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Rifle Scopes Metric mil reticle subtension...coincidence?

sscoyote

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Full Member
Minuteman
Jan 1, 2005
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Is it just coincidence that the 3.6 IPHY milliradian angle subtends exactly 10 cm. at 100 meters? I don't see how it could be designed to be so.
 
Re: Metric mil reticle subtension...coincidence?

By definition the miliradian subtends an arc that is 1/1000 the lenght of the radius.

So at 100 m one mil subtends 100/1000 = 0.1 m = 10 cm

And 100 yds = 300 feet = 3600 inches, so at 100 yds ome mil subtends 3600/1000 = 3.6 inches
 
Re: Metric mil reticle subtension...coincidence?

The "coincidence" comes from the metric system also being a <span style="font-weight: bold">decimal</span> system. A <span style="font-weight: bold">milli</span>radian by definition is an arc that subtens 1/1000th of the radius. The "milli"-prefix does not just apply to the metric system of lengths, like in millimeters, it is universally used with other units like milliwatts, milliseconds etc..

It may look like magic to someone who usually only deals with an archaic system that uses different units (yards, feet and inches) for distance and target size which are not easily convertible (12 inches in a foot, 36 inches in a yard). If one yard was 100 inches, 1 mil would subtend 10 inches at 100 yards and yards/inches would be just as "easy" when used with a mil-based reticle.

 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: David S.</div><div class="ubbcode-body">The "coincidence" comes from the metric system also being a <span style="font-weight: bold">decimal</span> system. A <span style="font-weight: bold">milli</span>radian by definition is an arc that subtens 1/1000th of the radius. The "milli"-prefix does not just apply to the metric system of lengths, like in millimeters, it is universally used with other units like milliwatts, milliseconds etc..

<span style="color: #FF0000">It may look like magic to someone who usually only deals with an archaic system that uses different units (yards, feet and inches) for distance and target size which are not easily convertible (12 inches in a foot, 36 inches in a yard). If one yard was 100 inches, 1 mil would subtend 10 inches at 100 yards and yards/inches would be just as "easy" when used with a mil-based reticle. </span>
</div></div>

Well said... people not used to it often do not realize or subestimate the advantages of a DECIMAL system
smile.gif
 
Re: Metric mil reticle subtension...coincidence?

Thks. Tiro and David 'preciate the responses. Will study on the 1:1000 aspect a bit more.
 
Re: Metric mil reticle subtension...coincidence?

So if the 1/6400th part of the circle is used then the "milli"- prefix is technically incorrect, and at 100 meters the subtension is no longer 10 cm. Is that not correct?

Have to look over Simeones writeup i have around here somewhere.

I understand the 1:1000 ratio, just forget about it sometimes when thinking in the Imperial system. Sure wish we woulda' switched when they proposed the change years ago. Though i'm sure it would've been costly, no doubt. As a lab tech we have to use metric all the time.
 
Re: Metric mil reticle subtension...coincidence?

As folks have already said, there was an expression you learned in high school that went like:

Arclength = Radius * Angle

In fact, since the concepts of arclength and radius are more simple, that is actually the formal definition of what an "angle" is. This is just a generalization of the expression

Circumference = Radius * (2 * pi)

so now we know the angle 2pi is equivalent to "all the way around the circle" and we call this unit of measure for angles "radians", i.e., a circle is 2pi radians. In this sense, the radian is the natural unit for describing angle.

Knowing this, it should be obvious that if both the angle (in radians) and the radius are strictly powers of 10, so should the arclength. It doesn't matter if you're measuring distance in meters, yards, feet, inches, whatever: as long as your adjustment is not too far from level, for any abitrary length unit, (x radians) at (y length unit) distance = (x*y length unit). This may be be why some prefer mils to MOA.

(There is some subtlety because when you talk about making a 1 mil adjustment on a flat sheet of paper 100 meters away, it's not exactly arclength but instead the arclength projected onto the plane of the paper, but for 1 mil, that difference is tiny).

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: sscoyote</div><div class="ubbcode-body">So if the 1/6400th part of the circle is used then the "milli"- prefix is technically incorrect</div></div>

No, it's still correct.

You're confused because the total number of radians in a circle is not unity or a power of 10. It's 2pi. I.e., 1 radian is not a full circle, 2pi radians is.

A milliradian is 1/1000 of a radian by definition. There are 2pi radians in a full circle, meaning there are 2000pi milliradians in a circle, so that each milliradian is 1/2000pi ~ 1/6283 of a circle.

But that really has no bearing. Just remember the arclength expression.
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: sscoyote</div><div class="ubbcode-body">So if the 1/6400th part of the circle is used then the "milli"- prefix is technically incorrect, and at 100 meters the subtension is no longer 10 cm. Is that not correct?</div></div>
That is correct, but the deviations are small enough to be neglected.

If you want to be super-anal about the accuracy of scope adjustments, I could list at least five different sources of systematic errors like the one you pointed out that in theory will make the adjustment/reticle of a scope incorrect, but fortunately most of them are irrelevant in practice for reasons like the fact that we are dealing with small angles. If we start to go "full circle" (literally) when thinking about the adjustments, a lot of stuff doesn't add up any more.
 
Re: Metric mil reticle subtension...coincidence?

The mil Reticle does not come to it's full advantage unless combined with the metric system.
Håkan
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lowlight</div><div class="ubbcode-body">don't use 6400, that is a rounded number, the true number is 6283 </div></div>

The true number is 6283.2

But since the acceptable error of each manufacturers different reticle is greater than the difference between either figure, it is gonna be okay to use 6400 since it allows for simpler mathmatics.

(Your results may differ)
 
Re: Metric mil reticle subtension...coincidence?

Thks. for the repies guys. I know that some have bastardized the true math by offering a rounded # of 6400, and that it's close to the true milliradian, but not exactly correct as stated above. It's what i wanted to know.
 
Re: Metric mil reticle subtension...coincidence?

All western rifle scope makers I know of use the true value of the milliradian (1/6283 of a circle), for clicks and reticles.
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: lockedandloaded</div><div class="ubbcode-body">
The true number is 6283.2
</div></div>

Well since we are splitting hairs, the true number actually has an infinite number of decimals which do not repeat in any type of a pattern. This stems from the fact that the number Pi (used to derive the above number) also has an infinite number of decimals which never repeat in a pattern.

Last time I checked a couple of years back, the record for the largest number of digits calculated for Pi was around 5 trillion.
 
Re: Metric mil reticle subtension...coincidence?

ARRRRGGHHHHHHHH!!!

My head hurts, I shoulda paid more attention in math...

So if the sum of all fears is equal to the american pie multiplied by the square root of all evil and is equal to the circumference of the spaceballs...


man I need to lay off the coffee....
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Commander Shepard</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: lockedandloaded</div><div class="ubbcode-body">
The true number is 6283.2
</div></div>

Well since we are splitting hairs, the true number actually has an infinite number of decimals which do not repeat in any type of a pattern. This stems from the fact that the number Pi (used to derive the above number) also has an infinite number of decimals which never repeat in a pattern.

Last time I checked a couple of years back, the record for the largest number of digits calculated for Pi was around 5 trillion.





</div></div>

I'd have written it to 6 trillion decimals, but my pencil broke
blush.gif


The 6400 figure is the result of the US Artillery rounding the figure UP to make it easier for crews to calculate with.
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: RedneckHunter</div><div class="ubbcode-body">ARRRRGGHHHHHHHH!!!

My head hurts, I shoulda paid more attention in math...

So if the sum of all fears is equal to the american pie multiplied by the square root of all evil and is equal to the circumference of the spaceballs...


man I need to lay off the coffee.... </div></div>

Oh, you must be one of them ee-lec-tronic-lay-zer guys, huh?
cool.gif
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: lockedandloaded</div><div class="ubbcode-body">[Oh, you must be one of them ee-lec-tronic-lay-zer guys, huh?
cool.gif
</div></div>


LOL, nope, I dont even own a rangefinder, I just keep squeezing the trigger till it runs away or fall down...
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Commander Shepard</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: lockedandloaded</div><div class="ubbcode-body">
The true number is 6283.2
</div></div>

Well since we are splitting hairs, the true number actually has an infinite number of decimals which do not repeat in any type of a pattern. This stems from the fact that the number Pi (used to derive the above number) also has an infinite number of decimals which never repeat in a pattern.

Last time I checked a couple of years back, the record for the largest number of digits calculated for Pi was around 5 trillion.
</div></div>

You're being irrational.


Great thread guys. It was very informative.
smile.gif
 
Re: Metric mil reticle subtension...coincidence?

The only thing worth pointing out is that when a mil is subtended at distance, the result is actually an arc (as said above) but we are using the chord of that arc. In small arc lengths or large diameter arcs, the difference is negligible, but, if we are splitting hairs...
 
Re: Metric mil reticle subtension...coincidence?

[/quote]

I'd have written it to 6 trillion decimals, but my pencil broke
blush.gif


The 6400 figure is the result of the US Artillery rounding the figure UP to make it easier for crews to calculate with. [/quote]

Actually that is really quite interesting to know--was wondering why somebody would bastardize the true subtension.

Always wanted to know the history behind the mil applications. Good stuff guys. Thanks!

For awhile i tried to figure out how they simplified the angular geometry to a simple 5 variable algebraic formula and found the answer in Robert Simeone's writeup. Nice to know the details of it...IMO.
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: TiroFijo</div><div class="ubbcode-body">All western rifle scope makers I know of use the true value of the milliradian (1/6283 of a circle), for clicks and reticles.</div></div>

The original Leupold M3A used a reticle based off 6400 it's why they say Army mils vs Marine mils. Back in the day, circa 1982, there was a difference.

No longer,
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lowlight</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: TiroFijo</div><div class="ubbcode-body">All western rifle scope makers I know of use the true value of the milliradian (1/6283 of a circle), for clicks and reticles.</div></div>

The original Leupold M3A used a reticle based off 6400 it's why they say Army mils vs Marine mils. Back in the day, circa 1982, there was a difference.

No longer, </div></div>


Lowlight, I'd be interested to know why you say there no longer is a difference between the US Army M3A reticle and the USMC spacing? I dont want to sound confrontive, just interested in the info you have that support that? There have been tons of early issue M3A scopes still mounted on M24 rifles (well, until recently before the new conversion to the XM2010 Sniper rifle).
 
Re: Metric mil reticle subtension...coincidence?

I was taught that the difference between Army and Marine mils was the dot size/shape in the different scopes. I'll see if I can find it.

Edit:
We used M3As, and were taught that the reticles were based off real mils. (Army Sniper School) This is what I was taught as the difference between Army and USMC mils.


ReticlesUSAvsUSMC.jpg
 
Re: Metric mil reticle subtension...coincidence?

SSSamuri, yes, dot shape/size is different.

The Leupold M3a Ultra has laser-etched mildots with perfectly concentric circle dots. The USMC Unertl 10X has painted dots onto the wire reticle, which caused them to become eliptical (football) shaped. That was the level of technology available at the time J. Unertl made them.

Also, the M3a has thinner outer posts (not the stadia lines) compared to the USMC version.
 
Re: Metric mil reticle subtension...coincidence?

Yep, that's what I was taught. But I was posting that as a prompt to what LL said about Army mil-dots being based off artillery mils. However, I just went back and read it again and he refers to 1982... the M24 wasn't adopted until 88. I'm curious now, is this some behind the scenes stuff, before the schoolhouse was up and running? I'm out now, but I still like to keep my history/facts straight.
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lowlight</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: TiroFijo</div><div class="ubbcode-body">All western rifle scope makers I know of use the true value of the milliradian (1/6283 of a circle), for clicks and reticles.</div></div>

The original Leupold M3A used a reticle based off 6400 it's why they say Army mils vs Marine mils. Back in the day, circa 1982, there was a difference.

No longer, </div></div>

But still, many "mil" system are still used even in western world 6000, 6300 etc.
And russians are still sticking with good ol´ 6000.

Thats why i prefer using only mrad term when talking about 6283,185307179586476925286766559 circle.
 
Re: Metric mil reticle subtension...coincidence?

JL (or anyone), do you know of any western <span style="font-weight: bold">rifle scope</span> maker that currently uses anything other than "true" milliradians?

On the topic of "USMC/football" vs "Army/round" dots, I think the oval dots have not been made by anyone for more than a decade now. It was basically a crutch due to manufacturing limitations at the time, the round dots and newer line/hatch based designs are much better IMO.
 
Re: Metric mil reticle subtension...coincidence?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: TiroFijo</div><div class="ubbcode-body">JL (or anyone), do you know of any western <span style="font-weight: bold">rifle scope</span> maker that currently uses anything other than "true" milliradians?

On the topic of "USMC/football" vs "Army/round" dots, I think the oval dots have not been made by anyone for more than a decade now. It was basically a crutch due to manufacturing limitations at the time, the round dots and newer line/hatch based designs are much better IMO. </div></div>

Far as I recall, only Dick Thomas at Premier Reticle did the Corps reticles for Unertl. I think they are still around, son runs it. But dont believe they can do Leupold reticles anymore. Maybe some of the old school benchrest optics guys can do them, they were the folks who boosted the magnification of factory scopes up to 36X and 48X