MOA is not 1.000" at 100 yards

[FL-NC]

Higher end sniper software expresses MOA in True MOA (TMOA) or Shooter's MOA (SMOA). With TMOA, the difference equals less than 1/2 MOA at 1000.

 

[Zerodefect]

What is this MOA you speak of?

I'm a MIL snob.

 

[Bart B.]

FL-NC, isn't the difference about 1/20th (.05) MOA at 1000?

What's a "mil?"

There are 2000*pi milliradians (≈ 6283.185 mrad) in a circle; thus a milliradian is just under 1⁄6283 of a circle, or ≈ 3.438 minutes of arc. Each of the definitions of the angular mil are similar to that value but are easier to divide into many parts.

1⁄6283 The “real” trigonometric unit of angular measurement of a circle in use by telescopic sight manufacturers using (stadiametric) rangefinding in reticles.

1⁄6400 of a circle in NATO countries.

1⁄6000 of a circle in the former Soviet Union and Finland (Finland phasing out the standard in favour of the NATO standard).

1⁄6300 of a circle in Sweden. The Swedish term for this is streck, literally "line". Sweden (and Finland) have not been part of NATO nor the Warsaw Pact. Note however that Sweden has changed its map grid systems and angular measurement to those used by NATO, so the "streck" measurement is obsolete.

 

[benEzra]

A lot of people just don't realize it's not a length measurement, it's an angle measurement. A "minute" of angle (also called an arcminute) is 1/60th of a degree, just like a minute of time is 1/60th of an hour.

By coincidence, an angle of 1/60th of a degree is just a smidge more than 1" at 100 yards, about 2.1" at 200, 4.2" at 400, etc., but it is technically an angle measurement.

 

[Walkalong]

After reading all these posts, does anyone wonder why we just use 1" per 100 yards to make it easy?

 

[mshootnit]

I've got a new standard for you to try. Three shots placed completely inside the area formed by the intersection of two perpendicularly placed short strips of ordinary black electric tape. Harder than it sounds.

 

[Warp]

I know OP. And I don't care in the slightest.

 

[FL-NC]

Walkalong- 1" per 100 is what every one I ever worked with does- most people don't have ballistic software anyway.

 

[Hardtarget]

I've never been able to, on demand, shoot 1"@100 yds for five shoots. So...I just don't worry about it. I must say...this has been an interesting read!

Mark

 

[FL-NC]

Zerodefect- I prefer mil/mil scopes, but the fact is that most US mil scopes have mil reticles and MOA adjustments. but even with mil/mil scopes I use MOA for 2 applications: 1.- in describing the capability of a given setup (rifle, scope, ammo- the assumption is that the shooter can do his/her part). 2.- In measuring the size of a shot group that has already been fired.

 

[FL-NC]

Bart B- you may be right about that. I should know, as I briefed it off of a slide umpteen times when I was a sniper instructor. The essence of the slide was "Its so small it don't matter so don't worry about it".

 

[Warp]

We go over this on the first day of Appleseeds, most shoots the number 1.047 is not even stated or mentioned.

One of the more universally understood pictorial (sp?) representations is a flashlight beam that expands outward as the distance from the light increases. 360* in a full circle, take that down to just 1* and it's still around 60" at 100 yards...we can't use that...but we can use 1/60 of that which is one "minute of angle" as that is approximately 1" at 100 yards AND 1" PER 100 yards...1 MOA is 1" at 100...2" at 200...etc...and backwards is 1/2" at 50 yards and 1/4" at 25 yards...and "an MOA is an MOA is an MOA no matter the distance" (close enough) and oh look those targets we have been shooting at 25 yards...they have 1/4" grid squares on them...those squares are...(somebody speaks up)...yes! 1 MOA! Look at that!


It doesn't get complicated for most folks until you start talking about ranging by using your front sight post or optic reticle on a known-size or approximately-sized object after pre-determining your front sight post/reticle's "size" as you see it when in position.



Interesting sidebar...how big is a red dot sight's "2 MOA dot"?

 

[lysanderxiii]

Interesting sidebar...how big is a red dot sight's "2 MOA dot"?

Well, seeing as the edge of the "dot" does not instantly go from "dot" to "no-dot" but fades out, the quest devolves to, "what are you measuring the on the dot, the region of maximum brightness, or the extreme fringe?"

 

[mahansm]

Let's not open that particular can of worms. I vaguely remember gaussian beams (an approximation to the distribution of light in a circular beam as from a laser) and just how fuzzy they were. About 34 years ago in graduate school...

 

[Warp]

Well, seeing as the edge of the "dot" does not instantly go from "dot" to "no-dot" but fades out, the quest devolves to, "what are you measuring the on the dot, the region of maximum brightness, or the extreme fringe?"

How about...how far from your eye is the dot?

 

[Arizona_Mike]

Well, seeing as the edge of the "dot" does not instantly go from "dot" to "no-dot" but fades out, the quest devolves to, "what are you measuring the on the dot, the region of maximum brightness, or the extreme fringe?"

Well, I did my doctorate in photonics and most technical people would use 1/e ~ 37%

Mike

 

[JohnKSa]

No pi/3 is a better approximation, an excellent approximation in fact (good to 6 decimal places) but still an approximation. ...
1 MOA at 100 YD is exactly 100[yd] * ATAN(1/60 deg) / (36in/[yd]). pi/3 deviates from this starting in the 7th decimal place.

Strictly speaking, Pi/3 is a very close approximation, but not exact. Pi/3 is the arc length of an angle of one minute for a radius of 3600 inches. What you are measuring on the target is the Tangent of one minute times 3600 inches. The difference is negiigibly small, About 3 e-8 inches.

That's interesting, I had never thought of it that way. Yes, if you consider 1MOA to be a linear measurement then pi/3 is very close but not exact.

1 MOA at 100 YD is exactly 100[yd] * ATAN(1/60 deg) / (36in/[yd]). pi/3 deviates from this starting in the 7th decimal place.

That formula works out to about 2.65--typo?

I think I know what you're trying to do but that won't provide the correct result because it approximates the isosceles triangle as a right triangle. That certainly isn't a practical issue given the tiny angle--but it doesn't provide an exact value.

You need to start with the isosceles triangle and split it into two right triangles, with the shared adjacent sides being 100 yards long, the two hypotenuses (the two sides of the original isosceles triangle) a hair over 100 yards long and the split angle being 0.5MOA. The exact aimpoint would be 100 yards away, but the ends of the tangent segment are slightly farther away than 100 yards.

Calculate the remaining side of one of the two identical right triangles and then double the result since that's only half the unequal side of the original isosceles triangle.

About 3 e-8 inches.

Same problem. If you run it as a single right triangle with one side 100 yards and an angle of 1MOA then you get a difference of about 3 e-8 inches compared to the length of the arc but the difference is actually a little smaller than that. It's actually an isosceles triangle with two sides slightly longer than 100 yards. You can split it into two right triangles with a shared side of 100 yards and the hypotenuses (the sides of the original isosceles triangle) each a hair over 100 yards. Each right triangle has one angle of 0.5 MOA.

The exact length of the tangent segment is 2 * 3600 * tan(1/120 degrees) inches. About 1.04719755858073 inches compared to about 1.0471975511966 inches for the length of the arc.

The difference in length between the arc and the tangent segment is about 7.38e-9 inches.

 

[benEzra]

Interesting sidebar...how big is a red dot sight's "2 MOA dot"?

Depends on the optic. I once had an old Tasco with (IIRC) a 4MOA dot, and it was a crisply defined circle, because you were looking at the reflected image of a circular LED. IIRC a 20/20 human eye is diffraction limited to around 1MOA for the mid-spectrum, so a person with 20/20 or better vision could probably resolve a 2MOA dot pretty well.

I know the dot of an Eotech is far smaller than 1 MOA, and "blooms" to 1 MOA due to the human eye's diffraction limit; that's why an Eotech's center dot doesn't get bigger when you slap a 4x magnifier on it, because it is still smaller than the eye's diffraction limit.

 

[Christopher B]

MOA

So to be super correct, perhaps we should say +/- 0.5 MOA.

Not that it matters, 1 inch at 100 yards is close enough for government work.

 

[Arizona_Mike]

That's interesting, I had never thought of it that way. Yes, if you consider 1MOA to be a linear measurement then pi/3 is very close but not exact.That formula works out to about 2.65--typo?

Yes typo in formula: 100[yd] * TAN](1/60 deg) * (36in/[yd]). Still don't know how you got 2 something, you should have gotten something really small with the typo. Did you use radians by accident?

So I gave some thought to the double tangent of the half angles and decided against it. It might be more legitimate if you are measuring the spread of a group around a point of aim however, I tend to think of it as the deviation from point of aim for most applications (like scope adjustments).

Mike

 

[Warp]

So to be super correct, perhaps we should say +/- 0.5 MOA.

Not that it matters, 1 inch at 100 yards is close enough for government work.

Who should say +/- 0.5 MOA, describing what, when?

 

[denton]

As has been pointed out, we'd all be better off if we could make the switch to the SI system (meters, kilograms) of measures, and I'll add: radians instead of degrees.

In radians, for small angles, the angle = sin of the angle = tan of the angle, and the distance between items on the target is just r*angle. So two items .05 radians (2.86 degrees) apart at the rifle would be .05*100 meters = 5 meters apart at the target.

The above approximations are quite good up to a few degrees.... er.... .05 radians (50 milliradians).

BTW, 1 minute of angle is .0003 radians to a good approximation. So a rifle that places two bullets .0003 radians apart will see them land .0003*100 = .03 meters = 3 cm apart at 100 meters. 1 MOA = .3 milliradians, to a good approximation. Of course, if you say you have a .3 milliradian gun, practically nobody in the US will know what you're talking about.....

 

[Bart B.]

Denton, does that mean sight adjustments and target ring spacings should also be based on the SI system (meters, kilograms) of measures, and radians instead of degrees?

What rear metallic sight lead screws' pitch be for a standard sight radius at a length to accomodate your new system?

 

[Christopher B]

Who should say +/- 0.5 MOA, describing what, when?

In reference to the 2 x TAN(1/120)x 3600 calculation.

 

[denton]

Denton, does that mean sight adjustments and target ring spacings should also be based on the SI system (meters, kilograms) of measures, and radians instead of degrees?

What rear metallic sight lead screws' pitch be for a standard sight radius at a length to accomodate your new system?

Oh dear... I've done it now. LOL.

It's not my new system at all. If only I were so capable! The system dates back to 1799. Shooters are one of the very few subgroups in the world that still measure shotgun shells in dram equivalents, and measure powder in grains. We're very slow to change.

Since metric thread screws fit right into the SI system, the calculations would be simpler for thread pitch.

Mil dot scopes are already using milliradians. Nothing new there.

There is nothing at all wrong with the system we have, except that a lot of the calculations are clumsy. The SI system is a lot cleaner, and much more commonly used in the world. I had to make the switch 40+ years ago, and that was painful, but worth it.

Calculations for shooting, sights, powder charges, cartridge length, etc. are all much easier in the SI system. Want to know your cartridge case capacity? Measure the mass in grams with the case empty, and then full of water. The difference is your case capacity in milliliters. End of calculations.