Convergence: Why your zero is only correct at two distances

Jul. 13, 2013 @ 08:02 PM

It’s a common misconception that once a bullet leaves the muzzle of a gun, it rises. When I was a young man I simply couldn’t understand what forces of nature caused this phenomenon to occur, yet the photos in the books always showed the bullet rising up above the line of sight when the parabolic curve of a bullet’s trajectory was illustrated.

The fact is that maybe it isn’t a misconception at all because the bullet has to rise above the line of the sights for it to hit where the sights are aligned because the bore of the gun is below the line of sight. To understand all this, you have to understand a little bit about how a bullet reacts to gravity once it’s fired. When a bullet is fired from a gun, it falls at exactly the same rate it would fall if it were dropped from your fingers. Gravity exerts the same pull on the bullet whether it’s traveling at 3,000 feet per second or dropping from a table. If we could see the flight path of the bullet, it would represent a parabolic arc with the rate of curve increasing with distance. This is simply because the further the bullet goes, the slower it is and since the effect of gravity is the same no matter how fast the bullet flies, the angle of drop is sharper at the slower speed. The confusing part of this is the relationship of the flight path of the bullet relating to the line that’s created by aligning the sight or sights.
Since the scope or sights on a gun are above the bore, they must be set to converge at the point where the shooter wants the bullet to hit. This means the line of sight can’t be parallel to the bore because the distance between the line of sight and bullet path would only increase as the bullet is pulled down by gravity. By setting the line of sight and the bullet’s path to converge at a certain point, the gun can shoot where the sight is aligned. A bonus of this is that, as gravity continues to pull the bullet down, it must converge again with the line of sight as it falls, giving two points where the bullet path and line of sight converge.
The Modern Sporting Rifle, the correct term for guns like the AR15, is a great example of this. The design of the AR15 allows the bore of the rifle to be very low under the sights. This allows less muzzle jump and facilitates staying on the target for a fast follow up shot. Since the scope on an AR15 is about three inches above the bore of the rifle, the AR15 is much more susceptible to problems with close zero. Bolt action hunting rifles have only about 1.5 inches of offset between line of bore (LOB) and line of sight (LOS) compared to the three inches of the AR15. An AR15 that shoots at point of aim at 25 yards will be about six inches high at 100 yards. The second convergence of LOS and LOB will be at 300 yards. A bolt rifle with a 1.5” offset will shoot only about three inches high at that same distance. This is because the angle of convergence is greater with the higher line of sight over the bore. These numbers are based on ammunition with muzzle velocities around 2700 feet per second, the approximate velocity of the .223 round and most currently used deer calibers.
A better base zero for the AR15 or other rifles with the scope much higher than the bore is to zero the rifle at 50 yards. The second convergence will then occur at 200 yards and the rifle will shoot six inches low at 300 yards. At 100 yards, the rifle will shoot 1.5 inches high and 1.5 inches low at 25 yards.
While the Modern Sporting Rifle is fast gaining a following among hunters, far more hunters use traditional bolt, lever, and semi-auto rifles with much less scope offset but the same issues apply, though the changes aren’t as extreme. Many Eastern hunters zero at the distance they assume they will most likely shoot. In North Carolina, few deer are shot at distances beyond a hundred yards and many hunters sight in at that exact range. If there is any chance the distance will exceed 100 yards by any significant amount, this is not a good idea. A rifle zeroed at 100 yards means the first convergence begins at 100 yards and the second convergence is probably only about 150. After that, the amount of holdover required for a longer shot becomes considerable.
A better solution would be to sight the rifle in to be dead on at 200 yards. This would put the bullet about two inches high at 100 yards and only about two inches low at 250 yards. This would allow the hunter to hold center on any shot between the muzzle and 250 yards and never deviate more than two inches, not really a factor considering the kill zone of a deer or even a groundhog.
It’s true that information like this might be a bit boring but the fact is that some knowledge and planning in setting up your base zero can pay big dividends if the occasion arises for a long range shot. A little planning can make the difference between a long range trophy and a long shot heartbreak story.

Dick Jones is a freelance writer living in High Point. He’s an NRA Certified Instructor and a member of the board of directors of the Southeastern Outdoor Press Association. He writes about hunting, fishing, dogs, and shooting for several NC newspapers as well as national and regional magazines. If you’d like to have him speak to your group, he can be reached at offtheporch52@yahoo.com or offtheporchmedia.com