Ballistics 201: Introducing a New Way of Thinking About Terminal Effectiveness – Force, Energy, and Work

NewtonradG11

One of the primary focuses of my study of modern small arms has been that of their terminal effectiveness, i.e. their “lethality” or “wounding”, although neither of these latter terms are exactly correct. Over the past several years, I have read a good deal of scientific and medical documents, first hand accounts, and treatises by experts, to come to the opinions I have today about the subject; Opinions which – I should note – are still evolving.

There is such a great deal that can be written about the subject of terminal effectiveness that it would be impossible for me to do so in one post of reasonable length here on this website. Therefore, I will have to release chunks of writing more slowly, rather than laying down a single complete primer on terminal effect. Because of this, today’s article will be necessarily incomplete; backing concepts will be covered in posts that have not been released yet. Still, there’s something important that I’d like to get to now, and that is energy and how it relates to one portion of the mechanism of wounding.

I say the “mechanism of wounding” because the process of an inert projectile impacting and affecting living tissue is a mechanical one, similar to how an automobile engine or a wristwatch are mechanical in nature. This mechanical foundation is expressed in the common literature of terminal effectiveness, where estimations are made of different calibers based on their kinetic energy or momentum on impact, as these indicate in one simple dimension how a caliber can interact with its target.

Wounding is not simple, however, and these two metrics fall short of providing a concise picture of terminal effect on living tissue. We’ve proven how, though momentum is highly relevant to the dynamics of a bullet impact, it doesn’t have much direct relevance to the wounding potential of a round. Likewise, although kinetic energy is directly related to wounding, it does not always inform the actual effect of a bullet on its target. Further, it needs to be said that wounding is only a part of the problem of terminal effect; it deals only with the physical damage to the target itself, not to the psychological effect of a gunshot, or other potential indirect effects.

Addressing wounding by itself, then, what actually happens when a bullet impacts a fleshy target and creates a wound? Since we believe that the universe behaves according to physical laws, wounding should be no exception. It should therefore be possible to create a descriptive (if not predictive) model of what happens to the bullet and the body during an impact. In Physics there are three quantities that appear to be immediately applicable to our problem; these are Force, Kinetic Energy, and Work. It is possible to take a very math-heavy approach in describing these three properties, but I want to focus on concepts instead, so I will try to avoid doing that. Let’s first take a look at what these three properties are, and what they do:

  • Force: An interaction that causes a change in the velocity of an object. It can be expressed mathematically as mass times acceleration (with a vector), and uses the Newton (SI) or lbf (English). Note that Force has components of mass, time, and velocity.
  • Work: When a Force moves an object over a displacement, then it is said to have done “Work” to that object. Expressed as force times displacement, it uses the Joule (SI) or ft-lb (English).
  • Kinetic Energy: A property held by an object in motion, defined as the work needed to accelerate the object to its velocity. It can be expressed as one half times mass times velocity squared, and also uses the Joule or ft-lb. Kinetic Energy is often just called “energy” when discussing firearms, although there are other types of energy as well.

What my readers should take away from this is that when a force is applied to an object such that it raises its velocity, it performs work, which increases the kinetic energy of the object proportionally to the work done. These three quantities are interrelated and describe parts of the same action. How does that apply to the mechanism of wounding? We’ll find out in the next installment!



Nathaniel F

Nathaniel is a history enthusiast and firearms hobbyist whose primary interest lies in military small arms technological developments beginning with the smokeless powder era. In addition to contributing to The Firearm Blog, he runs 196,800 Revolutions Per Minute, a blog devoted to modern small arms design and theory. He can be reached via email at nathaniel.f@staff.thefirearmblog.com.


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  • TheRealKivaari

    You’re argument is invalid? Seriously, guys?!

    • Major Tom

      And with the piece of worthlessness that is the G-11 in the pic too? Appalling.

    • No, I wouldn’t say “seriously”.

  • iksnilol

    To be honest, we’d never have this discussion if it wasn’t for the Hague convention banning explosive projectiles with less than 40 grams of explosive.

    • Major Tom

      Then there was the St. Petersburg Declaration that was still in force for those who didn’t sign onto Hague but were party to that…

    • Tassiebush

      I want my shell rifle!

  • DanGoodShot

    I’ll look forward to future installments. I like to learn atleast one new thing a day. I haven’t done that yet today. But I’m sure I will in the articles to follow! Looks promising.

  • Sean I Hayes

    When will higher orders of energy transfer rates and motion (e.g. power and jerk) make it to ballistic mechanics debate, or are we going to continue yelling brochure numbers at each other?

    • AirborneSoldier

      Likely this

    • RocketScientist

      Jerk (d3x/dt3), the time-rate-of-change of acceleration, and its next three derivatives, humorously named Snap (d4x/dt4) Crackle (d5x/dt5) and Pop (d6x/dt6) are essentially insignificant outside of mathematical or theoretical concerns. With a very very few exceptions they don’t represent physical/mechanical concepts or behaviors that are noticeable or have any observable impact on our day to day lives, aren’t correlable with any commonly experienced phenomena, and we can describe/model most mechanical systems with sufficient realism without even taking them into consideration. As an illustration, the further down that rabbit hole of derivatives you go, the closer and closer you get to what is essentially a step function that transitions from 0 to infinity at the exact first moment of displacement. Not a particularly useful concept.

      As for power its just the work per unit of time. I’m guessing its not discussed much as the impact/penetration of a bullet through a target occupies such a small moment in time its probably not worthwhile to consider time as a factor. It makes more sense to look at it as a point event. Further theres not a lot of difference in the duration of a bullet impact across a wide range of bullet velocities. Sure it might take a few more microseconds for a big slow 45 to penetrate compared to a 22-250, but that difference in time is not likely to significantly impact the wounding effects. On the very very small scale, the rate of transfer of energy (aka power) of the impact surely has some difference in localized heating of bullet/tissue, tissue liquefaction etc. But its going to be extremely difficult to model on such a small scale, and the natural variability of such events (depending on angle, clothing, minute surface geometry of the bullet, different tissue properties etc) would probably overshadow any effects easily attributable to any difference in time rate of energy transfer.

      • jungssean

        I guess I would disagree. I’ve seen the effects of temporary cavitation in wound generation criticized/doubted (even by trauma surgeons), but if you’ve hunted (or just googled it), I’m sure you’ve seen would channels [much] larger than what the projectile could have physically displaced, even considering expanding, fragmenting, or tumbling bullet designs. At some level, I would expect everyone can admit, temporary cavitation can lead to permanent tissue damage.

        The remainder of this post probably belongs as a comment to the follow-up, and is more or less simplified by his term “energy budget.”

        If we are willing to concede that temporary cavitation is meaningful, ballistic gelatin becomes much more useful. After some time in the YouTubes, it’s easy to see that loads with similar muzzle energies can cause much different cavitation shapes in ballistic gelatin which can be attributed to energy transfer rates.

        If we want to debate the effectiveness of different bullets and cartridges as means of damaging large animals (bipedal or not), then we should (a) have some understanding of the difference in response between our test media and actual intended media, and (b) be able to model and analyze the response of our test media. This is where our units need to convert from a mechanical projectile to a viscoelastic media.

        A lot of the above comments above have brought up the extremely transient nature of this case, and the follow-up article also brings up the projectile’s own deformation case after impact. I would bet money, second order functions will not be modeling these problems. Assuming I won that bet, why would we use them to describe our ammunitions’ performance?

        • RocketScientist

          I guess my point wasn;t clear enough. Not talking about permanent vs temporary cavity, not talking about ballistics gel testing, none of that. just speaking in broad terms about the large concepts you asked about (jerk and power being factored in, in addition to the common energy and velocity/acceleration). My point was that, based on my work experience with these concepts, I very seriously doubt including them in analysis would have any significant difference. If you came up with a model/governing system of equations that only included energy, and velocity/acceleration, and then went through the effort of making them more in depth and including time-rate-of-change of energy and time-rate-of-change of acceleration, the results you’d get would be virtually identical, but the process to develop them and use them would be significantly more cumbersome/complex. Or in other words, of course those concepts have SOME impact on things, at the analytical/theoretical/math level. But their impact on the real results are going to be SO SMALL compared to the effects of including acceleration and energy, that there’s likely no benefit or need to include them. Thats how these higher order derivatives work. There’s a reason most people are familiar with position, displacement (distance), velocity and acceleration, but almost no-one has heard of jerk, snap, crackle, and pop. Because for just about anything outside of a math book or a research lab, the first set of properties accurately describes 99.999% of the behavior we’re concerned about. The impact of the remaining ones get exponentially less and less.

          As a very crude example: if you’re trying to weigh yourself, everyone can see you’ll get a more accurate value if you take off your socks vs not. But compared to the major driving factor of measured weight (the weight of your actual body), going through the effort of removing your socks, or calculating their weight and subtracting them is not going to appreciably change the measured value. In fact the impact of their weight may be so small that its lost in the noise of measurement error, natural weight variation etc.

  • MarkVShaney

    Is “Terminal Effectiveness” your new buzzword to replace “stopping power”? I will repeat a previous assertion- so we can just skip to the end. “Terminal Effectiveness”, “Wounding”, “Stopping Power” is currently an undefined quantity. I will use an equation inspired by the Drake Equation.

    SP = E + F + B +/- T(v)

    Stopping Power = Kinetic Energy (momentum) + friction + biological factors (shot placement) +/- Target velocity at POI.

    This is your “descriptive model” that you called spurious nonsense last time.

    • Darkpr0

      The difference is that Work, Kinetic Energy, and Force are all engineering terms that are derived from real, measurable quantities. Everything is expressed in terms of combinations of mass, distance, and time. They are not picked out from thin air; they follow rules, like the Law of Conservation of Energy. They are useful because of what you can do with them, not because we pick them out of a brochure and plop them onto paper.

      Your math IS nonsensical. You are adding together factors that have nothing to do with each other. You have assumed that Kinetic Energy (an energy term in kg*m^2/s^2) is the same as Momentum (it is completely different, momentum is in kg*m/s), added it to friction (A force term in kg*m/s^2), added that to target velocity (a velocity term in m/s), and then just plopped on biological factors for giggles. Your math has literally nothing to do with anything. In fact, I challenge you to actually grab a calculator, measure out what you’ve put together, and produce data on anything. It won’t work for a very simple reason: The engineering formulae are all derived using fundamental rules of mathematics. Putting terms next to each other and calling them equal is not one of those rules.

      • ostiariusalpha

        Also, terminal effect is a consistently measurable alteration in the tissue, whereas stopping power is a highly variable behavior. You can shoot two different animals of the same species and size, with identical shot placement, and you will get very similar terminal effects, but not the same kind of stopping power. If you look at it from a defensive shooting perspective, one guy might faint from a wound, while another might keep charging despite that same exact wound.

  • ozzallos .

    You guys really want to carry the torch on this redefinition of stopping power, don’t you?

    • What I am trying to do is not a redefinition, as “stopping power” (or whatever you want to call it) never really had a definition to begin with. It’s always just been a loosely associated collection of observed behaviors. But there’s no reason to believe that gunshot wounds don’t follow Newtonian physics, so applying them there seems like it would help further people’s understanding, even if it doesn’t answer the “stopping power” question forever.

      • Kivaari

        We can’t take the “science” of Sanow and Marshall. It’s just too scientific.

  • Darkpr0

    I have popped myself a fresh bag o’ popcorn just to scroll through the forthcoming comments. They will sustain me today.

    On a more serious note, I’ve run numbers like these before and they get way easier if you approach it from a hydrodynamic perspective. You can take factors like the bullet’s geometry & stuff into consideration (with the help of some outside data like Brassfetcher & Ballistics by the Inch) and boil them down into factors like Coefficient of Drag. Biggest problem is computing how much permanent cavity is caused versus how much temporary cavity, but that’s endemic to the Work/Energy approach as well.

    • For computation, I would absolutely start from a hydrodynamic perspective. My goal here is to try to help people understand some of the fundamental mechanisms behind how these things function in tissue, which I think can really help boost understanding without even touching math.

      • Darkpr0

        That’s why I popped the popcorn :}

    • Tim

      Having just watched the Lucky Gunner high speed video of Hornady Critical Defense 380ACP into ball gel, I would say from an engineering perspective, especially considering the hydrodynamics/fluid dynamics, this would be a massive computational undertaking, even with a simpler wound channel such as with ball ammo. This is why the FBI and sites such as Terminal Ballistics Research rely on emperical experimental data.
      Even with ball ammo, the transient effects and associated hydraulic shock are completely unpredictable and of course, depend primarily on shot placement in an animal. In the simplified case of ballistic gelatin, the fact that five shots penetrate and expand and tumble differently gives some idea of the complexity involved. And this is in the final static result. Looking at high speed video shows the wound cavity expands in size by two or three orders of magnitude during the initial transient hydraulic shock event. The effect of this expansion on surrounding tissues and organs is completely undetermined at present.
      I applaud the effort of developing a model to predict or simulate terminal ballistics, but I think there’s a reason no one’s done it yet.

      • Right, that’s why I am not trying to create a model that you can use to simulate a gunshot; that would be insanely hard.

        Instead, I am trying to approach the physics of a gunshot with as little math as possible, so that my readers can easily follow along and get a grasp of the mechanisms involved in the physics of gunshots.

        Does that make sense?

      • Darkpr0

        Modern mathematics and simulation programs are plenty advanced to model this sort of behaviour. Compared to modelling the airflow around a full-size aircraft or inside a jet turbine (something that is done on a daily basis) this sort of axisymmetric calculation is pretty pedestrian. The problem is that it would take a fair amount of time and equipment investment (CFDs generally require supercomputers). Combine that with the fact that industries are generally quite suspicious of modern computational methods and it’s just not something anyone is willing to do. Even modern industry hasn’t got its head around finite element analysis (a phenomenally powerful and accurate tool), so in the firearms industry where people are afraid of concepts less than 100 years old it’s not a marketable thing. If you were to put up money for modelling of bullet hydrodynamics at a university, it would only be a matter of time before you get something that’s plenty accurate.

  • The_Champ

    Big game hunting, for me, has been highly instructive about how bullets kill living things. And it also sometimes shows seemingly inexplicable resilience on the part of shot critters.
    I’ve said it before, and I’ll say it again, anyone interested in the subject NEEDS to read a very nifty little website called “Terminal Ballistics Research”. It is authored by a Kiwi who has been a life long hunter and guide. He has shot or seen shot literally thousands of critters, and collected data on a large number of calibers and common bullet types. I highly recommend his cartridge research knowledgebase form some great insight into how effective particular bullets and calibers are.

    And spoiler alert, .223 is a lackluster killer at best, unless you can find some of that wonderfully tumblely FMJ 😊. And of course the newer military designs being fleshed out currently.

    • If I remember correctly, his cartridge histories need a little work, although his research on wounding is valuable.

    • CommonSense23

      5.56 is a lackluster killer compared to what? What round are we talking about? There has been plenty of excellent 5.56 rounds for a while now. Just the majority of the military hasn’t been using them.

      • I imagine he meant that in the context of hunting. Now, I think a lot of people unfairly dismiss 5.56 for hunting, but it’s still a little anemic for game like black bear or the larger deer varieties.

        • CommonSense23

          I’d would feel quite confident with 70gr for any deer in the states. I was routinely dropping 250 hogs with a 10inch at 200+ yards.

          • Yeah, but you and I can shoot, hahahah.

          • Gary Kirk

            Well put

          • iksnilol

            Alaska is a state, moose are a deer.

            5.56 against a moose is a bad idea, trust me there.

      • The_Champ

        Yes, in a hunting context. In the case of the above author, in the context of goats much smaller than humans. And I found it interesting that the above noted author was unable to produce hydrostatic shock with a .223, regardless of it’s high velocity.

        • Gary Kirk

          To be quite honest, I’ve found most animals are much more resilient than humans in any regard.. We’re more like taking groundhogs than goats or deer..

          • The_Champ

            Well I haven’t shot any humans but I’ve read plenty of examples of humans being extremely hard to kill with gunfire.

            And many examples of humans falling flat out of the fight with one non-lethal shot.
            Not sure what the norm is.

          • Kivaari

            Much of the time the US Army has used goats for ballistics research. I don’t know if they have simply shifted to ballistics gelatin. The Swedes used hogs the Chinese dogs. The Swede approach 40 years ago made a great deal of sense. They created a battlefield condition, where they would shoot a hog. Than a corpsman would give common field aid than the victim hog transported by truck or helicopter to a MASH-type hospital for surgery. Than destroyed. It was great training for combat medics and surgeons.

    • AirborneSoldier

      The old 55 grain did the trick well. The newer 62 and heavier loads stabilize better in flight for longer effective ranges, but require more penetration before it produces the old tumble effect that made 55 grain so deadly. I appreciate the author very much. Would love to see someone compile autopsy reports from the last 5 years or so after police shootings. Would likely expose trends in effectiveness, training, weapons types, etc. Id buy it.

      • CommonSense23

        55gr never relied on tumbling to be deadly. That’s a myth that was pushed by the military early on due to worrying about issues with meeting the Hague Conventions. 55gr relied on fragmentation. MK262 is a 77gr and fragments well. 62gr MK255 produces insane terminal ballistics. MK318 and M855A1 all produce excellenct wounding. And 70gr is a hunting round that is amazing.

        • Gary Kirk

          193s did rely on the overturning of the bullet as it entered tissue, think it was Pat Sweeney that did an extensive description of the “terminal ballistics” In his AR series of books.. Bullet composition has a lot to do with effectiveness.. The old 55s would fragment because of velocity.. As the bullet entered, it goes from air mass resistance to solid/liquid resistance.. Therefore the pointed/lighter end of said bullet so good at cutting air is now not good, now the heavier end wants to carry on using it’s mass.. So the bullet tries to to turn around, and with the velocity/bullet construction, generally tends to break apart.. Pieces go multiple directions inside said target.. Oh, wait.. With the 55gr 193s it was unintentional. Now we have 855A1, that achieves the same thing, But is also more accurate.. Damn modern ballistics..

          • CommonSense23

            Right it fragmented due to yawing at the speed it was flying. It wasn’t the fact that the round tumbled like Russian 5.54 which held together far superior than M193.
            And from every document I have seen relating to early 5.56 development. Western powers have been aware of small high speed calibers effective terminal ballistics due to fragmentation since the 1930s at least. If not earlier.

          • Paul Joly

            No, for example the fragmentation of the 5.56 at the crimp was discovered after the first design so it wasn’t intended at first.

          • Kivaari

            The 5.45 MOST of the time only turns 1 and 1/2 times ending up base forward. A bi-lobed rotation. The heavy steel jacket is so tough that it doesn’t go to pieces like the M193. Fackler’s USA tests says it was the least effective of the current issue rounds, circa 1989.

        • The_Champ

          Well I’d say tumbling and fragmentation go hand in hand, do they not?

          For what its worth, the author I mentioned above has found that certain brands of 55 grain FMJ bullets (specifically Norinco for reasons unknown) routinely tumble and fragment, especially when fired out of 1:12 twist barrels. With modern barrels in 1:9 and 1:7, tumbling is much less common.
          The terminal effectiveness when the bullets tumble at high velocity is pretty spectacular.

          • Gary Kirk

            Tumbling is the round not flying true (i.e. keyholing) Fragmentation happens after initial contact with target..

          • No, keyholing is keyholing. Tumbling can and does often happen in tissue.

          • Gary Kirk

            Ok, guess it means what I was talking about in my prior comment.. Never did get the concept of “tumbling”

          • Kivaari

            Some think it spins end over end multiple times. It normally goes 90 degrees, breaks apart with two major pieces ending up heavy end forward. Small chunks of lead and copper spread about. I’ve heard many say they “buzz-saw” as they pass through tissue. They don’t. Like Black Talon ammo some think it spins rapidly through the wound, when it turns like it does in the bore 1 turn in 16 (or what ever the twist rate is).

          • Gary Kirk

            Yes, if you take a look at my earlier post I went into the details you’re talking about. Just when someone talks about a round “tumbling” I immediately think of in flight..

        • Mk. 255 is totally lulzy. It would be such a great home defense load.

          • CommonSense23

            It’s what I use for HD. Its scary insane what happens when it hits flesh.

          • How did you get a hold of it!?

          • CommonSense23

            I was issued it.

          • Well, that would be one way, I suppose.

    • Federal 64gr .223 makes a good enough argument that I only have to let it speak up once to convince whitetails to stop whatever they’re doing. Shot placement > caliber.

      When it comes to hunting, I feel compelled to point out that unless your Kiwi source was an ANZAC, 5.56mm has brought down quite a few examples of a more dangerous kind of game than he’s ever faced.

      • iksnilol

        Biga$$ deer (moose) = more bullet resistant than whitetails.

      • Tassiebush

        In a Kiwi context they shoot a lot of pigs and deer. There’s a bunch of different types but a lot of the deer seem to be the heavier species like red deer. My understanding is whitetails are a smallish species in comparison.

      • The_Champ

        If you want to read the source you’ll see that the author is very big on achieving hydrostatic shock and an instant knock down kill. Generally speaking he recommends the .223 for critters no bigger than 130 pound, and cautions that a lot can and will go wrong if the shot made is less than optimal.

        In my neck of the woods, where big whitetail bucks can get to be over 300 pounds, I think the regulations restricting .22 cal round from big game hunting are mostly well thought out and correct. Something a little bigger should be used to achieve a more humane kill.

        This is quite different from saying that a .223 won’t kill a deer. Of course it will.

        • Personally, I haven’t had anything less than an instant knockdown kill on deer and hogs since I switched to passing up any shot besides a high neck, but point conceded about less-than-optimal shots; as Nathaniel F. points out below, you and I can shoot, but regulations are always written for a fairly low denominator, and “.243 or larger” is a perfectly reasonable and sensible requirement for hunting medium-sized or larger game. Dismissing .223/5.56 out of hand for a supposed lack of effectiveness, however, ignores its demonstrated real world effectiveness even in a Hague Convention compliant loading.

          • Joel

            I completely agree. One need only watch a video of 5.56 carbines being used on wild hogs from helicopters to see the round’s effectiveness.

            That said, it should be remembered that many rounds are better killers than they are stoppers.

        • Dan

          I agree with you the laws keeping .22 cal rounds from big game hunting are well thought out. While it will kill a deer, not everyone using it can make that shot. I’ve seen way too many people who sight the gun in the day they put the scope on and never again. I guess though if you suck at shooting size won’t matter anyway.

  • Kivaari

    This should be fun.

    • Gary Kirk

      Here come the armchair physicists

  • That is way over complicating things, unless you are designing bullets most of that isn’t applicable. As the designers have already calculated all that, and designed their bullets to work for a specific velocity range that will be most common when their bullets strike a target.

    For the end user all that matters is that velocity range where the projectile achieves IWBA standards (or whichever standards the bullet is designed for). If the bullet strikes the target outside that velocity range, both above and below, it may not work as expected.

  • Wanderlust

    The topic is pretty interesting. It always seems to gravitate back to ballistic gelatin though. Although in this era of 3D printing and cheap and very hard plastic Im surprised that hasent advanced to 3D printed skeletons with some basic organ systems to better model tissue after impact. Maybe a sufficiently complex physics model could make an approximation.

  • Mk. 255 =/= M855. I own several hundred rounds of Korean M855 equivalent. Mk. 255 RRLP is this stuff: http://www.dtic.mil/ndia/2006smallarms/kim.pdf

    Virtually only used by SOCOM with express approval, and very, very hard for a civilian to get.

    Not that there’s any reason for it to be, as it’s just a high-mass frangible bullet, but its terminal effectiveness against soft targets is off the hook by all accounts.