Minute Of Angle Linear Adjustment Help

[Ozen]

TL;DR Summary

I am in the process of developing a micro reflex sight but can't figure out how to compute the linear distance the LED should move for a 1 MOA adjustment.

I am working on developing a micro reflex sight and finally got the optical science of it sorted out, but now I reached a new impasse (hopefully the last really difficult one!). The device has to have an adjustment mechanism so the user can align the reticle with the bullet impact point, which sounds simple enough until we enter the realm of minute of angles. These funky units are "handy" in the sense that at 100 yards a 1 MOA reticle will be ~1 inch. Sure, it makes adjusting easy but from my perspective developing this sight it is nothing but a hassle. For reference, 1 MOA is 1/60th of a degree.

The problem I am facing is trying to compute the linear distance (in or mm) the LED must travel to have traveled 1 MOA. I asked around on reddit in the firearm community and I got a reply that 1/2 MOA is 0.0006in. However the user did not have the math to verify this and said they got it from an engineer at the company (firearm optics) they work at. I have not been able to figure out any way to replicate this answer.

I tried using trig to figure this out in the same method used to compute the physical dimensions for a reticle mask size (verified by data I dug up on an expired patent), but this yields a different result from the reddit guy. My math was:

2(focal length * tan (1/120)) = 8.14 * 10^-3mm [focal length = 28mm]

Obviously that is quite different than the reddit guys answer, which he could be wrong. So I dug around on one of the existing patents: https://patents.google.com/patent/US9958234B2/en?q=Reflex+sight&oq=Reflex+sight+&page=3. Image 7 depicts the adjustment mechanism they use, the socket holes next to it are ~3mm based on the footprint they use. Image 8 shows a nice section view, and we can see it can adjust ~1mm roughly in every direction. Each click on this device is 1 MOA. Unfortunately I do not have any of the actual dimensions so reverse engineering it is very limited to rough guesses I already stated. Just looking at their mechanism and comparing it with my computed value, it doesn't seem to fit quite right. Say it is 1mm exactly it can adjust in each direction, using my value above, we get ~122 clicks in each direction. From what I know about these sights, 40 clicks a direction is usually the max adjustment range (total of 80 on 1 axis). If we take that same logical deduction from before and translate .0012in to .03048mm we get: 1mm / 0.03048mm = ~33 clicks. That yields an answer that is closer to the usual adjustment range on these sights. But I need to verify this mathematically and to prove that it is correct and will adjust in 1 MOA.

So, I am seeking help on how to solve this problem mathematically. Any help you can offer is greatly appreciated!

EDIT/UPDATE: After digging around even more, it seems I might be mistaken with the typical adjustment range for these sights. the Trijicon RMR adjusts "157in at 100 yards) and the Vortex Venom is max elevation 130 MOA and windage 100 MOA. Noblex Sight C describes their range as ± 360 x ± 270 cm/100m.

It seems my way of calculating this may be correct, since 122 clicks would fall into what the competition has. If anybody could verify this or dispute this and describe how I am incorrect, it would be of great help.

 

[jrmichler]

First, let's get the geometry and terminology right. The figure below shows an angle, an adjustment distance, a pivot, and a length. With conventional iron sights, the front sight is the pivot, the length is the distance from the front sight to the rear sight, and the distance is how far you move the rear sight. The calculation for 1 MOA is:

Distance = tan(1/60 deg) X Length

Sample calculation for 1 MOA at 100 yards: Distance = tan(1/60 deg) X 300 feet X 12 in/ft = 1.047", which is very close to the rule of thumb that 1 MOA is 1" at 100 yards. You do need to watch your units. If you want distance in inches, the length needs to be inches.

In a telescopic sight, the pivot is inside the scope.

 

[sail]

Hello. I am pondering over the same problem. Had you been able to figure the mechanism out?
It would be a great help if I can use your guidance to do my calculations.

Also, were you considering the length ratio of 1 MOA over the 100 Yards distance to do the calculations?
I am also thinking of bringing in the reflection angles, as my LED sits a little behind the focus.