Measured Parallax Error in Hunting Scopes

[MrMauser]

Hello,
I wanted to share with y'all some results of a test I did measuring the maximum parallax error in 6 rifle scopes that are set to be parallax free at a fixed range.

I first noticed the magnitude of these errors when looking through a Zeiss Conquest 3-9x40 scope at a target 300 yards away. I found that without touching the rifle I could move the cross-hairs completely off the 8 1/2 x 11 sheet of paper just by slightly moving my head, all while maintaining a perfectly clear sight picture. I have shot targets to 500 yards with moderate regularity with and decent success but only with scopes with adjustable parallax and have never really qualified most of my "hunting guns", most of which have 3-9x40 scopes, beyond 100 yards. Searching across the internet I found countless posts regarding parallax errors and an often quoted formula which goes something like this:

(1/2)*D*abs(l-f)/f = PE

D = objective diameter
f = parallax free distance
l = distance where parallax error is being measured

For typical objective diameters this yields very small parallax error at the ranges in question. For a 40mm scope this should be around ~1.5 in. Since this didn't match the error I was seeing I decided to go through my various different hunting scopes and try to measure their parallax error. I once again stuck a target on a 8 1/2x11 sheet of paper and set it up at exactly 300 yards. I put my rifles in a rest and adjusted them to aim at the center of the target and then, without touching the rifle, moved my head as far left and right and up and down as I could and still keep a sight picture. Using the sheet of paper as a reference, I recorded the maximum parallax error to the nearest inch as best as I could resolve. The results are as follows:

Scope .......................................................PE
Zeiss Conquest 3-9x40 .............................. ~8in
West German Zeiss Diavari-C 3-9x36.............~2in
Leupold VX-II 4-12x50.................................~8in
Schmidt Bender Zenith 3-12x50...................~4in
Zeiss Victory Diavari 3-12x56.......................~7in
Nikon Monarch 2.5-10x42............................~2in

As you can see, a few of these scopes have a huge parallax error. The difference seems to be not only related to objective diameter as the formula suggests. I suppose this equation comes from some thin lens approximation that doesn't hold up to these modern complex optical systems. I was really impressed with the Nikon here, as it costs a fraction of many of these scopes. The West German Zeiss (I wish I had more of these great scopes) belongs on a hunting rifle that I have practiced with extensively to 400 yards in preparation of an Idaho elk hunt last year. The gun and scope both performed excellently and I noticed no problems due to parallax then. The Zeiss conquest bothers me the most. Its objective is only 40mm. I have loved these scopes for there clarity ( which side by side makes the VX-II look like crap),long focal lengths, and affordable price. I have about 10 of them now and I checked several to make sure I didn't just pick a lemon. I would image these are popular scopes. Does anyone here have them and have you noticed the same problem? I invite and encourage anyone who possesses any of these scopes to try this on their own. This amount of error makes them almost unusable at this range. The rifle that I first noticed this with does not have a straight comb, and with such a forgiving eye relief you can move your head forwards and backwards several inches which is all the while moving the cross hairs.

Well that kind of got winded. I hope someone made it down this far and I hope to hear back from some folks.

 

[BMF]

Interesting......what power did you have the scopes on? Or didn't it matter?
I'd be curious to see some more field experiments by people with other scopes.
Scopes in the 6-20ish x 50 range like:
Nightforce
Huskema
Meopta
Mark 4
Vari X III
Sightron SIII
Vortex PST
Higher End Bushnell's

 

[Len Backus]

Wonderful contribution, thanks!

 

[bruce_ventura]

Mr. Mauser,

I don't think you did the experiment you think you did. Your parallax error values for half of the scopes are way off. The max parallax error equation that you cited is accurate. It is based on simple geometry and the accuracy of the equation is insensitive to assumptions. The primary assumption is that light travels in a straight line. Over these distances, I think we can accept that assumption as valid. Readers should see the following link, in which the equation for max parallax error is very clearly derived:
Derivation of Riflescope Parallax Equation

For a scope adjusted to zero parallax at 100 yds, which should be the case for most if not all of the scopes you tested, the max parallax error at 300 yds would be equal to the objective diameter (1.4-2.2 inches). I don't need an equation to calculate that. The geometry is very simple. Yet you reported a parallax error of 7-8 inches at 300 yds for half the scopes.

The only way I could explain your results would be if the parallax free range for half of the scopes was a lot shorter - about 30-35 yds! I doubt that is the case, although I guess it is possible. It seems more likely to me that your measurements are off. If your measurements are correct, then you should send half of those scopes back to the manufacturer and have the parallax free range properly set to 100 yds or some other value that you prefer.

BMF,

Scope power doesn't matter.

All of the modern 6-20ish scopes that I can think of have either AO or parallax adjustment that will eliminate the parallax error at virtually any target range if properly adjusted. Maybe there is an odd one or two out there that have no AO or parallax adjustment. If so, they are rare and not worth worrying about.

 

[BMF]

That seems logical to me. I've tried moving my eye around the reticle before at various ranges at havn't noticed any significant deviation.
I wonder what's going on with MrMauser's scopes? Maybe it was hot and the mirage was high that day......or like ventura said, maybe the parallax wasnt adjusted properly. Anyway seems weird.
Brent

 

[MrMauser]

Thanks for the replies! The literature implies that the parallax error from the equation is measured from the optical axis and is half of the total error. The observations I made were from one extreme to the other. I will make an attempt this weekend to try and see where the focal point of these scopes are. By working the formula backwards it seems that a 40mm scope would have to be parallax free at around 50 yards to match what I am seeing at 300. The two scopes with the lowest error would seem to be parallax free at around 125-135 yards. If anyone out there has a 3-9x40 Zeiss Conquest I would really like to hear if they can make any similar observations. And yes it was blazing hot here in southeast Texas and will still be this weekend, unfortunately.

 

[MrMauser]

I visited this again for a short while on Saturday. I took the Zeiss Conquest 3-9x40 and checked its parallax at 100 yards. I suppose I shouldn't have been surprised that there was noticeable parallax error at this range. I moved a target back and forth in 5 yard increments until I finally found the parallax free range to be about 60 yards. I tested a different 3-9x40 Zeiss Conquest at 100 yards and found it to be perfect. I tried a third and found it to be off. I tried the Leupold VX-II and found it was also off (in addition, I battled when leveling this scope when I first mounted it before I found that the cross-hairs were not square to the turrets and leaned several degrees to one side). I didn't get the chance to see at what exact range these were focused, but regardless, I think some phone calls might be in order.