Why is it so

Gary,

The height of the tree and the angle of the shot has almost nothing to do with your hold over/under. It is the horizontal distance from your shooting position to the leaf that determines that.

That is true Bill but please explain a little further that one's perception of linear LEVEL distance takes a bit of reckoning when viewing at steep angles both uphill and down. Just shoot a 3D archery coarse and you'll learn it in a hurry. While I've never shot in Field Target I imagine if the course is in the hills it would be much the same.

True, I over simplified I suppose. Sometimes I get too wordy and other times I don't say enough. I have plenty of time on a 3D archery course but I shoot a longbow instinctively so I don't worry much about hold over or under.

No disrespect but at steep angles like 60-70-80 degrees, the effects of gravity do need to be calculated. Distance obviously needs to be taken into account. However...The steeper the angle, the less the gravitational forces effect the projectile and the lower you have to aim to compensate. This has to do with the adjusted sight height we used to zero our rifles on a horizontal plane. Shooting horizontally, like we normally do, the forces on a projectile are at their greatest, shooting at steep angles, up or down, the gravitational forces are a lot less but the adjusted sight height are the same. So, the steeper the angle, the less hold over you will need.

Not the most articulate explanation because I'm busy and typing fast. Sorry, it is accurate though.

Happy 4th. Stoti

The concept is that if you could drop a plumb line from the leaf you were shooting at, the required hold would be the hold you would use on level ground when shooting at a target that is at the same distance from you as the horizontal distance to the plumb line. If that isn't happening, there is a problem with the concept. My understanding is that it is an approximation, but I don't know much more than that.

Here is a much more articulate explanation of what I was trying to say...



There is a physical ballistic problem encountered when shooting on angles that causes the bullets point of impact to hit high. Shooting on angles is what every hunter experiences while hunting in mountainous terrain. Sheep hunters and deer hunters alike know all to well, that if their target is up or down on an angle, that they must aim low because the bullet will impact high. The reason for this has to do with gravity and the adjusted site height above the bore of the barrel.

When we zero in our rifle at 100 yards, we are shooting on a flat plane with the full force of gravity pushing down on the bullet. In order to zero properly and get the bullet to strike the bulls-eye, we need to adjust the sight height above the bore of the barrel for this particular condition, (shooting on a flat plane) so that when the bullet leaves the bore of the barrel it arcs up into the full force of gravity, and then drops down onto the bulls-eye.

However, when we shoot on an incline or decline (up or down on an angle) the force and effect of gravity is less on the bullet; but the sight height above the bore of the barrel remains the same, or adjusted for shooting on a flat plane.

Because of this, the bullet will have a flatter trajectory and strike the target higher than where our intended point of aim was. It is imperative that when we are shooting up or down on an angle that we eliminate the guesswork, and correct the straight line distance to the target or “sloped distance,” to the, corrected for gravity, distance to target.



Stoti

If and when shooting at an upward angle just pretend that the target is closer than it actually is. Mental note that is all.

When I was 11 years old, I had just gotten my hunting license and first deer tags. I missed a smoker buck on opening morning. He was down a steep hill only about 80 yards away, I shot right over his back and was totally confused and devastated, should have killed him easy. My dad gave me an explanation and I got my first life lesson on shooting up or down hill on a steep incline without compensating. As a young hunter, it was everything I had imagined and hoped for on opening morning...until I missed! 

Stoti

Yeah, as I said I over simplified. At steep angles and relatively long vertical distances other factors come into play. But the horizontal distance is still the most important factor. Plus I wasn't prepared to articulate the ballistic details. Too many beers in me for the Fourth. Hope everyone enjoyed theirs.

Somebody correct me if I'm wrong. If you take the scope hight out of the equation then the hold-over at 45 degrees should be exactly half of what it is at horizontal, at the same distance. At 90 degrees, no hold under or over at all. Any other angle is somewhere in between. That is not too hard to grasp.

I am deleting my attempt at an explanation because it leaves too many open questions in my mind. Maybe Wikipedia has something definitive on the subject.

Gary, yes that is how it supposed to work. You somehow determine the horizontal distance to the target, then use the hold you would normally use for that distance when shooting on level ground. In the wall example, the horizontal distance is the same for all targets, so the same hold would be used for each target no matter how high it is positioned on the wall.

In the typical hunting example, if you are shooting at 45 degree angle at a target that is 100 yards distant line of sight, the horizontal distance is about 70 yards, and you should use the hold you would normally use when shooting at 70 yards on level ground. If you instead use the hold you would normally use at 100 yards, the shot will go high. How you are supposed to calculate the horizontal distance in the field is another question. Normally you just hold a little low and hope for the best.

Gary. While I actually have to study this further and would have a hard time explaining it myself, I did see a good explanation of this by Ted. I think it may help to actually visualize it vs just reading the text. Check it out below:



https://youtu.be/zWYcsRr7T6E

Here’s another, not as entertaining, but good explanations:

https://youtu.be/wTSBcNgGMNo

gravity 

If you shoot 90 degrees (straight up), the pellet will cross the sight line (first zero) but never the second zero, and pass behind the shooter. So yes, we are talking gravity here, and the fact that the barrel is under the sight line. Transfer that to the upward angle....

Well the gravitational force on the pellet is the same constant whether it is horizontal or vertical (I suppose there is a small imperceptible difference going vertical above the starting point of reference/plane. However that wouldn’t be measurable by a layman. I think the holdover wouldn’t be the same at a steep angle because the gravitational force/wind have a mitigated impact on the trajectory’s horizontal drag. At say, 70% Angle, you would significantly less horizontal drag but you would still have some, and obviously you are substituting horizontal with the vertical impact of gravity and wind/humidity. I think the main thing is the flight pattern is different because of this reduced horizontal drag from your initial frame of reference. The way you should be able to see this is shooting at the same tree rather than the two trees, since you said one is further than the other.


I think Stoti’s reference to the flatter trajectory is the picture one should imagine. Instead of an asymmetrical parabola, the steeper the angle the more symmetrical that parabola is. You will still have the same drag forces in place and effecting the projectile, though the parabola shape of the flight pattern has been altered based on you initial starting frame+angle.