Quantizing Parallax

[woojos]

Does anybody have information or resources to better understand parallax? I get the principal, i.e. the goal is to set the reticle plane directly on top of the target plane.

Considering all my scopes have about a half turn adjustment to account for I'd say focus/target planes from ~0 to infinity, which we will associate with ranges from say 0 to 1400 yards, that's not a whole lot of precision in the actual adjustment.

My guess is it's not that big of a deal i.e. that you just need to be kinda close, but that would probably be more inexperience than intuition. I'm thinking I haven't put enough patience and effort into really dialling my parallax adjustment before tossing rounds downrange and that is effecting my marksmanship progress. I still do it, but I have a hard time distinguishing head movement causing rifle movement from actual parallax, and tend to think most of it is head movement instead of being really sure that my scope is parallax free. Most of my shooting is done within 200 yards, a situation I am working on.

Does parallax get to be a bigger issue at long ranges? Do you need to adjust parallax when dialing from a say a 500 yard target to an 800 yard target where time is an issue?

What POI or group increase would be associated with a parallax error? I'm guessing it would be a function of the distance between the reticle and focus planes and it's on my to do list to study this a bit and try to figure it out. I may write it up as a document if I ever reach a satisfactory answer.

Any input would be appreciated. I'm especially interested in any routines and habits you have developed or are developing to make sure you are parallax free before sending a round down range.

 

[George63]

put the stock on a bag and move the eye around without touching the rifle - on side adjust, some say to always come from the infinite setting - the ideal setting may change with change in magnification

 

[woojos]

I figured I was over thinking it.

 

[Flyboy22]

I figured I was over thinking it.

It gets less important the farther away you're shooting. The difference between focused at infinity and focused at 1000 yards is very small, whereas the difference between 100 and 200 yards is much larger. At first I thought I was moving the rifle as well, but after some practice I realized my parallax was still off. On my scope, I actually have to dial about 800m on the parallax to shoot at 300m (S&B 5-25 PMII). Basically, ignore the numbers on the dial, and err on the side of infinity

 

[LastShot300]

It gets less important the farther away you're shooting. The difference between focused at infinity and focused at 1000 yards is very small, whereas the difference between 100 and 200 yards is much larger. At first I thought I was moving the rifle as well, but after some practice I realized my parallax was still off. On my scope, I actually have to dial about 800m on the parallax to shoot at 300m (S&B 5-25 PMII). Basically, ignore the numbers on the dial, and err on the side of infinity

Really odd, never happened to me such a thing with any scope, let alone the PM II.

 

[woojos]

I have a Leupold Mark IV that doesn't label the parallax/focus knob. Not sure if the newer ones share that feature.

 

[Greg Langelius *]

Does anybody have information or resources to better understand parallax? I get the principal, i.e. the goal is to set the reticle plane directly on top of the target plane.

First, one needs to understand that combining focus adjustment with parallax is a compromise that scope designers impose on their customers. The two are dependent on each other, but not necessarily in any specific or consistent ratio. Understand further that where focal issues are concerned, the individual human eye is a crucial part of the system, that those eyes vary from user to use, and that corrective lenses add another complexity to any depiction that effectively makes it impossible for an optical manufacturer to standardize with infallible precision any matters related to focus and parallax.. Consequently, parallax compensation and focus are more often out of sync than in, dependent on the care (and cost) the makers assign to fabricating each example of a given model. Often enough, setting the scope objective/focus/parallax/whatever for a given distance will fail to achieve a precisely proper setting for any of those factors. Close, but often no cigar. This will also often vary among each and every scope of a given model in an entire shipment. It is an inherent problem in scope design/assembly across the industry, and getting it closer to being correct is one of the things that makes high dollar scopes as expensive as they are. Distance markings are a ballpark estimate at best, and adjusting for a sharp focus, then reading the distance is usually a good way to end up with a distance/drop error of significant proportion. If one wants to find the distance, I suggest using a laser rangefinder.

Considering all my scopes have about a half turn adjustment to account for I'd say focus/target planes from ~0 to infinity, which we will associate with ranges from say 0 to 1400 yards, that's not a whole lot of precision in the actual adjustment.

Adjusting for parallax is not about setting for a particular distance, but rather, an ad hoc compensation for a focal mismatch between the target image and that of the reticle. The mechanical and angular tolerances for optical components mounting are critical, and assembly lining that process can complicate the resolution of errors. It's not something that assembly testing standards handles well, and allowances may tend to be ridiculously lax. Again, close, but often, no cigar. Consequently, a direct and correct correlation between focus adjustment, parallax compensation, and a specific distance is only marginally proportional to the distance markings on the focus adjustment

My guess is it's not that big of a deal i.e. that you just need to be kinda close, but that would probably be more inexperience than intuition. I'm thinking I haven't put enough patience and effort into really dialling my parallax adjustment before tossing rounds downrange and that is effecting my marksmanship progress. I still do it, but I have a hard time distinguishing head movement causing rifle movement from actual parallax, and tend to think most of it is head movement instead of being really sure that my scope is parallax free. Most of my shooting is done within 200 yards, a situation I am working on.

It is a big deal; so much so that parallax is easily the most misunderstood and also the largest single cause for dispersion in the entire marksmanship process. It doesn't need to be, but due to this misunderstanding and the failure to take it properly seriously, it usually is. Benchrest shooters take it very seriously and this is one reason why their dispersions are so much smaller than most of ours. The nod/wag head maneuver is the best and most directly available method to detect parallax mismatch and to verify success in its precise/effective compensation.

Another thing to recognize is that many scopes do not offer parallax adjustment at all, and are supposed to be arbitrarily set for an arbitrary distance. For rifle scopes, it is usually 200yd, and for handgun scopes, it is usually 50yd, but I would not want to bet in favor of those distances being anywhere near consistent and precise. As far as dot scopes with no magnification are concerned, I have not been able to conclusively determine whether parallax is or isn't an issue, the literature is contradictory.

Longer eye relief scopes (Handgun and Scout scopes) would appear to me to be more significantly affected by parallax, maybe even by (an) order(s) of magnitude)

Does parallax get to be a bigger issue at long ranges? Do you need to adjust parallax when dialing from a say a 500 yard target to an 800 yard target where time is an issue?

No, parallax becomes a bigger issue as and to the degree that it is mismatched. It is not related as much to a given distance as it is to the optical/angular factor by which the adjustment is off. I.e., a compensation distance error of 200yd is more serious than an error distance of 100yd, but is (mostly...) unrelated to the actual distance of the shot. This is an oversimplification of a complex factor, but for the purposes of understanding, it will serve to convey the important relationships.

What POI or group increase would be associated with a parallax error? I'm guessing it would be a function of the distance between the reticle and focus planes and it's on my to do list to study this a bit and try to figure it out. I may write it up as a document if I ever reach a satisfactory answer.

Parallax error is important because it is an aiming error. While there may be some degree of predictability/qualifiability, I would not want to attempt any procedure for resolving it. But one can get some idea of its magnitude by doing the head nod/wag maneuver. The degree of parallax dispersion will relate (but not necessarily directly) to how much the reticle moves across the target image. I don't think that attempting to document anecdotal results would result in being able to provide a reliable prediction capability.

Any input would be appreciated. I'm especially interested in any routines and habits you have developed or are developing to make sure you are parallax free before sending a round down range.

Cutting to the chase, parallax error may be quantifiable; but I seriously doubt that attempting such is going to result in a consistently reliable tool. About the most effective thing one can do about it is to employ the nod/wag technique of identifying and adjusting it out, so that it can be eliminated from the list of issues that detract from marksmanship precision. I am not at all positive that atmospheric issues can be completely ruled out of the process, so it may not be completely a matter of setting it for the current conditions and forgetting about it for the duration for that string of fire. Being a "belt and suspenders sorta guy" myself, I see little harm to doing the nod/wag before each shot. Where time interferes, I suspect it becomes a matter of taking a chance and accepting what consequences may follow.

FWIW, I worked with a NASA contractor for the Apollo 10, 11, 12, 13, and 14 Moon Landing missions, and was directly responsible for QC and process monitoring in areas including the production of the Command Module windows, and the optical media employed in the network of solar optical telescopes (priced at $200,000 apiece in/around 1969) employed around the equator for monitoring solar weather during the spaceflights. It was a long time ago and while the theoretical stuff has gotten somewhat fuzzy, the knowledge was a significant part of my job, and dealing with the practical aspects/consequences of parallax was a major factor in a lot of it.

Greg

 

[sled_mack]

I agree with what Greg said. Especially the part about quantifying the error.

But it leads me to another question - can we eliminate the effects of parallax by having a very consistent cheek weld? I think (but I can't say for sure) that if the eye is perfectly centered behind the scope that parallax is not an issue? Is this correct?

The reason I ask - I just shot a match where we had to engage targets from 275 to 1050 yards, which we had just ranged using our scopes. We had about 20 seconds between shots. That is just enough time to locate the next target, dial elevation, and get a shot off. My solution for parallax was to set it for about 700 or 800 yards, and focus on the rest of the fundamentals for each shot.

If time allows, I try to adjust it out the best I can. But if I am under tight time limits, especially with varying target difference, I pick something close and run the stage. Based on my experience (which is not that much compared to others) parallax is crucial for tight groups, but not as important for hits on steel targets.

 

[hlee]

But it leads me to another question - can we eliminate the effects of parallax by having a very consistent cheek weld? I think (but I can't say for sure) that if the eye is perfectly centered behind the scope that parallax is not an issue? Is this correct?

Yes, parallax is only a problem in as much as the line of sight (center of eyeball to point of aim) is offset from the line created by the crosshair and the point of aim on the target. If these are always in perfect alignment then parallax is not an issue. This is why the nod/wag method is so effective at showing parallax issues.

 

[woojos]

Greg, can you recommend any basic references if one wanted to become a more familiar with common scope designs (FFP/SFP), their associated adjustment mechanisms, and the appropriate lens equations that would provide a more complete understanding of this?

 

[Sterling Shooter]

OP,

The issue with parallax is, with whatever eyeball to eyepiece relationship, it may appear you have properly pointed the rifle with consistent alignment when that is not actually the case. That's why both parallax adjustment and recognition of a consistent eyeball to eyepiece relationship are important.

Depending on offset and eye relief, with the ACOG parallax could be in the 19 inch arena at 600 meters when the shooter's eyeball is less than square with the eyepiece. Not understanding the actual origin for the error the shooter might assume wind was not correctly countered.

As Greg alluded, parallax is akin to sight misalignment which, being angular error, increases with distance.

 

[Greg Langelius *]

Greg, can you recommend any basic references if one wanted to become a more familiar with common scope designs (FFP/SFP), their associated adjustment mechanisms, and the appropriate lens equations that would provide a more complete understanding of this?

Sorry, no; I can't.

The reason I can't is because, for me, that sort of thing falls into the box labeled "too much information". When one attains an age such as mine, one recognizes that life and time are getting shorter, and that information about things one is never going to do (in this case, designing optical appliances) requires more time and effort than the knowledge one attains can ever be worth.

I will never need to know such things because the solution is simple, adjust the parallax out, and the problem is solved. More information is more a distraction than assistance. When I come across a reference/link, I ask myself what I would do with the additional info.

The mind, unfettered, is a remarkable resource. It processes simple questions, like the last one, in the blink of an eye. Developing a thought process that will pause at the right time and ask such generic and simple questions becomes a liberating agency allowing one's ever decreasing store of remaining lifetime to be employed with more efficiency.

I can only wish I had learned that simple relationship far sooner. If I had known such things when I was 21, I could have applied the ensuing 46 years far more effectively. Don't wait until you're my age to figure that one out.

But it leads me to another question - can we eliminate the effects of parallax by having a very consistent cheek weld? I think (but I can't say for sure) that if the eye is perfectly centered behind the scope that parallax is not an issue? Is this correct?

Yes, you're on a productive track. When the eye's optical axis aligns with the scope's optical axis, parallax is eliminated. But a cheekweld is not that easily repeated. IMHO, the best way to find the proper cheekweld is to do something similar to the nod/wag maneuver (i.e. quartering the reticle) every time one addresses the firearm, as we are establishing the foundation from which we can reestablish the sight picture. In this way, the cheekweld becomes repeatable, and parallax is simultaneously resolved.

One can still shoot a non-parallax-adjustable scope without being chained to accepting unresolved parallax. The nod/wag maneuver can allow one to reduce/maybe even eliminate any parallax mismatch. But actually adjusting it out allows far quicker recovery from recoil and the setup for an accurate followup shot. Too many wounded animals escape because the parallax was not/could not be adjusted out. Reestablishing a proper eye/scope optical axis alignment for each following shot is crucial to effective rapid fire. As another informed poster has said on this forum, the only effective way to perform rapid fire is "One shot at a time...". This includes verifying eye/scope optical axis alignment.

The way to perform this is called "Quartering the reticle", and is very similar to the nod/wag maneuver, except the reticle and target are not the points of interest. Rather, we are looking to establish a midway point between the image limits (which correspond to the boundaries of the eyepiece exit pupil) which we recognize as a dark edge of the observed image. One performs the nod/wag to the extent that image shadowing is encountered, left/right and up/down. The better we can reestablish the cheekweld at the precise center of those observed limits, the closer our eye/scope optical axis alignment will be.

For those interested, the size of the exit pupil in mm is equal to the size of the objective lens in mm, divided by the power of magnification. That's actually only the maximum possible size, the true size will be slightly smaller due to optical anomalies like spherical aberration, etc. So a 50mm objective adjusted to 25x will render an exit pupil of 2mm diameter. This is actually very small as such measurements go, and is a valid recommendation for smaller magnifications and larger objectives in applications where sustained and rapid fire are encountered. This works better because a larger exit pupil will have a larger and more forgiving central sweet spot. I find it is best to start with a lower magnification on my variable, allowing faster target acquisition and a better followup capability, and then adjust up only as time and circumstances permit for more precise sight picture resolution.

Greg

 

[sled_mack]

hlee and Greg - thanks for the follow ups.

I've also heard that parallax is "much less" of an issue at magnifications of 10x and below. Knowing that every general rule has exceptions, is this something considered to be "generally true"?

I certainly try to dial out parallax when time allows. But when engaging multiple targets at multiple distances under tight time limits, it is not possible. But I may be gaining some advantage by dialing an "average" parallax and lowering my magnification to about 10x to get a bigger field of view to locate new targets more quickly.

Woojos - I hope I'm not taking your thread too far off topic. My suggestion to you would be to try shooting it to see the difference. Shoot a group with the knob turned fully in one direction, then a group in the other direction, then with the parallax dialed out. Repeat that a second time, but the second time try moving your head side to side and up and down - just a bit, just to where you see shadowing on one side of the sight picture. Without getting any deeper in theory, this will show you the effects of parallax. If you really want to be thorough, repeat again at a lower magnification and moving your head to see if the lower magnification reduces the error. I may try this myself when I have a chance.

 

[woojos]

Woojos - I hope I'm not taking your thread too far off topic.

Nope, its making for a good discussion.

The reason I started thinking about this is I thought my parallax was adjusted and I shot a nice tight group. On my second string, about halfway through, I switched from a cheek weld to more of a chin weld in trying to get more behind the rifle. The round impacted about 1" left of POA. I didn't call it a flyer because everything else felt good and I purposely tried changing my head position. I figured parallax was the most likely culprit.

 

[hlee]

hlee and Greg - thanks for the follow ups.

I've also heard that parallax is "much less" of an issue at magnifications of 10x and below. Knowing that every general rule has exceptions, is this something considered to be "generally true"?

I certainly try to dial out parallax when time allows. But when engaging multiple targets at multiple distances under tight time limits, it is not possible. But I may be gaining some advantage by dialing an "average" parallax and lowering my magnification to about 10x to get a bigger field of view to locate new targets more quickly.

Woojos - I hope I'm not taking your thread too far off topic. My suggestion to you would be to try shooting it to see the difference. Shoot a group with the knob turned fully in one direction, then a group in the other direction, then with the parallax dialed out. Repeat that a second time, but the second time try moving your head side to side and up and down - just a bit, just to where you see shadowing on one side of the sight picture. Without getting any deeper in theory, this will show you the effects of parallax. If you really want to be thorough, repeat again at a lower magnification and moving your head to see if the lower magnification reduces the error. I may try this myself when I have a chance.

Without doing any math or real heavy thinking, my intuition says that parallax errors are no less of a problem at lower magnification, however, they are substantially less noticeable. A 1 moa shift is easily observable at 24x but may well go undetected at 6x. Parallax is an angular error. The magnification does not change the relationship between the various sighting axes, but increased magnification does allow one to more effectively see the error associated with the relationship.

 

[Greg Langelius *]

Not taking the time to quarter the reticle on successive shots, even under limited time frames, is not my kind of logic.

Considering outcomes, a saved round costs no more points than a clean miss, but a well aimed shot garners more points than an off-center hit; and on a two-way range, unproductive shots can help an opponent locate you better without any gain for you. As was said, "One shot at a time...", and to me, that means each shot takes as much time as is needed to ensure it counts. Anything less is a waste of points, opportunities, and can lead to tragic outcomes under the wrong circumstances.

Suppression fire is, I guess, acceptable; as long as at least one somebody is trying for a legitimate aimed hit. I assume that's the purpose the Designated Marksman slot was intended to accomplish; but a hastily aimed shot in a match makes no legitimate sense to me.

Greg

 

[sled_mack]

Greg,

When you say quartering the reticle, you mean centering the reticle within the scope (or more specifically, within the exit pupil), correct?

If so, I agree. That is part of the fundamentals of the shot. I tend to think of it in terms of sight picture, but I think we are talking about the same thing.

I'm not a two-way range guy, so my context is matches. If a stage is "up to 10 shots in 90 seconds on one target", I might actually dial out parallax before the first shot. And as you said, each shot takes as long as it takes - 5 slow hits score better than 7 fast misses. Matches are won by avoiding zeros on all stages first.

A match director can force a speed per shot situation. Consider a stage where there are 10 targets. The MD is going to call out a target identifier and start the clock. A hit gets you another target called out and the clock reset, a miss and you are done. If you don't fire inside the time limit, you are done. Taking the time to dial parallax would be a stage killer. Quartering the reticle/sight picture, along with adjusting NPA, breathing, and trigger control need to be practiced such that they can be applied quickly.

The second scenario is very workable. Just because I am not adjusting parallax for each shot, doesn't mean I'm not aware of it. I set the scope to some pre-determined setting before starting the string and move on. What I choose to set it to will depend on the target ranges and sizes. Big targets up close offer some cushion, so I'll set the parallax longer. Really small targets close, and bigger targets out long, I might set parallax closer. So I'm aware of parallax, I set it for a reason, and I rely on my fundamentals (sight picture specifically) to over come the difference in parallax setting and make the shot. It isn't a perfect solution, but the point of the stage is to force an imperfect solution.

There is no doubt this all gets far more difficult when we move up from the prone position where cheek weld and eye relief become much more difficult to reproduce exactly each and every time, under time limits.

For other tasks, like zeroing a scope or load development, I take a lot of time to dial out parallax before taking the first shot. I also check sight picture for each shot very carefully.

I'm not suggesting that parallax isn't important. But I am saying that it needs to be prioritized based on the shot being taken - and all within the context of match shooting.

 

[Greg Langelius *]

I agree completely on all points.

I see parallax compensation as a means of reducing error, rather than as a means to achieve perfection. Demanding perfection is a futile pursuit, just ask any really serious BR shooter. What we do is about striving for successively better personal bests. One shot at a time, until your "good is better", and your "better" becomes a new "best".

I, too, am trying to prioritize the issue, and to offer fallback techniques that can still achieve a "better" when the entire process cannot be achieved.

hlee; yes, parallax creates an angular aiming error. I still think I can make a case for parallax error reduction at lower magnification.

First, the lower magnification produces a narrower field of view. This means the angular extent for potential error is likewise reduced.

Second, the broader exit pupil allows a wider area within which to resolve angular error. I believe this makes it easier to find a good cheek weld and therefore to further reduce parallax-induced aiming error.

Now this is all personal speculation, so I could easily be wrong about all or part of this (at least) particular viewpoint.

Greg

 

[steve123]

I've often wondered if it were possible to have a separate parallax adjustment from the scopes adjustable focus ???

 

[Greg Langelius *]

Me too. Hoping a scope techie is reading this.

 

[Aeon1]

I've often wondered if it were possible to have a separate parallax adjustment from the scopes adjustable focus ???

Why would you want that?

 

[steve123]

Why would you want that?

Because when the image is perfectly focused for a persons eye the parallax error isn't always dialed completely out, so that persons only choice is to choose between having some parallax and a focused crisp image, a out of focus image with 0 parallax error, or somewhere in between the two choices. I personally hate blurryness! This is one of those situations that fit into the "where life just isn't fair" category, haha.

 

[Greg Langelius *]

Why would you want that?

I'd want it because so many scopes come out if the box with the combined focus/parallax adjustment so far o/o sync that for many shooters, long range shots become a choice between having good focus or good parallax, with the other off by a significant amount. Since many shooters are rather unaware that parallax even exists, the usual outcome is a bad parallax adjustment and a rifle performance that gives the shooter the fits; sometimes it shoots great, and other times most definitely not.

Bring able to adjust each separately may allow better precision and less confusion. I can't say so definitely because I've never been above to fins a (affordable) scope that allows each to be adjusted separately

Greg

 

[Aeon1]

Ah ha, I thought that's what you would be after!

If a scope is adjusted properly you typically can have your cake and eat it too. To set up a parallax adjustable scope so focus and parallax come in together you first rough in the ocular/diopter for a sharp reticle. Quick glances into the scope at a bright non-descript background and adjust the ocular to get the reticle sharp. Set the gun up on the bench so it's stable. Adjust the focus on a distant object and check for parallax, if none your good. If parallax exists pick a direction and move the ocular a small amount, refocus and check parallax, did it get better or worse? If better keep repeating the ocular adjustment, refocus, check parallax procedure until focus and parallax come together. If the parallax got worse turn the ocular the opposite direction and follow the same directions. It's pretty much always worked for me so go try it and let us know how it does for you.

If you wear glasses or contacts you may have other issues beyond what scope adjustments can do for you. Example, with one of my scopes if I try to shoot with a particular pair of corrective glasses there is no way I can eliminate a double vertical crosshair effect.

 

[steve123]

You must have good eye's. I used to but as I get older they gradually worsen. No matter how much I fiddle with the diopter, parallax and image focus, one of the three will be off.

Hmm, I wonder if a special eyeglass subscription would make a difference to even up the compromise???

 

[Greg Langelius *]

My eyeglasses are provided by the VA, and my VA optometrist is a shooter and formulates my prescription to optimize my shooting vision. I have no idea if or what he does differently. In my case, the eyeglasses appear to provide a vertical upright wire, and a slanted horizontal wire. I really doubt it's possible to get good shooting eyewear that does all things as well as perfect uncorrected vision; I'm happy with what I can get. Being totally honest, I think we all take too much for granted and quibble far too quickly about modern shooting optics.

Greg