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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.
"...It absolutely does, in some situations. And it absolutely does not, in some others...." I have never encountered that situation.
"...But AT EACH RESPECTIVE DISTANCE, one is aiming dead center with the crosshair to hit that spot...." As long as the POA is intersecting the intended POI, I can't see how the viewing position changes the amount of gun cant error.
Please diagram the exception so I can better understand what you are describing.
Below is a response nervoustrigger posted to my open sight vs scope photos early in this thread-
nervoustrigger
The question is whether a high scope is more susceptible to cant error than a low scope. To answer this question, which of these two experiments would best answer it?
1. An experiment with two scopes
2. An experiment with a scope and a "not a scope".
A scope allows one to re-zero for every shot, either by using using stadia markings (mildots) or by dialing. Open sights do not do that except in a crude, improvised way analogous to holding over with a plain crosshair reticle absent of any mildots.
This illustrates PERFECTLY why those who believe the Szottesfeld view DON'T UNDERSTAND. Consider-
When a shooter "aims" through a scope, there is a straight line from EYE to RETICLE to TARGET. The optics can be manipulated to focus or to change aim point (think ANGLE HERE) but even after such change, there is still a straight line from EYE to RETICLE to TARGET. That line after internal scope manipulation is still there, it's still straight, but it has been changed IN RELATION TO BORE.
When a shooter "aims" with open sights, there is a straight line from EYE to REAR SIGHT to FRONT SIGHT to TARGET. The open sights can be manipulated to change aim point (the same manipulation of angle that a scope accomplishes, just external and mechanical vs. internal and optical). That line after manipulation is still there, it's still straight, but it has been changed IN RELATION TO BORE.
The scope is relatively more precise while the open sights are relatively more crude, BUT THEY DO EXACTLY THE SAME THING. They create a LINE OF SIGHT. Why even bring mention of "re-zero for every shot, either by using using stadia markings (mildots) or by dialing" into the response to my photos? Everyone who has ever used a scope knows what they do. It isn't a revelation and has absolutely NO bearing on the photos and discussion, other than a level of precision in aiming. But the need to mention that ILLUSTRATES the Szottefeld fatal error-it ALWAYS bases it's view on a single "re-zeroed" distance.
scotchmo-"Please diagram the exception so I can better understand what you are describing."
You've basically already done about half of that, but as with every person who holds the Szottesfeld view, you stopped a bit short. That is the FATAL ERROR for Szottesfeld. Go back to your B0 and B90 diagram. Redo that illustration using a SIDE ON view but with a SINGLE PAGE SHOWING THE HIGH SCOPE, BORE, AND THAT CONVERGENCE ANGLE TO TARGET and a second SINGLE PAGE SHOWING THE LOW SCOPE, BORE, AND THAT CONVERGENCE ANGLE TO TARGET. REMEMBER to use a COMMON DISTANCE TO TARGET (the basis for the two zero method). Place the scope and muzzle to the left side of both diagrams and the target near the center. Leave some space to the right of the "target". These separate page drawings are still accurate and still show exactly the same relationships as your B0 and B90 drawings but it is easier to "see" the relationship between the two different heights. It's exactly the same illustration of the relationship, just less cluttered and people can view them more easily. As you've noted in the past, you often view things in terms of bore line while I focus on scope line and that is fine. It doesn't matter because they are connected by the scope rings. Fixed in relation to each other. To me, it is simply easier to "see" the relationship if you keep the scope horizontal and show the inclined bore below. But do it as you wish. Once you have those two pages, lay them side by side and look at them. You will see an angle between scope (you can also call the scope the LINE OF SIGHT or LOS, it's all the same) and bore on each individual drawing. But with each "scope height" set to a common base zero distance (distance to "the target", the ANGLES will be different. The lower scope height will produce a SHALLOWER angle of convergence from muzzle to target while the higher scope height will produce a STEEPER angle of convergence from muzzle to target.
Now the critical part. EXTEND EACH "BORE LINE" PAST THE "TARGET" and across the page to the right. You will observe that, as you get further and further beyond the "target" (increasing range), both lines continually DIVERGE FROM LOS but the steeper angle of the higher sight causes it to progressively be FURTHER DIVERGED from LOS in relation to the low sight line as distance increases. The SPECIFIC SCOPE HEIGHT produces a SPECIFIC CONVERGENCE ANGLE. DIFFERENT for each HEIGHT but specific to each. BEYOND the target, the CONVERGENCE becomes DIVERGENCE (simple geometry).
Now imagine firing a pellet from the LOW scope height setup using a perfectly vertical "gun cant" (meaning no cant is present). Assume 20 YARD ZERO. With the low sight (assume 2") and at 20 yards, the pellet "rises" (in relation to LOS, absolutely not in relation to gravity, common sense) exactly 2" to hit the target. BEYOND the target, it "rises" a bit more (again and as always, in relation to LOS) as gravity continually works to pull the pellet DOWN and now back TOWARD LOS. Assume the pellet manages to rise 1" above LOS before gravity halts the "rise". The pellet then continually "falls" (constant gravity at work) as it travels until it AGAIN crosses LOS. That is the SECOND ZERO for the LOW SIGHT, and assume it is at 40 yards.
To continue, now imagine firing a pellet from the HIGH scope height setup, still using a perfectly vertical "gun cant" i.e. NO CANT. Same as before. But now assume the scope height is 4" (the higher scope). That pellet "rises" (as above, in relation to LOS, not gravity as that isn't possible) exactly 4" to hit the target. BEYOND the target, that pellet "rises" a bit more as well but just a bit more than the low scope due to the ANGLE. Assume it manages to "rise" 2" above LOS (remember, the low sight only managed to "rise"1") then as always gravity continues to pull it DOWN and back TOWARD LOS. But because it has risen a bit higher and is travelling at about the same velocity, it "travels" a bit further until gravity (always there, always a contant") pulls it down to again intersect LOS. That is the SECOND ZERO for the HIGH SIGHT. But it is at a bit longer range because it "rose" a bit more above LOS. Assume the second zero in this case is 50 yards.
Last step. We are going to hold both "guns" vertical (0 "gun cant", not canted) Now aim the crosshair of the LOW SIGHT at the center of the "target" at the second zero distance (remember, it is at 40 yards). Shoot and you hit dead center. Because the pellet "rose" a bit above LOS and fell EXACTLY back onto LOS at that second zero distance. Now CANT 45 degrees in either direction. Doesn't matter which direction but lets assume a CLOCKWISE CANT AROUND THE LOS. WHY DO I SAY CANT AROUND LOS? Because when we shoot, we aim with the scope, or the open sights, or a red dot. That is the LOS. EYE to "SIGHT" (whatever it is) to TARGET. ALWAYS a STRAIGHT LINE. We DO NOT aim with the bore. Bore and LOS are connected physically, but we AIM with the LOS. AND it doesn't matter what particular TYPE of sight we use. They only vary in PRECISION. ALL are adjustable. Back to taking the shot. When canted and shot, the LOW setup will hit LOW and RIGHT with the CW cant direction. GRAVITY determines how much it will DROP. Always a constant, always working. But how much it hits LATERALLY is determined by the ANGLE OF DIVERGENCE and measured NOT from the bore BUT from the 20 yard base zero distance. WHY? Because that 20 yard distance was SET by the common zero distance for low and high scopes when we set up the two DIFFERENT HEIGHT SCOPES and sighted both in at 20 yards.
But now follow the same process as above with the HIGH SIGHT setup. Shoot "level" (again 0 "gun cant", not canted) and the pellet still "rises" above LOS (but it still "rises" a bit more than the low height setup AGAIN due to the angle). But the SECOND ZERO for this setup is 50 yards and that is the "target" distance that we are holding dead center on to hit dead center-50 yards. At 40 yards with the HIGH setup, the pellet is still a bit ABOVE LOS (remember, it "rose" a bit higher due to the angle) but gravity is pulling it straight down TOWARD LOS. At 50 YARDS, it has been pulled (straight down, by gravity) back onto LOS. We aim center with the HIGH SCOPE and hit center, AT 50 YARDS. NOW cant exactly the same as we did with the LOW SIGHT. Same amount of "gun cant". What happens at the 50 yard SECOND ZERO "target" distance? It hits low and right. As above. But because the ANGLE is steeper (from the original setup of HIGH vs. LOW and again, a SET angle for each setup but a DIFFERENT angle DUE TO HEIGHT), the HIGH setup impacts MORE laterally at 50 yards than did the low setup at 40 yards.
All this stuff can be difficult to visualize. Why? Because we are trying to reconcile the functions of ONE straight line (LOS) connected to a SECOND straight line (bore line) at an ANGLE (a SET angle for each SCOPE HEIGHT but a DIFFERENT angle for each SCOPE HEIGHT due to the common base zero distance used at setup for the 2 zero shooting method) all operating under the force of GRAVITY which produces a CURVED TRAJECTORY. But there are a couple of physical facts operating across all of this. GRAVITY works (affects) the pellet only in the vertical plane. It doesn't move the pellet left or right, only down. AND the ANGLE only works in the vertical plane, AS LONG AS NO CANT IS INTRODUCED. So in the uncanted position, we have both GRAVITY AND ANGLE working only in the vertical plane. BUT once we introduce ANY amount of cant, what happens to the forces. GRAVITY is a constant. It absolutely continues to work but only (and always) in the vertical plane. But think about the ANGLE function. As we begin to cant, we take some of the vertical effect of the angle (100% in the vertical with no cant) and transfer it to the horizontal. More cant and more transfer from vertical to horizontal. By 90 degrees of cant (gun on it's side) we have 100% of the ANGLE now operating in the horizontal and 0% working in the vertical. All the while through the canting process, gravity has not varied in either force or direction. IT GETS VERY HARD TO EASILY VISUALIZE THE COMPLICATED INTERRELATIONSHPS.
This statement is false-"scope height above bore does not affect cant error". It is false because it suggests that scope height above bore NEVER affects cant error. Even good ole Szottesfeld admitted that scope height above bore DOES affect cant error, in "certain instances". A shooter can dislike those instances or prefer to shoot in a different manner than those instances, and that is perfectly valid and scope height might well NOT effect cant error for those methods. But that is a PREFERENCE for a certain "instance" (or method) of aiming and shooting and IN NO WAY INVALIDATES THOSE "OTHER" INSTANCES, A person can say that "holding over with the crosshair is an aiming error" but it sure seems odd that if I know the drop for a given distance and I know that a target is at that distance, I can hold over WITH THE CROSSHAIR with no gun cant and I'll hit the target. But using the same method, if I introduce gun cant then I miss the target while "aiming" at exactly the same point. I'll ask a question again that I've asked before, how can anyone state that this is an "aiming error". Even Szottesfeld admitted that this works as I've described, admitting that the miss would be more for a higher mounted scope. This statement is true-"scope height above bore does not effect cant error if you click to zero". Perfectly valid. Because it isn't overgeneralized and doesn't mislead those who are trying to understand the topic into thinking that IN NO CASE WILL SCOPE HEIGHT EVER AFFECT CANT ERROR.
