Reticle Perpendicularity


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dscottdennison
March 9, 2012, 09:33 AM
I recently purchased a new long range scope, and while I was shopping around online I came across some incorrect information regarding reticle perpendicularity. Many people were experiencing slightly canted reticles (in relation to turrets) and were frightened that this would somehow put them 3 feet or more off target at the coveted range of 1000 yards!

So, I just wanted to do a little math and clear things up.

First, let me just say that it is not all that difficult to notice as little as a 1 degree variation in angle by eye at the reticle. Some people were stating as much as 5 degrees of variance between reticle and turret! That's an extreme case, and most were talking well under that, so I will use 2.5 degrees for my calculations. It seems that canted reticles are not all that uncommon, but I will show you that it is nothing to worry about. All of this also holds true if the reticle and turret are aligned but the scope is installed slightly tilted one way or the other. So, those scope leveling systems are just another bit of marketing BS in the gun world...

Imagine a right triangle in the same plane as your reticle while looking through the scope, pointing downward. If you align the reticle squarely, and your turret is angled 2.5 degrees off to the right, the bottom angle of your triangle is obviously 2.5 degrees. For this example, I will use MOA measurements. At 100 yards, 1 MOA is about 1.047 inches. We will figure out how many inches of horizontal variance result per click of a 1/4 MOA per click scope with a turret that is offset by 2.5 degrees from the reticle.

1/4 x 1.047 = 0.26175" This is the hypotenuse of your triangle, since this is how much each click of the turret raises the reticle, but the turret is offset, not the reticle. Now we have the simple equation: sin(2.5 degrees) = x/0.26175, where x = the horizontal leg of your triangle. This X value is how much horizontal variance will result for each click of your scope. Doing the math, we find that X = about 0.0114. So, just making up a number of 30 MOA of correction needed to get a large caliber rifle to 1000 yards while zeroed at 100 yards, this comes to about 1.37 inches of horizontal variance.

In simple terms, if you zeroed your rifle at 100 yards, drew a perfectly vertical line through the bullseye, cranked up 30 MOA and fired another group while aiming at the same bullseye, the group would be less than 1.5 inches off to the right of the vertical line.

Therefore, the only people who need to worry about a few degrees of cant between reticle and turret (which is evidently pretty common) are those who are worried about 1.5 inches at 1000 yards...

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dogmush
March 9, 2012, 10:44 AM
Yes but.....and this is what you're missing:

It's actually pretty dang difficult to shoot at 1000yds, and if you're going to be any good at it, you try to limit all possible variences. It's not that 1.5 inches is all that much, it's that that's another 1.5 inches on top of wind drift, mirage, trigger pull, barrel heat, and everything else that affects the impact. to get good long range groups you have to limit, or take into account, as much of that as possible, and reticle cant is one of the easier things to take care of. Either get a scope without reticle cant, or measure it and work it into the dope.

dscottdennison
March 9, 2012, 10:52 AM
or measure it and work it into the dope.

Measure it and work it into the dope is good advice.

What you want to limit are inconsistent variables. If it were 2 inches off this time, 5 inches off the next, 14, the next, 1 the next, this would be a bad thing. 1, 2, 10, 20 or however many inches off CONSISTENTLY is of no concern.

Many people mix up the terms precision and accuracy, and their actual definitions become cloudy among the flood of marketing BS.

Zak Smith
March 9, 2012, 12:14 PM
If the reticle is crooked compared to the direction of elevation movement, and the knobs are always used for elevation and windage adjustments, and the direction of elevation travel of the erector is straight up and down, then it does not matter: you are always using the reticle crosshair center for the hold point.

dscottdennison
March 9, 2012, 12:24 PM
I'm not sure I understand what you are saying, Zak Smith.

What I was saying is that if the erector is crooked when the crosshair is made square, the the adjustments made with the elevation knob will not be exactly vertical, so your up and down movement of the reticle center point will move off center slightly.

If using the reticle for a holdover (Kentucky windage) and not using some sort of target turret, then none of this matters whatsoever.

Zak Smith
March 9, 2012, 12:34 PM
I was describing the opposite case of what you just described.

dscottdennison
March 9, 2012, 12:42 PM
So, if the reticle were crooked and the erector were vertical? Gotcha.

Although that would be pretty annoying.

Zak Smith
March 9, 2012, 12:43 PM
Yes, but potentially less error prone

dscottdennison
March 9, 2012, 12:52 PM
Well, then you would probably try to correct for it by tilting the rifle while shooting anyway... Or your mil dot ranging would be a little crooked...

Either way, when the error is as small as I've shown, it's all negligible

d2wing
March 9, 2012, 02:42 PM
The verticle plane of the reticle and the bore must be the same. If the path of the bullet is offset and intersects the line of sight at one hundred yards you have two triangles, one base at the muzzle and crosshairs, another at the poi and and the target as seen through the scope. The sin will be increased with elevation, the bullet would cross the line of sight much closer to the muzzle. But if they are not on the same verticle plane they will not intersect at all and no triangle will be formed. If you are talking about both the verticle plane of the reticle and and the bore center being offset a tiny amount with elevation adjustment that makes sense. Is the angle you are referring to the horizontal offset?

Skribs
March 9, 2012, 02:51 PM
Many people mix up the terms precision and accuracy, and their actual definitions become cloudy among the flood of marketing BS.

Could you enlighten me as to the difference?

dscottdennison
March 9, 2012, 03:24 PM
Could you enlighten me as to the difference?


http://celebrating200years.noaa.gov/magazine/tct/accuracy_vs_precision.html

dscottdennison
March 9, 2012, 03:34 PM
The verticle plane of the reticle and the bore must be the same. If the path of the bullet is offset and intersects the line of sight at one hundred yards you have two triangles, one base at the muzzle and crosshairs, another at the poi and and the target as seen through the scope. The sin will be increased with elevation, the bullet would cross the line of sight much closer to the muzzle. But if they are not on the same verticle plane they will not intersect at all and no triangle will be formed. If you are talking about both the verticle plane of the reticle and and the bore center being offset a tiny amount with elevation adjustment that makes sense. Is the angle you are referring to the horizontal offset?

I'm not so sure what you are saying, and I don't know if it is clear what I am saying... I wish I could be speaking in person and drawing pictures and etc.

Anyway, the travel of the bullet is not being changed at all, and actually neither is the sight picture. Just imagine zeroing your scope at 100 yards and then cranking it up to hit bullseye at 1000, then adding 2 clicks to the right of windage. That is basically the same thing that would be happening in the scenario I was describing. Just like adding a tiny bit of windage without actually adding windage.

Hope that didn't make it even more confusing...

Skribs
March 9, 2012, 03:41 PM
So accuracy means you're shooting centers on point of aim, and precision means you consistently hit the same spot?

That's what I thought you meant, just wanted to clarify.

dscottdennison
March 9, 2012, 03:54 PM
That graphic comes up a lot when talking about accuracy and precision. I can remember it from text books way back when. It applies to everything, but the illustration of target shooting just lends itself very nicely to the topic and is easy to understand. If you notice, that looks to be a surveying site that was just the first that came up when I googled.

But yes, precision is basically repeatability, with each measurement comparing closely to the last, but not necessarily being "correct". Accuracy is basically getting close to the "correct" measurement, with no reference to the previous measurements.

d2wing
March 9, 2012, 05:21 PM
Ok I know what you mean now. But isn't 1/4 inch at 100 yards 2.5 at 1000. If the angle stays the same the height is a function of the length isn't it. If you add a limit of accuracy such as .5 moa it becomes more important. Not too important to plinking but can make the difference in a match.

chaser_2332
March 9, 2012, 07:52 PM
This is why u test ur retical and tracking of your scope. To avoid dumb variables that's shouldn't be there

dscottdennison
March 9, 2012, 11:16 PM
D2wing, I think you are thinking about the wrong plane.

Chaser, I think you missed the point. The point is that this small variation does not matter.

Longrifle2506
March 10, 2012, 12:15 AM
Thanks for posting that. I was wondering about that because my brand new Leupold is slightly canted. My father told me not to worry and he said it's no big deal because Leupold actually allows for a certain amount of cant; I'm sure it's not much; but they do allow a little. This is valuable information though, for those who are worried about it.

I just level the top turret to get my reticle close; then use a plumb bob to fine-tune what little degree of cant may remain.

Really, the reticles in My Bushnell Elites, weavers, and Nitrex scopes were all perfectly perpendicular to their turrets. They were all built at a facility in Japan named "Light Optical Works." They build awesome optics. I just bought my very first Leupold after reading how the new VX-3 was improved so much versus the Pre-2009 VX-III and it's more expensive than my Elite 4200's. But the canted reticle can easily be noticed by the naked eye; although its still minor. Leupold makes more scopes in 8 weeks, than Swarovski, Schmidt & Bender, Kahles, Leica, and Zeiss(and one or two others) build in a year; Combined! Ya know, that kind of mass production might scare some folks away; but I'm impressed with the VX-3; I really do wish they didn't allow canted reticles though.

SharpsDressedMan
March 10, 2012, 12:19 AM
Perpendicularity might just be the biggest word ever used on THR.

Driftertank
March 10, 2012, 12:53 AM
Disestablishmentarianism....

:P

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