This article originally appeared over at the First Strike sub-forum of M. Carter Brown. That thread can be found here. Check it out if your interest in the subject extends to the community’s reaction and inputs. I’ve broken it up here on the blog into a series since the different aspects of rifle scope design are so broad that I didnt feel comfortable adding them on to this post as they get written. Each one is really it’s own subject and deserves a more dedicated treatment. 

It’s been kind of scattered over some previous work on the subject, but today we’re collecting the subject under one advanced topic discussion and expanding on it little.

Bullet Drop Compensation. The basic goal of the BDC reticle is to allow the shooter to rapidly range the target and compensate for that range within the reticle itself rather than with the physical elevation adjustment knobs. We want to make that process as smooth and fast as possible.

Left: Russian PSO-1.
Center: ACOG. Note that the horizontal bars widths’ are equivalent to the perceived width of the target at the ranges indicated by the tick mark.
Right: An example of the current reticle design.

The russian style is a two step system, where you use the rangefinder on the left to find the range and then go to the actual cross hair to compensate. The ACOG is an improvement over this style in that the ranging method is built directly into the reticle. Personally though, I never liked how the ACOG implemented periodic range finders rather than continuous range finders, so this reticle design will incorporate the range finder into the aiming reticle like the ACOG, but does so in a continuous manner like the Russian scope.

Windage Compensation. In addition to bullet drop, we also want to account for wind. The relatively large and slow First Strike rounds we shoot are very very susceptible to wind drift, so as a matter of necessity, we must then include some means of compensating for it in our reticle.

A simplified reticle image. The dot on the target model represents the intended point of impact.

Additional Features. You can do a lot more than just BDC and wind with the reticle.

Limit lines. This feature is in essence, is a horizontal line that indicates the maximum range at which a perfect shooter under perfect conditions may expect a 95% hit probability. In reality, using the military trained average shooter error rate, this line indicates approx. 50% hit probability. The idea is to give snipers an estimate of success before firing and potentially giving away their position.

Head BDC. Since the head is exposed more often than full torso and since it’s perceived width at any given range is less dependent on the shooters angle to the target, a BDC funnel calibrated to a slightly oversized human head (to account for the mask) would give us more reliable accurate range finding ability within those ranges that the head can be easily sized.

Running Target Leads. Paintball is a dynamic game. We’ve made the reticle here with speed in mind, but some targets won’t sit still for even the split second required to range and fire. For the worst of the offenders, i.e. running targets, there’s an additional line that uses the flight time of the round at various distances to match that hang time with the speed of the target so that they intersect at the same time down range. This follows the same aiming methodology described above for windage compensation.

Head Circle. A circle placed at the center of the crosshair who’s diameter corresponds to the perceived size of the human head at the zero range for rapid head-shot accurate hits within 25 yards.

Other Features. We still have a lot of space on the side of the reticle between the windage and the lead lines. I’m thinking about doing some russian style ranging devices in this space, (which I go into more detail below) or failing that more running target lead lines. I figure that shooting in winds above 5 mph isn’t going to be practical so more windage lines are probably a no-go. Theres a lot of space there though, so if you have an idea for a reticle feature feel free to post it.

Reference image for some of the above reticle features.

Consider. You’ll note that in the above reticle images, the BDC funnel might become difficult to use at extended ranges. This is an unavoidable consequence of diminishing range returns. For example: the range difference between 0°-1° is huge compared to the difference between 4°-5°. At the same time the angular size of the target, which we use to define the width of the funnel, suffers from the same diminishing returns as the target gets further and further away. The rate of this diminishing return is a little exaggerated with First Strikes because of their relatively low aerodynamic efficiency.

For this reason, I’m thinking about adding range tick marks to the side of the BDC funnel (over the last half or so) and putting a Russian style rangefinder in the free space of the reticle to allow an alternative method of range finding and compensation for these longer ranges.

For clutter reasons, I’m not sure if I want to add this, but with the added FoV in the new version (which I haven’t coded yet) the BDC funnel will probably be parallel for all practical purposes at the 100+ yard range and the alternate method may be necessary. I’m also not sure how I want to implement it. There are a lot of different ways to do it… Let me know if you want to see it and/or how you’d like to see it implemented.

Selectable features. Obviously we’ve talked about a lot of features here. They’re all great but you only have so much mental capacity available to distinguish between relatively close intersecting lines. For this reason not every feature will make it into the final reticle design. Longer term though, if there’s something that you absolutely have to have, depending on the reticle etching process I end up going with, it might be feasible to build a simple feature toggle utility to allow shooters to customize what reticle features go into their specific scopes. For the limit line feature you could also input your own accuracy SDs and get a 95% confidence line customized to you and your system.

Bonus. I built a poor man’s zemax, heres a look at the reticle input and output and a brief explanation of how it works.

The reticle side of the house.

The inputs are hand copied values from the ballistics modeling software. It’s a complicated application of trig, but the general idea is to take those values, and use them to build triangles that return the X and Y plot point for the reticle’s comp lines. You then copy the X and Y values produced in the output section and plug them into a function finder. You take the function that they work out to be, and the constants indicated by the values themselves, and program them into some data visualization software (Python’s Pyx add-on module in this case) to produce an image of the reticle. You then take the image and etch it into your glass using any number of readily available options. @Trinity: The deflection category indicates wind deflection.

Update: Since the specific reticle features are such a concern, I think what I’m going to do is etch super thin copper sheets instead of glass. This isnt too crazy since super thin wire is routinely used as the basis for crosshairs in old and modern scopes. It’s cost, flexibility, and accuracy (its used to make circuit boards) means that we should be able to do on-the-fly customizable reticles…

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