Your story presents a good opportunity to demonstrate the power and simplicity
of the SI unit for plane angles, the radian. Since we're talking about small
angles, just divide the diameter of the grouping by the distance. For those
of us less talented than your one-eyed acquaintance, we might measure our
skills in milliradians (mrad). The calculation is,
Grouping in mm / distance in m = angle in mrad
For example,
25 mm / 25 m = 1 mrad
100 mm / 100 m = 1 mrad
50 mm / 25 m = 2 mrad
Very interesting! I had never thought of small angles in terms of radians before, let alone doing the "group size / distance equals angle." I ran a couple of examples with my calculator, and it actually works! (Not that I doubted John, but I just had to verify it.)
I'm going to write a note to American Rifleman with this info, as they occasionally print stuff that includes "moa" (minute of angle).
I ran the calculation with a 1 m group at 10 meters, and this approximation is still very close: 100 mrad per John's formula, 99.669 mrad by exact calculation. And even beginners can shoot that size of group.
Thanks for the info!
Your acquaintance was shooting
15 mm / 91.4 m = 0.16 mrad = 160 urad
Alternatively, if we know our goal and want to calculate the pattern size
angle in mrad * distance in meters = grouping in mm
For example,
0.8 mrad * 20 m = 16 mm
MORAL: the SI unit radians is BETTER (simpler, easier to use) than the non-SI
unit degrees for many applications. In customary units, it's just a lucky
coincidence that 1 arcminute is about 1 inch at 100 yards.
For general reference, and somewhat in reply to a private post by Terry Simpson, people at different skill levels, shooting a good rifle at 100 meters:
beginner
intermediate
expert
sharpshooter
