Re: Is something wrong with my scope?
Sorry if anyone thinks this is condescending...it's not meant to be. I think pictures make it easier to visualize this concept.
The length of the arc subtended by angle "theta" at distance "r" is equal to the fractional circumference of a full circle the angle subtends. In other words, it is the length of the arc between where the two lines (separated by angle theta) cross the circle at some distance "r". It's easy to think of this as a shot group diameter. Note that the angle "theta" in this picture is not drawn to scale (in actuality it would be several hundred MOA the way it is drawn).
In this case, theta is 1/21,600 of a full circle (360 degrees in a circle x 60 min per degree = 21,600 min in a full circle). So, you get (1/21,600) x 2 x pi x r. If r = 100 yd (3600"), then "arc100" = 1.0472". Thus 1 MOA at 100 yd = 1.0472".
Note in the figure that for "arc200" the distance is 2 x r, and for "arc300, the distance is 3 x r. For r = 200 yd (7200"), then "arc200" = 2.0944". For r = 300 yd, "arc300" = 3.1416". Thus, 1 MOA equals increasing arc length as the distance "r" increases.
This translates to accuracy and using your turrets to change point of aim in the following way. A 1 MOA rifle should produce groups of 1.0472" at 100 yd. If other factors such as wind, etc., are ignored, the same 1 MOA rifle will produce groups of 2.0944" at 200 yd, 3.1416" at 300 yd, and so forth. It may be hard to conceptualize, but in theory, a 1 MOA rifle should give just over 10 inch groups at 1000 yd. The same principle is true for turret clicks. If the turrets are listed as 0.25 MOA per click, then this has been calibrated at 100 yd. This means that at 100 yd, one click will move the point of aim by 0.25 MOA, or 0.2618" (1.0472" per MOA x 0.25).
At 200 yd, one click will move the point of impact by twice the distance it would at 100 yd. Therefore, at 200 yd 1 click = 0.5 MOA (0.5236"). At 300 yd, it will move the point of impact three time the distance it would at 100 yd. Therefore, 1 click at 300 yd = 0.75 MOA (0.7584").
In actuality this is not completely true as the "click" value remains constant at 0.25 MOA per click, you are simply increasing the length of the arc subtended by that angular value as the distance increases (ie. the arc subtended by 0.25 MOA at 200 yd is 0.5236"). But for practical shooting purposes, the click value goes up as distance goes up.
The formula to calculate this is as follows:
target distance (yd)/100 yd] x calibrated 100 yd click value (MOA)
For the examples in the thread:
200 yd/100yd x 0.25 MOA = 0.5 MOA per click; to change point of impact by 4.2 MOA, you'll need ~ 8 clicks
At 300 yd, it will be 0.75 MOA per click; to change the point of impact by 15.6" (14.9 MOA) ~ 20 clicks.
As far as turret calibration, I agree with Savageman110, you probably want to test it at the range at least once to be sure how good the calibration is. I just did this recently for my Nightforce 3.5-15x50. At 200 yd, it moved the (group) center point of impact by exactly 0.72" as the average of 3 separate groups. I have 0.1 milrad turrets, which should be equal to 0.36" at 100 yd or 0.72" at 200 yd. So it's pretty much dead on.
In any case, I'm not sure this is any clearer than any of the other explanantions above, but if you look at the picture carefully, it may help clarify the relationship between increasing distance and setting turrets on your scope.
