"He pivoted slightly, found a bush coned in snow, which he took to be of three feet girth. By covering it in the scope with mil-dots and racking through the math - the black mass covered two dots; multiply the assumed one meter in heigth by one thousand and divide by two to get the approximation of a thousand yards: say, less than a thousand but more than nine hundred yards he held four dots high."
There are a couple issues, separate from the shooting related issues:
1. The most glaring issue is the math error.
One meter (in width or height) x 1000 / 2 = 500 not 1000. If he can't divide 1000/2 to get 500, he's got serious problems with doing math in his head.
2. He references target girth of 3 feet and then uses target height of 1 meter. I don't know anyone who can tell the difference between a 3 feet (1 yard) wide target and 1 meter wide target at 1000 yards or 1000 meters.
I also don't have any real issue with a shooter who grew up with the imperial system estimating target size in feet or inches and then converting that to cm or m for range calculation purposes.
But the shooter should be using a consistent target dimension (height or width) when ranging, and
The shooter should be working in consistent units.
There are some shooting issues as well:
A. Range estimation with a mil dot using meters.
The formula for range estimation with a mil dot reticle in meters is:
Target Height in meters / Height in mils x 1000 = Range to target in meters.
(Obviously you can also measure target width and the mil subtension in width as well.)
Either way, if a 1m target subtends 2 mils, then the range is 500 yards.
1m / 2 mils x 1000 = 500
With the order of operations rules in math you can multiply or divide in any order for this calculation, so it can also be solved as:
1x1000 / 2 = 500;
which is easier in your head and probably would have avoided the mistake he made.
B. Range estimation with a Mil dot using imperial units - yards
Lots of self taught long range shooters, in particular civilian shooters, will use yards with a mil dot reticle. It's workable but it's less elegant.
The easiest way to do it is to work in yards.
Target height in yards / height in mils x 1000 = range to target in yards.
If a target is 24" wide, you'd use .75 yards, then divide by the mils and multiple by 1000 to get the range - or some combination of that:
.67 x 1000 = 670 (which is super east in your head as all you're doing is moving the decimal) and then divide 750 by the mills. If the target is subtending .5 mils in the reticle, then it's 670/.5 = 1340 yards. (which is easier to do in your head by multiplying 670 by 2 rather than dividing 670 by .5, as mathematical it's the same thing, just a lot easier).
C. Range estimation with a Mil dot using inches, and with mixed units
Unfortunately, I encounter shooters who use inches for estimation of target size, and the formula for inches is more difficult to do in your head:
Target size in inches x 27.77 / Height in mils = range to target in yards.
So for a 24" target, you have to multiply 24 x 27.77 and then divide it by the height in mils.
24x27.77 = 666, and then 666 / .5 = 1332 yards.
I can't crunch those numbers in my head, so a calculator becomes a go/no go item if you're using that approach.
Almost as and are the shooters who want to use target size in inches and then use range to the target in meters.
In this case the formula is:
Target size in inches x 25.4 / Height in mils = range to target in meters.
The math is just as hard:
24x25.4 = 609.6, and then 609.6 / .5 = 1219 meters (which is 1333 yards).
In summary, all of the above get you to the same range, but it's a lot easier to generate that range in your head ,or on a calculator, if you stay with yards and yards, or meters and meters and not get sucked into estimating target size in inches.
D. Significant figures and limiting variables
Some folks will no doubt show up and flame me for the error in the yards calculation, but that's a 7 to 8 yard difference over a 1300 plus yard range, and thats well within the other errors in the system.
For example you are estimating the target width or height in mils and there's always a range of error there, both in terms of estimating exactly how many mils the target subtends, and then estimating exactly how tall or wide the target happens to be.
Short guys will mil farther away than tall guys even when both are standing identical distances away from you. So at best you are estimating a standing target you assume is average height, and unless the target aligns exactly with the dots in the reticle, you're estimating how many tenths of a mil the target is actually subtending. Both estimates introduce potentially significant errors.
Way too many people get hung up on "precision" while failing to realize that the precision they can achieve is constrained by the most inaccurate variable in the calculation.
In that regard, I'm ok with the shooter in your text ball parking the range estimate, based on the ball park estimate of the size of the bush. There is no sense measuring with a micrometer, when you are going to mark the line with chalk and then cut the board with an axe.
E. Mil dot differences.
There are also differences in mil dots that can effect the accuracy in miling the target
For example the reticle in a US Army issue scope will use round dots that are .2 mil wide (.1 mil each side of center). They are spaced 1 mil apart, which means there is only .8 mil between them and 1.2 mil from outside edge to outside edge and 1 mil from inside edge to outside edge.
The USMC on the other hand uses football shaped mil dots that are also 1 mil apart center to center and inside to outside edge, but they are .25 Mil wide and .75 mil apart.
In addition, there are mils and there are artillery mils. A mil is an angel measure that is technically 1/6283rd of the circumference of a circle. However the artillery types rounded that to 1/6400 of a circle, as it was accurate enough for artillery purposes.
Some scopes use 1/6400 as a mil, while other use the more exact 1/6283 for a mil.
I wouldn't get too hung up on the it if the scope is using 1/6400, as it's not the least accurate number in the calculation.
F. There are also MOA reticles
About 90% of current military trained shooters use Mil, in large part because most military forces work in meters, it also keeps things neat and tidy, and mil corrections are a little easier to record and communicate as "5.2 mils" is more compact to write or say than the equivalent "17.75 MOA", which has twice the digits.
However if the shooter in the story is old school, not current/recent military or is civilian he or she might prefer mils.
There are advantages to the system for a shooter more comfortable with imperial units.
1 mil = 3.438 MOA, so 1/4 MOA adjustments are slightly more precise than .1 Mil adjustments.
For those folks who are better at estimating target size in inches, the math is super easy:
Target size in inches / Target size in MOA x 100 = range to the target in yards.
In the example above a 24" wide target that subtends 1.8 MOA would be 1333 yards away:
24/18 = 1.33, 1.33 x 100 = 1333.
The advantage of the smaller MOA unit is that there is less extrapolation between hash marks in the reticle than their is between mil dots, so the estimate is potentially more precise.
The same complications occur when you start mixing units or when you start mixing MOA and mils.
Both Mil and MOA work, so just pick an angular measure, pick your units of distance, keep them compatible to simplify the math, and then stay with them.
As for the ballistics, if the shooter is holding 4 mils high at a ball park 950 yards range, then he'd have to either a) have about 6 mils in elevation already put on the scope or b) have a basic zero of about 700 yards to expect to hit a target 950 yards away with a 4 mil hold.
But that's assuming the use of a .308 with M18LR ammo. Without knowing the cartridge and rifle being used it's hard to comment in much more depth.
In any case, from a technical perspective, it makes sense to match the reticle, the units and his style of shooting to the shooters back ground and training, as well as with the era in which the story occurs.
For example, in the immediate post Vietnam era when scopes were still simple, adjustable turrets less reliable, and snipers could still do math in their heads, it was not uncommon to have a 500 meter basic zero on a .308 using a fixed 10x scope with a mil dot reticle. The shooter then used the reticle to apply the additional windage and elevation holds for shots at longer range. And in the M118 (173 gr FMJBT bullet) days, the engagement ranges with a .308 are normally 500 to 800 meters. Shooting from less than 500 meters often meant the sniper took unnecessary risks of exposure, and shooting from much farther than 800 meters meant the probability of a first round kill fell to unacceptable levels.
Modern laser range finders that provide a much more precise estimate of range are what have made the PKs on long shots more acceptable past 800 meters with cartridges like the .308.