The critics like to jump on this one.Some try to do less typing.They do not go through all the exercises to create the perfect PC statement .
Most of us could understand this thread without the following,but for the nit-pickers,and those who might just mis-understand,its really simple.
The theoretical "angle of departure" of the bullet from the axis of the bore is zero.Its straight.Now,imperfection of the bore or crown may introduce error,and recoil and or barrel harmonics may influence where the axis of the bore is pointed,but the angle of departure is theoretical zero.
But,there is another line.That would be line of sight.
Assuming the sights are above the barrel,if there were zero angle,the line of sight and the line of bore would be parallel.By definition,parallel lines never intersect.So there is no range where the POI would be the POA.
Gravity begins to act on the bullet the instant it leaves the bore.The bullet begins to drop immediately from the extension of the axis of the bore.
If the axis of the bore is where your mind is,there is no rise,only drop.
Its reall simple,not much to think about.
However,for those who are trying to discuss the usefulness of the rifle,and hitting things at range,the discussion is far more about the relationship of the sights to the flight of the bullet.
Assuming the rifle is sighted to hit POI/POA at a longer range,some portion of the bullets flight will be above the line of sight.
If a shooter wants to talk about "Rise" I will understand what he is trying to discuss and not muddy the water trying to impress with how brilliant I am.
To the OP,make yourself a drawing.Most trajectory data will provide you with "MOA" which really is Minute of Angle,or 1/60th degree.You can lookat all that in charts or software.But for your angle,the up close initial sight in range is the long leg of a triangle.Sight height above bore is the short leg.
Use a common unit of measure,divide the range into the sight height and it will give you the tan of the angle.Hit INV TAN function on your calculator and it will give you the angle.It will be decimal.If it is 1,or greater,write that down,then subtract the 1. there will be a 0.xxx decimal value for the fraction of angle.Multiply by 60 and it will give you the MOA value.
So,in common language,if you are sighted at 200 yds,the bullet must first "rise" the distance of the sight height.They might cross at ,say 30 yds.Your up close,initial sight in distance.Very little gravity drop has occurred.Line of sight intersects line of bore You have a triangle.While it won't be perfect,that is pretty much the angle you re looking for,I think,. That will give you enough info,rise over run,to calculate an angle.
Range to the short range target,and sight height above bore.
Then the bullet will "rise" to the peak of the midrange trajectory.That might be at about 150 yds.Then it will fall to point of impact on the target.