The issue is one of geometry. The scope's ling of sight will be essentially parallel to the bore, at about 1.5 to 2.0 inches above the bore. If you zero the scope at 100 yards, you have to tile the barrel up just a little bit because the bullet starts falling to the ground as soon as it leaves the confines of the bore. In this case, the angle of bore will be about 2 to 3 minutes of angle up from zero and that will be just enough for the bullet to "rise" up to the 100 yards zero before going back down again.
For instance, in JBM, I did a quick ballistic plot with an MV of 3000FPS, an increment of 10 yards, a range of 200 yards, a zero at 100 yards and a sight height of 2.0 inches above the bore.
These are the numbers I get: Left is distance in yards, right is inches below the line of sight. 0 -2.0 10 -1.6 20 -1.3 30 -1.0 40 -0.7 50 -0.5 60 -0.3 70 -0.1 80 -0.0 90 0.0 100 -0.0 110 -0.1
As you can see, the bullet reaches its apogee at 80 yards and then starts going back down after 100 yards.
Now, depending on the height of the sights (the line of sight) above the bore, the barrel can be pointed further up or down to reach that 100 yards.
If the sight height is higher, the apogee of the trajectory will be reached further downrange, In the case of a height of 3 inches, that occurs at 100 yards and the bullet starts going down after 120 yards.
If the sight is even higher, then the bullet actually continues to rise after the 100 yards zero is reached and in the case of a height of 4.0 inches, the apogee is reached at 120 yards when the bullet is actually 02 inches above the 100 yard zero and remains so for the next 20 yards before going down again. It actually crosses the light of sight once again at 170yards downrange. So this is where you have the same zero at two different distances, 100 and 170 yards.
As was discussed already, there are combinations of velocity, sight height, barrel tilt and so on that allow one to use the near zero of the trajectory and know that the far zero will be at a specific distance, much further down range. For example the 24meter/250meter for the rifle/ammo specified above.
That's a neat way of getting a decent zero at 250 meter, but just shooting at 25 meters.
In my game where the zero is 1000 yards, even with my 2.0 inch sight height, the bullet first crosses the line of sight inside of 8 yards and the actual distance is extremely critical, down to inches, which makes it very difficult to use. So, I shoot at tall targets at 100 yards and I see how far above the point of aim the bullet hits. For my load, that's about 35 inches high at 100 yards for a 1000 yard zero.
The neat thing though, is that I can use a boresight laser indoors to aim at 8 yards and confirm the 1000 yard zero. Of course, not many high-magnification scopes focus down that close, and you have to measure the distance EXACTLY.
I hope this helps.
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