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Help a newbie...What MOA definitions always leave out...

So I am a long time hunter, but just really started getting fanatical in the last year in regards to reloading and improving accuracy. I joined a private range near my home about a year ago with a 500 yard line, but due to Covid it has been shut down. I live in Western WA, so long range lines are hard to come by.

I recently re-scoped two of my rifles, a 338WM and a 7RM with Leupold VX5 3x15x44s. These are my first scopes that I really have ever intended out of the gate to actively dial elevation with. Previously I just held over, or kept my hunting ranges within MPBR. This has led me down the rabbit hole of understanding MOA adjustments, and I think I am 99% there in terms of being crystal clear. I don't have any family or friends that I can rely on to answer this question, so I am turning to this forum for confirmation that I am understanding this 100% correctly.

For the sake of clarity, both these scopes are MOA, 1 click equals 1/4 MOA. I have both these rifled zeroed at 200 yards, shooting sub MOA, around 1.5 inches. With the handloads I have developed for both, we are going to round to a nice even number, and say that my ballistic charts at 500 yards show a 40 inch drop.

I am crystal clear on an MOA being an angle of measurement, 1 MOA at 100 yards equals 1 inch, 200 yards equals 2 inches, 500 yards equals 5 inches. I am seeing that in my head very clearly now. I also understand that same single 1/4 inch click at 100 yards equals .5 at 200yds, .75 at 300yds, an inch at 400, and 1.25 at 500 yards.

So going back to my nice even round 40 inch drop at 500 yards. A 40 inch drop equals 8 MOAs at 500 yards. So an 8 MOA adjustment will put me dead on at 500 yards. Here is where I need your help to make sure I am understanding this correctly though. An 8 MOA adjustment for that 500 yard shot will put me 16 inches high on my 200 yard target that I am zeroed at. 16 inches high at 200 yards, not 40 inches high? So confirm this for me please, the problem is that my mind thinks of drops in relation to my zeroed range, ie 200 yards. I hear a 40 inch drop and my previously unenlightened mind thinks that is a 40 inch drop in relation to my 200 yard zero. The error would be to literally dial up 40 inches high on a 200 yard target...

The way I am 99% sure I understand it now, please confirm, is that when we talk MOA and ballistics, we aren't talking drop from my 200 yd zero. Rather we are envisioning that MOA angle straight as an arrow stretching out to infinity. The 40 inch drop we are referring to is not really off my 200 yard zero, but rather how far it drop from that imaginary MOA line. An 8 MOA adjustment at 500 yards puts me 40 inches above where I want my point of impact to be, and then bullseye.

Please confirm if that all sound right?!?! Thanks
 
It is not often that someone is able to take a simple concept and give it enough of a twist that it no longer makes sense. Of course the 40 inch drop is off your 200 yard zero. Call it 40 inches or call it eight moa. it's the same thing. When you are eight minutes low, you must adjust up eight minutes. Not too surprisingly, this will move the point of impact up 8 moa at all ranges. In essence, you are moving your line of sight DOWN 8moa. Howis that for a confusing concept? WH
 
I am certainly no master ballistician, but this is how I understand it.
On a 200 yd zero, dialing up 8 MOA will equal 16 inches, like you noted. The reason it's not 40 MOA is because your bullet arcs (some more, some less) into the target. As it gets farther from the muzzle, it loses momentum and energy, and starts dropping faster. So it's not really a beautiful symmetrical curve, but more of a sharp drop as it loses steam. You are dialing for your destination - 500 yds - not for a perfect arc of 40 inches high at 200 to compensate for the 40 inch drop at 500.

ETA - Just saw the Cleckner video post. He is very good at simple explanations for shooters of all abilities. His book is pretty good.
 
Get the free version of the Strelok app for your phone and start playing with it as well. It's not perfect but you will get an idea of what your bullet is doing.
 
If you dialed up to 40” high at 200 ie 20 moa you’d be on at around 825 yards. The drop is from the line of sight as looking through the scope not looking through the bore. The bore is pointed up. Do you have a ballistic app on your phone?
 
I do have the hornady ballistics app on my phone, but just really starting to learn how to use it. I have read a lot of articles and watched a lot of videos to get to where I'm at, it really isn't that simple a concept, or there wouldn't be a million articles and youtube videos dedicated to this very thing. That NSSF video did confirm that my thinking is on the right track. Thanks for your help.
 
So I am a long time hunter, but just really started getting fanatical in the last year in regards to reloading and improving accuracy. I joined a private range near my home about a year ago with a 500 yard line, but due to Covid it has been shut down. I live in Western WA, so long range lines are hard to come by.

I recently re-scoped two of my rifles, a 338WM and a 7RM with Leupold VX5 3x15x44s. These are my first scopes that I really have ever intended out of the gate to actively dial elevation with. Previously I just held over, or kept my hunting ranges within MPBR. This has led me down the rabbit hole of understanding MOA adjustments, and I think I am 99% there in terms of being crystal clear. I don't have any family or friends that I can rely on to answer this question, so I am turning to this forum for confirmation that I am understanding this 100% correctly.

For the sake of clarity, both these scopes are MOA, 1 click equals 1/4 MOA. I have both these rifled zeroed at 200 yards, shooting sub MOA, around 1.5 inches. With the handloads I have developed for both, we are going to round to a nice even number, and say that my ballistic charts at 500 yards show a 40 inch drop.

I am crystal clear on an MOA being an angle of measurement, 1 MOA at 100 yards equals 1 inch, 200 yards equals 2 inches, 500 yards equals 5 inches. I am seeing that in my head very clearly now. I also understand that same single 1/4 inch click at 100 yards equals .5 at 200yds, .75 at 300yds, an inch at 400, and 1.25 at 500 yards.

So going back to my nice even round 40 inch drop at 500 yards. A 40 inch drop equals 8 MOAs at 500 yards. So an 8 MOA adjustment will put me dead on at 500 yards. Here is where I need your help to make sure I am understanding this correctly though. An 8 MOA adjustment for that 500 yard shot will put me 16 inches high on my 200 yard target that I am zeroed at. 16 inches high at 200 yards, not 40 inches high? So confirm this for me please, the problem is that my mind thinks of drops in relation to my zeroed range, ie 200 yards. I hear a 40 inch drop and my previously unenlightened mind thinks that is a 40 inch drop in relation to my 200 yard zero. The error would be to literally dial up 40 inches high on a 200 yard target...

The way I am 99% sure I understand it now, please confirm, is that when we talk MOA and ballistics, we aren't talking drop from my 200 yd zero. Rather we are envisioning that MOA angle straight as an arrow stretching out to infinity. The 40 inch drop we are referring to is not really off my 200 yard zero, but rather how far it drop from that imaginary MOA line. An 8 MOA adjustment at 500 yards puts me 40 inches above where I want my point of impact to be, and then bullseye.

Please confirm if that all sound right?!?! Thanks
If you REALLY want to become fanatical about reloading and accuracy, trading 1.5" groups at 200 yds for 1.5" groups at 600 yds, then there are a group of shooters in SW WA that you should get to know. I think they shoot locally in Eatonville at 550 or 600 yds. They also shoot at other ranges not terribly far away at 600 and 1000 yds. Two of those shooters post here, @Jet and @newbieshooter
 
To answer your question succinctly...yes, you have it right. If dialed 8 moa up to account for your 500 yard drop, then you would be 8 moa (16") high at 200.

But, as has been said, the key to doing this correctly is to stop thinking in inches altogether. They do you no favors.

Memorize or record your adjustments in moa. So your 500 yard drop is not 40"...it is 8 moa. So you aren't dialing 40", you are dialing 8 moa. Do the same for your wind holds.

The average moa user thinks this way: " My drop is 40 inches...40 inches at 500 yards is 8 moa...there are 4 clicks per moa...so dial 32 clicks...". So a couple minutes later you finally get the shot off.

The proper way: "My 500 yard drop is 8 moa...I need to dial to the '8'...". So 15 seconds later the shot rings out.
 
As others have said, you need to stop thinking about inches entirely; it's 100% irrelevant as it pertains to dialing scopes. Seriously, stop. :)

You can choose any number of ballistic programs, the Hornady 4DOF is the best product Hornady makes, and it's free. Even better you can use a handheld Kestrel. Regardless, either will ask for some basic information to formulate a drop chart. One of the required inputs to create a drop chart will be the range at which you zero'ed your rifle (along with other things such as elevation, temp, etc.)

Once you have the chart built out, the drops will have been established based on your zero range; Inches don't matter at all. If it says 8MOA to 500 yards, then dial in 8 MOA. That's all there is to it.

Personally, I'd zero at 100, but that's just personal preference. Carry a rangefinder with you while hunting, and if you can range it, you can dial to it. Bang. Flop.
 
After reading your post a couple times, here's what I think is giving you trouble. Two extended rays (lines) define an angle (see cartoon below). If you rotate those rays around the central axis, they describe a circle at a given distance, which is what people are referring to when they use "inches" rather than MOA or mils. So at increasing distance, a given angle describes larger and larger circles. All well and good, I think you've got that down.

I suspect your issue with grasping the concept of angular subtension as it applies to the difference between your zero (drop) at 200 versus 500 yd (or any other two distances) lies in the fact that the rays that define an angle, as well as our line of sight to the target are all straight lines. However, the flight path of the bullet is a hyperbola, a curved line. The difficulty in visualizing this may be compounded by the fact that we aim the rifle slightly up in the air to account for the effect of gravity on the bullet, as well as that the line of sight (riflescope) sits an inch or two above the bore of the rifle. Thus, a bullet's trajectory starts out below the line of sight, and crosses it the first time at some fairly close distance on its way to the target. The bullet eventually reaches the height of its trajectory and starts nosing back down. It will again reach or cross the line of sight at some farther distance.

When we "zero" a rifle at some distance, what we are really doing is matching the second point at which the bullet crosses the line of sight to the target to the exact distance of the target. In other words, our bullet, now on its downward path will again cross the line of sight exactly at the distance of the target, thus being "zeroed" or centered vertically on the target face. I have illustrated this with a crude cartoon below. You can see that the upward angle required to zero the bullet trajectory at 500 yd is ever so slightly higher than the upward angle required to zero the bullet at 200 yd. In fact, the initial trajectories of the two bullets wouldn't be hugely different, only a little bit. However, even a very slight change in the launch angle of the bullet is enough to cause it to hit the vertical center of the target at either 200 yd, or 500 yd. Obviously, a slightly higher launch angle is required to mitigate the effect of gravity and zero the bullet at 500 yd than at 200 yd. When you twirl the elevation turret on your scope, all you are really doing is changing the attitude of the scope with respect to the bore axis. For example, when you dial more elevation, you are actually moving the reticle downward with respect to the bore axis and your line of sight. Thus, when you then bring the reticle aiming point to bear on a target, the barrel will be actually pointing slightly higher than it was before the elevation adjustment, because you moved the reticle downward when you dialed more elevation using the scope turret.

The end result of hyperbolic bullet trajectory versus a straight line of sight is that any adjustment you make to the scope to change the launch angle of the bullet will, by definition, have a greater effect as the distance increases. The bottom line is that although there is a well-defined mathematical relationship between elevation adjustments (i.e. scope elevation turret adjustments) at varying distances, you don't need to know any of those formulas or conversions. All you need to do is either know your drops at given distances (i.e. write them down), or use some type of ballistic calculator/app that provides you with that information for your specific load/setup. After that, all you need to do is remember that mixing and matching elevation or windage adjustments at different distances is like comparing apples to oranges. Again, this is because the effects of gravity and/or wind on a bullet trajectory are not linear with respect to distance.

Another way to think about the issue you described above is simply to look at two drop charts. I used JBM Ballistics to generate these two drop charts with a fairly common .208 Win load, and set the zero points at either 200, or 500 yards, everything else being the same. What you can see when you compare the two outputs is that when you zero at 200 yd, the bullet will hit 8.6 MOA low at 500 yd. Likewise, if you zero at 500 yd, the bullet will be 8.6 MOA high at 200 yd. What this tell you is that you need 8.6 MOA more elevation adjustment to go from a 200 yd zero to a 500 yd zero. In other words, the launch angle for a 500 yd zero needs to be 8.6 MOA higher than it does for a 200 yd zero. I think what is causing you problems is that you're mixing and matching with the distances. The outputs from ballistic calculators are internally consistent when you use different distances as your "zero", but the differences in the outputs solely represent the differences in the launch angles required to zero at the two different distances. Using your exact numbers, you needed 8 MOA to go from a 200 yd zero to a 500 yd zero. That adjustment would then put you ~16" high at 200 yd. 16" high at 200 yd equals 8 MOA, exactly the amount you dialed up from your 200 yd zero to reach 500 yd.

FWIW - this stuff can be pretty confusing at times. Hopefully, some of the explanations in this thread help you wrap your head around it a little better.
 

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I love that Tangent Theta chose that name for their scopes because the size of something in the vertical plane at some distance is the tangent of that angle (theta). This is “sub tension”— slice a perpendicular plane through the two legs of the angle and it’s the distance in that plane.
 

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