Letter Re: Scot’s Product Review: Burris 2-7xx32mm Handgun Scope on the Mexican Mauser

Good morning, Hugh,

In reading Scot’s excellent review of the Burris 2-7X Extended Eye Relief rifle scope he mentioned using a ballistics program to determine a 200 yard zero which would also allow hits within four inches of point of aim at 250 yards. Inadvertently, I think, Scot broached the topic of Point Blank Range with that sentence.

If one watches movies and television dramas, one probably believes Point Blank Range to be several inches to a few feet in front of a firearm’s muzzle. It is not. The definition of Point Blank Range is:

“The maximum distance at which a center sighting hold on a target of specified size will produce a strike on that target from the muzzle to that maximum distance.”

It is, of course, dependent upon bullet trajectory and will vary based on the firearm and/or ammunition employed and the target. Determining point blank range is simple using ballistics software, an ammunition manufacturer’s trajectory chart, or it can be determined by actual measurement on the range.

Regarding trajectory, here’s a question: If a rifleman is standing on a perfectly flat plane not subject to curvature of the earth holding a firearm parallel to that flat plane, accompanied by an observer who holds a bullet at muzzle height identical to the one being fired, and the observer releases the bullet at the same instant the fired bullet exits the muzzle, which bullet strikes the ground first?

They will both strike the ground simultaneously because gravity is a constant and acts on both bullets identically. The only difference is one bullet contacts the earth at the observer’s feet and the other at a distance down range. Where the fired bullet strikes the ground is determined solely by velocity – gravity begins acting on it immediately after it leaves the muzzle, dragging it downward at an acceleration rate of 32 feet per second for each second it falls, and it will continue to accelerate downward until it either reaches terminal velocity (gravitational acceleration is balanced out by air resistance) or it reaches the ground and stops falling. The faster the bullet moves , velocity allows bullet to travel horizontally farther before the downward acceleration of gravity brings it into contact with the ground; it’s completely a function of horizontal distance traveled per unit of time because gravity is a constant force exerted over time.

To move point of impact farther away than several hundred feet requires the firearm’s muzzle be elevated to release the bullet at an upward angle to counteract the effect of gravity. Since gravity is a constant force it still begins acting on the bullet as soon as it leaves the muzzle, so the upward angle of the bullet’s path soon begins to turn downward, eventually reaching the ground. The path is usually depicted as an arc, but with one significant difference: past the trajectory midpoint – the highest point of the bullet’s arc– the downward arc steepens because bullets slow due to air resistance the farther they travel, requiring more time to cover a particular distance, and gravity is a constant force. The slower the bullet travels the steeper the downward trajectory curve.

For my example I’ll use a common 8.5X11.0 inch sheet of copy or printer paper as a target, which allows shots 5.5 inches high or low to strike the paper, and generic 5.56X45 ammunition. With 55 grain projectiles and a 20 inch barrel length, published velocity from one ammunition manufacturer is 3240 feet per second. Bullets have a ballistic coefficient – labeled “BC” in the trajectory tables – which references the shape of each particular bullet and the associated air resistance, necessary for precise trajectory computation but for now we can ignore it.

According to the manufacturer’s data tables, this bullet and velocity allows the convenience of a “dual zero”, in this particular case a point-of-aim zero at 40 yards produces another point-of-aim zero at 200 yards, with a trajectory midpoint of 1.4 inches above the point-of-aim zero point occuring at 125 yards. The usual “line of sight above bore distance” for iron sights or scopes is about 1.5 inches, so we’ll use that. A 1.4 inch midpoint height means the bullet not quite reaches line of sight at its trajectory midpoint.

Using the same ballistic data and our 8.5X11.0 inch paper as a target, a 310 yard point-of-aim zero produces a midpoint high of 5.2 inches above point-of-aim zero, which occurs at 175 yards. At 370 yards the bullet is 5.5 inches below point-of-aim zero. That means if this rifle and ammunition combination is zeroed at 310 yards and aimed at the center of our 11-inch high paper the bullet will strike somewhere on the paper at any distance from the muzzle to 370 yards, so 370 yards is the Point Blank Range for this particular rifle/ammunition combination. To hit a target 11 inches in height at any distance from the muzzle out to 370 yards with this rifle/ammunition combination one needs only to aim at the center of the 11 inch target.

Given the energy level of 55 grain projectiles, and the effect of crosswind, 370 yards is probably a bit too far. Most users of 5.56X45 ammunition would select a 250 yard point-of-aim zero, which produces a point blank range of 320 yards on our 11 inch paper target, and a trajectory midpoint of just under 3 inches above point-of-aim. At 300 yards this combination is 3.6 inches below point-of-aim, which shows how quickly the trajectory drops as the bullet slows – in the 20 yards between 300 and 320 it falls just over two inches, and that two inches puts it at the very bottom edge of the 11-inch paper target.

Another point – many misunderstand the mechanics of shooting uphill or downhill. It is often assumed that a rifle zeroed at a horizontal distance needs to be aimed higher if the target is uphill, or lower if it’s downhill. Remember, gravity is a constant – what matters most is not the distance uphill or downhill but the horizontal distance the bullet travels. An uphill target 300 yards away by rangefinder and 100 yards higher in elevation is only 282 yards distant horizontally, meaning gravity acts on the bullet for 282 yards, not 300; “holding over” to compensate for “shooting uphill” will result in a miss. To score a center hit one would need to aim slightly lower. The same gravity rules apply when shooting downhill. (On mild inclines and/or at close distances the effect is negligible, but on smaller targets or at greater distances the difference is enough to determine whether your dinner plate is full or empty).

Selecting a target size different from our 8.5X11.0 inch paper would result in a different point blank range, and requiring a different point-of-aim zero distance as well. With deer, for example, a common game animal, the vital area in which to place a heart/lung shot is usually described as an 8-inch circle. This would require a point-of-aim zero at a closer distance since the radius of an 8-inch circle is 4 inches; using the same rifle/ammunition combination as above (not that 55 grain 5.56 ammunition is suitable for deer), a 230 yard POA zero produces a 288 yard point blank range with a trajectory midpoint of 2.3 inches occuring at 140 yards. Allowing for normal error would suggest a closer point blank range – approximately 265 yards would produce a drop below point-of-aim of about 2.4 inches, nearly matching the trajectory high point of 2.3 inches, keeping all shots well within the critical 8-inch circle all the way out to 265 yards.

Point blank range works the same on every firearm/ammunition combination, from .22 rimfires to cannons. The advantage of knowing the point blank range of one’s firearm and ammunition combination allows successful shooting at unknown range targets without guessing at distance or the “hold over” required to score a hit. Competitive shooters compute the trajectory of their loads precisely because points scores are at stake, and winners are often decided by small fractions of an inch. Those of us who go afield don’t need that level of precision, but knowing where your bullets will strike at distance could be the difference between meat for the pot and opening another can of beans.