Wednesday, February 6, 2008

A few of the many types of black-powder guns

Anyone walking down the aisles of a sporting goods store featuring black-powder supplies will agree that muzzleloader users face an unusual mix of choices. Available rifles are based partly on nostalgia (Hawken, Kentucky rifles etc.), partly on new technologies (in-line ignition, pyrodex pellets etc.) and partly on preferences acquired from using other, more modern, weapons such as short-barreled carbines. To make matters worse, there are usually racks of bullets of various shapes and weights. How does one decide what to use? It’s not that no one is willing to give advice. It seems that every store clerk and every muzzleloader owner has some advice to give. The problem is, “whose advice do you take?”

A good piece of advice might be to refer to ballistics tables. They are available from gun manufacturers, are found in many books and can be accessed on the web. It usually turns out that the tables are incomplete. You might be able to find the right gun or at least the same barrel length as the gun you are interested in, but to also find the bullet and powder charge you are interested in, all tested together, would be a stroke of luck. It is hard to extrapolate from the tables and come up with a good guess for some value not expressly given, such as the muzzle velocity for a certain gun/powder/bullet combination that you might want to try. The variables don’t behave in a linear sort of way and attempting to read between the lines could be deceiving. There are some interesting web sites that feature calculators where one can plug in various parameters such as bullet mass and powder charge and view a calculated result. Since the result is offered without explanation, it still leaves a person wondering why things turn out the way they do.

I have to admit that I got started with muzzleloaders the same way most people do – basically clueless. I bought my first gun because it was on sale. I bought the bullets the store clerk told me to buy. The powder was the only kind on the shelf. I practiced shooting until I felt good at it. Then I went Elk hunting, had a clean shot, and missed. My ego wouldn’t allow me to think that I flinched or that I blew off a twig somewhere between the Elk and me. It had to be that the bullet dropped more than I thought it would at that distance. After that incident I switched to lighter bullets and have had good success hunting Whitetails ever since, but I often wondered if there really was a good reason for the change.

I don’t like doing everything by trial and error. I know that sometimes a little experimentation is necessary but there ought to be some guiding principles that can help a person wade through some of the decisions. The science of ballistics is, in some respects an art, but there are some fundamental laws of physics that can be applied to guns and bullets. Attempting to apply those laws can be a little tricky. The real world is filled with complications and the laws of physics, as usually presented to a lay audience, tend to leave out the effect of complications that prove to be small contributors. This means that the simplified laws are necessarily incomplete and cannot fully account for every situation. Even so, it is helpful to consider some of these laws.

Conservation of momentum and conservation of energy are a fundamental part of physics and, as far as anyone knows, always correct. To apply them, though, in ordinary situations like this, I will leave out some small contributing complications. I’ll start with conservation of momentum. Stated simply, conservation of momentum means that, after the gunpowder explodes, the momentum of the bullet is equal and opposite to the momentum of the gun - where momentum refers to the product of mass and velocity. Clearly, for any given momentum value, the smaller the mass, the greater the velocity.

Conservation of Momentum

(mass of the rifle) x (rifle velocity) = - (mass of the bullet) x (bullet velocity)
Conservation of Energy
The energy available from the explosion is divvied up between the gun and bullet. Now the word “available” is a little questionable. The explosion not only affects the motion of the gun and bullet, but it also produces a lot of heat. Who knows how much energy produces heat and how much produces motion? I sure don’t, but there is a useful “catch all” phrase that one can apply. It is “everything else being equal”. In other words, if everything else is equal, then the amount of energy going into motion of the gun plus the bullet ought to remain the same for any given powder charge no matter what the bullet is like. I am over simplifying things a bit but this is a good place to start.

It turns out that the energy of a moving object depends on the mass and square of the velocity. If energy is conserved, and “everything else is equal”, then the mass of the gun times the square of its velocity plus the mass of the bullet times the square of its velocity should remain constant. I’m not going to list a bunch of equations. Suffice it to say, if you write the equations for momentum and energy and deal with them both together, simultaneously, then you ought to be able to predict the velocities, momenta and energies of both the gun and the bullet after the powder explodes. Working it through is fairly easy. It only requires a little algebra. The results are both expected and a little surprising.

I’m going to ask you to stretch your imagination a little. Let’s start out by imagining a gun and its bullet having exactly the same mass. Actually, it will be more like a bomb exploding into two identical fragments than a gun and bullet, but please bear with me. Both fragments will have exactly the same momentum (in opposite directions) and exactly the same energy. Now let us consider one of the fragments having half the mass of the other. After the explosion, both will have equal and opposite momentum values but the smaller of the two will have twice the energy of the other. The sum of the energies will remain constant. If the smaller of the two has one-fourth the mass of the other, it will have four times the energy. The sum of the energies will again remain constant. The process will continue, as one fragment gets smaller and smaller its share of the total energy will continue to get bigger and bigger. The result of the changes in mass will be to continually decrease the momentum of each fragment and continue to increase the imbalance of energies. The sum of the two energies will remain the same as before and the two new momentum values will still be equal (but individually lower than before) and opposite in direction.

The situation for an actual gun and bullet is a little different because the mass of the gun doesn’t change when the bullet’s mass is changed, but if bullets are made smaller it will still be true that, in this simple model, their energy should increase and the recoil energy of the gun will decrease correspondingly. As bullets continue to decrease in size, the energy effect on the bullet will become less noticeable while the recoil effect on the gun will continue to be very noticeable to the shooter. Consider this example; A bullet whose mass is one hundredth of the mass of the gun will have an energy about one hundred times greater than the recoil energy of the gun. The bullet will have approximately 99 percent of the total available energy. Cutting the bullet mass in half could bring the energy up to between 99 and 100 percent of the total. This is barely noticeable. However, at the same time, the gun’s share of the energy will be nearly cut in half and that is noticeable.

The fact that bullet mass has a very noticeable effect on recoil was made clear to me during a target practice outing. Two of us took our muzzleloaders into the Arizona desert to sight them in. We took turns shooting and calling out results while observing the target. One time I heard an especially loud report, saw a bunch of gravel fly up a few yards in front of the target and something bounce into the target leaving a jagged hole. I yelled, “What happened?” and heard back, “I don’t know but it kicked like a mule”. A few seconds later the reply continued, “I can’t find my ramrod.” There was a lot of recoil in that shot but very little muzzle velocity. I suspect that a strong kick sometimes creates, for a shooter, an illusion of a more energetic bullet when the opposite is actually true.

When these predicted results are compared with ballistics tables there are a few discrepancies. The ballistic tables are, of course, correct. They represent actual measurements, whereas, the “everything else being equal” generalizations mentioned previously just make educated guesses. As expected, the predictions agree fairly well with the muzzle velocity trends and which bullets drop the most. Light bullets are usually faster and drop less. They drop less because; being faster, they have less time to fall before reaching the target. The prediction that light bullets have slightly greater muzzle energies shows greater discrepancies in the tables. Most of the discrepancy probably comes from the propellant gases carrying away a part of the energy. A point of diminishing returns can be reached where the bullet energy actually drops as the bullet mass declines and the gasses carry away a greater portion of the energy.
The barrel lengths, referenced in the tables I looked at, were 24 inches. That seemed a little short to me and I wondered if “everything else” was really equal when it came to barrel length. Could it be that a bullet, moving slower at first, had more time in the barrel to absorb energy from the expanding gas in a longer barrel, and were there other significant factors such as a longer frictional path that I had simply overlooked? The truth is I’m not sure. I would have felt better if I had more data for the 29-inch barrel in my gun but that information was sketchy.

I remembered the racks of muzzleloaders in the gun stores. The barrel lengths vary tremendously. Replica Kentucky rifles have barrels nearly 40 inches long and on the rack right beside them might be a carbine with a 20 inch barrel. Many of the replicas may have longer barrels than is actually necessary, but there is a reason why barrels in black-powder rifles tend to be long. A gunpowder explosion is fast but it is not instantaneous. It takes a little time for the powder granules to completely burn and an even longer time for the gasses produced by the explosion to expand and push the bullet out the barrel. The black-powder explosion, especially for the larger granules of the FFg rifle powder, is of a longer duration than an explosion of the modern rifle powders that cannot be safely used in a muzzleloader. The longer barrel may be necessary to allow for maximum effect. I suspect that short barrels tend to be popular because they make the gun easier to handle, not because they are more efficient.

My predictions may not have agreed completely with the tables, but being unsure about a percent or two doesn’t seem all that important. It is important that I can hit a target without having the bullet drop too much with distance, and that the recoil isn’t a major distraction. I’ll settle for having a general understanding of the effects of bullet mass on muzzle velocity and gun recoil. Actually, there may be a back door way of assuring that a lighter bullet will leave the barrel with more muzzle energy that its heavier counterpart. Gun manufacturers generally furnish recommendations on how much powder can safely be used. It’s not unusual to see larger powder charges listed for lighter bullets. This makes sense. The gun isn’t going to receive as big of a wallop with the light bullet, so that leaves room for a more powerful explosion.

I started out looking for some guiding principles and ended up with a model for a rifle in which the exploding gunpowder shares its energy between the gun and the bullet. Making the bullet smaller generally produces a higher muzzle velocity and less recoil for the rifle. Unfortunately, the model leaves one major unanswered question. Can a bullet be too small? Of course it can, but the reason for the answer doesn’t come only from the gun. It comes mainly from the bullet.
Bullet Choices

After a bullet leaves the barrel it starts slowing down because of air friction. The laws of motion used in physics to describe the effect of force on moving objects predict that for a given force, the rate at which the velocity decreases will vary inversely with the mass, in other words, the larger the mass, the less the deceleration. Physics also predicts that drag forces are greater at higher velocities. Both of these predictions favor heavy bullets over light ones, as long as “everything else is equal”.

The physics of drag forces is extremely complicated and there isn’t any simple way to understand how it works. High velocity motion causes drag due to surface friction and turbulence produced in the bullet’s wake. Turbulence may seem unimportant, but turbulent air has a lot of energy and that energy had to be transferred away from the moving bullet. That fact makes turbulence a huge contributor to drag. Two other factors, in addition to velocity, stand out as being very important when trying to understand drag. They are cross sectional area and bullet shape or profile.

Let’s start out by considering a round ball and compare it with a cylindrical bullet that has a spherical front. A ball and a spherical faced cylindrical bullet that have identical cross sectional areas may experience somewhat similar amounts of drag but, since the cylindrical bullet has more mass, it will decelerate at a lower rate. A similar argument can be used when the bullet strikes a target. If the surfaces exposed to retarding forces are nearly the same and the bullets enter the target with the same velocity, the cylindrical bullet will be more penetrating than the ball. Exactly how much velocity is left when either bullet reaches the target, though, depends on how long the drag forces have been acting. If the distance is great enough, the ball could even be moving more slowly than the heavier cylindrical bullet when it eventually hits the target.
The ball seems to be a bad choice. A cylindrical bullet makes more sense, especially if the profile is streamlined and made more cone-like to reduce drag even further. The big question is, “What is the best balance between a bullet being light to achieve high velocity and low recoil, and heavy to maintain speed and have adequate penetration when it eventually hits the target?” I can visualize some highly opinionated conversations regarding that question where the participants all end the conversation without having budged. For myself, I base the decision on my own experience.

I mentioned earlier that I had switched to lighter bullets after a missed shot and have had good luck ever since. Personally, I stick to the light end of the range of bullet weights that are typically found in the stores because they provide a high velocity and are more than adequate when it comes to penetration. I think 200-300 grains is a far better choice than 400-500 grains. In fact, I’m sold on a 180-grain bullet for Whitetails.

I used to hunt deer with a 12-gauge shotgun and slugs. It seemed like the heavy slugs went right through the deer while still retaining a lot of energy. Usually the exit wound didn’t appear much different than the entrance wound. To me this is energy lost. Energy is extremely important since it is the energy of the bullet dissipated in the target that does all the damage. Getting the bullet to expand or deform and lose its energy quickly is an aspect of bullet design that enables the transfer of energy to the target. It seems to me that a simple lead bullet can be too penetrating if it isn’t designed to expand adequately when it hits the target. I know there are many who will disagree with this opinion, believing that bullet penetration is more important than energy transfer. I guess for most of us, hunting experience will sway a person toward one opinion or the other.
The Plastic Sabot

If one agrees with using a smaller bullet for the advantages of higher muzzle velocity and a flatter trajectory, there is a great way of cutting down bullet weight and surface area while at the same time providing a means where the various bullet types, which allow for greater energy transfer, can be fired in a muzzleloader. This is what plastic sabots accomplish. The sabots reduce the diameter (caliber) of the bullet, thus reducing the cross sectional area causing drag. Guns of different calibers may actually fire the same bullets, as long as the appropriate sabots are used.

Another factor, which plays an important role in selecting a black-powder rifle, is the rifling or twist. One of the great advances in the evolution of firearms is the invention of rifling. The gyroscopic action of a spinning bullet keeps the bullet moving forward without wobbling or tumbling. It is similar to a spiraling football. Bullets vary greatly in the amount of twist needed to stabilize their flight. Round balls require very little twist, while rounded cylindrical bullets with sabots may need a lot. The only way to know if a gun has enough twist for a given bullet is to test fire it. Once you have found a bullet design that is consistently accurate, keep using it. Causing a bullet to spin does take a small amount of energy, which is subtracted from the energy of forward motion. The rotational energy is fairly easy to estimate and turns out to have only a tiny effect on muzzle velocity.

I’m sure there are some who will question the need for having a set of “guiding principles” from which choices can be made. I guess for me, the need is to have a way to tie things together more than it is a way getting specific information. Hopefully, other muzzleloader shooters will find this small amount of physics useful to them too.

The statements made in this article are generalizations based on principles of momentum and energy conservation and Newton’s laws of motion. They are not intended to cover all possible factors that affect the performance of firearms. The reader is urged to study the actual measurements found in firearm test reports and ballistics tables

Lynn Schultz
P.S. A "thank you" goes to Roger Whatley, an engineer and avid black powder hunter from Georgetown Texas, for correcting a mistake in my original post.