CANT , and it's effect ?

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Oh by the way, the 2 scope experiment you assert will require welding or some other such Herculean effort...it’s quite easy with this little fella:



It seems your haste to deride me further didn’t work out quite like you’d hoped.
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Feel free to utilize that to ACTUALLY DO SOME SHOOTING AND DOCUMENT THE RESULTS. I'll be watching for such so that I can say "you didn't do something right" as another supporter of the Szottesfeld group basically said would be the reason for results that didn't agree with his. As I noted-circular logic, just lacking the logic. And I see you still haven't addressed-WHAT ELSE ROTATED? Not surprising.


 
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Bandg, the answer to your question is represented in Scott’s diagram where circled.


Because the severity of cant error is determined chiefly by the amount of drop (for the small cant angles typical of normal shooting), the error is small for close shots and grows ever larger with increasing distance.

That is a characteristic of cant error bound to my example only in the most tenuous way.

I look forward to seeing you substantiate how two identical points of aim produce different errors.
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Again, feel free to DOCUMENT WITH ACTUAL SHOOTING. As above, I'll certainly be watching for such.
 
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A quick take for tonight. 20th wedding anniversary was today so it was a bit of a late start.

The basic info:

1. QB79 HPA with short LW barrel running RWS Super Field pellets at 780fps (modest velocity and relatively poor BC pellet to ensure sufficient drop)
2. Mounted 2 scopes. Low one at 1.65" above bore, high one at 3.87" above bore.
3. Zeroed both scopes at 30 yards.
4. Shot groups at 50 yards through each scope to determine holdover (1.5 mildot for low scope, 0.8 mildot for high scope)
5. Canted gun 45° and shot a group via the low scope.
6. Canted gun 45° and shot a group via the high scope.

The 2-scope setup:


The groups at 50 yards with the rifle canted 45 degrees:




The vertical error for each group is virtually identical at 2.7". The horizontal errors are 7.2" and 7.5" for the low and high scopes, respectively, which represents a 4% difference. For a crude test cobbled together in an hour, I think it sufficiently demonstrates the concept.
 
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Congratulations on your 20th wedding anniversary. I hope you had a nice celebration and that you get to celebrate again in '41.

Notice in that 2 scope setup above ( and yes, it did take effort) that, IN HIS OWN WORDS, the vertical error was "VIRTUALLY IDENTICAL" (2.7" specifically) while the horizontal error (7.2" for low scope and 7.5" for high scope) wasn't quite "virtually identical" but was deemed to be close enough to "sufficiently demonstrate" the concept. Interesting.

A few things to consider-

1)First and MOST IMPORTANT=nervoustrigger has said before (correctly) that using mil-dot holdover "IS THE SAME AS CLICKING TO ZERO". Sound familiar?

2)WHY are there "virtually identical" vertical differences while there is observable difference in horizontal position? Anyone care to weigh in on the possibilities for that WHY?

3)WHY are the groups so different in both size and shape? Sure seems it would be easier to be accurate with the lower scope (it really looks like a much more "normal" or average" scope mounting position to me) and shoot a better group so WHY is the lower scope group so much worse (as a group only) than is the higher scope group? Interesting? Relevant?

4)A relatively common analysis technique for such comparisons would be to eliminate some of the "noise" by throwing out an equal number of the MOST DIVERGENT units (shots in this case, or potential errors in general terms) from each group. The focus here is on the horizontal, so throw out the lower left and lower right shots from the low scope group (these appear to me to be the most divergent 2 shots from the "center" of that group horizontally) AND throw out the left most and right most shots from the high scope group. Still trying to understand the major difference in relative group sizes, but I guess it isn't really important😊. Doing this doesn't seem to shift the high scope group center much (if any) in the horizontal plane. To me, the same process would seem to shift the low scope group center slightly further left. Not by much, but FURTHER LEFT, and such a shift increases (albeit slightly) the horizontal difference between the low and high scope groups. Interesting? Relevant? Each reader would need to answer for themselves.



All in all, an attempt at a comparison that is to be commended for the effort taken. But unlike the poster above (who already agreed with the experimenter), I DO NOT see how one can view this as a relevant illustration of the differences in question. As noted , there is an awful lot of "noise" in the shooting results that seem to be less than "logical" IMO. Second, it had already been stated, by nervoustrigger himself, that using mil-dots for holdover was THE SAME AS clicking to zero. Seems we've "circled" back to that familiar term again. Interesting?



Previously, I laid out a shooting comparison that Michigander "ran" (AND THAT I STILL STAND BY) which showed that, indeed yes, the higher scope clearly created more horizontal error than did the lower scope in that comparison. I've done physically the same process that Michigander "ran". But Michander then discounted that OBSERVED result (his "but" qualifier recall, and the same "circular reasoning" by Szottesfeld supporters that I've mentioned before) by noting that the difference observed "was because" the lower scope PRODUCED a closer second zero distance (remember, a common base zero for the two) than that PRODUCED by the higher scope. Absolutely true. AND ALWAYS WILL BE. A physical arrangement (such as rigidly mounting a scope to a rifle) produces a physical condition. A PHYSICAL CONDITION IN THE VERTICAL PLANE AS WELL AS IN THE HORIZONTAL PLANE, IF CANT IS INTRODUCED. Once mounted, the physical relationship is fixed and doesn't change. Such can be viewed as providing both advantages and disadvantages, as is the case with a relatively lower or higher scope. But the 2 different MOUNTINGS (LOW/HIGH) produce those different physical CONDITIONS that will PRODUCE different physical RESULTS. THAT described mounting process/comparison is fixed. UNLESS THE SHOOTER "CORRECTS" THE DIFFERENCES. REQUIRING in your reasoning (as Michigander did, representing the Szottesfeld view) that the two physically produced different second zero distances (PRODUCED DIRECTLY BY THE TWO DIFFERENT HEIGHTS OF THE TWO SCOPES) must be set equal to each other (as Michigander asserted) means that, once again, in doing that "setting equal" one would have "circled" back to click to zero shooting. And, as nervoustrigger has previously stated, using mil-dots is "the same as" clicking to zero.

Lots of "circular" with only egocentric "logic" in this stuff, IMO.

I don't shoot like a field target competitor on any regular basis. I don't change my scope settings (clicking) in many instances at all unless rezeroing. I use a two zero shooting method. In my method of shooting, HIGHER MOUNTED SCOPES PRODUCE MORE CANT DISPLACEMENT FOR ANY GIVEN DEGREE OF CANT, AND MORE OF THAT ERROR AS DISTANCE INCREASES. No 'but" exception. And THAT INSTANCE ALONE invalidates any overgeneralized statement which claims that "scope height has no effect on cant error". Even Szottesfeld was sensible enough to admit this. If you shoot the way I described, then what I have described (and what Michigander noted before "circling back" to click to zero) will happen. If you shoot using another method, you will need to evaluate for your specific approach to determine the effect on your method.
 
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Yes, holding such an arrangement at a 45 degree angle is not conducive to small groups at 50 yards. No cheek weld and no opportunity to support it in the shoulder. Nonetheless, the “observable difference” is not only insignificant in terms of percentage (4%), but also in absolute terms, 0.3”, an amount much less even than the difference in the scope heights. 

To the extent there is a difference, I expect it lies with the casual way I arrived at the 1.5 and 0.8 mildot holdovers and the precision in applying them to an unwieldly gun held at an awkward angle. In other words, the identicalness of the two aim points wasn’t quite perfect.
 
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Maybe you shouldn't have been so "casual" in order to produce better results. And maybe your "I expect" is correct. And maybe you "should" have gotten those WORSE results WITH the WORST position having NO CHEEK WELD and NO SUPPORT=the high scope. BUT YOU DIDN'T. I'll say again, interesting😌. And I EXPECT no resolution to this that doesn't come to each shooter through his/her own efforts.

Shooters can try to repeat your efforts if desired. Shooters can try what I described previously with Michigander, if desired. Or they can ignore both of us with no real complications to themselves other than possibly a miss that can't always be easily explained. It's still (as of today) a free country.
 
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I try to be, and I absolutely do not see how I was saying ANTHING remotely like you insinuate. Am I incorrect in my conclusion above? Didn't address that. Interesting. I respect who and what I chose to respect. It's earned, not demanded. But thanks for trying.

As I've said, correctly I believe, each shooter can try these "experiments" for themselves, and should IMO if they want to understand the issue here.
 
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Many times now we have acknowledged that scope height matters when using improvised holdover…the scenario with a simple crosshair, aiming high and expecting it to fall to the target.

Meanwhile scope height makes no difference when using mildots or dialing the turrets. That is to say as long as the POA matches the intended POI, scope height does not matter. It is a fact that is not at all intuitive. As I said earlier in the thread, I stubbornly denied it for years until I tried it. So yes, I too encourage others to try the experiment to see for themselves. However for those without the time, materials, or inclination to set up the experiment, it is hopefully obvious that two identical points of aim cannot produce different errors.
 
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Many times now we have acknowledged that scope height matters when using improvised holdover…the scenario with a simple crosshair, aiming high and expecting it to fall to the target.

Meanwhile scope height makes no difference when using mildots or dialing the turrets. That is to say as long as the POA matches the intended POI, scope height does not matter. It is a fact that is not at all intuitive. As I said earlier in the thread, I stubbornly denied it for years until I tried it. So yes, I too encourage others to try the experiment to see for themselves. However for those without the time, materials, or inclination to set up the experiment, it is hopefully obvious that two identical points of aim cannot produce different errors.
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"...as the POA matches the intended POI, scope height does not matter...."

That is the crux of it.

Can I envision an instance where POA does not match the intended POI, AND the gun is canted? Sure.

Two instances where POA does not match intended POI:

#1) Using mil-dot holdover or clicks that are wrong for the target distance. POA does not match intended POI.

#2) Holding cross hair (aiming) on a point above the intended POI in order compensate for drop. ("improvised holdover"?) POA does not match intended POI.

Have I ever purposely used "improvised holdover"? Sure, on rare occasions, knowing very well that I must then take extra care to avoid introducing additional cant errors related to scope height/reticle cant. I think that is the instance that bandg is talking about.
 
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Many times now we have acknowledged that scope height matters when using improvised holdover…the scenario with a simple crosshair, aiming high and expecting it to fall to the target.

Meanwhile scope height makes no difference when using mildots or dialing the turrets. That is to say as long as the POA matches the intended POI, scope height does not matter. It is a fact that is not at all intuitive. As I said earlier in the thread, I stubbornly denied it for years until I tried it. So yes, I too encourage others to try the experiment to see for themselves. However for those without the time, materials, or inclination to set up the experiment, it is hopefully obvious that two identical points of aim cannot produce different errors.
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"...as the POA matches the intended POI, scope height does not matter...."

That is the crux of it.

Can I envision an instance where POA does not match the intended POI, AND the gun is canted? Sure.

Two instances where POA does not match intended POI:

#1) Using mil-dot holdover or clicks that are wrong for the target distance. POA does not match intended POI.

#2) Holding cross hair (aiming) on a point above the intended POI in order compensate for drop. ("improvised holdover"?) POA does not match intended POI.

Have I ever purposely used "improvised holdover"? Sure, on rare occasions, knowing very well that I must then take extra care to avoid introducing additional cant errors related to scope height/reticle cant. I think that is the instance that bandg is talking about.
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"Target distance" again. So what you have written is partly, but not totally, addressing the issue. Your last two lines above try to address it, but they are still dismissive of the method (i.e. "rarely" and "reticle cant") because YOU (and many who shoot the way YOU do) never (or "rarely") shoot that way. As to "reticle cant", once the mounts are tightened the GUN follows the RETICLE. Why try to represent it as anything other than simply committing a CANTING ERROR. Also, read my 20 yard zero illustration which Michigander took the time to "run" over his program. A second similar but distinct method of "aiming" from "IMPROVISED" holdover (and distinct as well from click-to and mil-dot holdover methods) that also produces more cant error with the higher scope at the respective distances. To me, the refusal to acknowledge THOSE THINGS illustrates the issue. TWO separate illustrations of HOW a higher scope can produce more cant error than a lower scope and yet some still support the overgeneralized statement(s), overgeneralized because they insinuate that NEVER could such occur, that "scope height does not effect cant error" or "scope height has no effect on cant error" or any other way it has been phrased. That is false, incorrect, in error, or whatever other negative one wants to apply to it. False BECAUSE there are exceptions (YOU don't have to like or even use the exceptions but OTHERS MAY) and the exceptions aren't accepted in the statement. They are actually DISMISSED by the statement. THAT is the fallacy of the statement. Thus the statement is false and misleading to those who may be in the process of making sense of the topic in relation to how THEY SPECIFICALLY DO THEIR SHOOTING. In that 20 yard zero illustration case, you are "aiming" directly at intended POI for each case, both a near and far zero, with a high vs low scope (a method that MANY shooters may utilize in THEIR shooting) but in a different manner than click-to-zero or mil-dot holdover. THAT produces the same "greater error with greater scope height" situation as does the SO CALLED "improvised" holdover. Some may use that "improvised holdover" (and they probably don't view it as so seriously "improvised") regularly with complete success FOR THEIR NEEDS. Some may use the "20 yard zero" method I had previously mentioned, then use EITHER mil-dot or click-to or "improvised holdover" for further distances. Others (FT shooters and Szottesfeld supporters certainly) seem to dismiss most if not all of that as inadequate, or in error, or "improvised", or whatever other term might be used, in spite of the fact that many may use such methods with complete success FOR THEIR NEEDS, because THEY (FT and Szottesfeld supporters) use a specific method and seem to hold the view that it is the only way one should shoot. And in spite of the case that many may use those OTHER (non-FT or Szottesfeld) methods with complete success FOR THEIR NEEDS, those OTHER methods have almost always have, almost always do now, and almost always will into the future, cause increased cant error with higher scope height and longer distances. Seems it cannot be made any more simple than this. If this doesn't resonate with any specific individual(s), then there will NEVER be agreement between those individuals and myself. Because there ain't just one way, and no person's (or group's) way is BEST for all others.
 
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#1) Using mil-dot holdover or clicks that are wrong for the target distance. POA does not match intended POI.

#2) Holding cross hair (aiming) on a point above the intended POI in order compensate for drop. ("improvised holdover"?) POA does not match intended POI.

...
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... TWO separate illustrations of HOW a higher scope can produce more cant error than a lower scope ...
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#1) Using mil-dot holdover or clicks that are wrong for the target distance. POA does not match intended POI.

#2) Holding cross hair (aiming) on a point above the intended POI in order compensate for drop. ("improvised holdover"?) POA does not match intended POI.

Then I'll add another that I have yet to imagine or understand (I'm not following what you are trying to describe but won't deny that it could exist):

#3) Other aiming methods that are affected by scope height in different ways.



BTW: #1 and #2 are not examples where higher scopes produce more cant error. They are instances where different height scopes produce different cant errors. Low scopes worse for far targets, and high scopes worse for close targets. Those two instances are equally applicable to when a scope is canted (rotated) in the mounts but the gun is otherwise uncanted (center of scope directly above bore).
 
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"BTW: #1 and #2 are not examples where higher scopes produce more cant error. They are instances where different height scopes produce different cant errors. LOW SCOPES WORSE FOR FAR TARGETS."

We will NEVER agree if you view this quoted statement as correct. It is not correct and illustrates a complete lack of understanding of the entire concept. #2 is easily tested by ANYONE who wants to take the time to do so and is the STRONGEST opposing viewpoint to Szottesfeld.

In fact, this is EXACTLY what Szottesfeld was forced to "concede" at the end of his article due to accurate pushback from long range firearms shooters. Yet he "stood by" his overall statements. And that point of view made him overgeneralized and thus incorrect.
 
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You guys are smart people! It's interesting the opposing views and honestly the hard thinking part is a bit out of my wheelhouse.

So setting all the in's and out's of your debates aside this is what happened to me.

I tried using a bubble level in the form of a Horus ASLI I attached to my scope tube. I used the top of the elevation turret and leveled it to match the top of the pic rail on my rifle with that same level, then made the Horus match them. 

Long story short, on uneven terrain, I was able to win a long range steel series twice, using this Horus system on my rifle "as well as NOT using" the Horus system on my rifle approx half that time over a 3 year period. My conclusion was I couldn't tell the difference in my scores. Since then I've just left the ASLI off. This is of course highly unscientific and unconventional but "I think" small CANT errors get washed up with other things like wind and the precision of the rifle. I was also holding over and holding off most of the time vs dialing dope, and the targets averaged 1.5 moa. Scope height was 2.1" IIRC. I did however make the top of the turret level to the pic rail back then when I didn't use the ASLI. I know that most of the shooters back then had levels on their rifle and they used them but obviously it wasn't the deciding factor on who won or not. They also dialed most of the time.

It's shameful I guess but I don't like how the left side of the horizontal crosshair appears sloped down when the scope is level while using a level on the rifle???? Instead I set up the rifle and scope so the crosshair appears right to me even though it really isn't level. Oh well, I'm happier and it doesn't seem to affect my scores.

The way I look at this subject as far as normal shooters shooting at normal sized targets is - don't sweat it. Just give some attention to getting the horizontal crosshair as even as your eyes tell you and fire away. 

I have no doubt there is a effect with CANT, but I can't tell in my shooting, not enough to have a level on my rifles. 


 
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Others may chime in who do UNDERSTAND. The scotchmo statement above ILLUSTRATES the lack of understanding, but he had to "accidentally" stumble into admitting it. Their logic and presentations are ALWAYS circular and confusing. But scotchmo has made a very clear statement that is easily understood as incorrect with just a bit of reasoning, although he did so while ATTEMPTING to discredit what I've been saying.

My 20 yard zero illustration, which Michigander "ran" and provided numbers for and which anyone can read above in this thread, illustrates EXACTLY that scotchmo is completely incorrect in HIS EXACT STATEMENT MADE ABOVE. IMO, such an incorrect statement ON a topic ILLUSTRATES lack of COMPLETE understanding OF the topic.

I'll try to explain it one more time. ASSUME a 20 yard zero for an AIR RIFLE with a low scope. A CONVERGENCE ANGLE of BORE to LOS is CREATED by the height of mounting. Their MUST BE that angle to have any zero distance (20 yards in this example but it can be any distance chosen) where the two (bore and LOS) meet to hit a target. ANY HIGHER MOUNTING of the scope produces a STEEPER angle between bore and LOS. SIMPLE GEOMETRY. What the Szottesfeld supporters don't seem to be able to grasp is that THOSE 2 DISTINCT ANGLES CONTINUE TO INFINITY. Stated another way, they both DIVERGE FROM LOS BEYOND THE TARGET, just as both CONVERGED from muzzle to target. But BEYOND the target, those 2 distinct angles (STEEPER for ANY HIGHER SIGHT) then DIVERGE from LOS, as noted, TO IFINITY which means also TO ANY INCREASING DISTANCE. Since, through simple geometry, the HIGHER sight PRODUCES a steeper angle, the HIGHER sight will result in MORE DEVIATION FROM VERTICAL THAN WILL THE LOWER SIGHT beyond the target. HOLDING OVER AS IN #2 ABOVE (with the "crosshair" as noted by scotchmo) which scotchmo states will produce MORE error for a LOWER scope is obviously incorrect to anyone who understands simple geometry and can separate such from the "gorilla dust" of any formulas or any talk of drop or anything else at all. ONLY THE ANGLE matters for this. ONLY. Yes, drop occurs. But that is eliminated from consideration here by the HOLDOVER (which scotchmo VIEWS as an incorrect or "improvised" method because he doesn't do it that way, but which he stumbled into mentioning here). The different "incorrect" holdovers necessary in this example for the 2 different scope heights (specific for each height at any given distance) for the low vs high scopes CORRECTS for the drop for each at any given correctly "held over for" distance. BUT both crosshairs in this example are still being held ON THE VERTICAL and the ONLY THING causing movement away from the vertical IS THE ANGLE ONCE CANT IS INTRODUCED. ONCE AGAIN, STEEPER ANGLE (FROM ANY HIGHER SCOPE BY SIMPLE GEOMETRY) results in MORE error from vertical for the higher scope WITH increasing distance beyond the target. NOT more error from vertical for the LOWER scope (read scotchmo's "INCORRECT") statement above, BUT more error from vertical for the HIGHER scope. Incorrect is incorrect, no matter WHY it is incorrect.

As Steve mentioned, one can shoot well without considering all this, under many circumstances, And as he mentioned, the distinctions aren't particularly easy to VISUALIZE for many people. But very long range firearms shooters understand this distinction and pressed Szottesfeld on it (see the Szottesfeld "concession" at the end of his article and note how he apparently viewed the issue as a less than particularly valid way to shoot because HE didn't shoot that way). And I believe that air rifle shooters MAY begin to understand this with the push toward longer range air rifle shooting. Of course, if those long range air rifle shooters only click-to-zero (or mil-dot holdover) then they may never catch the distinction. Those two "aiming methods" (click-to-zero or mil-dot holdover) may certainly cover MOST of the shooters. I don't know the percentages of such. It doesn't ALWAYS cover me and others. But there IS a difference.

I believe that the reason the Szottesfeld view shooters cannot grasp this is because they have a "tunnel vision" that ties them to both viewing EVERYTHING in terms of click-to-zero (or mil-dot holdover, which nervoustrigger and I believe scotchmo as well have STATED is "the same as" click-to-zero). This tunnel vision is illustrated by the constant referral to "target distance", "distance must be common", etc. IMO, that "tunnel vision" always causes them to "circle back" (the circular logic I have mentioned) to those Szottesfeld views in their reasoning and trying to apply those views to EVERYTHING.

This isn't particularly easy to follow. But it is possible to illustrate for ALMOST ANY shooter to themselves. EVERY shooter that has a rifle and a scope (yes, it will work the same way with a pistol but pistols are just harder to shoot accurately) COULD do these experiments for themselves and see the distinctions. The distinctions are there and would be immediately visible to ANYONE who wants to do the physical comparison to high vs. low scope with a common zero using the crosshairs as the holdover aiming point at any distance beyond the aiming point. For high vs. low scopes, MORE MOUNTING HEIGHT=MORE HORIZONTAL CANT ERROR and MORE DISTANCE=MORE HORIZONTAL CANT ERROR.

Let the "circling" begin. 
 
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What the Szottesfeld supporters don't seem to be able to grasp is that THOSE 2 DISTINCT ANGLES CONTINUE TO INFINITY. Stated another way, they both DIVERGE FROM LOS BEYOND THE TARGET, just as both CONVERGED from muzzle to target. But BEYOND the target, those 2 distinct angles (STEEPER for ANY HIGHER SIGHT) then DIVERGE from LOS, as noted, TO IFINITY which means also TO ANY INCREASING DISTANCE. Since, through simple geometry, the HIGHER sight PRODUCES a steeper angle, the HIGHER sight will result in MORE DEVIATION FROM VERTICAL THAN WILL THE LOWER SIGHT beyond the target.
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I think I follow what you’re saying, and yes it’s true that the steeper angle produces a greater divergence between the line of sight and the bore’s axis with ever increasing distance. That’s okay so long as we know what mildot to use. It’s not so okay if we are aiming high with a crosshair reticle…meaning we lack reticle subtensions to establish a precise point of aim.

But even with the advantage a mildot reticle, I’m still handicapped if I don’t know the distance. Because if I don’t know the distance, I don’t know what mildot to use. If my distance estimate is wrong, my aim is wrong. It’s an aiming error.

AS IN #2 ABOVE (with the "crosshair" as noted by scotchmo) which scotchmo states will produce MORE error for a LOWER scope is obviously incorrect to anyone who understands simple geometry...
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That happens because the steeper angle of the high scope produces a line of sight that is a closer match to how the pellet is falling off at a distance. That’s why the high scope would produce less error when using the “just aim high” approach, because the correct point of aim is still fairly close to the crosshair (compared to aiming with a low-mounted scope, where the proper POA would be further down the reticle).




 
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