Why is the mildot reticle the accepted standard, when it appears that MOA reticle ranging is much easier and far less prone to math errors?
In order to make a range calculation via a mildot reticle one uses the following calculation:
Height of item in yards x 1000/Mils read = Distance to item in yards
This of course requires the shooter to convert the inch dimension of the item into yards. A 48 inch fence post would have to be converted to yards. A mental cogitation is required to come up with 1.33 yards, which we then multiply by 1000 and divide by mils read.
While it is no huge deal to convert the size of the target to yards, it is one place in the entire equation where a mistake might be made.
So basically, the mildot ranging equation--in reality--looks more like this:
Height of item in inches divided by 36 (to convert to yards) x 1000 divided by Mils read = Distance to item in yards
Much-o room for error-o there if you ask me! /ubbthreads/images/graemlins/smile.gif
But consider the MOA graduated reticle...
The equation is: Target size in inches/MOA x 100. That's it.
So, let's say that a shooter spots a 15 inch target at an unknown distance.
The mildot reticle indicates that this target is 5/6ths of a mil, or about .83 mils. The shooter then must convert this 15 inches to yards. He crunches out 15/36 (36 inches in a yard), for about .42 yards of target size. He then multiplies that .42 figure by 1000, and of course gets 420, which he divides by mils read, which in this case is .83 mils. He comes up with 506 yards, which would be about right. It would be about right, that is, if he managed the math--at every step--correctly.
The MOA reticle shooter looks at the 15 inch target through his scope and sees that it occupies 3 MOA on his scope's MOA graduated reticle. Since the calculation is target size in inches/MOA x 100, he can easily do this in his head. 15/3x100 = 500 yards.
Of course if the MOA reading is not an even number, ONE division calculation might have to be scratched out on paper, or punched into a calculator.
Say the target was a 20 inch plate and and it took up 3.3 MOA on the reticle. It would be necessary to divide 20 by 3.3, which would require (for most of us) a calculator or pencil and paper to be absolutely certain we got it right. That would give about 6, and times 100 would mean the target was at 600 yards.
You can always do the "times 100" in your head, of course.
So what I'm saying is that the worst the MOA shooter is going to have to calculate on paper would be ONE division calculation, and this only in the instances when the target was not an even MOA in size (granted, more than half the time probably).
But the mildot shooter is likely to have to number crunch to convert the target size in inches to yards (1st externally assisted calculation), then he can multiply by 1000 in his head, but there will almost certainly be another number crunch when he must divide this number by the number of mils. Since mils are about 3.6 times bigger than MOA increments, the mildot shooter is going to end up on a fractional division a helluva lot more often than the MOA shooter will.
I realize that the MilDot Master exists, and that many guys shooting mil reticles will be using it. However, when we justify knowing how to range with the scope's reticle in lieu of a laser rangefinder (LRF) by advancing the (very real) notion that the LRF can fail, we must by that same token understand that a MilDot Master card can be lost or damaged.
Regarding the single division calculation necessary for the MOA based range call... If we could come up with a way to do this ONE division calculation in our heads, the rest would be easy--and we could call the range without ever looking up from the scope.
One thing that might help us do this single calculation in our head is to move the decimal in the division equation one place to the right.
Example: A known 14 inch tall target is occupying 1.6 MOA on the reticle. This would require dividing 14 by 1.6, but this product would be the same as 140 divided by 16 (move decimal one place to the right for each number). To me, 140/16 is easier to do than 14/1.6
Since 16 goes into 140 eight times (8 times 16 = 128) I can figure immediately (while I'm still looking through the scope) that the answer is going to be 8 and some fraction of 16--in this case, 12/16ths if you follow me. (I get the 12 by deducting 128 from 140). 12/16 is 3/4, or .75. So the target is 8.75 times 100, or 875 yards out.
True, when the MOA fraction is an odd number, rather than an even one, the calculation would become a little tougher to do in one's head. However, you would (statistically speaking) end up on an even MOA fraction about half of the time.
For the times when you do end up on an odd MOA fraction, it might go something like this: You see a known 16 inch target which occupies 4.3 MOA in your scope. In your head, you divide 16 by 4.3 (which is the same as 160/43. You immediately know that it's going to be 3 and some fraction of 43. Still working only in your head, you say "Three times 43 equals 129, and 160 minus 129 equals 31, so the target is 3 and 31/43rds (times 100) away from me."
What would we do with 31/43rds? That blows chunks! /ubbthreads/images/graemlins/laugh.gif But 31/43 is going to be about the same as 3/4. (The numerator rounds to 30, and the denominator rounds to 40). That would mean that we come up with .75 in our "guess-timate" rather than the calculator's .72 number. Not so bad, we're off three yards. If we're dealing with a fraction like 38/47, we would round that up to 40/50, and get .80--when the calculator actually does say about .80... If we were to have something like 21/39, we would simply say 20/40, or .50 in this case. The calculator would say about .53, so I'd be within three yards here. This works. /ubbthreads/images/graemlins/wink.gif
Rounding to the nearest "friendly" number in a manner as described above, or in your own unique way--whatever works for you--can become routine enough that range caluclations would be quite close. And with the MOA reticle, you would be able to do this, as a rule, without ever looking up from the scope.
What if we get an odd fraction at a longer range? For instance, a target which is known to be 20 inches takes up 2.7 MOA on the reticle. That's 20/2.7, or 200/27. Twenty-seven goes into 200 seven times (7 x 27 is 189) and this leaves 11 left over. So we have 7 and 11/27ths. That rounds to 10/30, which is of course one third, which means 33 yards. The target is about 733 yards away according to our calculation. The calculator says 740 yards. While seven yards might seem like a large error, it would likely not be enough to cause a miss on a 20 inch target quartered in the crosshairs. A seven yard ranging error in this instance would mean less than a five inch error in where the bullet strikes. (175 SMK @ 2600 fps MV).
Note: If you round down the numerator, and the denominator is "5", then round down the denominator for the closest estimate. If you round up the numerator and the denominator is 5, round up the denominator. For instance, if you end up with 14/25, you would round down the 14 to 10, so round down the 25 to 20. That would give 10/20, or .50 in this case. The actual number given by the calculator for 14/25 is .56, so you'd be off six yards here. That would be somewhere around 7 inches vertical at 1000 yards with the 175 SMK launched at standard velocity.
We may not always be able to do these calculations in our heads, but in cases where it may be necessary, the technique would be good to know. If you have a spotter assisting you, and you each do the math in your heads and come up with the same number, that would be most excellent! I would of course use a calculator and hit the nail on the head if a calculator was handy and using it was convienient. But if I were in pouring rain, or in sub zero temps, I might find that my handy-dandy little calculator was on the blink. /ubbthreads/images/graemlins/blush.gif No matter, with a good understanding of the MOA reticle it is possible to get very close to the actual range of a target without ever looking up from the scope--because this reticle pattern is MUCH more condusive to doing the math in one's head than is the vaunted mildot.
If ranging with the scope's reticle seems imprecise when compared to an LRF, it is. However, you will not always get a reflective enough target for your LRF to work, and in some cases, the battery will die, or the unit will simply fail you. Knowing how to reticle range can be important.
So, to recap...
By using a reticle divided in MOA, I believe we gain these advantages:
1. We reduce the number of division calculations to only one. Since division calcs are the ones that the average bear is most likely to "goof up," I think keeping this number to a minimum is best. Even if we are using a calculator, increasing the number of calculations would--statistically speaking--increase the chances of an incorrect range call.
2. In many cases, the division calc will be almost automatic, as in an 18 inch target which takes up 3 MOA. That gives 6, which means 600 yards. This "even denominator" situation will occur 3.6 times to every one versus the mildot reticle (there are 3.6 MOA in a mil). And even when you do get an even mil (such as an 18 inch target at 500 yards) you've still got to convert the 18 inches to yards by dividing 18 by 36 and then multiply that by 1000).
3. In most cases, the mildot scope is going to have MOA windage and elevation cranks. With the MOA reticle the cranks will match the hash marks on the reticle, an advantage, I believe, when dialing to move the shot a specific amount (i.e. you see your shot hit the ground 2.5 MOA low of the target. This simply means grab the elevation turret and adjust it 2.5 MOA for the next shot. This precludes having to convert mils to MOA in order to decide how much to move the turret).
As always, I'm open to feedback on these notions. If you can suggest a better way to handle the math--or if you feel I'm being unfair to the mildot ranging system, please add your comments. /ubbthreads/images/graemlins/smile.gif
Dan
In order to make a range calculation via a mildot reticle one uses the following calculation:
Height of item in yards x 1000/Mils read = Distance to item in yards
This of course requires the shooter to convert the inch dimension of the item into yards. A 48 inch fence post would have to be converted to yards. A mental cogitation is required to come up with 1.33 yards, which we then multiply by 1000 and divide by mils read.
While it is no huge deal to convert the size of the target to yards, it is one place in the entire equation where a mistake might be made.
So basically, the mildot ranging equation--in reality--looks more like this:
Height of item in inches divided by 36 (to convert to yards) x 1000 divided by Mils read = Distance to item in yards
Much-o room for error-o there if you ask me! /ubbthreads/images/graemlins/smile.gif
But consider the MOA graduated reticle...
The equation is: Target size in inches/MOA x 100. That's it.
So, let's say that a shooter spots a 15 inch target at an unknown distance.
The mildot reticle indicates that this target is 5/6ths of a mil, or about .83 mils. The shooter then must convert this 15 inches to yards. He crunches out 15/36 (36 inches in a yard), for about .42 yards of target size. He then multiplies that .42 figure by 1000, and of course gets 420, which he divides by mils read, which in this case is .83 mils. He comes up with 506 yards, which would be about right. It would be about right, that is, if he managed the math--at every step--correctly.
The MOA reticle shooter looks at the 15 inch target through his scope and sees that it occupies 3 MOA on his scope's MOA graduated reticle. Since the calculation is target size in inches/MOA x 100, he can easily do this in his head. 15/3x100 = 500 yards.
Of course if the MOA reading is not an even number, ONE division calculation might have to be scratched out on paper, or punched into a calculator.
Say the target was a 20 inch plate and and it took up 3.3 MOA on the reticle. It would be necessary to divide 20 by 3.3, which would require (for most of us) a calculator or pencil and paper to be absolutely certain we got it right. That would give about 6, and times 100 would mean the target was at 600 yards.
You can always do the "times 100" in your head, of course.
So what I'm saying is that the worst the MOA shooter is going to have to calculate on paper would be ONE division calculation, and this only in the instances when the target was not an even MOA in size (granted, more than half the time probably).
But the mildot shooter is likely to have to number crunch to convert the target size in inches to yards (1st externally assisted calculation), then he can multiply by 1000 in his head, but there will almost certainly be another number crunch when he must divide this number by the number of mils. Since mils are about 3.6 times bigger than MOA increments, the mildot shooter is going to end up on a fractional division a helluva lot more often than the MOA shooter will.
I realize that the MilDot Master exists, and that many guys shooting mil reticles will be using it. However, when we justify knowing how to range with the scope's reticle in lieu of a laser rangefinder (LRF) by advancing the (very real) notion that the LRF can fail, we must by that same token understand that a MilDot Master card can be lost or damaged.
Regarding the single division calculation necessary for the MOA based range call... If we could come up with a way to do this ONE division calculation in our heads, the rest would be easy--and we could call the range without ever looking up from the scope.
One thing that might help us do this single calculation in our head is to move the decimal in the division equation one place to the right.
Example: A known 14 inch tall target is occupying 1.6 MOA on the reticle. This would require dividing 14 by 1.6, but this product would be the same as 140 divided by 16 (move decimal one place to the right for each number). To me, 140/16 is easier to do than 14/1.6
Since 16 goes into 140 eight times (8 times 16 = 128) I can figure immediately (while I'm still looking through the scope) that the answer is going to be 8 and some fraction of 16--in this case, 12/16ths if you follow me. (I get the 12 by deducting 128 from 140). 12/16 is 3/4, or .75. So the target is 8.75 times 100, or 875 yards out.
True, when the MOA fraction is an odd number, rather than an even one, the calculation would become a little tougher to do in one's head. However, you would (statistically speaking) end up on an even MOA fraction about half of the time.
For the times when you do end up on an odd MOA fraction, it might go something like this: You see a known 16 inch target which occupies 4.3 MOA in your scope. In your head, you divide 16 by 4.3 (which is the same as 160/43. You immediately know that it's going to be 3 and some fraction of 43. Still working only in your head, you say "Three times 43 equals 129, and 160 minus 129 equals 31, so the target is 3 and 31/43rds (times 100) away from me."
What would we do with 31/43rds? That blows chunks! /ubbthreads/images/graemlins/laugh.gif But 31/43 is going to be about the same as 3/4. (The numerator rounds to 30, and the denominator rounds to 40). That would mean that we come up with .75 in our "guess-timate" rather than the calculator's .72 number. Not so bad, we're off three yards. If we're dealing with a fraction like 38/47, we would round that up to 40/50, and get .80--when the calculator actually does say about .80... If we were to have something like 21/39, we would simply say 20/40, or .50 in this case. The calculator would say about .53, so I'd be within three yards here. This works. /ubbthreads/images/graemlins/wink.gif
Rounding to the nearest "friendly" number in a manner as described above, or in your own unique way--whatever works for you--can become routine enough that range caluclations would be quite close. And with the MOA reticle, you would be able to do this, as a rule, without ever looking up from the scope.
What if we get an odd fraction at a longer range? For instance, a target which is known to be 20 inches takes up 2.7 MOA on the reticle. That's 20/2.7, or 200/27. Twenty-seven goes into 200 seven times (7 x 27 is 189) and this leaves 11 left over. So we have 7 and 11/27ths. That rounds to 10/30, which is of course one third, which means 33 yards. The target is about 733 yards away according to our calculation. The calculator says 740 yards. While seven yards might seem like a large error, it would likely not be enough to cause a miss on a 20 inch target quartered in the crosshairs. A seven yard ranging error in this instance would mean less than a five inch error in where the bullet strikes. (175 SMK @ 2600 fps MV).
Note: If you round down the numerator, and the denominator is "5", then round down the denominator for the closest estimate. If you round up the numerator and the denominator is 5, round up the denominator. For instance, if you end up with 14/25, you would round down the 14 to 10, so round down the 25 to 20. That would give 10/20, or .50 in this case. The actual number given by the calculator for 14/25 is .56, so you'd be off six yards here. That would be somewhere around 7 inches vertical at 1000 yards with the 175 SMK launched at standard velocity.
We may not always be able to do these calculations in our heads, but in cases where it may be necessary, the technique would be good to know. If you have a spotter assisting you, and you each do the math in your heads and come up with the same number, that would be most excellent! I would of course use a calculator and hit the nail on the head if a calculator was handy and using it was convienient. But if I were in pouring rain, or in sub zero temps, I might find that my handy-dandy little calculator was on the blink. /ubbthreads/images/graemlins/blush.gif No matter, with a good understanding of the MOA reticle it is possible to get very close to the actual range of a target without ever looking up from the scope--because this reticle pattern is MUCH more condusive to doing the math in one's head than is the vaunted mildot.
If ranging with the scope's reticle seems imprecise when compared to an LRF, it is. However, you will not always get a reflective enough target for your LRF to work, and in some cases, the battery will die, or the unit will simply fail you. Knowing how to reticle range can be important.
So, to recap...
By using a reticle divided in MOA, I believe we gain these advantages:
1. We reduce the number of division calculations to only one. Since division calcs are the ones that the average bear is most likely to "goof up," I think keeping this number to a minimum is best. Even if we are using a calculator, increasing the number of calculations would--statistically speaking--increase the chances of an incorrect range call.
2. In many cases, the division calc will be almost automatic, as in an 18 inch target which takes up 3 MOA. That gives 6, which means 600 yards. This "even denominator" situation will occur 3.6 times to every one versus the mildot reticle (there are 3.6 MOA in a mil). And even when you do get an even mil (such as an 18 inch target at 500 yards) you've still got to convert the 18 inches to yards by dividing 18 by 36 and then multiply that by 1000).
3. In most cases, the mildot scope is going to have MOA windage and elevation cranks. With the MOA reticle the cranks will match the hash marks on the reticle, an advantage, I believe, when dialing to move the shot a specific amount (i.e. you see your shot hit the ground 2.5 MOA low of the target. This simply means grab the elevation turret and adjust it 2.5 MOA for the next shot. This precludes having to convert mils to MOA in order to decide how much to move the turret).
As always, I'm open to feedback on these notions. If you can suggest a better way to handle the math--or if you feel I'm being unfair to the mildot ranging system, please add your comments. /ubbthreads/images/graemlins/smile.gif
Dan
