Advanced Marksmanship 27.77 Why?

[Maggot]

In a class I took they gave us the constant of 27.77.

Take the height of a known object near the target, say a tire at 30" and multiply the two. 27.77 X 30 = 833.1

Then use 833.1 and divide that by the # of mils of the target, say a man and he measures 1.2 mils then he is 694.25 yds away.

The question then is, what does the 27.77 represent? How is that # determined?

 

[DocRDS]

1000/36

Why those numbers?

1 mil ~ 1 yard at 1000 yards (its an angle--kinda like the 1 inch = 1MOA at 100 yards)

target size in yards x 1000 / mil measurement.

target size in inches x 1000/36 x 1/mil measurement.

Take a known target at distance in inches x 27.77/mil measurement.

(its acutally a much better approximation).

SOH CAH TOA

Tan = Opposite/Ajacent

Distance to Target (adjacent) = Opposite/Tan(mils)

Tan = sin/cos

For SMALL angles, cos = 1, sin x = x

Distance = target size/x (angle in radians)

 

[Maggot]

1000/36

Why those numbers?

1 mil ~ 1 yard at 1000 yards (its an angle--kinda like the 1 inch = 1MOA at 100 yards)

target size in yards x 1000 / mil measurement.

target size in inches x 1000/36 x 1/mil measurement.

Take a known target at distance in inches x 27.77/mil measurement.

(its acutally a much better approximation).

SOH CAH TOA

Tan = Opposite/Ajacent

Distance to Target (adjacent) = Opposite/Tan(mils)

Tan = sin/cos

For SMALL angles, cos = 1, sin x = x

Distance = target size/x (angle in radians)

I dont doubt youre right but thats over my head. I was just asking about the 27.77 and what is that one # derived from?

 

[Tmm01]

Since your target is in inches, an inch would be 1/36 of a yard that equals .277777 and when you multiply that by 1000 you get 27.77777 by rounding it off you get 27.78 or 27.77777

 

[308pirate]

I dont doubt youre right but thats over my head. I was just asking about the 27.77 and what is that one # derived from?

His explanation is correct but very hard to follow.

Here's the answer in short: target size in inches x 1000 yd/36 inches x 1/mil measurement.

Since 1000/36 = 27.77777 the formula becomes target size in inches x 27.78 yds/inch x 1/mil measurement of target

All the units cancel out except yards, as it should be.

 

[DocRDS]

Sorry I get excited sometimes.

27.77 is indeed 1000/36

@Maggot in your initial example you shouldn't have two items. Measure the thing with the known height in your scope.

So if you know the tire is 30" measure the TIRE in your scope in mils. This of course gives you the distance to the tire. (I assume the man is just nearby).

And for those of you wondering about the "approximation" of 1 mil = 1 yard at 1000 yards, for practical purposes you can say they are equal. The difference is in the 6th or 7th decimal point, not like MOA where its 1.047

1.00000033333 is the "official" measurement (yards subtended by 1 mil at 1000 yards) or 36.000012 inches so using 1000 and 36 is fine.

 

[Maggot]

Sorry I get excited sometimes.

27.77 is indeed 1000/36

@Maggot in your initial example you shouldn't have two items. Measure the thing with the known height in your scope.

I see, then youre comparing apples and apples...

But wouldnt that throw off the equation.

Sorry, Im mathematically dyslexic.

 

[DocRDS]

Nope its just a simplified math. In right triangles, if you know 2 parts, you can find the third. It doesn't matter of those parts are lengths or angles.

You know 2 out of 3 things in a formula: Angle of the "target", linear size of the "target" using those two you find the "distance" to the target. The 1000 and 36 come from converting inches to yards (36) and mils to radians (1000)

Distance = size/angle (distance and size need to be same units, angle MUST be radians for this to work)

Distance (yards) = size (yards)/angle(radians)

Distance (yards) = size (inches) / [angle (radians) * 36 ] --> Change size to inches--introduces the "36" to stay "yards" if my height is in inches, I divide by 36, so my DISTANCE remains in yards!

Distance (yards) = size (inches) * (1000/36) * 1/angle(mils) --> convert radians to mils 1 radian =1000 mils


Think of it as
D = H/A (distance = Height/Angle). 1000/36 is simply to get the correct units 1/36 from the Height and 1000 from mils.

You know (or can estimate) H and A, so you just math it out to get D.

 

[Maggot]

Nope its just a simplified math. In right triangles, if you know 2 parts, you can find the third. It doesn't matter of those parts are lengths or angles.

You know 2 out of 3 things in a formula: Angle of the "target", linear size of the "target" using those two you find the "distance" to the target. The 1000 and 36 come from converting inches to yards (36) and mils to radians (1000)

Distance = size/angle (distance and size need to be same units, angle MUST be radians for this to work)

Distance (yards) = size (yards)/angle(radians)

Distance (yards) = size (inches) / [angle (radians) * 36 ] --> Change size to inches--introduces the "36" to stay "yards" if my height is in inches, I divide by 36, so my DISTANCE remains in yards!

Distance (yards) = size (inches) * (1000/36) * 1/angle(mils) --> convert radians to mils 1 radian =1000 mils


Think of it as
D = H/A (distance = Height/Angle). 1000/36 is simply to get the correct units 1/36 from the Height and 1000 from mils.

You know (or can estimate) H and A, so you just math it out to get D.

Gonna have to study on that for a bit. Thanks.

 

[308pirate]

Gonna have to study on that for a bit. Thanks.

 

[Trigger Monkey]

The question then is, what does the 27.77 represent? How is that # determined?

It's funny, they never explained that to us, it was more like

because