With all the discussion of lead free pellets, I have had a look at modelling a direct comparison of the group sizes between two pellets, one made of lead and the other made of zinc. I chose the usual 0.22 15.9 grain JSB type pellet and just substituted zinc for the lead. The zinc pellet weight came out at 10.04 grains, a bit lightweight but OK for this comparison. The results should be much the same for tin pellets, as the densities of zinc and tin are very similar (7.13 for zinc and 7.31 for tin).
Stability and group sizes are affected by a very large number of things, but one of them is the balance between the physical properties of the pellet, such as mass and moments of inertia, and the aerodynamic properties. If the aerodynamic and physical properties are balanced for a given design of lead pellet, and you change from lead to zinc, then you are changing the all important balance, which should change how the pellet works. I am trying to see how much the group sizes change and if different twist rates are needed for the different pellet materials.
Many of the non-lead pellets appear to be the same or similar designs to the lead ones. This work compares the group sizes for a lead and a zinc pellet of identical shape, fired at the same muzzle velocity (900ft/sec) and with the same defects present in the pellets. As the pellet designs are identical, the same aerodynamics have been used for both the lead and zinc pellets, but with the different mechanical properties.
The defects are based on some work I did some time ago looking at the effect of twist rates on group sizes for non-perfect pellets. For this exercise the pellets have a centre of gravity which is 0.1mm (4thou) away from the pellet centreline, and a 1.25mm diameter flat spot on the front of the nose close to the pellet edge representing a dent or cavity. The barrel twist rates used range from one turn in 82 inches up to one turn in 7 inches.
The aerodynamic data is based on experimentally derived data as far as possible, with some extra coefficients estimated using standard aerodynamic estimation techniques. The pellet physical characteristics have been calculated using a simple program which has been tested for accuracy against standard shapes with known mass and inertial properties. The trajectory modelling program is a six degree of freedom model which has been fully tested to government standards.
The group sizes at 30 and 50 yards for both the lead and zinc pellets have been calculated and compared. The resulting variations in group sizes with barrel twist rate is shown in the two diagrams below for 30 and 50 yards range. Each dot represents two trajectory runs, one with no pellet defects to give a zero error point and one with the pellet defects to give the error size and thus the predicted group size.
Don’t worry about the size of the groups predicted, that is just a function of the size of the pellet defects used, which were pretty severe, for this exercise in order to show up the differences. The important things are the relative sizes of the lead and zinc groups and how they vary with barrel twist rates.
The 30 yard results are the easiest to look at first, as the lead (pb) pellet results are always better than the zinc (zn) results. The zinc group sizes are generally, 30% or more, larger than the lead ones. The results at 50 yards are largely the same, but there is something strange happening at twist rates around one turn in 50 inches, where the zinc pellet suddenly looks much better. Looking at the variation in the pellet yaw angle with range for this twist rate, the maximum yaw seems to increase to a much larger angle than normal, indicating a dynamic instability which then to slowly damps down. This can be seen in the diagram below, showing the vertical yaw angle as a function of range for this particular case
.
One possible explanation is something known as spin yaw resonance producing spin yaw lock in, which happens when the yaw and spin frequencies are the same or very close. The yaw wave length shown above is close to the barrel twist rate, which would support the resonance theory. Resonance usually gives larger errors. In this exercise though, the orientation of the pellet defects used produced a vertical error giving a high impact point. The extra drag produced by the yaw angles shown above caused the pellet to fall as the range increased, so it may just be a coincidence that the error is small at the chosen range because the extra fall of the pellet due to the increased drag counteracted the vertical error of the pellet defects.
The best twist rates for both the lead and the zinc pellets seem to be similar, with the zinc having a slightly smaller bandwidth of suitable twist rates.
The results do not mean that a lead pellet will always give smaller groups than a zinc pellet. A zinc pellet with no defects which is a perfect fit in a barrel will be as good as a lead one in terms of group size. What it does mean is that a zinc pellet is much more sensitive to defects and is much more fussy about the barrel fit than a lead one. A zinc pellet will have to be made much more accurately and be a better fit in the barrel to match the lead pellet group sizes. Using lead pellet designs and production methods as a basis for zinc pellets is unlikely to give suitable results in a wide range of guns and barrels due to the above sensitivity.
The effects of cross winds have not been included in the above results for group sizes.
Stability and group sizes are affected by a very large number of things, but one of them is the balance between the physical properties of the pellet, such as mass and moments of inertia, and the aerodynamic properties. If the aerodynamic and physical properties are balanced for a given design of lead pellet, and you change from lead to zinc, then you are changing the all important balance, which should change how the pellet works. I am trying to see how much the group sizes change and if different twist rates are needed for the different pellet materials.
Many of the non-lead pellets appear to be the same or similar designs to the lead ones. This work compares the group sizes for a lead and a zinc pellet of identical shape, fired at the same muzzle velocity (900ft/sec) and with the same defects present in the pellets. As the pellet designs are identical, the same aerodynamics have been used for both the lead and zinc pellets, but with the different mechanical properties.
The defects are based on some work I did some time ago looking at the effect of twist rates on group sizes for non-perfect pellets. For this exercise the pellets have a centre of gravity which is 0.1mm (4thou) away from the pellet centreline, and a 1.25mm diameter flat spot on the front of the nose close to the pellet edge representing a dent or cavity. The barrel twist rates used range from one turn in 82 inches up to one turn in 7 inches.
The aerodynamic data is based on experimentally derived data as far as possible, with some extra coefficients estimated using standard aerodynamic estimation techniques. The pellet physical characteristics have been calculated using a simple program which has been tested for accuracy against standard shapes with known mass and inertial properties. The trajectory modelling program is a six degree of freedom model which has been fully tested to government standards.
The group sizes at 30 and 50 yards for both the lead and zinc pellets have been calculated and compared. The resulting variations in group sizes with barrel twist rate is shown in the two diagrams below for 30 and 50 yards range. Each dot represents two trajectory runs, one with no pellet defects to give a zero error point and one with the pellet defects to give the error size and thus the predicted group size.
Don’t worry about the size of the groups predicted, that is just a function of the size of the pellet defects used, which were pretty severe, for this exercise in order to show up the differences. The important things are the relative sizes of the lead and zinc groups and how they vary with barrel twist rates.
The 30 yard results are the easiest to look at first, as the lead (pb) pellet results are always better than the zinc (zn) results. The zinc group sizes are generally, 30% or more, larger than the lead ones. The results at 50 yards are largely the same, but there is something strange happening at twist rates around one turn in 50 inches, where the zinc pellet suddenly looks much better. Looking at the variation in the pellet yaw angle with range for this twist rate, the maximum yaw seems to increase to a much larger angle than normal, indicating a dynamic instability which then to slowly damps down. This can be seen in the diagram below, showing the vertical yaw angle as a function of range for this particular case
.
One possible explanation is something known as spin yaw resonance producing spin yaw lock in, which happens when the yaw and spin frequencies are the same or very close. The yaw wave length shown above is close to the barrel twist rate, which would support the resonance theory. Resonance usually gives larger errors. In this exercise though, the orientation of the pellet defects used produced a vertical error giving a high impact point. The extra drag produced by the yaw angles shown above caused the pellet to fall as the range increased, so it may just be a coincidence that the error is small at the chosen range because the extra fall of the pellet due to the increased drag counteracted the vertical error of the pellet defects.
The best twist rates for both the lead and the zinc pellets seem to be similar, with the zinc having a slightly smaller bandwidth of suitable twist rates.
The results do not mean that a lead pellet will always give smaller groups than a zinc pellet. A zinc pellet with no defects which is a perfect fit in a barrel will be as good as a lead one in terms of group size. What it does mean is that a zinc pellet is much more sensitive to defects and is much more fussy about the barrel fit than a lead one. A zinc pellet will have to be made much more accurately and be a better fit in the barrel to match the lead pellet group sizes. Using lead pellet designs and production methods as a basis for zinc pellets is unlikely to give suitable results in a wide range of guns and barrels due to the above sensitivity.
The effects of cross winds have not been included in the above results for group sizes.
