Cast Bullets. F=MA, V=AT

Shooting bullets is a science. Anyone who tells you it is an art is someone who doesn’t know how to properly record their knowledge in a way that can be transmitted to others. So you could say that shooting cast bullets is a rather empirical part of the science. There are aspects of art, the craftsmanship, the pride in creating something, the tricks of the trade to make consistent bullets. But the art meets science in making consistency, understanding how your rifle has a particular geometry, and what are the causes of inaccuracy at a given velocity.

There are two simple equations in the title of this post. The first is that force equals mass times acceleration. The second equation is that velocity equals acceleration multiplied by time. I’ve been pondering why lots of people report that the same techniques work for them, and I’ve come up with what I consider a reasonable explanation for the facts about how to optimize both velocity and accuracy for a given rifle with cast bullets.

The problem with cast bullets is lead. Lead is soft, dense, malleable, and has been the choice of bullets for literally centuries. As velocity increases with a rifled firearm, the rotational velocity on the bullet also increases. This means if you double the velocity, you also double the rotations per minute (rpm). You can quite literally spin a bullet so fast that it tears itself apart. Other cast bullet shooters have noted the “rotational accuracy limit” for cast bullets. While not a hard and fast set of rpm numbers, they are empirical guidelines to understand that once you cross them, odds are accuracy will be negatively impacted. There are a lot of techniques to get beyond these limits such as changing the bullet alloy, changing the lube, paper patching, among other techniques.

The second part of this problem is how easily lead deforms, the malleability of the substance. It takes force to deform something, and in order to get a high velocity (V) we need to have a lot of acceleration (A) or a lot of time (T). Since the length of your rifle barrel has a practical upper limit (which is the biggest factor on how much time your powder has to accelerate the bullet) we are stuck adjusting the acceleration to ensure that the bullet isn’t radically deformed during the firing process. Some handloaders index their cartridges to ensure everything is consistent, some breach seat the bullet into the bore and then load the powder filled brass behind the already set bullet, others change the powder burn rate to (by changing powders) until they’ve found the one that gives them max velocity for max accuracy in their rifle.

All of these techniques are valid, and all of them are supported with empirical evidence of hundreds if not thousands of experiences with custom and factory rifles shooting every type of cast bullet imaginable. And eventually they all came to the one point where their rifle just couldn’t shoot a bullet faster and maintain any level of accuracy.

So far we haven’t talked about any particular bullet mold, lead alloy (and what different metals do to hardness, fill out, etc), or casting techniques. All that is largely the “art” part of creating ammunition where individual taste (or budget) dictates the performance parameters of the end product.

Through a few years of research, distilling down what the “art” into a checklist of things to monitor has produced the following list. They are in no particular order because any single thing on the list will destroy accuracy if not properly addressed. This is the science of the project, being able to choose among all the various options to address one of these points is the “art” if you will.

1. Bullet fit. Empirical data says that your bullet should fit into the throat, and be engaged in the rifling upon chambering. Lots of different bullet designs work, the key is fit.

2. Bullet alloy should be hard enough to withstand the pressures (the main Force in the F=MA equation) generated by the powder. Lots of different alloys work, the key is to be hard enough to consistently engage the rifling and come out the muzzle in the same shape from shot to shot. A deformed bullet is an inconsistent bullet.

3. Lubrication. Some folks use regular bullet lube, some paper patch, some powder coat. They all work, but the key is that the bore is not leaded between shots. Without a consistent bore condition you won’t have consistent internal ballistics, which means no consistent external ballistics, which means lousy accuracy.

4. Consistent transition from brass to barrel. If your chamber is off bore with the barrel, this can be quite a challenge as it will make deforming the bullet much easier to do (see point 2), once again a deformed bullet is an inconsistent bullet. This means brass prep and brass consistency is extremely important.

5. Consistent internal ballistics from the primer/powder combination, including pressure curve and barrel harmonics. Leaving the barrel at the same point in muzzle whip at the same velocity from shot to shot is necessary to have consistent external ballistics. Key here is that all of the bullets must also be the same shape to fly the same path (see point 2 and 4).

If you can address those five points, you will (eventually) find the maximum velocity with which your rifle can accurately shoot cast bullets. Or you will find the maximum accuracy with a particular cast bullet regardless of velocity. It may be slower than you want, and if it is a factory barrel it is probably going to be slower than you want.

Now with that in mind, back to the equations from the title. If force is mass times acceleration, then mass is force divided by acceleration. To put it more bluntly, mass is an inherent resistance to force. And while you can get good accuracy with any bullet weight, heavier for caliber bullets seem to produce better results. If rearrange the equation again, so that F/M=A, then V=TF/M, or F/M=V/T. What this should intuitively tell you is that increasing the mass should “spread out” the acceleration, and by doing so decrease the overall force acting on the bullet at any given time.

So how does this work? Well if you have a static charge of powder, then the lighter the bullet the easier it is to move, and the easier it is to deform (there is simply less mass there to resist deformation). But since we don’t have a static powder charge, we can change powder burn rates to do two things.

  1. Maximize the “area under the curve” for chamber pressure.
  2. Minimize maximum chamber pressure.

A normal chamber pressure curve immediately goes to a high spike, then degrades down to atmospheric pressure. This works great for jacketed bullets with their gilding metal support. It won’t work so well for use with softer cast bullets. So by using slower powders, the initial rise in pressure is more gradual, giving the bullet time to turn some of that pressure into acceleration, and acceleration into velocity, so that as the chamber pressure gets higher the bullet is already further down the bore and gaining velocity at a steady acceleration.

Sometimes this hobby really is rocket science. With modern powders it is very easy to launch a cast bullet so fast from a normal twist rate barrel that it loses all accuracy (the lead deforms from centrifugal force and stops flying in a predictable and repeatable manner. Going beyond that limiting rpm requires a tougher bullet, obviously (back to the 5 point checklist).  Some of the more hardcore hobbyists are having rifles built with slower twist rates to launch bullets at high velocity without going too high on the rpms. This limits the maximum bullet weight (as weigh increases, bullet length increases, requiring a tighter twist to stabilize a bullet in flight) but there’s no such thing as a free lunch.

There should be one more caveat, and that is this: sometimes you can do everything right and the rifle just won’t like it. Nothing to do but change the bullet design, or powder, or primer, or any of the dozen other details that go into creating your own ammo.

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3 Responses to Cast Bullets. F=MA, V=AT

  1. B says:

    Speaking from experience in art, like casting alloys, is the ability to control chaos. In most art however you can layer and paint over but in casting it’s a one way street. I believe Picasso said something like… art is the skill of throwing a pat of butter on a hot skillet. You can account for heat, butter size and throwing technique but everytime you throw it, it comes out different 🙂

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  2. DW says:

    I do a fair amount of reloading to keep costs down, and sometimes I will cast lead bullets for my 9mm pistols – basic wad cutter loads for practice and such. But I have never considered casting bullets for my .223 rifles. I have always purchased the bullets in bulk, usually 55 grain in fmj or the hornady spire tips.

    So I am curious, do you cast bullets for your .223 rifle? If so it must require some special cast alloy to work. I don’t want to get to far into the weeds here as it seems like this would be way beyond what I can do in my workshop. But if you have had any success that you can divulge, I would be interested, as I can see this being a critical need in a grid-down scenario. Primers of course, are the other grid down show stopper, don’t have a good solution for that either.

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    • rthtgnbs says:

      No, I don’t have molds for anything smaller than 7.62, and I like heavy bullets at that. The lightest weight cast bullet mold I have is a Lee 8mm because at the time it was what I could get in 8mm, although that has been remedied with a Lyman spitzer design.

      For 223 going the commercial jacketed bullet is probably the way to go unless you have a 1:12 or 1:14 twist barrel. I don’t ever plan on casting for 223 simply because all my ARs are 1:8 or tighter barrels now, and it can be a pain to develop a load that cycles the action without over spinning the bullet.

      If you have a bolt action rifle, it’s probably the perfect platform for cast rifle bullets, no matter the chambering, and you can develop useful short range loads even with a tight twist.

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