When I was up in Wisconsin in mid-October, my father-in-law George and I went to the range to sight in the rifle. And to shoot my Glock. I was feeling pretty cocky after we'd shot the rifle from 25 yards. We moved back to 100 yds, and I couldn't even hit the paper reliably. I was humiliated. He eventually was able to hit the target reasonably well, but I still couldn't. He pointed out that I was moving the rifle all around while aiming. [Ed. I didn't think to tell him that that was the same way I play pool. Also unsteady.]
I want to shoot well enough not to embarrass him: he seems to take pleasure when I do well in the family competitions -- driving a golf ball across the pond, deer hunting.
First time I went to the local range, I was 'way off at 25 yards. I adjusted to deadeye status, but my shots at 100 yds were so far off I shot below the paper most of the time. Not humiliation, but confusion.
I started thinking about the ballistics of it all. When a thought came to me. Maybe my scope was massively misaimed.
Here's the idea. A bullet flies along a parabola, falling under the pull of gravity. The whole idea of "sighting in a rifle" is to make the scope's straight-line view intersect with the bullet's flight on the way up. For my 30-06, that shorter distance is 25 yards. Shooting farther away, the bullet continues to rise for a little while, then it starts to sink. The idea is to have the bullet hit the target you see (straight-line) both at the near point (e.g., 25 yards) going up and at the far point (in my case, 100 yards) going down.
My conjecture was that I was hitting the 25-yard target on the way down. If that was true, the bullet would continue to fall another 75 yds, missing the aim-point 'way low, sometimes off the paper altogether.
Like a mathematician, I began trying to devise formulas that would confirm my conjecture by estimating the amount low my shot would be at 100 yards. That didn't work out. I couldn't find the right approach on which to bend my formerly considerable mathematical talent. But I thought of another plan.
I went back to the range (very busy this close to deer hunting season). I began at 100 yards and assumed I was hitting 'way low. 7 of my first 8 shots missed the paper altogether. I cranked the scope up and up and up. Eventually, I got my shots onto the paper reliably. I then tried to refine my settings at 25 yards, but there was no room to shoot there, so I used 50 yards. There I was shooting low, confusing me since I should be high at 50 yards. But I polished the aim, then went back shooting at 100 yards.
Success! my shots were within 5 inches of the bull's eye. I adjusted twice, then put the last 3 shots inside the center circle, one touching the red dot.
Beyond the accomplishment (I did this!), now I feel like I won't be an embarrassment to George.
[Still wish I could figure out the equations for how much a shot will change by changing the scope a quarter of a degree......]