The Essential Ed Lowry on Shotshell Velocity and Patterns

ACTUAL MUZZLE VELOCITY

It has been the industry practice to give the initial velocity of a shotshell load as its velocity at three feet from the muzzle, as measured with a coil disjunctor. This situation is further complicated by the fact that the physical configuration of the shot column at three feet causes the coil disjuntor to produce a somewhat misleading measurement.

For example, when a moving shot column passes through a full choke constriction, the column strings out to several times its original in-bore length. The front pellets quickly separate and are immediately in free flight. Moreover, at three feet from the muzzle, these front pellets are the only ones in free flight since the remaining pellets in the column, although no longer in contiguous contact, have not yet begun to disperse and are still traveling in the turbulent wakes of others. The coil disjuncter actually produces the average velocity of the entire shot column. But it is the velocity of the forward pellets that determines the average downrange performance of the whole shot charge.

Hence, in order to ascertain the actual velocity at the muzzle, two corrections to the three foot measurement must be made. The first one increases the three-foot value by an amount that depends on pellet type and pellet size and by the amount of choke constriction.* The second correction then simply produces the muzzle velocity necessary to give the (corrected) resulting three-foot velocity.

The basis for this was established in an extensive experimental program by the Winchester Research Department in 1969.

MEASURING THE PATTERN

A shotshell pattern is a large signature sheet on which is recorded the impact locations of pellets from a moving shot cloud. Its purpose is to provide a measure of lateral pellet dispersion at some predetermined downrange point. In current practice the standard measure of this dispersion is the pattern percentage. To obtain its value, the user places the signature sheet on a flat surface and then determines the largest number of pellet holes that can be covered by a 30 circle. The pattern percentage is this number, divided by the total number of pellets in the load, times 100.

The customary downrange location of a signature sheet is at 40 yards. Hence when a gun-ammunition combination is said to give a certain pattern percentage, it is generally understood (unless otherwise specified) that the percentage number refers to its average value at 40 yards.

THE BELL-SHAPED CURVE

After the pellets in a shot charge clear the muzzle, and are in free flight, each of their individual flight paths experiences a number of deflections which vary randomly in both direction and magnitude. The deflections of any one pellet, moreover, are unaffected by those of any so that the pellets all move independently. Yet, collectively, their points of impact produce a definable frequency distribution on the signature sheet.

The dispersion of pellet holes on a signature sheet conforms to the so-called "normal" or "Gaussian distribution", more familiarly known as the "bell shaped curve". This was reported by Journee in his 1902 "Tir de Fusils de Chasse", subsequently corroborated with hundreds of patterns at the Western Cartridge Co. (now the Winchester Division of Olin Corp.) in 1946 and also publicly reported by Oberfell and Thompson in 1957. A further number of extensive experimental programs at the Winchester research range established the effects of range, choke constriction, shot size and atmospheric conditions on pattern values.

EFFECT OF ATMOSPHERE ON PATTERNS

For ballistic purposes of reference, "Standard Atmospheric Conditions" are: a temperature of 59 degrees F (15 degrees C); a barometric pressure of 29,54 " (75 cm) mercury, at sea-level; an absence of wind ; and a relative humidity of 50%. Deviations from these reference conditions will have the following effects on ballistic performance.

Temperature A rise in temperature causes a drop in air density and, thereby, a drop in the drag forces that decelerate a moving pellet and that induce its dispersive (i.e. patterning) behavior.
Barometric Pressure A rise in barometric pressure causes a rise in air density, and thus an increase in the aerodynamic drag force. At near sea-level (1000 foot altitude or less) conditions, which characterize the overwhelming amount of populated land in the U.S., the normal changes in barometric pressure cause such a small change in air density that the ballistic effects are negligible. However, the effect of altitude on the average barometric pressure can be considerable.
Wind Head and tail winds (i.e. those moving toward or away from the shooter) have a small effect on downrange velocities and an almost negligible effect on patterning. A cross wind has essentially no effect on effect on velocity or dispersion. However, a cross wind can cause sensible lateral movement of the shot cloud.
Humidity Humidity, even rain, has a negligible effect on downrange ballistic performance and is therefore not considered.

SHOTSTRING EFFECTS

As a cloud of pellets flies toward a target its individual pellets disperse, both laterally (patterning) and longitudinally.(shotstring). The way that a shot cloud disperses laterally is covered by the "Shotshell Patterning" and by the "Target Hits" sections of this Shotshell Ballistics program. This lateral dispersion is further covered under "Miscellaneous Topics". While pattern measurements are readily obtainable, as is done with downrange signature sheets, the measurement of a shotstring is not so easily managed. Methods for shotstring measurements are covered in the three references listed below.

The pertinent property of a shotstring is its length. This is usually specified (in the US) as the shortest length that includes 90% of the load's pellets at 40 yards from the muzzle. The key question about a load's shotstring centers on the relative effect of its length on the load's lethal effectiveness this question breaks down into two parts: the effect on pellet energy delivery and the effect on the total number of hits delivered against the target.

The effect of shotstring length on energy delivery is difficult to ascertain. A long shotstring, which represents a large spread in pellet travel-times, suggests that the trailing pellets in the shot cloud are meaningfully smaller and/or more distorted than the leading pellets. But the actual degrees of pellet size variation and of pellet deformation are not easily predictable. Moreover, since the actual value of the shotstring length for any given shotshell load can only be roughly conjectured, a procedure with poorly known input values is only marginally useful. For this reason the "Shotstring Ballistics" routine does not predict downrange ballistic behavior. Instead it aims simply to illustrate the nature of the shotstring problem and chooses to do this with at the one range, namely at 40 yards.

However, the way that shotstring length affects the average number of target hits, (without reference to delivered pellet energy) is more readily ascertainable. This is demonstrated here with the help of the following arbitrarily chosen example:

Ammunition 12 gauge, 1-1/4 oz of #2 steel shot, 3-foot velocity is 1365 ft/sec; 80% of pellets hit within 30" circle at 40 yards (assumed);

Target Size 20 square inches (e,g, the vulnerable area of a mallard);

Target Range 40 yards;

Target Speed 70 ft/sec, traveling at right angle to the line of fire;

Flight Time 0.126 seconds, for shot to travel 40 yards;

Lead Distance 8.82 feet (106"), traveled by target while shot travels 40 yards

Shotstring Ratio of Average Number of Hits if Shooter's Lead

Length in Shot Velocity to Is Dead Is Off by

Feet Target Velocity On 10 Inches

0 9.94 6.90 3.43

5 9.94 6.60 3.38

10 9.94 5.96 3.26

15 9.94 4.86 2.97

20 9.94 3.97 2.65

References:

1 - Bob Brister - Shotgunning, The Art and The Science, (Chapter on The Shot String Story) Winchester Press, 1976

2 - Gerald Burrard - The Modern Shotgun, (Chapters V and VI) A.S. Barnes and Co., Inc. New York, 1961

3 - E.D. Lowry - The Effect of a Shotstring, The American Rifleman, November 1979

FELT RECOIL

Various experiments have shown that the disagreeable "kick" sensation experienced by the shooter correlates primarily with the kinetic energy that has been imparted to his recoiling gun. The total sensation is probably influenced by other factors that are difficult to measure, such as the method of holding, the resulting noise, etc. But a gun's recoil energy can be established from the known properties of the gun and of the ammunition.

Determination of a shotgun's recoil energy follows directly from the laws of motion established by Isaac Newton. One direct consequence of these laws is the principle of the conservation of momentum. It tell us that if we let

W be the gun's weight.

V be the gun's recoil velocity.

ws be the shot charge weight.

ww be the weight of the wad.

v be the muzzle velocity.

pw be the propellant weight.

pv be the average velocity (at the muzzle) of the propellant gases.

Then

[W times V] is equal to: [(ws + wv) times v] plus [pw times pv].

For a given gun and shotshell load, six of the above quantities are assumed to be either measurable or known. The seventh, the gas velocity (actually the velocity of sound in the propellant gases), is approximately 4,000 feet per second for shotshell propellants. Hence, if all quantities are given in pounds or feet per second, then it follows from algebraic manipulation and from the definition of kinetic energy that the gun' s recoil energy is given as

[M times V squared] divided by [2 times g], where

g is the gravitational constant and assumed as 32.16 ft/dec/sec.

LAG TIME

An example can demonstrate the meaning of lag time. Suppose that a projectile, aimed at a target 40 yards downrange, leaves a gun muzzle at a velocity of 1,200 feet per second. If there were no air resistance the projectile would travel the 120 foot distance in one tenth of a second.

But, there is air resistance in our atmosphere. Suppose also, for our example, that the projectile is a #2 steel shotshell pellet and the atmosphere is at standard conditions (59 degrees F and 29.54" barometric pressure). In this case the pellet would require .1457 instead of .1000 seconds to travel the120 feet. Thus air resistance slows the pellet and causes it to arrive .0457 seconds late. The .0457 second delay is the "lag time".

The meaning of lag distance is definable in a similar manner. If there were no air resistance during the .1457 second travel time it takes the #2 steel pellet to travel the 120 feet, then it would travel at 1200 ft/sec for .1457 seconds. In such a case the pellet would travel a total distance of

(1,200) times (.1457) = 174.84 feet.

The extra distance, 174.84 - 120 = 54.84 feet (call it 55), is the extra distance that did not get traveled because of the rearward push of air resistance. This 55 foot distance is the "lag distance".

FLYING SPEED OF GAME

Approximate Flying Speeds of some Gamebirds

(in feet per second)

GAMEBIRD MINIMUMSPEED MAXIMUMSPEED MEDIANSPEED

black duck 50 90 70

blue-wing teal 70 90 80

bob-white 60 80 70

brant 70 90 80

cackling goose 80 100 90

california quail 60 80 70

canada goose 70 90 80

canvasback 90 100 95

cinnamon teal 70 90 80

gadwall 65 85 75

golden eye 60 90 75

green-wing teal 70 90 80

mallard 50 90 70

mourning dove 50 80 65

pheasant 60 90 75

pintail 60 80 70

redhead 75 95 85

ruffed grouse 40 60 50

sharptail grouse 50 70 60

snow goose 60 90 75

spoonbill 50 90 70

turkey 60 90 75

widgeon 65 85 75

BALLISTIC COEFFICIENTS

A shotshell pellet's ballistic coefficient is a comparative measure of its ability to overcome the force of air resistance. It is numerically equal to the pellet's sectional density divided by a so called form factor, which is an index of pellet shape. The pellet's sectional density is equal to its weight (in lb) divided by the the square of its diameter (in inches). The form factor for a truly spherical pellet is equal to one (1.0). Hence, for an undeformed, spherical pellet, the ballistic coefficient is simply equal to its sectional density.

If two dissimilar pellets have the same ballistic coefficient and are launched with the same muzzle velocity, their velocitites (and flight times) at any downrange point will be the same. Thus, as seen in the table below, a #5 steel pellet and a Buffered Lead #8-1/2 pellet will have identical downrange velocities (and flight times) if they are each of equal roundness in flight and if each is launched with the same muzzle velocity.

SECTIONAL DENSITY OF SOME EXAMPLE SHOTSHELL PELLET TYPES

SHOTSIZE STEEL BISMUTH IRON-TUNGSTEN BUFFEREDLEAD

#9 0.080" 0.0119 0.0147 0.0157 0.0168

#8½ 0.085" 0.0126 0.0156 0.0167 0.0178

#8 0.090" 0.0134 0.0165 0.0177 0.0189

#7½ 0.095" 0.0141 0.0174 0.0187 0.0199

#7 0.100" 0.0149 0.0183 0.0196 0.0210

#6½ 0.105" 0.0156 0.0192 0.0206 0.0220

#6 0.110" 0.0164 0.0202 0.0216 0.0231

#5 0.120" 0.0178 0.0220 0.0236 0.0252

#4 0.130" 0.0193 0.0238 0.0255 0.0273

#3 0.140" 0.0208 0.0257 0.0275 0.0294