Why do they call it a "minute of angle"?

[MachIVshooter]

You have that backwards Wally. 100 meters is roughly equivalent to 110 yards. So with the distance growing 10%, the minute of angle will grow 10% as well. So a MOA will become 1.14" at 100 meters.

Wyman

Nope. You've inverted the correlation of the numbers, and angular measurements remain regardless of distance. MOA is MOA, no matter if it's 10 yards or 10,000. What changes is the distance of arc, which will be ~10% (actually 9.36%) longer at 1 meter than one yard. Since a 1" group @ 100 yards is actually .95 MOA, 1 MOA at 100 meters becomes 1.04".

The sweet spot for 1" groups really being 1 MOA for practical purposes is at 104.7 yards, halfway between 100 yards and 100 meters.

 

[Bart B.]

For all the metric afficianados, the French first established a meter as one ten-millionth the distance from the North Pole to the equator.

 

[Catpop]

Jim, I learned the same thing about a year ago on this forum. I used surveying trig functions to prove it.
Good to see you're still at it!

 

[lastofthebreed]

And all along I thought that minute of angle was a measurement of the time it took a sixteen year old heterosexual male to read all the articles is this months Playboy magazine. Lurn sumthin new ever day don't we Bub?

 

[stoky]

I think I'd like bowling more if
ther

e were a catapult involved.

A bowling ball fits perfectly (well, close enough) in welding gas cylinders...............some black powder and your good to go.

 

[benEzra]

FWIW, those MOA can be divided into sixty seconds of angle as well, just like a time minute has sixty seconds.

Yup, you sometimes see arcseconds referenced in astronomy, though milliradians/etc. are used a lot also. Arcseconds (or seconds of angle/seconds of arc) would be overkill for measuring groups, though, given that 1 arcsecond works out to just over 1/60th inch at 100 yards or 1/6th inch at 1000.

 

[WestKentucky]

Right - it's an oddity to see 1' = ~1" !!!

Going a little nautical, of a different scale, I just can't fathom a life chained to using a rod to call mark twain!! ;-)

Reckon there's a township with a good range? Maybe a few square fields of good ground left to farm? Wait...this is nautical stuff, not land. Chains are for cajuns.

 

[Varminterror]

I forget where I heard it, I was in grammar school... but fathom, chain, and rod are all units of length measure, and calling "Mark twain" is to notify the captain (or rather the pilot, in river vernacular I'm told) the river depth is two fathom.

 

[JohnKSa]

A fathom is 6 feet and is used, as you say, for water depth measurements.

The chain is typically used for surveying distances. There are a number of chain measurements, but the most common is probably a 66 foot chain--1/80th of a statute mile.

The rod is also used as measure for surveying distances. It's a fourth of a chain, 16.5 feet.

Rods and chains relate well to acres, or perhaps vice versa, I suppose.

1 MOA at 100 meters becomes 1.04".

1 MOA at 100 meters is about 1.145"

100 m * 100cm / 2.54 cm/inch * 2 * pi / 21600 minutes = about 1.145"

 

[Varminterror]

Since a 1" group @ 100 yards is actually .95 MOA, 1 MOA at 100 meters becomes 1.04".

Math is coming out wrong on this too - 1moa at 100m (328.08ft) is 1.145"

328.08ft x 12"/ft x tan(1/60) = 1.145"

That's not REALLY the formula, since it accounts for an isosceles triangle instead of two right triangles half as wide like we should, but since 2x tan(Theta/2) = tan(theta), it comes out the same, so I simplified.

What MachIVshooter calculated is as if you shot a 0.95" group at 100yrds, then subtend/project that group out to 110yards, or ~100m. Not a .95moa group (1" at 100yrds). The mistake was the confusion of inches and MOA here's his math: .95" x 110/100 = the 1.04" he calculated BUT the group size wasn't 0.95", it was 1.0", which he correctly cited as 0.95MOA. Again, at 100m, 0.95moa (rather 0.955...) is 1.09", not 1.04", and 1moa at 100m is ~1.15".

The below would be the correct relationships:

A .95" group at 100yards would come out to 1.04" at 100m (.907moa)

A 1" group at 100yards (0.95moa) would come out to 1.09" at 100m.

A 1moa group at 100 yards is 1.047" and at 100m is 1.15".

 

[JohnKSa]

The sweet spot for 1" groups really being 1 MOA for practical purposes is at 104.7 yards, halfway between 100 yards and 100 meters.

1MOA = 1" at about 95.493 yards

 

[MachIVshooter]

Math is coming out wrong on this too - 1moa at 100m (328.08ft) is 1.145"

328.08ft x 12"/ft x tan(1/60) = 1.145"

That's not REALLY the formula, since it accounts for an isosceles triangle instead of two right triangles half as wide like we should, but since 2x tan(Theta/2) = tan(theta), it comes out the same, so I simplified.

What MachIVshooter calculated is as if you shot a 0.95" group at 100yrds, then subtend/project that group out to 110yards, or ~100m. Not a .95moa group (1" at 100yrds). The mistake was the confusion of inches and MOA here's his math: .95" x 110/100 = the 1.04" he calculated BUT the group size wasn't 0.95", it was 1.0", which he correctly cited as 0.95MOA. Again, at 100m, 0.95moa (rather 0.955...) is 1.09", not 1.04", and 1moa at 100m is ~1.15".

The below would be the correct relationships:

A .95" group at 100yards would come out to 1.04" at 100m (.907moa)

A 1" group at 100yards (0.95moa) would come out to 1.09" at 100m.

A 1moa group at 100 yards is 1.047" and at 100m is 1.15".

Yeah..........I shouldn't have been typing this morning. Last night was a rough one, and I'm still a little foggy What can I say? As a full time single dad, I make the most of it when the kiddo is with grandparents for a night

 

[Bart B.]

Of course, the sight angle change moves impact a tiny bit more at right angles to the LOS than in a circular arc. For simplicity, let's pretend the target plane is dished and equidistant at all points on its surface to the sight.

The standard service rear sight on Garands with a 32 tpi leade screw moves its base in windage 1/128th inch per click. How much in inches at 100 yards does that change the line of fire angle relative to the line of sight with the elevation set all the way:

Up?

Down?

Is the change in elevation per click the same? If not, what is it?

Same rear sight's used on M14's. How much does it change POI at 100 yards with a shorter sight radius than M1's have? I'd bet it's the only iron-sighted rifle that with its rear sight all the way up, windage clicks are virtually exact trig MOA units moving POA 1.0471975364... inch at 100 yards.

There's two MOA standards; one for sights on arms, one for math with angles. Ne'er the twain will meet in harmony until we all accept that. We've done it for mils (4 standards) and miles (3 standards).

 

[Arizona_Mike]

Interestingly, this is related to why a nautical mile is 6000 yards

1 nautical mile is 2025.37 (~2000) yards. Clearly you meant feet.

Mike

 

[sscoyote]

You guys need to set the equations up using Dimensional Analysis (remembered that one from school), so your units cancel correctly. It helps keep the ratios correct.

 

[JohnKSa]

...Dimensional Analysis...

Force = mass * acceleration-->(units kg*m / s^2)

Kinetic Energy = 1/2 * mass * velocity squared--> (units kg*m^2 / s^2)

Kinetic Energy / distance = 1/2 mass * velocity squared / distance --> (units kg*m / s^2) <Same units as Force>

Force = 1/2 mass * velocity squared / distance

Force = Kinetic Energy/distance. If a moving object hits a target medium with kinetic energy KE and the target medium stops the object by decelerating it over a distance of D; the force applied to the target medium is equal to KE/D.

Momentum = mass * velocity--> (units kg * m / s)

Momentum / time = mass * velocity /time --> (units kg * m / s^2) <Same units as Force>

Force = Momentum/time. If a moving object hits a target medium with momentum M and the target medium stops the object by decelerating it over a time of T; the force applied to the target medium is equal to M/T.

 

[cc-hangfire]

I'm just finding this thread, & I have to add my 2 cents.

In current surveying, civil engineering, and land descriptions, angular measurements are an everyday matter. There are 360 degrees in a full circle, 60 minutes in a degree, and 60 seconds in a minute. I currently have between 40 & 50 construction plan sets or property boundary drawings on my desk, and every on them have boundary lines or property lines labeled with distance & bearing, & the bearings are all showing degrees, minutes, & seconds.

Others have covered the ballistic variation of these terms - primarily our one degree is called one angle in ballistics. (Surveyors & engineers would say "minute of degree" whereas shooters say "minute of angle"; just a difference in trade jargon terms)

You'll also find this angular measurement system in latitude & longitude (shown on many maps), but that'd be another long & dry post.

 

[cfullgraf]

It all sounds clear as mud, eh?

I enjoyed all the information. Brings back memories of Engineering in college back in the "dark ages".

 

[stoky]

It was adapted to ameliorate the alliteration of finding fall in fathoms for fast in furlongs / fortnight.

 

[pert near]

 

[Bart B.]

It's often thought that the biggest number is a Googol; a 1 with one hundred zero's after it.

Then someone came up with a bigger one: Googolplex. That's a 1 followed by a Googol of zero's. There's not enough matter in the known universe to make a sheet of paper to print a Googol of zero's 1/10ths inch diameter. on. To say nothing about the size of a pencil to write them. That sheet of paper would have to be 37 light years square.

 

[stoky]

 

[Dr T]

Yep! I meant 6000 ft. thanks for the catch, Mike.

By definition, a mathematician is someone who writes A, says B, and means C. Since I was trained as a pure, not applied, mathematician, it is all theoretical. but at heart I am really an empiracist.

 

[Arizona_Mike]

at heart I am really an empiracist.

Classicist Victor Davis Hanson tells a story of giving an invited lecture on Ancient Greece when a student barged in and started shouting denouncing him for being a classist, then grabbed all the pizzas that were on a table at the back of the lecture room and stormed out.

So shame on you for being an empi-racist.

Mike

 

[jim in Anchorage]

My God what have I started. So what is a ft/lb anyway? Just lifting a pound 1 foot? Or is it like horsepower with time in the equation?