Comparing the Precision of Tin and Lead Slugs

[ballisticboy]

This is a first look at what may happen if slugs have to be made from an alternative to lead. The material I have used for the modelling is tin. The slugs are all .22 calibre based on a commercial design, with a hollowpoint nose just short of one calibre long, and a cylindrical aft portion of different lengths to give different slug masses. The design is fairly standard for slugs, with many of the currently available lead slugs being very similar in shape and size and can be seen below.



Slug overall lengths varied from 6.7 mm to just over 11 mm. Slug masses for the tin slugs varied from 12 to 24 grains, while the identical slugs made from lead varied from 19 to 37 grains. The muzzle velocity for all the slugs was fixed at 950ft/sec. The use of a fixed muzzle velocity is an initial starting point.

I could have used a fixed muzzle energy, but some of the tin slugs then end up travelling at supersonic velocities or some of the lead slugs would be travelling very slowly. To start the examination I wanted to introduce some fixed parameters to simplify the modelling which  already required intensive production of many types of data files.

To produce an error at the target end of the trajectory, I first used an initial yawing rate of ten radians per second on each of the slugs. The maximum range in all cases was 75 yards.

The first job was to calculate the mass, centre of gravity and inertial moments for each of the slugs. These characteristics are necessary for the rest of the input data files and for the stability calculations. The next job was to predict the aerodynamic properties of each slug using the calculated centre of gravity. The aerodynamic prediction program is a specialised version of a program created many years ago, an early version of which is on the JBM website. The accuracy of the predictions when compared to known values was  /-10%. For the slugs in this exercise, even if the errors are larger, the comparisons between the tin and lead slugs should be valid as the same aerodynamics are being used.

For rifle bullets, it is generally considered that a stability factor of 1.5 is the minimum required for good performance. For this reason, I calculated the barrel twist rate needed to have a stability factor of 1.5 for each slug, both lead and non-lead. The calculated twist rates needed for the required stability factor were then used in the trajectory modelling for each slug. The table below shows the slug lengths, mass and barrel twist rates for both the tin and lead slugs.



The table immediately shows up some problems for shooters and designers. For a given length of slug the tin one is much lighter, which is to be expected, and it requires a higher twist rate for the same stability factor. For the gun owner this means that unless he changes his barrel for one with a higher twist rate a shorter slug in tin will be required compared to a lead one, which will make the mass loss even greater. For example, a gun with a 22 inch twist rate will only be able to fire tin slugs of around 12 grains instead of the 25 grains for a long lead slug which could be used previously. The gun will also need adjustment to reduce the muzzle velocity if supersonic speeds are to be avoided.

There are also problems for slug manufacturers as well. Tin slugs will need increased barrel twist rates if the slug mass is to be preserved. Take a 24 grain slug mass as an example. A 24 grain lead slug will only need a 23 inch twist rate, whereas a 24 grain tin slug needs a 13-inch rate. Selling a slug which requires such a high twist rate to the general public, as opposed to enthusiastic experienced shooters willing to change their barrel, could prove challenging.

The graph below shows how the necessary twist rate varies with slug length for both the tin and lead slugs.



If the slug mass is of interest, the comparison for tin and lead slugs is shown here.



Remember, these numbers are for slugs fired at 950ft/sec. For higher muzzle velocities, faster twist rates will be needed.

For each slug, both lead and tin, two trajectories had to be run, one with no yaw rate on the slug and one with the 10 radians per second yaw rate at the start of the trajectory. There was a slight problem in that the modelling suggested that the shorter slugs suffered from a dynamic instability leading to increasing yaw and a slight spiralling effect at the end of some trajectories. To overcome this, a straight line was fitted to the error calculations (initial yaw rate errors give a linear increase in error with range). The slugs are probably not going to be dynamically unstable in real life, it is just very difficult to predict it accurately, particularly for small projectiles.

The predicted group sizes at 75 yards range for both the tin and lead slugs as a function of slug mass is shown here.



The group sizes look very similar. Looking at the group size as a function of slug length gives an easier comparison.



There are actually two curves there, but the lead one lies directly underneath the tin curve, something we would not expect. It would appear that with the same initial error, stability factor and muzzle velocity, slugs of the same length will give the same group size.

The group size results in tabular form for a fixed initial yaw rate are shown below.



This exercise is supposed to be concentrating on projectile error sources and looking at how the slug reacts. With the different twist rates for tin slugs, it seems unlikely that projectile based error sources would give the same initial yawing rate as the slug leaves the barrel. To take account of this, the 10 radians per second yaw rate was kept for the slug requiring the slowest twist rate and all the other slugs yaw rates were adjusted in proportion to their barrel twist rates. The resulting initial yaw rates for each slug are shown below.



The group size results are now very different for tin and lead slugs. Below you can see the group sizes at 25, 50 and 75 yards for the lead and tin slugs.



In this case, for a given slug length the lead slug always gives smaller groups than the equivalent tin slug, about 20% less. This is more in agreement with the results of a pellet study comparing pellets made of zinc and lead. The group sizes as a function of slug mass at 75 yards are shown here.



According to this chart, a lead slug of much greater mass can be fired for the same group sizes as the shorter, much lighter tin slug. Finally, for shooters with a fixed twist rate, the diagram below shows how the group size for tin and lead slugs varies with twist rate for the fixed stability factor.



Below are the group size results for twist rate related yaw rates at 75 yards in tabular form.



So what does it all mean? These are some initial thoughts, there is a lot of data to look at and a lot of observations which can be made. For shooters, unless you change the barrel on your gun to have a much faster twist rate, you will only be able to use much lighter and shorter slugs in tin than you could in lead. To avoid the new tin slugs travelling at supersonic speeds, you will also have to reduce the muzzle energy of your gun. Tin slugs of the same mass as some lead slugs can be used, but they may be too long to fit in the magazine and will need an even higher twist rate.

For slug makers, the problem will be how do you make a tin based slug which can use pellet type twist rates without going ultra short and light. Making a tin slug the same mass as a lead slug can be done, but it will be much longer and may well not work with standard twist rate barrels or fit in magazines.

There are still lots of variables which can be changed such as different stability factors, different error sources in the slugs, different muzzle velocities or constant muzzle energies. Each one could change the resulting group sizes, but tin slugs will always need much higher twist rates in the barrel than the equivalent length or weight lead slug.

[rsterne]

Thanks for taking the time to do all those calculations and write the article, Miles.... Lots there to think about, for sure.... With some parts of the World getting rid of lead for projectiles, this could become increasingly important.... As you say, unless you are replacing lead with tin directly (at only 65% of the weight), accuracy is likely to suffer, and even then a faster twist rate may be required....

One thing we need to remember, regardless of the projectile, using too fast a twist rate is generally not the best for accuracy.... Not as critical as too slow a twist (unstable and tumbling) to be sure.... but it emphasizes any slight imperfection in the projectile, increasing initial yaw, and ultimately group size....

Bob

[Back_Roads]

 Great read, I have been experimenting with cast tin and lead slugs, your calculations look to be in the ballpark with my initial test results.
 Inspired me to go cast up some of my latest .177 slugs in tin for my next range experiment. I still have to do further testing in the larger calibers that I first experimented with over a year ago, so many options so little time
 Have you run the numbers for a BBT say in .22, I have had decent results with them in tin with my custom Airforce Escape UL, worth more testing IMO.

[BigBird]

So what does it all mean? These are some initial thoughts, there is a lot of data to look at and a lot of observations which can be made. For shooters, unless you change the barrel on your gun to have a much faster twist rate, you will only be able to use much lighter and shorter slugs in tin than you could in lead. To avoid the new tin slugs travelling at supersonic speeds, you will also have to reduce the muzzle energy of your gun. Tin slugs of the same mass as some lead slugs can be used, but they may be too long to fit in the magazine and will need an even higher twist rate.

Interesting.  I have limited knowledge to figure out the models but it is really good information we "need to start thinking about".

I see the "drawbacks" you identified as advantages except for more drag in the bore and less expansion or metplat. I'm thinking slug slingers now, probably more than 12 FPE. Magazines shouldn't define the gun. They will just have to make them longer.  Future technology will eventually catch up with problems that we are thinking about now. 

Like how will we use airguns without lead, depleted uranium, meteorite or tungsten and if it is tin how do we design the twist and loading port.  They would probably have better BC, maybe closer to PB bullets.  I'm thinking some PB barrels might have a good twist. Even some PB magazines can be used.  I'm thinking of a design where you could incorporate one in the traditional PB position for loading.  I think with problems come innovation. 

Although this is a single shot it is probably using this Tin technology already.
https://www.altaros.cz/en/pcp-rifles/119-altaros-m24.html


Sorry this is not a plug and I don't have any stake in the company.  I just think it's cool.

[JuryRigger]

With the complete ban of lead projectiles seeming inevitable (at least some day-not talking about current politics in the slightest!!); this information is invaluable.
Many, many thanks; much appreciated.
Jesse

[ballisticboy]

Great read, I have been experimenting with cast tin and lead slugs, your calculations look to be in the ballpark with my initial test results.
 Inspired me to go cast up some of my latest .177 slugs in tin for my next range experiment. I still have to do further testing in the larger calibers that I first experimented with over a year ago, so many options so little time
 Have you run the numbers for a BBT say in .22, I have had decent results with them in tin with my custom Airforce Escape UL, worth more testing IMO.

I haven't run any BBT's in tin, just lead. I was concentrating on the usual slug design to start with and can move on to alternative designs in the future. There are still many more questions to be answered, which will hopefully eventually help with non-lead slug designs and their use.

[MJP]

There is no no viable substitute for lead, and there never will be.
Tin is harder and too light, and way too expensive.
Copper and brass way too hard. So we end up with nothing or something expensive and not as working.

Sabots and tungsten maybe. That works in my guns but I don't think the authorities want us to use armor piercing projectile?

These green folk have no idea what is really harmful to people, or the environment, or do they? Lead is so heavy that it sinks to the bottom if in water, but plastic in the other hand.

Marko

[Back_Roads]

 I use tin projectiles when pesting, as I leave the carcass for the critters higher on the food chain to get a free lead free meal. Not a fan of plastic either, melts to the barrel at higher powers, and there is enough of it in the environment already.

[rsterne]

Pure tin is about BHN 10, so certainly not too hard for use in an airgun.... and it melts at a lower temperature than lead, so easy to cast.... It is softer than 5% tin in lead, for example.... Expensive, yes.... 

Bob

[BigBird]

There is no no viable substitute for lead, and there never will be.
Tin is harder and too light, and way too expensive.
Copper and brass way too hard. So we end up with nothing or something expensive and not as working.

Sabots and tungsten maybe. That works in my guns but I don't think the authorities want us to use armor piercing projectile?

These green folk have no idea what is really harmful to people, or the environment, or do they? Lead is so heavy that it sinks to the bottom if in water, but plastic in the other hand.

Marko

Agreed.  Not to detract from the science here which has no political motive. The lead vs tin argument really IS a politically correct action (one that doesn't make sense or really has no ground in reality but enough argument to gain followers who feel good about the rhetoric and promote it regardless).  For us in the U.S.A. I think we have to use maybe California as a thermometer in this case.  I have no idea.  Have they banned lead there or anywhere?  Has any country banned it?

Tungsten is too expensive too.  Instead of shooting expensive tungsten a friend of mine loads pea gravel in his PB shotgun shells to comply with waterfowl hunting laws.   Gets a new barrel when it wears out.  It's cheaper even when you figure in a new barrel.  And that's the craziness of these laws too.

So, hey, there's a ban on lead shot there.  I think that is US federal.

[ballisticboy]

Tungsten is too expensive too.  Instead of shooting expensive tungsten a friend of mine loads pea gravel in his PB shotgun shells to comply with waterfowl hunting laws.   Gets a new barrel when it wears out.  It's cheaper even when you figure in a new barrel.  And that's the craziness of these laws too.

I seem to remember from the tank ranges that there are pollution problems with tungsten as well. When I was looking at using mini tank ammunition type long rods for sniper ammunition, I asked some of the management to find out if it was allowed, but I was retired before there was any answer.

[BigBird]

Tungsten is too expensive too.  Instead of shooting expensive tungsten a friend of mine loads pea gravel in his PB shotgun shells to comply with waterfowl hunting laws.   Gets a new barrel when it wears out.  It's cheaper even when you figure in a new barrel.  And that's the craziness of these laws too.

I seem to remember from the tank ranges that there are pollution problems with tungsten as well. When I was looking at using mini tank ammunition type long rods for sniper ammunition, I asked some of the management to find out if it was allowed, but I was retired before there was any answer.

I think people can find problems with any substance.  Although I found this:

"Some forms of tungsten can move readily though soil and groundwater under certain environmental conditions. ... Scientists have shown that exposure to tungsten can stunt the growth of plants, cause reproductive problems in earthworms, and trigger premature death in certain aquatic animals."

https://phys.org/news/2009-01-health-environmental-tungsten.html?&ampcf=1

Well, maybe I agree to a certain extent. I think earthworms "biology" is already messed up enough!

[subscriber]

Heavy going, but insightful!

How do I vote this thread up?

[JuryRigger]

Heavy going, but insightful!

How do I vote this thread up?

It used to show in the header bar along the top of the page, but not seeing it??
Edit-looks like that function is completely turned off here....
Jesse

[subscriber]

I had no idea that group size could be calculated/predicted.  I am surprised that the best slug lengths are so short.  Is that with the stability factor at 1.5 for all cases; or a fixed barrel twist?

[rsterne]

The stability factor is 1.5 in all cases.... The calculations are assuming a given initial yaw, caused by imperfections in the slug, caused by the CG not being in the center of the form.... As the slug exits the muzzle, and the slug changes from rotating around the center of form (the center of the bore) to rotating about the CG, it yaws due to gyroscopic precession.... The longer the slug, and the faster the twist rate, the greater the initial yaw.... The more perfect the slugs, the less the initial yaw, of course.... Changing the relationship between the CG and the CP of the slug will change how that yaw damps out (the slug goes to sleep) or increases (tending to developing a spiral).... again all related to velocity and twist rate....

Bob

[subscriber]

I thought that a longer slug provides a better lever for the correcting moment, to force the projectile to follow its projectile with less yaw?  Assuming the center of form and center of mass are also further apart.

Are rifle bullets "long and pointy" only for high BC?  Would shorter ones be more stable; and shoot smaller groups (at the expense of effective range)?

Obviously, an out of balance slug can upset things - all else being equal.

[rsterne]

Miles can give you a better answer to your first question....

Regarding the second, yes, long bullets can have a better form factor, but a lot of their higher BC comes from their greater SD.... However, they do require a faster twist, and in a crosswind they will have greater "aerodynamic jump" (vertical deflection from that crosswind), and likely greater "throwoff" from bullet imperfections as well.... As the bullet turns to face into the "relative wind" (the vector sum of its forward velocity and the crosswind velocity) that yaw causes it to deflect upwards or downwards, depending on the direction of the crosswind and the direction of the twist.... and also depending on if the CG is ahead of or behind the CP.... This causes groups to slope in gusty winds, rather than being strictly horizontal.... However, if the BC of the shorter, lighter bullet is lower (as we would expect), it's crosswind drift will be greater....

As you can see, in real world conditions, a long bullet with a good BC has some advantages (flatter trajectory, less drift).... while a short bullet with a poorer BC, but shot in a slower twist barrel, has other advantages (less throwoff and jump).... This balancing act between long and short bullets is one of the reasons you seldom find bullets with extreme length/diameter ratios being use in benchrest competitions.... The upper limit is about 5:1 (with 4:1 being more common), and the lower limit is probably about 2:1 (to get a decent BC).... A lot of really great PB bullets are about 3-4 calibers long, but many of those are too high an SD for airgun use, because of our low pressures.... In addition, their advantages may be greater when Supersonic, so our "ideal" L/D ratio may well be 2-3 calibers long, (maybe even less?)....

The bottom line is, you still have to find the one that works best in your barrel, and/or vice versa.... Miles may have additional comments as well....

Bob

[Back_Roads]

 So was the Lone Ranger onto something with his silver bullets or am I confusing that with werewolf hunting  Either way I'm on a tin & lead budget.

[subscriber]

OOPS:  Meant trajectory for bolded projectile.

I thought that a longer slug provides a better lever for the correcting moment, to force the projectile to follow its projectile with less yaw?