduce cant errors.
I'm not going to address your belief in the "myth" of scope cant, Most every aspect that pertains to it is being covered in my debate with bandg.
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