Shotgun Patterning from First Principles: Part II

In the first part of this article, we explored the justifications for the use of patterning as an indicator of shotgun performance and explored some of the variables which ought to be controlled or otherwise accounted for if patterning is to provide useful data. We discussed the need for thoughtful interpretation of the data on the grounds that some of the variables affecting the operation of shotgun cartridges cannot be controlled (e.g. the environmental conditions).

In this section, we will focus on the reasons for the patterning approach which has become the de facto standard of measuring shotgun performance in the last century or so and examine the fundamental mechanics of shot clouds and patterns and how they come about.

Why Pattern?

In the first section of the article, we sought to answer the question “why pattern a shotgun?” in the sense of justifying the value of patterning to the ethical sportsman. Here, we ask the same question, but in a different sense: why is patterning – as opposed to any other form of testing or measurement – the best approach for determining a shotgun’s likely performance in the field?

The answer lies in the practical difficulties of taking accurate, three-dimensional photographs of a shot cloud in flight. It has been done, using extremely fast-exposure stereoscopic cameras which can create holographic-type images which show each of the pellets’ positions in space at the time the photo is taken. The difficulty for the SmallBoreShotguns team in adopting this approach is that it really requires a laboratory-cum-firing range and a huge budget. Since we (and almost everyone else) are in possession of neither, a two-dimensional impression of the passage of a shot cloud through a sheet of paper or cardboard is the next best option.

Shot Stringing

Of course, shot clouds are not two-dimensional. Rather, they appear – at their best – when viewed from the side as ovate “blobs” of 3′ or so in length flying towards the target. At their “worst”, where the differences in velocity between first and last pellet are large, they may be up to 20′ in length and appear (again viewed from the side) as a slowly expanding “sausage” shape.

Having understood this effect, known as “shot stringing”, one might be tempted to argue that the accumulated strikes of the pellets in such a shot cloud on a piece of paper or cardboard cannot properly represent the performance of that cartridge on a game bird.

One often hears it said that a bird in flight moves so fast that, by the time the last pellet in a cloud passes through the airspace in question, the bird will be gone and that one must thus hit and kill it with the first pellets in the shot cloud, or fail to hit it at all. In turn, this (apparently) renders any pattern test useless, since one cannot identify which are the holes made by the the “first” pellets and which were made by the supposedly ineffectual “later” pellets from the back of the cloud.

Unfortunately, a quick look at the numbers demonstrates these beliefs, where held, to be false.

Suppose that a wood pigeon crosses at a right angle to one’s natural shooting position in front of a hide. The bird might be flying at 40mph, or perhaps 60mph on a windy day. Suppose also that it is 50 yards distant when it crosses in front of us and that we are shooting a particularly awful cartridge which produces shot strings of around 20′ in length at that range.

At 50 yards, our #6 shot might only be travelling at 600fps which means the first pellet in the shot string will arrive approximately 0.0333 seconds ahead of the last pellet. In that time, our bird traveling at 60mph (88fps) – will travel approximately 3′, which seems a lot until we remember that the average full-choke pattern is around 5′-6′ in diameter at that range.

Even in this extreme example, our imaginary wood pigeon can hardly escape the pattern area in the time between the arrival of the first and last pellets. To even require the pellets arriving at the back of the shot string to make our kill, the first 80-90% pellets – which we know to have been accurately placed – must miss the bird entirely. This is highly unlikely for a centre-of-pattern shot.

Bigger shot, looser chokes, slower bird, shorter range and a cartridge producing shorter shot strings will all further reduce the likelihood of a miss due to shot stringing effects.

Since most of the above mitigating factors are likely to be present in 90% of hunting situations, we cannot find any reasonable argument for the significance of shot stringing, which has rightly been relegated to an irrelevant curiosity in the study of shotgun performance. Assured of its insignificance, we can be confident that a two-dimensional image of the passage of a shot cloud through a given plane is a sensible basis from which to draw conclusions about the behavior of shot clouds impacting targets or birds.


Experience tells us that shooting a single pattern and treating it as representative of the performance of our gun is a mistake, but why should that be so? The answer requires us first to understand why shot spreads and how both shot-to-shot variation in the same cartridge and brand-vs-brand variation of different cartridges occurs.

Shot Spread

The tendency of the shot propelled from a cartridge, down a gun barrel and into the environment depends on many things, but the most significant is way that the shot interacts with the atmosphere.

Ballistics shows us that a perfectly spherical projectile is inefficient but that, if it does not spin, it will tend to fly in a straight line with a path modified only by acceleration due to gravity (i.e. it falls in an arc, towards the ground). At any point about the axis of travel, the drag function describing the way in which friction and resistance from the air slows it down is identical: the projectile experiences no lift or deviation because of uneven passage of air around it.

The forces involved in the operation of a shotgun are substantial. The pellets in a 1oz load accelerated to 1400fps in 22″ of a shotgun barrel experience acceleration forces of somewhere in the region of 4000N (and this is a conservative estimate – peak forces are likely to be much higher). This is roughly the same as the resistive force required to stop a family car from a speed of 12mph in 1 second!

Considering the latter scenario, it is not difficult to imagine that some damage would be done to a car, impacting, for example, an immovable concrete wall, even in a low speed crash. Perhaps bumpers would be broken, bonnets would be crumpled, lights would be smashed? It is therefore not difficult to imagine that small lumps of soft lead experiencing simillar forces inside a gun barrel will likewise be damaged, deformed or sheared by collision with other pellets, wad, barrel wall and suchlike.

It is this pellet damage which most significantly contributes to the spread of a shotgun pattern outward from the initial axis of flight.

A sheared or damaged sphere is less ballistically-efficient than a perfect sphere and will have a drag function which describes uneven airflow over its surface. The unbalanced drag forces which that function describes have the effect of altering the pellet’s direction of flight: it is drawn in the direction of the part of the surface experiencing the highest drag force, much as the uneven shape of a plane’s wing causes a difference in pressures over and under the wing, generating lift.

Given the forces and pressures involved, it is very likely that, even in the best performing shotgun loads, no pellets remain entirely undamaged. The question of performance relies then on doing the least possible amount of damage to the shot, whilst propelling it in the right direction to hit our target.

In fact, it could be said that the cartridge that we want is the one that most consistently damages it’s pellets on our barrel and choke, such that the drag functions of the individually-damaged pellets cause their movement outwards from the axis of the barrel by a distance considered to be most useful or appropriate at a given range!

Per-Brand Variation

The chances are that, if one were to pick any three brands of cartridges with the same loading marked on the box (e.g. 28g / #6) from a dealer’s shelf at random and fire several of them at a pattern board through one barrel of one gun, the result would be three different sets of patterns representing, on average, three entirely different levels of performance.

The reasons for this will doubtless have something to do with the contents of the cartridge cases and – as we have described above – in almost all cases will be related to how well the shot inside was protected from or was able to resist damage / deformation under the conditions of firing.

Perhaps one of our three imaginary brands contained shot with a particularly high antimony content, making it especially hard. Increased hardness will cause the pellets to resist deformation in the “crush” of firing and at the choke, leaving them more-nearly spherical than those made of softer lead. They will be less affected by uneven drag forces and therefore less likely to fly out of the shot cloud or will do so more gradually.

Perhaps another brand contained a particularly progressive powder which accelerated the shot column to full speed over a distance of 22″ rather than 11″. The force exerted on that column will be only half that of the other two cartridges, theoretically reducing damage to the pellets.

Perhaps the third cartridge contains a compressible section in the wad which cushions the shot during its accelleration? Perhaps it has a rolled turnover which provides less resistance to the departure of the shot column from the case? Or perhaps it contains a powdered buffer to insulate the pellets from internal collisions?

In short, the components used to construct a given cartridge may or may not reduce the degree to which the shot column is affected by the forces generated by the powder burning behind the wad. “Better” shotgun performance, most often associated with a slower outward expansion of the shot cloud (and indeed, a shorter shot string), is usually associated with the use of components which reduce as far as possible the deformation of individual pellets.

Shot-to-Shot Variation

Since we cannot eliminate pellet deformation (and arguably would not want to, since it might make our bird shot loads behave rather more like slugs / rifle bullets), we rather aim to achieve a predictable, consistent amount of pellet damage, such that those pellets are propelled from our gun in as similar way as possible for every single shot. This gives us confidence that our gun will work consistently at the ranges for which it is calibrated and than we will not unexpectedly wound quarry with a “bad firing”.

Variability in components exists within a single brand of cartridges as it does between brands, albeit – one hopes – to a significantly lesser degree. Contrary to oft-received wisdom, the most expensive cartridges (particularly in the world of clay shooting) are not the most “powerful” (the term having almost no meaning in shotgunning) but the most consistent; those that are made most carefully with the most similar components with the aim of every cartridge performing as near-identically as possible.

Of course, even with the finest manufacturing tolerances, perfect consistency is impossible. If it were possible (and if every other variable could likewise be controlled), we would expect each individual pellet in every cartridge to be damaged in the same way, each time the gun was fired. This being the case, we would expect that gun to throw identical patterns with every shot – such that one could overlay them and observe the alignment of every pellet hole.

Since this kind of consistency is clearly impossible to achieve, we must therefore express the performance of gun, choke and cartridge as an average performance over a number of tests. We can then judge the performance by answering two questions. Firstly, is the average performance of a kind appropriate to our shooting situation? Second, is the standard deviation of the average small, indicating a highly consistent cartridge?

Degrees of Deformation

It would be ludicrous to attempt to label every pellet in a series of cartridges and compare those individual pellets’ trajectories. If we did, however, we would probably find that, whilst no two trajectories for a pellet originating in a given position in the shot column were the same, all positionally-equivalent pellets would have a trajectory of a similar character, the exact form of which would depend on their initial position in the cartridge and the kind of deformation they experienced on firing.

For example: pellets on the outside of the column, in contact with the barrel wall, will be “scrubbed” whilst they travel down the barrel. We would probably see that those pellets had a characteristic flight path out of the pattern (“fliers”), whilst those from the center of the column flew truer (i.e. more nearly to the imaginary line extending out of the gun along the barrel axis). We might also expect the pellets originating from the front and the back of the column to have been flattened by impact with the crimp or the wad. These would probably lose velocity more quickly than those pellets in the center of the column and predominantly be found at the back of the shot string.

A shot column contained in a cylindrical cartridge is approximately axially-symmetrical. Given this and given that there are hundreds of pellets in most mainstream cartridges, we can be reasonably sure that in any such cartridge, there will be many pellets in geometrically-equivalent positions before the cartridge is fired.

Furthermore, for a given bore size and shot column height, the proportion of the shot charge in each of the significant positional areas (e.g. in contact with the barrel wall; in contact with the wad; in the center of the column; etc.) will be broadly the same. Narrower bores and longer shot columns will place more pellets in contact with the barrel walls; larger bores and shorter shot columns will do the opposite.

It is safe to assume that pellets originating from a given positional “area” will be, on average, more or less damaged than those originating in other areas. For example, a pellet in the center of the shot column cannot be “scrubbed” – there will be too many other pellets in the way for it to make contact with the barrel wall as the column passes up the barrel.

It is also safe to assume that, for pellets originating in any one area, there will be a range of pellet deformation from light to severe. The amount of energy absorbed by each individual pellet will exist around an average governed by the overall conditions of firing and other factors. Until the shot column spreads apart, most of the energy of pellet-to-pellet collisions will be absorbed via deformation of the pellets themselves, since they cannot necessarily rebound with a change of direction or velocity until the column leaves the confines of the barrel.

It is reasonably safe to state that those pellets in contact with the barrel walls or originating towards the rear of the shot column (i.e. close to the wad) will usually be those which are most damaged, but we cannot say definitively that this is the case.

(In fact, the millions of collisions between pellets, wad and barrel walls which occur after the firing pin strikes the primer are entirely predictable, as is the distribution of collision energy and resulting pellet deformation – but the SmallBoreShotguns team has neither the required equations or computing power available to model that situation.)

Regardless, the situation is complex and even having understood the mechanisms by which pellets may be damaged, there is overlap in the amount of damage between pellets originating in one positional area and another. Considering all of the shot together, there will be a range of degrees of damage, from those nearly-undamaged to those which are, for ballistic purposes, essentially destroyed. Most pellets will be deformed to a degree between these two extremes.

If the damage caused to each individual pellet in a shot cloud was quantifiable, we would in fact find that the degrees of damage were approximately Normally-distributed around an average, according to the kind of passage they had experienced down the bore of the gun. This is a hugely important point: if the degree of damage each pellet experiences, on average, is predicted by a function of the Normal distribution then so is the kind of trajectory each pellet will follow.

This conclusion means that although we cannot predict the flight path of individual pellets, we can measure the probability of a pellet ending up a given distance from the theoretical point of impact (i.e. the point on the line extending down the axis of the barrel, which intersects our target) at a given range and, having established that probability through repeat testing, use that as a reliable predictor of future behavior.

A shotgun pattern provides the means to measure that probability, being a fixed image of the distance of each pellet from the central point of aim, at a given distance. By fixing the conditions of measurement via a threshold value (i.e. the 30″ circle), we can express the probability function describing pellet deformation and trajectory for a given gun, cartridge, choke and range as an easily-expressible percentage likelihood of any given pellet ending up inside or outside of the circle. In turn, these percentages can be compared to express relatively impressive or relatively poor performance.

Conclusions to Part II

We hope that, in reading what we have written above, our readers will now understand that the creation of a shot cloud occurs because of the conditions prevailing under firing and their effect upon the pellets to be projected from the gun.

We hope also that they will recognize the three significant causes of pellet deformation: contact with the barrel wall; impact with the closure of the cartridge; impact by the wad.

We hope, thirdly, that they will recognize the practical difficulties in measuring exactly the behaviour of individual pellets and accept the value of an approach based upon probability and in turn accept the now well-established use of the Normal distribution in modelling degrees of pellet deformation and the likelihood of their deviation from the theoretical point of impact.

We hope, finally, that in accepting the three conclusions drawn above, the value of patterning in measuring average pellet deviation from the theoretical point of impact, as an indicator of pellet deformation and cartridge performance both in terms of absolute performance and as a measurement of consistency, has been established.

In the third part of this article, we will look at the mathematics required to analyze a shotgun pattern and the methods by which useful information about the characteristics of our cartridges can be gleaned from them.