Some time ago I carried out some work looking at pellet spiralling (https://www.airgunnation.com/threads/pellet-spirals.1297114/) and how it could be reduced at ranges up to 100 yards. The conclusion was that increasing spin damping could reduce spiralling to negligible sizes, but of course as shooters we can do little to change the pellet design. All we can do is reduce muzzle velocities and try to obtain a barrel with reduced twist rate based on what others have found, or what manufacturers are prepared to offer.
Of the two .22 designs used in the study, it was obvious that one was more likely to suffer from large spirals than the other. Based on the evidence of an earlier thread comparing lead and lead free pellets of the same design (https://www.airgunnation.com/threads/lead-and-lead-free-pellets.1283547/), it seemed that filling in the pellet tail to increase weight made them more susceptible to yaw growth and thus spirals. The main reason for this was the change in the centre of gravity (CG) position, moving it back towards the base to make it much nearer to the aerodynamic centre of pressure (CP), thus reducing the aerodynamic moments (Cma) about the CG. The calculated values of Cma for the heavy pellet are always much lower than those for the pellet with a hollow base and a forward CG.
I started off by taking a heavy pellet design and running trajectories out to 100 yards using standard calculated values for Cma and twist rates varying from 16 to 32 inches per turn. The actual group sizes calculated are a function of the pellet based errors assumed, which are fairly severe. The important thing to look at is how the group size varies, rather than its actual size. I then arbitrarily increased the numerical value of Cma by 0.1 and repeated the exercise, and repeated the exercise again by increasing the numerical value of Cma by a further 0.1. As expected, the trajectory modelling showed that the increases in Cma reduced the sizes of the spirals and thus the group size.
This was done for two velocities, 800 and 1050 ft/sec. These velocities were chosen as they include the speeds at which the values of Cma start to change due to Mach number effects, and thus group sizes. The 800 ft/sec simulations were repeated for a medium weight pellet design to see if similar results were obtained.
The big problem is that you cannot really randomly increase the size of Cma for a pellet without changing its design. Making it longer is the easiest method to increase Cma, but that immediately changes the mechanical moments of inertia, which also changes the pellets behaviour and thus the group sizes. I had a lot of data from the literally hundreds of simulations, but it was difficult to see trends as there were too many things varying all at once, even though this was a simulation with many variables kept constant which would vary in real life testing.
In all my previous threads I would have shown three or four diagrams by now, but there was so much data, and it was so confusing I have not shown anything so far.
There is one variable which the trajectory model prints out which contains a number of the variables causing the difficulties, and that is the gyroscopic stability factor. For this reason, I decided to try plotting out the calculated group sizes as a function of gyroscopic stability factor to see if it showed up any trends.
The next problem is that gyroscopic stability factor varies as the pellet moves along its trajectory, so which value could be chosen? In the end, I decided to work out the average stability factor for each of the trajectories for each of the chosen ranges and muzzle velocities. Now the data began to make some sense.
Below are the results for the heavy pellet type fired at 1050 ft/sec at four different ranges. Each dot is for a different barrel twist rate, giving a different average SG value.
Now there appear to be definite trends that we can see. The diagram below shows all the different trajectories on one graph for both pellet designs. It looks a bit of a mess at first, but there is something we can see.
If you look closely you can see that for all the different speeds and pellet types there appears to be an optimum value of average SG for the minimum size groups. This average value appears to lie between -2.5 to -3.5.
So what use is knowing the optimum average value? By knowing the SG value needed, it is possible to calculate the optimum twist rate required for the ranges of interest. The twist rate for 100 yards will be different from that needed at 50 yards, so barrels would need to be optimized for specific purposes. It does not mean that a barrel optimized for 100 yards could not be used at 25 yards, but the groups would not be the smallest possible at 25 yards. The difference would probably be small at short ranges where groups are small anyway, so a barrel twist optimized for the longest ranges would give the best overall performance.
But is this of use to shooters? Optimizing your twist rate will not suddenly turn a poor barrel into a brilliant one. It will help to make a good pellet barrel combination give the smallest groups, particularly for long range competition shooters.
However, not many shooters will have the ability to calculate the twist rate needed. It requires some pretty involved computer programs and aerodynamic calculation, plus detailed properties of the pellets themselves. Manufacturers of guns and pellets should have the joint knowledge and programs to produce pellet gun combinations which are optimized for each other. I say should as, based on the comments of a representative of a large manufacturer in a recent article, it would appear some do not. Strelok, which had supposedly been used for twist rate information, is not suitable for this work and was never intended to be used for such detail design. Some manufacturers of barrels may be able to carry out the research, or employ someone who can do it, I do not see why not, there must be people who could do the work needed.
One word of caution. The work still needs expanding to other pellet designs, calibres and with other inputs of pellet manufacturing errors. The data so far suggests the optimum SG value will not vary a great deal, but it needs confirming. This is really only the start of the work.
Of the two .22 designs used in the study, it was obvious that one was more likely to suffer from large spirals than the other. Based on the evidence of an earlier thread comparing lead and lead free pellets of the same design (https://www.airgunnation.com/threads/lead-and-lead-free-pellets.1283547/), it seemed that filling in the pellet tail to increase weight made them more susceptible to yaw growth and thus spirals. The main reason for this was the change in the centre of gravity (CG) position, moving it back towards the base to make it much nearer to the aerodynamic centre of pressure (CP), thus reducing the aerodynamic moments (Cma) about the CG. The calculated values of Cma for the heavy pellet are always much lower than those for the pellet with a hollow base and a forward CG.
I started off by taking a heavy pellet design and running trajectories out to 100 yards using standard calculated values for Cma and twist rates varying from 16 to 32 inches per turn. The actual group sizes calculated are a function of the pellet based errors assumed, which are fairly severe. The important thing to look at is how the group size varies, rather than its actual size. I then arbitrarily increased the numerical value of Cma by 0.1 and repeated the exercise, and repeated the exercise again by increasing the numerical value of Cma by a further 0.1. As expected, the trajectory modelling showed that the increases in Cma reduced the sizes of the spirals and thus the group size.
This was done for two velocities, 800 and 1050 ft/sec. These velocities were chosen as they include the speeds at which the values of Cma start to change due to Mach number effects, and thus group sizes. The 800 ft/sec simulations were repeated for a medium weight pellet design to see if similar results were obtained.
The big problem is that you cannot really randomly increase the size of Cma for a pellet without changing its design. Making it longer is the easiest method to increase Cma, but that immediately changes the mechanical moments of inertia, which also changes the pellets behaviour and thus the group sizes. I had a lot of data from the literally hundreds of simulations, but it was difficult to see trends as there were too many things varying all at once, even though this was a simulation with many variables kept constant which would vary in real life testing.
In all my previous threads I would have shown three or four diagrams by now, but there was so much data, and it was so confusing I have not shown anything so far.
There is one variable which the trajectory model prints out which contains a number of the variables causing the difficulties, and that is the gyroscopic stability factor. For this reason, I decided to try plotting out the calculated group sizes as a function of gyroscopic stability factor to see if it showed up any trends.
The next problem is that gyroscopic stability factor varies as the pellet moves along its trajectory, so which value could be chosen? In the end, I decided to work out the average stability factor for each of the trajectories for each of the chosen ranges and muzzle velocities. Now the data began to make some sense.
Below are the results for the heavy pellet type fired at 1050 ft/sec at four different ranges. Each dot is for a different barrel twist rate, giving a different average SG value.
Now there appear to be definite trends that we can see. The diagram below shows all the different trajectories on one graph for both pellet designs. It looks a bit of a mess at first, but there is something we can see.
If you look closely you can see that for all the different speeds and pellet types there appears to be an optimum value of average SG for the minimum size groups. This average value appears to lie between -2.5 to -3.5.
So what use is knowing the optimum average value? By knowing the SG value needed, it is possible to calculate the optimum twist rate required for the ranges of interest. The twist rate for 100 yards will be different from that needed at 50 yards, so barrels would need to be optimized for specific purposes. It does not mean that a barrel optimized for 100 yards could not be used at 25 yards, but the groups would not be the smallest possible at 25 yards. The difference would probably be small at short ranges where groups are small anyway, so a barrel twist optimized for the longest ranges would give the best overall performance.
But is this of use to shooters? Optimizing your twist rate will not suddenly turn a poor barrel into a brilliant one. It will help to make a good pellet barrel combination give the smallest groups, particularly for long range competition shooters.
However, not many shooters will have the ability to calculate the twist rate needed. It requires some pretty involved computer programs and aerodynamic calculation, plus detailed properties of the pellets themselves. Manufacturers of guns and pellets should have the joint knowledge and programs to produce pellet gun combinations which are optimized for each other. I say should as, based on the comments of a representative of a large manufacturer in a recent article, it would appear some do not. Strelok, which had supposedly been used for twist rate information, is not suitable for this work and was never intended to be used for such detail design. Some manufacturers of barrels may be able to carry out the research, or employ someone who can do it, I do not see why not, there must be people who could do the work needed.
One word of caution. The work still needs expanding to other pellet designs, calibres and with other inputs of pellet manufacturing errors. The data so far suggests the optimum SG value will not vary a great deal, but it needs confirming. This is really only the start of the work.
