Calculation of the ideal pattern width for a given target and shell


Introduction.

You may have heard others talking about the fringe of the pattern or the effective pattern diameter. Sometimes the fringe will be described using terms like, 'the diameter at which the chance of two pellet strikes drops below 95%'. This page will explain how the effective pattern width is found, how it can be optimised and what the 95% figure means. It is a little heavy going but bear with it.  

Choosing the optimum spread for a given target is complicated by two things:

1) The shot pattern is random. This means one must work out the worst case pellet density rather than the simpler average pellet density.

2) The shot distribution is not uniform but relatively dense in the centre and thins out progressively with distance from the centre of the pattern. The rate of thinning out is much more difficult to calculate than a simple straight line and it is this that makes working out the effective pattern width difficult. 

Effect of pellet density and randomness.

Because the pellet patterns are random, in order to ensure a pellet strike on the target the AVERAGE pellet density must be much higher than 'one pellet per target'. Just what average pellet density is needed to ensure at least one pellet strike (or at least two or more) on the target is shown by the graph of Figure 1 below.

 

Figure 1. Variation in hit probability versus average pellet density.

For the following discussion, pellet density is measured in 'pellets per target'. This may seem odd but actually makes things easier to follow because one does not need to constantly convert from pellets per square inch to the size of the target. The game shooter uses a smaller number of large pellets with a more open pattern, the clay shooter the opposite. What is important is not absolute pellet densities per se, but 'pellets per target'.

The details of the graph are as follows:

  • The horizontal axis shows the average pellet density of a pattern.

  • The vertical axis shows the probability of the required number of strikes on the target being achieved.

  • The six lines show the relationship between average pellet density and probability of one or more, two or more, three of more etc up to six or more pellet strikes on the target occurring. 

Assume that it is required that at least one pellet strikes the target. This is the dark blue line. The label '1' shows that with an average pellet density of two pellets per target, there is a ~86% chance of at least one pellet striking the target. Following the dark blue line along to the label '2' and it shows that an average pellet density of four pellets per target gives a ~98% chance of at least one pellet striking the target.

Because one pellet strike alone might just clip the edge of the clay, it is maybe better to work with the probability of two pellets striking the clay. With luck at least one of them will be a good hit! The pink line shows the chances of two or more pellets striking the target and what average pellet density is needed to achieve a certain probability of the two or more pellet strikes.

The vertical line with labels '3', '4' and '5' shows what an average pellet density of six pellets per target can achieve. The label '3' shows that there is ~72% chance of five or more pellets striking the target. The label '4' shows that there is a 85% chance of four or more pellets striking the target. Going up to the label '5' and it is seen that the average pellet density of six pellets per target gives a 98.3% chance of two or more pellets strikes on the target or 99.8% of at least one pellet strike. This is probably a good pellet density and hit probability combination for a good trap or skeet shooter where high scores are expected. 

Note that label '3' denoted that there was a 72% chance of five or more pellets striking the clay, this means that a pattern spread for a skeet or trap gun to give the almost guaranteed one pellet strike will very often deliver much more than this. Six plus pellets striking a clay will deliver a very impressive break, most likely at least some 'smoke'. 

The key point is this: To ensure breaks 99%+ of the time, the choke may well appear too tight 70% of the time. Also, the very random nature of the pellets makes it near impossible to tell by eye whether the spread is optimal or really too tight and denying pattern width.

The next thing to do is move from 'pellets per target' to a measurable spread on the pattern plate and work out how wide a useful pattern can be had for a given shell . . . . .  


Maximum pattern width giving a desired average pellet density. 

24g (7/8oz) skeet shell example.

Ever since I started patterning with my skeet gun I had that feeling that it threw too wide a pattern. Now I'll prove that it does. I use 24g shells to reduce recoil. The Winchester X3+ gives very repeatable spreads shot to shot and also has a relatively high pellet count of 550 pellets per shell. This should give the best chance of good pellet coverage.

The pellet density is always greater (on average) in the centre of the pattern. The effective width of the pattern is simply the radius/diameter inside which the average pellet density is high enough to deliver the required number of pellet strikes after allowing for random shot to shot variation in the pattern.

Having found that a good skeet shot would benefit from an average pellet density of six pellets per target to give a 98.3% chance of two or more pellets striking the clay and a 99.8% chance of at least one pellet strike, all that needs to be done is to find the pattern spread that maximises the area over which the average density is six pellets per target.

The graph below shows how the average pellet density varies versus distance from the centre of the pattern (multiplied by two to convert the radius to an effective diameter). 

 

Figure 2. Pellet density versus diameter for a 550-pellet shell and an edge-on clay target.

The six lines show different spread widths (i.e. patterns from different chokes) and how their densities vary versus distance from the centre of the pattern. 

The 75% spread figure is the number generated by the Shotgun-Insight software. The 27" 75% pattern is close to that thrown by my skeet gun at 21yds. From the Eley Handbook, this is actually more open than true cylinder. The sporter with 1/2 choke throws a pattern of ~16" at 21yds. Hence the six different spread lines on the graph above show the range of pattern densities from a little wider than cylinder to ~3/4-choke.

Looking at the horizontal line where 'average pellet density' equals 6, it can be seen that the 27" wide pattern of my skeet gun does not actually deliver this density even in the middle of the pattern. 

This is a useful point to move away from the pure theory of patterns to the practicalities of skeet and the vagaries of the shooter. 

 

Effects of different distances in skeet.

First, the distances skeet targets are taken at vary from as little as 7-10yds up to ~24yds for the second shot of the doubles on stand 4. So, for all the incomers, this skeet gun with its very wide pattern offers a slight advantage. Furthermore, the incomers tend to offer a larger target area so the pattern can't really ever be too wide. 

For shooters who are quick and take the going away birds before the centre peg, say at 19yds, the pattern width will be close to that of the 24" 75% trace shown in the graph of Figure 2, i.e. the pellet density in the centre 8" is now above the 6-pellet threshold. For very quick shooters who get the going away bird at approximately 2/3 of the distance to the centre peg the pattern density will be between that of the 21" and 18" 75% patterns shown in Figure 2, i.e., just about optimum for this gun and shell. 

The problems with coverage occur for the ~24yd going away second bird on stand 4. The pattern only gives about a 91%/98% chance of a double/single pellet strike respectively even in the very centre of the pattern and maybe only ~85%/96% double/single hit probability at 5" from the centre (i.e. 10" diameter). While this sounds really bad, there is only one of these shots per round of 25. So even if 1 in 10 birds pass through the pattern, this is only 1 bird in every 10 rounds of skeet. This would trouble the very best shots, but not most intermediate and casual shooters. 

There is another complication with skeet when it comes to optimising chokes. For the shooter who takes high 1, 2, 3 and 4 over the centre peg, it is the first shot that is most distant. However, for the second bird on the doubles at stand 4, it is the second bird that is most distant and would benefit from the tighter choke. Changing barrel selectors on stands is not recommended because it can disrupt concentration, get forgotten and maybe lead to the option bird being lost when the shell is put in the wrong barrel. This is why skeet is best shot by taking the first bird just before the centre peg with a skeet 1 choke, and the skeet 2 choke is just right for the second bird on stand 4. For the other incomers, they are assumed to be straight forward for a good shot so the over choke of skeet 2 is not really a problem. 

 

Rating the shooter (an honest assessment of one's abilities)!

Now we come to the vagaries of the shooter. The optimum spread also depends on the skill of the shooter. There is no point worrying about whether the coverage in the centre is 99.0% or 99.99% if the shooter can only place the clay in the centre of the pattern 75% of the time! For the casual shooter, it would be much better to trade some guaranteed coverage in the centre for some extra luck on the fringe. If one compares the 27" 75% spread and the 18" 75% spread in the graph of Figure 2, one can see that at the 25" diameter mark on the horizontal axis, the wider spread is giving an average pellet density of ~2 versus ~1 for the tighter spread. Referring all the way back to Figure 1, one can see that an average density of 2-pellets gives ~86% chance of at least one pellet strike on the clay whereas at 1-pellet per target average density, down to ~60%. For the less precise shooter this would be a real benefit which is why beginners do so much better with open chokes.

However, for the shooter who wants a pattern that does not let them down if they do their part, this gun with the 550-pellet shell would benefit from some more choke. It is a close call between the red and pale-blue traces (18" and 21" 75% patterns respectively). The red 18" trace maximises the 6-pellet average density spread to about 13" and is only slightly poorer at the 20" diameter. At 24yds distance the red trace is equivalent to approximately 3/8 to 1/2 choke, the pale blue trace is ~1/4 choke. 

It is a personal judgement call as to which is the best. Both offer a useful enough central pattern to deliver kills for good shooters. The pale blue slightly more open trace looses about 1.5" coverage at the 6-pellet average density level but by offering slightly denser patterns at a 20" diameter and outwards might help with those awkward clays that move around in gusts of wind. It could be summarised thus, 'Enough density to guarantee kills when conditions and the shooter are good, enough margin of error for when conditions are poor'. 

The red trace is actually pretty close to a 'Skeet 2' choke pattern, so in a very long and drawn out way, we have just shown why 'Skeet 2' chokes are good for the longer going-away birds.    

This link shows where skeet 1 & 2 are in the order of chokes: http://www.colonialarms.com/chokespecs.html

 

Effect of increasing the pellet count for the skeet shell.

The skeet gun is about 30 years old. Back then 1-1/8oz loads were still allowed for English Skeet. This would give a load of ~657 pellets. ~650 pellets is also offered by some 28g (1oz) Italian 9.5s and some of the recent dedicated skeet shells. Shown below is the same type of graph but for a 657 pellet shell. This now looks better with near guaranteed coverage in the very centre. For shots taken before the middle peg (follow the purple or pale blue trace) this is near optimum. For a slow shooter such as myself, slightly tighter chokes could increase the effective pattern from ~8" to 12-15". This may not sound much, but actually gives a 2-4 times increase in effective pattern area. That's why choke choice is important!!

 

Figure 3. Pellet density versus diameter for a 657-pellet shell and an edge-on clay target. 

 


28g (1oz) No. 7.5 trap shell example.  

Trap shooting is a little bit like skeet in that high scores and edge-on clays are the order of the game. Clearly if the skeet gun could benefit from a 'little bit of choke' when it has a 550+ pellet count and a 21yd target, a trap gun shooting at ~30yds+ using fewer larger pellets will benefit from a lot more choke.

Just for the purpose of an example, a 1oz No. 7.5 will be considered. This has ~400 pellets.

The ideal average pellet density will still be six pellets to give the ~98% chance of at least two pellets striking the clay. The difference now is that the clay will be assumed to be 'trap view', i.e. showing a little larger target area than a true edge-on clay. The other advantage as far as selecting chokes is concerned is that the distances are known and the second shot is always further out than the first.  

The green or red traces look like the best choice. This applies whether the target is the first shot at ~30yds or the second at ~40yds. The only difference is that practically delivering a 18" 75% pattern at 40yds will require a lot more choke than delivering the same pattern at 30yds.

At 25yds the sporter with 1/2 choke gives a 75% pattern spread of ~19". Scaling to 30yds would give a 1/2 choke spread of ~23" which is close to the purple trace on Figure 4. The red trace showing an 18" 75% spread is about 80% of the width of the 23" estimated for the 1/2 choke which suggests the red trace corresponds to a tight 3/4 choke at 30yds. 

For the second shot, delivering this same pattern at 40yds is most definitely a job for full choke! If they can be proved to work, something just little bit tighter than 'full' might be beneficial.

That's why dedicated trap guns typically come with 3/4 & Full chokes!!

 

Figure 4. Pellet density versus diameter for a 400-pellet shell and a 'trap view' clay target.

 



 
 
 
 
 
 
   

(c) Dr A C Jones