Can maximum potential parallax error be quantified?

arcticcathonda

arcticcathonda

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I have a question that relates to maximum potential parallax error.
Can this be quantified if I of know target distance as well as what distance parallax is set for? I found an equation online that I believe was posted by the optical department of Leupold; however I am not too sure.

Consider this example:
Let’s say my target is 800 m away and I not knowingly forgot to adjust my parallax setting from my previous engagement distance of 300 m. In a perfect world (0- wind, 0 MOA gun etc) with all other variables constrained, how much can that error in parallax contribute to the maximum group size when using my 56 mm objective on my Nightforce?

The Formula I found:
Max error (mm)= {0.5 X objective (mm) X [ range to target (m) – range focus (m)]}/ range focus (m)

Max error (mm)= {0.5 X 56mm X [ 800 m – 300m)]}/ 300m
Max error (mm)= 46.7 mm or roughly 1.84”
Does this seem right to folks?
 
I am not sure about the formula ... But i know if the distance you are shooting is much farther or closer than the set paralax and your eye is not perfectly square with the retical, you can miss by feet.

I have just sold one vx3 4.5-14 boon and crocket and i have another one that will be going up soon as well. Neither of the scopes have AO. Leupold has set there fixed paralax at 150 yards. This is a problem for me because at close range in the timber say... 50 yards or less, if your on uneven ground offhand bending around a tree and you have what seems like fraction of a second or maybe a second to take a shot at a very skitish blacktail, With all those variables compounded by an eye that is not aligned perfectly with the retical and a paralax that is out by 100 yards , even though the crosshair is on your game ... You can miss by feet.

If you take a rilfe with a scope that has fixed paralax at 150 yards, rest your cheek on it look into the scope at something at 30 yards and move your head side to side while keeping your eye on the retical... the retical will bend side to side across the entire objective. If you take the exact same scope with paralax adjustment and dial the adjustment down to 50 yards, the retical is far more stable with far more room for error at the same 30 yards when moving your head around.

Of course the fixed 150yard leupolds are great between 100 and 200 yards ... where most game is taken.

Also guys that are hunting in the flat lands where they dont have all these variables that could possibly get them off cant probably will not encounter these issues. The fixed scopes will work fine at close range if you are conscious enough to make sure your eye is perfectly aligned with the retical and the gun is level at close range in the heat of the moment.

Now lots of guys will say they never let these variables get to them but ... Of course " buck fever " prevails over cooler heads.

I have a VX3 with front focal adjustment now for the timber. Im am currently waiting for nightforce to come out with the new compact hunter that ive been hearing so many rumours about. If it takes until next year i will wait.

I have just sold 2 of my 3 leupolds that do not have paralax adjustment and agian the 3rd one will be gone soon. I personally will never own another scope that does not have the paralax adjustment.

to conclude, im certain that there will be signifacant error when shooting longrange with your paralx set incorrectly

I am looking forward to anyone that wants to add to this thread.
 
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The error is small and insignificant in many applications, but enough to separate winners from losers in target shooting. Set your rifle up on a rest and move your eye around. You will see the potential for error when it is misadjusted.
 
The first thing to mention is that if you eye is perfectly in line with the centerline of the scope and reticle, parallax error no matter what it is set to is zero, you will always hit exactly where your aiming assuming everything else involved in the shot is perfect. So this depends entirely on how well you eye is line up with the centerline of the scope, if you look diagonally say through the very bottom of the ocular assembly and subsequently through the reticle and top of the objective lens, that would provide you with the maximum possible parallax error in terms of physical position.

To maximize it further you would have your reticle focused in a plane as far away from your target's plane as possible, say if you target was at 1000yds and you have parallax dialed in at 10yds. Mathematically what this would equate to may be possible to figure out, but in my mind it would depend on both the objective diameter as well as the length of your scope, so to see the length missing out of that seems off, as well as your resultant 1.8" calculation.
 
So I spent the last hour researching and I think I've got a better formulae to figure it out. Wikipedia states that you can figure out the distance one plane is behind the ocular using the distance your scope is calibrated at to be parallax free and the distance the target is at as a ratio times your focal length distance which on most scope is 100mm.

(1000m/10m)/100mm=1mm

This value then gets amplified based on magnification, take a S&B 5-25;

1mm*25= 25mm difference between the focus plane of the reticle(25mm behind the ocular) and the focus plane of the target (at the ocular)

For a S&B 5-25 @ 25magnification, the exit pupil is 56mm/25mm=2.64mm which is the diameter of the scope image at 70mm behind the ocular (eye relief)

Thus the maximum your eye could be off dead center would be 1.32mm and still see the image at the proper eye relief.

So if you take a triangle that is 1.32mm high and 70mm(eye relief)-25mm(distance reticle plane is closer to your eye) and do some trig(I'll spare you) you get 1.68 deg angle

This angle is the same angle that the reticle would be off the target at 1000m, so if you move the rifle to put the 1.68deg off reticle back on the target you end up with a new triangle

This triangle has an angle of 1.68deg and a length of 1000m, which after a bit of trig, turns out a 29.3m difference between the point of impact and the target at 1000m.

Assumptions:100mm focal length(nobody seems to list this on there manufacturer site), and that the wikipedia focal plane distance formulae isn't bull####.

Hope this helps, was fun looking at this, if I'm wrong on any of this, let me know!

Cheers,

Andrew
 
blacktemplar, that end result of your math can't be right. When you move your eye around the reticle doesn't move anywhere 29.3m at 1000 yards. Also, I've read parallax doesn't increase with magnification, it simply gets easier to detect.
 
Screw the formula. Just clamp the gun into a vice, look through it at a grid-type target, move your head as far over to one side as possible while keeping the reticle in view, and note where the reticle is resting on the grid. Then move your head as far as possible in the opposite direction, and again note the grid position. Measure the distance between these two points, divide by 2 and you should have the maximum possible error due to parallax at that distance for that scope. This should serve to not only answer the question, but to illustrate how unrealistically extreme it is to fret over "maximum" possible error. That maximum error as calculated seems to be limited, in practical application, by the field of view allowed by the eyepiece. You just can't go far enough over to create many yards of apparent reticle movement. In practice, even if your head position isn't absolutely perfectly centered, it's probably going to be within 5 percent of dead center. The further off you go, the more obvious and extreme the misalignment becomes, and you will naturally correct it.

Especially for big-game hunting, adjustable objectives are a PITA. They adjust parallax and also image focus...no matter what setting you adopt, you will wind up looking at a critter that is so much closer or further that he is out of focus, causing you to #### around with the adjustment and making you look like one of the goofs in the TV hunting shows...you know, the guys that force you, the watcher, to shout at the TV "Shoot! SHOOT!!! You dumb %*$#, SHOOT!!!" while they fiddle with this, adjust that, shift their grip, wiggle their butts, scrape their feet and generally waste time while the animal stands ready to run. Play with this stuff at the range, by all means. But I really don't think you want to sell all your regular scopes and "upgrade" to AO scopes for general use.

Of course, you could just set the parallax at some intermediate distance, say 100 or 150 yards, and trust that for most hunting shots the parallax error will be so small as to not matter. Oh, wait...that's where all those scopes are already set...hmmmmm....

And a parallax error of FEET when shooting at a 50yard target with a regular, 150-yard-parallax scope? Sorry, but I don't believe that...and I suggest that anyone who does should try to duplicate that error at that range. I'll bet its more like an inch or two, at most. If you can manage to miss a deer by FEET at 50 yards, I think you need a better alibi than that.
 
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