Now I'm NOT saying your wrong with your train of thought.....but.... when my .22 scope is sighted in say at 50-75 yds. I've never had a problem hitting a squirrel head on the ground or almost directly overhead. How would a properly sighted in rifle scope know what angle it's shooting at...? Maybe I'm missing something I'm not aware of or am misunderstanding your meaning....?
When I was shooting pro archery and teaching I taught many folks how to shoot archery at different angles. Mainly it was downward but upward would apply also. If you were sighted in correctly at 20 yds. and were in a tree stand at any height all that was needed was bending at the waist to the correct angle for the sights to work from above as on the ground.
When shooting horizontally the sights are adjusted to slant downward so the sight-line intersects the falling trajectory of the bullet. Normally twice, @ the near and far zeros, but it could be adjusted to just hit the apex or not at all.
But, when you fire vertically there is no bullet drop to cause a trajectory and the path is straight line. Gravity slows the bullet in its upward travel, but does not cause a deviation to the straight path. Perfectly vertical shots are rare. The target would have to be directly overhead. But nearly vertical has similar issue.
In close shots with a shotgun like your goose example are not affected enough - similarly any close shot is not affected by small sighting issues. Shooting at any angle other than as sighted in affects the projectile path vs the sightline.
Vertical shooting can be accurate if your sightline is established exactly parallel to the bore axis. Then you would be off by only the distance between the center-lines of the bore and scope. Consistently for the entire path of the bullet, until it fell back into the barrel assuming no wind. The navy used to calculate wind and speed correction by a perfectly vertical shot ( not a real fast weapon) and seeing how far away it hit the circular target when it returned. Simple math.
In most situations the sight makes you tilt the barrel up so the bullet's trajectory intersects the sightline. The farther away the more you need to tilt. 'Give it a little more bead'
At close range the sights are usually not far off for any circumstance, and even sighting along the barrel is sufficient. Some archers use that as well, looking down the arrow with no sights and aiming higher as distances get longer.
If that didn't do it I could grab some diagrams off a search.
www.smithsonianmag.com
