Long post warning... this is a long post, with technical ballistics stuff in it.. if you don't like long technical posts, don't fecking read it. If you do read it and moan about it, you can't say I didn't warn you - no one forced you to read it and you were warned.
Originally Posted by verminator
When the barrel is horizontal, the full force of gravity is acting upon it, pulling it down. When the barrel is tilted to full vertical, gravity is no longer bending it downwards and therefore pointing higher than expected.
Now take that sentence and replace the word 'barrel' for the word 'trajectory' and you've actually just explained why the POI changes when shooting at an angle and it's the same whether you're shooting up or down.
It's not the barrel that's bending - it's the reduced effect of gravity on the trajectory that means your pellet will strike higher than it would have done if the full effect of gravity was applied to the trajectory.
So..... take this example...
If you shoot on the horizontal, at 10 yards the effect of gravity on your trajectory will mean that the pellet will drop by just a few mm. If you now take that gun and point it directly up, the trajectory of the pellet is a straight line (up). The difference between shooting on the level and shooting straight up, is the difference that gravity makes to the trajectory - which is a few mm at 10 yards.
To put some numbers into that -
If you shoot on the horizontal with a 12fpe .177 - at 10 yards your pellet would drop about 5mm due to gravity.
If you take that same gun and point it directly up or down, the pellet will no longer drop 5mm, the pellet will strike 5mm higher than if you'd shot it on the horizontal (the difference is the difference in the effect of gravity which at 10 yards is just 5mm).
If instead of shooting directly up or directly down, you shot at a 45 degree angle, you'll get half of the effect of gravity pulling the trajectory down as you would have done if you'd shot on the level. So the difference would now only be about 2.5mm.
Taking that example, if you shoot at a target 10 yards away at a 45 degree angle (half way between 0 and 90 degrees) - you halve the effect of gravity on the trajectory (approximately) which means your pellet will land 2.5mm higher than if you'd shot on the level.
Does that make sense? - I'm still struggling for time to draw diagrams, but since you already understand the idea, I might not have to draw one (I'm hoping).
If you were to say... write a ballistic calculator application to calculate exactly what all of those drop figures actually are for every distance and every angle (I've done this, coz yes, I really am that sad) - you come up with a great big spreadsheet of numbers. If you look at that spreadsheet you'll see that if it's less than 15 yards (no matter what the angle is - up or down) then the difference in POI is so small, you won't notice it. It's less than 7.5mm in the worst case, so easily enough to hit a 15mm kill without having to worry about any of this angle stuff.
Similarly, if you shoot at an angle of 15 degrees or less, you're only reducing the effect of gravity on the trajectory by about 17% and again looking at this huge spreadsheet you'll see that the shift in POI is so small that you really don't need to worry about it because even in the worst case, it's not bigger than 7.5mm which is still enough to take down a 15mm kill by aiming exactly how you would have done if it was on the level.
Coming onto the Rifleman's Rule.. why is it wrong?
Well... it's actually never right in the first place. At the very best, it's a rough approximation of change in POI. It doesn't account for scope height in that approximation, which means that anything closer than the top of your trajectory (which is usually around 25 yards) is going to be spectacularly wrong. In some cases beyond 25 yards, the rifleman's rule isn't a bad approximation - but ask yourself, do you want to rely on a 'rule' that at best is only a rough approximation and at worst is spectacularly wrong? Bearing in mind that most of the steep elevated targets in HFT are sub 25 yards and the sub 25 yard range is where the Rifleman's rule gets it very wrong.
If you want an easy to remember practical answer it's already been given in this thread by Maestro and Steve P and it's this....
If the target is less than 15 yards OR it's less than 15 degrees (up or down) just ignore that it's an angled shot and shoot it as though it was on the level - the worst you'll be out is just a couple of mm.
If it's further than 15 yards AND it's more than 15 degrees - aim inside bottom of kill.
That rule which I've called the "Airgunners rule of 15's" (it was me that made that rule up) is easy to remember and will do for the vast majority of any inclined shots you're ever likely to see at an HFT event, so just use that and don't worry about gravity or bendy barrels or rifleman rules or any of that bollox. Just remember 15 is the magic number and get on with your day.
There's a couple of other problems you might also face when shooting an inclined shot.. the biggest problem is that knowing where to aim is only half the battle.. holding your gun still, dealing with cant and parallax error and a difference in hold are the other half of the battle. The rule of 15's is ballistically correct, but.... you might find your pellet doesn't hit where ballistics says it should - and that'll be down to your screw up, not gravity.
Springers also behave differently with inclined shots - again, it's not ballistics, it's well.. something else I won't go into because this post is long enough.