In the first two parts of this series (Part 1, Part 2) we have discussed sight adjustment for a fixed distance only. Our calculations used the lengths of the sides of similar triangles. But it is much more useful to think in terms not of the sides, but of the angles, of the triangles. This change will enable us to set general rules for sight adjustment at any distance, without having to do as much math in the field.
We typically measure angles in degrees – there are 360 degrees in a full circle. A useful thing about angles is that an angle is the same at any distance. So if we know how to adjust our sights based on angles, we can adjust for any distance without re-doing all that division. If you shoot within an accuracy of one degree, what does that mean on the target?
A standard distance in shooting is 100 yards. If you are at the center of that circle, the radius is 100 yards. Remember this formula from school?
Circumference = 2πR
One degree is 1/360 of the circle, so the arc of one degree of a circle at 100 yards in inches is:
Arc = 2π (3600”)/360 = 62.8318”
So if you were accurate within 1 degree at 100 yards, you would miss the x-ring by five feet. Obviously a degree is too coarse a measure. So each degree is split into 60 minutes of angle (MOA).
(Note: Geometry purists know that the straight-line distance on the target from bullseye to impact is not an arc, but a chord. However, the difference in length between arc and chord at this small an angle is measured in molecules, so it is practically irrelevant.)
A minute of angle is a useful measure, because 62.8318”/60 is 1.0472” at 100 yards. For rifle shooting purposes we can simplify that as 1 inch at 100 yards. After all, the error of that approximation at 1000 yards is less than ½ inch, easily within the x-ring of a high-power rifle target – or any other practical 1000-yard target. The picture illustrates the change in POI of 1 MOA at various distances (click to enlarge):
So if we know how our sights adjust in terms of MOA, we can quickly figure how many clicks we need to zero at any distance. As we saw in Part 1 of this series, we need to know two things about our rifle:
- The amount of sight movement per turn and per click (if it has click detents);
- The sight radius – distance between front and rear sights.
Let’s look at two 10/22s, one with 18.5” barrel and Tech-Sights TSR-200 sights, 23” radius; and the other with 22” barrel and a Williams FP rear sight, 25” radius. First, how much movement is one turn or one click:
- TSR-200 36 TPI, 5 clicks per turn: 1 turn = 1”/36 = .02778”, 1 click = .00556”
- Williams FP, 48 TPI, 20 clicks per turn.: 1 turn = .0250”, 1 click = .00125”
Now, what would be the effect on POI at 100 yards of adjusting each of these? Remember the formula:
I = A × D/R
- I= POI change on target
- A = Sight adjustment movement
- D = distance from front sight to target
- R = sight radius
For 18.5” barrel, TSR-200:
- 1 turn: .02778” × 3600/23 = 4.3482”
- 4.3482”/1.0472 = 4.1522 MOA per turn
- 1 click = 4.3482”/ 5 = .8696”
- .8696”/1.0472 = .8304 MOA per click
- ≈ 5/6 MOA per click (5/6 = .8333)
For 22.0” barrel, Williams FP:
- 1 turn: .0250” × 3600/25 = 3.600”
- 1 click = 3.600/20 = .1800”
- .1800”/1.0472 = .1719 MOA
- ≈ 1/6th MOA per click (1/6 = .1667)
If you are adjusting the front sight for elevation, remember that the formula is:
I = A × (D+R)/R
For the 18.5” barrel with Tech-Sights, the math is:
- 1 turn: .02778” × 3623/23 = 4.3760”
- 4.3760”/1.0472 = 4.1787 MOA per turn
- 1 click = 4.3760”/ 5 = .8752”
- .8752”/1.0472 = .8358 MOA per click.
- ≈ 5/6 MOA per click (5/6 = .8333)
The difference between the front and rear sights is so small as to be negligible. The Lyman front sight on my 22” rifle is not adjustable.
In practical terms, I would estimate 1 MOA/click on the Tech-Sight, and if I had to move more than 6 MOA I would add one click for every six. For example, if my POI was 1” left at 25 yards (or 8” at 200 yards), that’s 4 MOA = 24/6ths, I would adjust the rear sight to the right (turning the dial clockwise) by 5 clicks. Yes, that would overcompensate by 1/6 MOA, which is about .04” at 25 and .33” at 200.
If my 25-yard group was 3.5” high = 14 MOA (84/6), I might raise the front sight and lower the rear by some combination of 17 clicks (17 × 5/6 = 85/6). Note that there is a limit to the range of adjustment. The Tech-Sights front sight has a maximum elevation of 18 clicks from its lowest position, and the rear a maximum of 40 clicks from its lowest position. If for some reason you needed a taller front sight, Tech-Sights offers one as an accessory or you can use an M16A1 front post. The Nodak front sight post has a range of adjustment of about 10 turns, or .300”, and its MOA value is about 4.5 MOA per turn on an 18.5” barreled 10/22.
If your rifle and its sights are set up differently from these, now you know how to run the numbers for your system to establish the MOA value per turn or per click. Write down if you need to. Once you know your rifle’s sights in terms of MOA, you can make any sight adjustments in the field easily.
Optical scopes are much easier. Their “sights” are all inside the tube, so the adjustment is independent of barrel length and is already calibrated in MOA. Most scopes have click adjustments and their precision is marked on the turrets. Better quality scopes have ¼ MOA clicks, and cheaper ones have ½ MOA clicks.
If you have any questions on this article and how it applies to your 10/22, please post them in the comments.