Hunters fling the term Max Point Blank Range (MPBR) around the internet as though it possessed some unique magic whereby their favorite hunting rifle can put a bullet in a deer at a mile with no hold over. Even seasoned gun writers use the term with abandon and never share the whole truth about it with their readers. It’s time to debunk the myths which surround this concept.
A Numbers Game
There are two MPBR’s: theoretical and calibrated. The first, the one most people believe is the only, is a simple mathematical construct based on data obtained from ballistic tables, which themselves are deceptive to the uninitiated. The second is the theoretical MPBR adjusted (calibrated) for the specific variables each rifle and load combination generates.
The easiest way to understand MPBR is to imagine a horizontal pipe, usually six inches in diameter, which extends from the rifle’s muzzle toward infinity. The pipe’s size can vary to accommodate different sized targets. The bullet travels within this pipe. Because the barrel centerline is tilted up relative to the sight line, a bullet rises from the muzzle when fired, reaches apogee (the highest point in the arc) at the pipe’s top; falls back under gravity through the zero point the sights are set at, which is also the pipe’s centerline; and exits out the pipe’s bottom (perigee) on its way toward Earth. The two variables at work are the pipe’s diameter, which corresponds to a game animal’s vital zone, and the bullet’s path based on the rifle’s zero range.
Here’s a hypothetical example. A load is zeroed at 200 yards. The bullet’s path rises to three inches above line of sight at 100 yards and sinks three inches below at 250 yards (bullets do not drop in a linear fashion; they lose velocity as a function of aerodynamic drag and drop due to gravitational pull). The theoretical MPBR for this round is 250 yards which means a hunter would not have to adjust their rifle’s scope or employ hold over to shoot an animal in the vitals up to 250 yards. Sounds easy, doesn’t it?
|Theoretical MPBR for a 10 inch kill box.
The unfortunate truth is a hunter who relied on this theoretical MPBR would likely undershoot the animal’s vital zone if the critter stood exactly 250 yards away, and overshoot if it stood at 100 yards. Why?
The theoretical MPBR has no basis in reality; it’s just a number. The theoretical MPBR needs adjustment for one more variable—the rifle’s accuracy. No two bullets fired from a gun hit at exactly the same point of impact (POI), this is proven by shooting multiple shots at a single aim point. The bullets form a group measured in Minute of Angle (MOA), Milliradians (Mils), or inches. This dispersal, or grouping, is because the shooter, rifle, and ammunition all contribute small imperfections which introduce variability. The shot group represents a given rifle’s true accuracy with any particular load.
What Accuracy Really Is
The best way to imagine accuracy is to envision an ever widening cone which extends from the gun’s muzzle to infinity. The bullet’s mathematical trajectory runs down the cone’s centerline. I call this the “Cone of Probability” or COP. Military snipers call it the “kill box.” Assuming nothing else goes awry, every shot fired will land somewhere inside this cone at a given range. It is impossible predict exactly where inside.
For example, a gun and ammo combination which prints a one inch wide group on a paper target at 100 yards should print two inches at 200, three at 300, and so on, as the chart below (courtesy, accurateshooter.com) shows. It is this cone which the shooter must factor into the MPBR calculation in order to derive a real world number.
How to Calculate Your Real MPBR
Let’s calibrate the MPBR derived in the article’s first section with the accuracy obtained on the firing range. Just superimpose the COP over the mathematical trajectory generated by the MPBR. Again, the rifle is zeroed at 200 yards. At 100 yards the bullet is not exactly three inches high, rather it is in a one inch circle of probability around that theoretical point; perhaps half an inch higher or lower (1 inch ÷ 2 = 0.5, the average within the circle). The bullet will strike within a two inch circle around the 200 yard zero point, and as much as 1.25 inches low at 250 yards (2.5 inches ÷ 2, added to the theoretical POI).
Zero is Relative
To account for the COP in this case, the zero point must move back toward the rifle’s muzzle until the apogee occurs at the range the COP’s top hits the top of the pipe, and the COP’s bottom hit’s the pipe’s bottom. The range the COP meets the arc’s perigee gives us the calibrated MPBR.
Don’t Fear the Math
The calculus needed to derive the calibrated MPBR is complex, but modern ballistic software makes the actual work for the hunter relatively simple. Once the COP for a particular rifle and ammo is known in MOA, Mils, or inches, just use simple division to find where the COP’s top hits apogee based on the zero point entered into the program. Change the zero point until the rise above line of sight generated by the software hits three inches adjusted for the COP, then read further down the trajectory table the software generates and find the perigee range based on the COP’s bottom.
Here’s an example. Your rifle shoots 1 MOA groups. You enter a 200 yard zero into the software. The resulting table predicts a 3-inch apogee at 100 yards. You COP at 100 equals roughly 1 inch. Divide 1 inch by 2 = 0.5 inches. Add 0.5 inches to the table’s apogee (3 + 0.5 = 3.5 inches). You’re calibrated apogee is 0.5 inches above the theoretical kill box. Move the zero back until the COP added to the theoretical apogee equals 3 inches. Now, you’ve calibrated the arc to your actual rifle.
From here it’s easy to find the calibrated MPBR. Move down the table from the zero point in ten yard increments. At each point, calculate the COP for that range and divide by two. Add the result to the drop in inches listed on the table. Repeat until you find the range where this calibrated number equals 3 inches drop and there’s your real-world, calibrated MPBR. You’ll find calibrated MPBR depends on accuracy. The tighter the MOA, the longer the MPBR.
You can run as many simulations as you like with various weather parameters to get a better picture how your gun will perform. Remember, you must still go to the range to double-check your gun, with you at the trigger, shoots close to the prediction.
A Change Would do You Good
In the example at the article’s beginning, the calibrated MPBR might move from the theoretical 250 yards to 225, or even less. A big difference when an animal may give you just a few seconds to shoot and there is little time to consult the bullet drop table attached to the rifle’s stock. You do have a drop table, don’t you?
Real Numbers Make Real Success
With some basic data: muzzle velocity, bullet ballistic coefficient, and MOA, you can find the real MPBR for any given set of atmospheric conditions and know at what range to begin scope adjustment or hold over. The real MPBR puts meat in the freezer, the theoretical one only strokes egos.