You have to remember that most sighted in barrels point (slightly) upwards. Because there's a slight upward angle there's also a slight amount of vertical thrust. So you have to factor in the changing balance between decreasing vertical thrust (worked out by a triangle of velocities) & increasing gravitational pull.
I think you mean there's a vertical velocity, yes--throughout the entire flight of the bullet except at one point in its trajectory, where vertical velocity is zero. But no thrust--it's ballistic flight we're talking about, and 'no thrust' is the very definition of ballistic flight. But I think I know what you meant--it's just that using that term could really throw folks off, I think. There's also no
increasing gravitational pull--it's the same throughout the entire flight of the bullet. If you meant increasing downward
velocity, yes--a 32 ft/s increase for each second the bullet is in flight. But, it's important I think to appreciate that this increase in downward speed takes place during the entire flight of the bullet, whether the bullet is moving upward, downward or horizontal. While I think I understand what you meant here as well, we just wouldn't want folks to think that somehow the pull of gravity is changing over time--but yes, the vertical speed component of the bullet due to the constant pull of gravity over time definitely is.
But I don't see what this has to do with reading a ballistic chart, which is all the op wanted to understand.
As for 'drop' and 'path', in the tables I've seen at least, the term 'drop' refers to the distance the bullet has moved away from the
bore axis...think in terms of the comment made above regarding tables that assume the gun barrel is perfectly horizontal. This value has nothing at all to do with line of sight, zeroing the gun or any other aspect of sighting in a gun or hitting a target, near as I can tell. It's just how far the bullet drops, at a given distance from the muzzle, if the bore is parallel to the ground.
'Path' is the distance, again, at a specified range, between the bullet and the line of sight. It's the only metric that has much meaning, as far as I know, when it comes to aiming, 'sighting in' or zeroing. At least this is how I understand it. Where the bullet it going to hit (that is, where we predict it's going to hit) a target is only of interest in the context of where the gun is aimed (line of sight), and that is what path represents.
So, 'path' would be the one you use, as 'drop' has no practical use I'm aware of when it comes to shooting a gun. 'Drop' is something that would be useful for comparing the performance of bullets, as it directly reflects the identical circumstances of bullet launch--there's no complication of the bullet being aimed upward to increase range (and change trajectory). So, you're comparing apples-to-apples, so to speak.
