Range Estimation Brain Teaser – Part II
Well, a few months ago when I wrote the last article, I had a few tests I decided to run at our spring Precision Optics Workshop and the great folks who attended were all willing guinea pigs.
In the previous article, I postulated that the ability to accurately estimate the range to a target using a graduated scope reticle would be limited by the capabilities of the human eye, and that capability would be somewhere between 1 and 5 arc-minutes, but I didn’t exactly know where to set the bar. My best guess, given glass quality and atmospheric effects was about 2 arc minutes.
To test this, we played a little game with 10 participants. 5 “shooters” with optics greater than 20X and 5 “shooters” using optics less than 20X. The scopes used were a fairly representative sample of the common glass out there, everything from sub-$1000 Athlons and Vortexes to $2500+ Kahles and Nightforce. The sample group came from a variety of experience levels and age groups as well. The groups were presented with 2 targets at 100 yards, each having a series of staggered lines, varying in length and thickness by .1 inch for the less than 20 power optics group, which corresponds to roughly 1 arc minute at 10 power magnification, and by .05 inch for the over 20 power optics group, which also corresponded to roughly 1 arc minute.
The participants were tasked with judging the width and length of 5 lines and putting them in order of shortest to longest and thinnest to thickest.
In addition, a series of 5 steel targets were placed at distances from 180 to 520 yards and the participants were given a short amount of time to mil and calculate the distance to each target.
Lighting conditions were bright but not direct sunlight.
The results of the tests indicated that 80% of the <20X participants correctly judged the length of the staggered lines and 100% correctly judged the width. The >20X group judged both the length and width 100%. So… that means the average person is able to reliably resolve differences of 1 arc minute through their optic (adjusted for magnification). One thing that might have skewed the results of this test was that all of the lines were relatively close together on a standard sheet of paper. Had they been spread out further, it might have made it more difficult to compare the lengths and widths.
On the 5 steel targets, results varied.
Target #1 was placed at 180 yards and estimates ranged from 170 to 210. Average 10% error
Target #2 was at 210, estimates ranged from 204 to 227. Average 4% error
Target #3 was at 290, estimates ranged from 235 to 317. Average 13% error (likely an outlier)
Target #4 was at 380, estimates ranged from 330 to 370. Average 8% error
Target #5 was at 520, estimates ranged from 429 to 510. Average 10% error.
When we compare the percentage error with the charts generated for the previous article, adjusted for target size, distance, and magnification, the visual acuity gets closer to 2 arc minutes.
So, without doing a lot more math, because really… who needs that in their life? Our little experiment shows that my original guess wasn’t bad. The average person with average glass can estimate target distance with an acuity of approximately 2 arc minutes of angle, meaning we should be able to get on generous target fairly reliably out to 600 yards. After that; glass quality, shooter experience, eyesight, and flat-shooting cartridges are needed to improve the odds.