D.M., may his days be blessed, done the English translation of the "Inclined fire" series of articles. He is too modest to claim proper credit, but without his help this site would not be. My gratitude is as deep as thorough.
It all began when I failed to kill a paper plate. There's always a first time. For me that first long range inclined fire opportunity was an 8 inch paper plate at 600 m, approximately at 30 degree angle downhill.
With no wind to speak of it looked totally doable. I held one meter low - and missed with my first shot. And with the second. And third. And fourth. It wasn't clear where the shots went because grass hid the impacts. With no tracers the situation appeared grim.
But I did not panic, no, not at all. Instead I recalled the science from the NDS book and applied it right away. NDS heuristics brough immediate fruits - I missed again. And again. And again.
After taking a time-out, I recalled "Rifleman's rule", another heuristic. Applied it quickly and just as quickly missed. And missed again.
Paper plate died only after a friend lent me his ballistic calculator. It turned out that I did not miss by much, but that was enough to understand that I'm on the wrong path.
We have some pretty steep hills here in Switzerland, so it's not enough to hit a paper plate horizontally.
I started reading what's been written about inclined fire so far, like you're doing now.
Definitions (what are we talking about -- a must read to understand the rest)
When angles matter, and when they don't
Comparative analysis of existing approximation methods (NDS, Rifeman's rule, Improved Rifleman's Rule, Sierra's)
The best method -- 2I2R (invented it all by my little self)
And how to use it in real life
[See also: all notes on inclined fire as a single page.]
Brace for impact.
TL/DR summary for the lazy ones
(If all of a sudden Zombie Apocalypse strikes, and you just don't have time to read it all.)
|Domain:||up to ≃400-500 m|
|Complexity:||moderate -- 1 table lookup, 2 mathematical operations|
|Cons:||inelegant and useless|
|Conclusion:||Zombies would laugh their heads off|
|Domain:||30º, < 500 m. Maybe a little more if holding a correction.|
|Complexity:||very simple -- 1 table lookup, 1 mathematical operation, often automated|
|Pros:||beautiful simplicity, independence from rifle and caliber, no need to amend or extend existing ballistic tables|
|Cons:||surprisingly limited applicability|
|Conclusion:||Not far away zombies suffer|
|Domain:||up to ±30º -- all distances. Up to ±40º -- within 800 m with additional hold|
|Complexity:||easy -- 1 table lookup, 1 mathematical operation|
|Pros:||reasonable accuracy, simplicity, can use existing tables.|
|Cons:||depends on zero distance|
|Conclusion:||Zombies start getting really, really scared.|
|Domain:||as far as the eye can see|
|Complexity:||complex! 2 table lookups, 3 mathematical operations|
|Pros:||accuracy is as good as it gets|
|Cons:||too complex to be useful in the field, requires extra data (regular ballistic tables are not enough)|
|Conclusion:||Zombies would have time to eat your ass off before you sort out the dope.|
|Domain:||all practical angles, distances, and calibers|
|Complexity:||easy -- 1 table lookup, 1.5 mathematical operations|
|Pros:||accuracy, simplicity, can use existing ballistic tables|
|Cons:||only works with 100m / 100 yd zero; procedure depends on click value|
|Conclusion:||Zombies stand no chance|