SHOTGUN PATTERNS AND RANGE

*By Marshall Williams.*

I have enjoyed small bore shotguns for many years and usually shoot them effectively. Many shooters disdain small bores feeling they lack killing power at any reasonable range. For example, one friend objected to my using a .410 to shoot quail over his bird dog, because he feared all my misses would ruin his dog. Because he was a good friend (and had a good bird dog) I deferred to his wishes and used a bigger gun, albeit with a very light load. But neither of us shot anything which was out of range of my .410. Shooting small bore guns has made me conservative in range estimation: I always try to keep my range limitations in mind. While small bores have shorter effective ranges than large bores, or more correctly, while light shot charges have shorter effective ranges than heavy shot charges, the reduction is less than one might imagine. I suspect that many shooters think range is directly proportional to shot charge, and, therefore, a one ounce load will kill twice as far as a one-half ounce load. While the difference in range is significant, it is much less than that. The effective range of a shotgun depends on two things: pattern coverage and pellet energy. In order to make a killing shot, the pattern must put enough pellets on the target to insure an adequate number of killing hits, and the pellet energy must be sufficient to inflict killing wounds. To illustrate by extremes, a half ounce of 9s, about 292 pellets, would provide a killing pattern on geese to perhaps sixty yards, however, at that range, a goose might not notice if a number 9 hit him. In contrast, a half ounce of 2s, about 44 pellets, would provide adequate energy on doves beyond sixty yards, but pattern density would not insure a hit beyond the closest of ranges. Obviously what is needed is an adequate number of pellets hitting with the required energy at a reasonable range. For practical purposes, a shotgun pattern spreads in direct ratio to the range. This is true for all degrees of choke, but more open chokes spread at a faster rate. According to an accepted rule of thumb, the diameter of a full choke pattern increases about one inch for each yard of range; the diameter of an improved cylinder pattern increases at about 1 3/4 inches per yard of range. Thus, constriction affects the rate of spread. Figure one represents the approximate spread of a full choke pattern over a distance of 40 yards. The three circles represent the approximate size of the pattern at ranges of 20, 30, and 40 yards.
As a simple matter of geometry, the area of a pattern increases in geometric proportion as range increases. By reference to figure 1, we see that the circle at 40 yards is twice the diameter of the circle at 20 yards, but has four times the area of the 20 inch circle. The diameter of the 40 inch circle is larger in diameter than the 30 inch circle by the ratio of 4 to 3, and the ratio of its area is larger by squares or by a ratio of 16 to 9. Assuming I drew figure 1 accurately, counting the little squares within each circle, should disclose only-quarter as many squares in the 20 inch circle, and nine-sixteenths as many squares in the 30 inch circle as are in the 40 inch circle. From this, we can deduce that
the 20 inch circle requires only one-fourth as many pellets as the 40
inch circle requires to produce the same density of pattern, and the 30
inch circle would require 9/16 as many pellets. It turns out that this
ratio is the ratio of the square roots of the weights of the shot charge.
Mathematically, this is called an inverse geometric ratio. By arbitrarily
assuming that one ounce of shot is effective at 40 yards, Because the pattern spreads at a constant rate, for a given degree of choke, the allowable aiming error as a function of angle is the same at all ranges. This angle of error is the same in any direction, up, down, or sideways, away from the imaginary centerline of our pattern. At forty yards, a full choke pattern will be about 40 inches in diameter. However, patterns tend to be denser at the center than at the edges. Thus, at 40 yards, a full choke pattern will have about 70% of its shot in a 30 inch circle. The 30 inch circle represents only 56% of the 40 inch pattern area. Further illustrating this density, on average, about 45% of the pattern will be in a 21.2 inch circle. The significance of the 21.2 inch circle is that it has exactly one-half the area of the 30 inch circle. Thus, 45% of the 40 yard full choke pattern will be in only 28% of the pattern. The other factor in killing power is pellet energy. At 20 yards, pellet velocity and energy will be much higher than at 40 yards. If we assumed a size 7 1/2 pellet had adequate energy for our target at 40 yards, a size 9 pellet would have comparable energy at 20 yards. One-fourth of an ounce of 7 1/2s would give us the same pattern coverage at 20 yards that one ounce of 7 1/2s would give at 40 yards. One-quarter of an ounce of 7 1/2s contains about 88 pellets. A quarter ounce of 9s has about 146 pellets. Thus, if 88 pellets would give us the pattern percentage required at 20 yards, and number 9s give us comparable energy, we could substitute number 9s and use a more open choke, and have equal energy coverage in a larger pattern. The larger pattern would be 26.76 inches in diameter. If we were satisfied with the 20 inch pattern, we could substitute 9s and lighten the shot charge. Eighty-eight divided by 146 shows that only .15 ounces of 9s, about 1/6 ounce of 9s, would give the same density of pattern and energy at 20 yards as a full ounce of 7 1/2s would give at 40 yards. Without careful consideration, much the foregoing will disconcert many readers. Is Williams saying that 1/4 of an ounce of 9s is more effective than one ounce of 7 1/2s? Of course not. One ounce of 7 1/2s will be more effective than 1/4 ounce of 9s at any range. That is the problem, at 20 yards, the larger shot charge may be so effective that it becomes destructive and ruin game for eating. As a general rule, if you are using a shot size which provides adequate penetration for your game, the pattern will become too sparse to hit your target before your shot's penetration becomes inadequate. Pattern fails before penetration.
TABLE 1 Because a shotgun pattern tends to spread in direct proportion to range, the relative range of a shotgun, as a function of pattern coverage only, and without regard to penetration, is proportional to the square root of the shot charge. If we arbitrarily set 40 yards as the maximum effective range for one ounce of shot, we get the following comparative ranges for smaller shot charges.
Reprinted curtesy of Shotgun Sports Magazine, P.O. Box 6810, Auburn, CA 95604. www.shotgunsportsmagazine.com |