Ballistics 201: Introducing a New Way of Thinking About Terminal Effectiveness – The Energy Budget

NewtonradG11

Since we know that gunshot wounds follow physical laws – Newtonian mechanics, specifically – we can use physical quantities to describe what happens to a bullet when it enters a fleshy target. In a previous post, we were introduced to three physical quantities: Force, work, and kinetic energy. To see how these apply to a gunshot, let’s use the example of a hollow point bullet as it impacts and penetrates 10% ballistic gelatin.

Ballistic gelatin is essentially a solution of pure collagen (which is the primary protein in connective tissue) in water, and we can think of ballistic gelatin as acting much like water at the high speeds of a bullet impact. Indeed, jacketed hollow point bullets designed to expand in gel and tissue expand very nicely when shot into water, too. So first, let’s consider the design of a modern hollow point projectile, the below sectioned example being monolithic for simplicity’s sake:

MHP

We can see that the cavity in the bullet is bell-shaped. When the projectile is shot into gelatin, the media outboard of the cavity flows around the bullet, just like it would with a standard full metal jacket projectile. However, the gelatin in the path of the cavity itself has nowhere to go; it can enter the cavity, but then it becomes trapped as the bullet’s momentum carries the projectile forward. This creates a great deal of hydraulic pressure inside the cavity, which in hollow point bullets is harnessed to cause expansion. The forces generated by the forward movement of the projectile against the fluid act on the walls of the cavity, which have already been weakened during the manufacturing process by deep score marks. If the forces are high enough, the bell breaks into petals, which are then forced open even further by the oncoming gelatin, creating a “mushroom” or “flower” shape.

38_Special_mushrooming_side_view

This expanded .38 Special hollow point bullet illustrates how the hydraulic pressure has forced the walls of the hollow cavity outward, rupturing them along pre-made fracture points that become the edges of petal-shaped structures.

 

These forces acting on the bullet and the tissues together comprise the work done by the projectile. This work is a function of the energy of the bullet as it loses velocity in the target. There is a misconception that it is the “energy dump” of a projectile that causes wounding, but that’s actually backwards. Since there is a relationship between energy and work, a very rapid energy dump and deceleration by a projectile implies a large amount of work being performed on the projectile and target in a very short amount of time. It’s this work, expressed by a deforming or tumbling projectile cutting or crushing tissue, that is the true actor in wounding.

This has some interesting implications if we also consider the structure of small arms projectiles. Let’s take a look at a very simple model of two fragmenting projectiles of the same design made of the same materials with a given toughness. First, remember that the physical property of toughness is a measure of how much energy a material can absorb per unit volume before it ruptures, given in units of Joules per cubic meter or foot-pounds per cubic foot. Toughness is far from the only mechanical property of a material that should be considered for a thorough analysis of projectile impacts, but to keep the example simple we will consider it alone.

Let’s consider a 55 gr (3.56 g) gilding metal jacketed lead projectile that is .224″ caliber. In order for this bullet to fragment, the gilding metal jacket must rupture under the force of impact. Due to its design and toughness, this can occur only at energies of 1,000 Joules or higher. We can calculate the minimum fragmentation velocity of the bullet by solving the kinetic energy equation for velocity:

1,000 J = 0.5 * 3.56 g * .001 kg/g * V^2

Which gives us 750 m/s velocity, or 2,460 ft/s as the velocity at which the projectile can fragment.

What if we double the weight of the projectile by increasing its size? Doing this gives us a projectile that is 0.282″ caliber and weighs 110 gr (7.13 g). Does this projectile still fragment at energies of 1,000 Joules or higher? If the projectile is scaled up exactly, the answer is “no”; the toughness of the projectile is given as per unit volume, which means that (assuming fixed density and the same construction), a jacket that is twice as heavy will require twice as much energy to rupture. Since the bullet is twice as heavy, we can see that the new equation solves out exactly the same as the old one:

2,000 J = 0.5 * 7.13 g * .001 kg/g * V^2

V = 749 m/s

This is one reason we observe that velocity is so important for terminal effectiveness. There are only two ways to increase the energy of a projectile: Increase the velocity, or increase the bullet weight. However, increasing the bullet weight often (though not always) also increases the durability of the bullet and raises the amount of energy needed to cause upset to the projectile in the form of expansion, fragmentation, or another effect. Therefore, it is by raising the velocity of a projectile that the most dramatic gains in wounding are often seen; this is simply a way to raise the projectile’s energy (and therefore ability to do work) without also making the projectile tougher and more resistant to deformation.

It is more difficult, but becoming increasingly common, to design projectiles that require less force (and thus energy and work) to deform or disrupt, and which therefore can do so at lower velocities than ever before. Good examples of rifle bullets that have been well-crafted to expand or fragment at much lower velocities than were previously normal include the new M855A1 and M80A1 EPRs, the Mk. 318 and Mk. 319 SOST projectiles, and mono-alloy bullets like those from Barnes. This solution, provided the resulting bullet is not too weak to hold up in flight, is an excellent one, and its widespread adoption has greatly increased the effectiveness of rifle calibers that previously suffered from poor performance.

This brings me to a core concept that I don’t think is often explicitly outlined. That is that higher impact energy allows for more work to be done, increasing the wounding potential of a projectile, but it does not ensure more severe wounding. In other words, kinetic energy (along with other less relevant quantities) is often treated in the literature as if it is a measure of the wounding power of a round. This is not the case; rather energy is more like a wounding budget, which can be spent very efficiently to produce more serious wounds, or very inefficiently, therefore producing lackluster wounds. This is how a .50 BMG round can produce less severe wounds than a 5.56mm round with a tenth of the energy, provided the former spends its energy inefficiently (e.g., by not upsetting and creating a “through and through” wound) and the latter spends its energy very efficiently (e.g., by fragmenting early and dramatically).

It seems useful, then, to coin the term energy budget as a shorthand for this concept. Using this term instead of “kinetic energy” helps to illustrate that the higher energy level may imply greater wounding capacity and terminal effectiveness, or it may not. This separates out the issue of empirically-observed terminal effectiveness, and makes it more clear why impact energy is a useful quantity to compare between rounds. For example, if I say that 7.62mm has more kinetic energy than 5.56mm, this implies to the listener/reader that I mean 7.62mm is a superior wounder, even if I don’t. However, saying 7.62mm has a higher energy budget than 5.56mm makes it clear that I mean there is more energy available in the larger caliber which can be used in the ways described in this series to cause more severe wounds, but not necessarily that 7.62mm will be the better wounder.

A great deal of research and development has been conducted to reach the level of understanding we have now, which has in turn given us some very effective projectiles even in modest calibers. Of course, it would be nice if there were a simple equation that would tell us exactly how effective a given round would be based just on its bullet weight, caliber, and velocity, but unfortunately the subject of wounding and lethality is far, far too complex for such simple models. Hopefully, though, what I’ve written here helps the understanding more than it hurts.



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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  • iksnilol

    I’mma be honest, the G11 looked off due to the blue shade of it, https://uploads.disquscdn.com/images/d18bf553fe28a6f09db959197dfaf8a174f8310333410beb609d1f43e130c691.gif and that mildly annoyed me.

    • Giolli Joker

      Brilliant!

  • UKShuggy

    So… basically what you are describing is the Expected Kinetic Energy or EKE model, based on the theories of Sturdivan from the ’70s. This theory proposes that the damage caused by a bullet is proportional to the Kinetic Energy deposited in the target.

    • Nope.

    • Paul Joly

      Keep in mind that bullet do damage mostly by laceration, this is done via the bullet material. So more material = more mean to do laceration/damage ; but those fragments of material move thanks to their kinetic energy. The size, shape, material proprieties of these fragment also matter. All we need to do now is do some iterations.

  • Gorilla Biscuit

    So what would the minimum fragmentation velocities be for the M80A1 and MK319 as compared to their smaller family members in 5.56?

    • I don’t know, that has yet to be (publicly) empirically established.

  • MPWS

    There is error in order of units in sample calculation. 1Joule = 1kg . 1m . 1s^2; not 1g. Use of metric units is preferable.

    • You are correct, the error was a result of the shorthand I use for energy calculations.

  • TC

    The GAO estimates that U.S. troops expend 250,000 rounds for every enemy combatant killed. Clearly, the focus of ammunition development should be ‘hit probability’. Doesn’t matter how deadly a bullet is if it doesn’t hit its target.

    • Those 250,000 rounds aren’t wasted, because modern tactics involve suppressing fire and firing while maneuvering.

      Certainly, general Army marksmanship is poor as well, but you can’t fix that with a new bullet.

      • That has always struck me as a simplistic and misleading metric. Most of the time it is calculated by dividing the total ammunition acquired during a time period divided by the guesstimated enemy casualties. Even when it is drilled down to ammunition expended during a given time period, they typically include ammunition expended in training. So even if you practice to be a better shot, your round per kill ratio still remains high.

        • MPWS

          I have seen this number before as it is apparently traded from source to source. It is likely it was established shortly after WWII and Korean conflict. Assuming that rifles fired powerful .30.6 ammunition which caused invariably deviation from point of aim, it may not be valid today. But I am not aware of any new statistic in that direction; neither anyone seem to be concerned with that aspect. It appears to of general belief that new optics present the fix. Today priority is of different kind (aka lightweight ammo).

      • Tom01

        Those numbers have never been close to correct. I don’t know what bean counter keeps coming up with them but even commo sense should tell people it is BS.

        If it really took a quarter million rounds to off one opponent an infantry company couldn’t carry enough ammo to be combat effective.

        Yes, ammo is always expended at a higher rate than people would think, but not nearly that much.

        Take the attack on Abu Ghraib in 2005. Our ARR said the entire camp spent 15,000 to 17,000 rounds in total, a bit over 10,000 of which were 5.56. That was a camp defense with high round counts due to a lot of auto fire.

        For engagements outside of a camp the round counts were lower. Usually in the hundreds to a few thousand depending on circumstances.

        I always assumed the crazy numbers came from the total ammo shipped to a theater divided by number of enemy casualties. Only way I can think of to reach insane numbers like that.

        • Yeah, I agree that those numbers are just “total expenditure / total enemy casualties”, which inflates them. My point was different, which is that misses are valuable in modern infantry tactics.

        • RocketScientist

          Pretty sure those numbers include training/qualification, etc in the total as well.

    • iksnilol

      To be fair ,that does include training.

      • Kivaari

        My kid was a M249 gunner in Iraq, and never fired a round of ammunition in training or combat. That makes for inefficient soldiers, unless you count the Hummers repaired and stripped of parts to get others running. Some shops changed tires on hummers for a year and never fired a weapon for a year.

    • Uniform223

      Its easy to say that in BRM and in training you can shoot a full magazine and hit 25 (or more depending on the skill level of the shooter) out of 30 possible targets. In the REAL WORLD outside of the comfortable/relaxed environment… things become incredibly DIFFERENT!

  • MPWS

    I do recognize that author of this work has cautioned about complexity of wounding mechanisms and its unpredictability. However what concerns me for some time while reading these kind of sources is that the only mode of disabling opponent is considered full expansion of bullet energy/ work into tissue of target.

    I am not entirely convinced it has to be the only mechanism which acts on opponent’s physique and is harmful to him/her. Even superficial wounding without deep penetration are disconcerting and causing extensive discomfort/ pain. It is known that most nerve ending are in shallow layer just under skin. Besides, even if penetration does not take place (say while target wears protective armour), the terminal energy/work transfer is substantial and has detrimental effect such as bruising, loss of balance, mobility and so on.

    • As I mentioned in the post yesterday, this is only accounting for the actual wounding, so it’s not a complete picture of terminal effect, which includes several other factors.

  • Jonathan Ferguson

    Great post Nathaniel. I think we all need a remedial Physics class to get our heads around these ideas and move away from the simplistic “energy dump” idea.

  • Darkpr0

    Energy budget is an effective method for determining cartridge performance potential. Probably the major issue is that the bullet is what translates that potential into a wounding profile, but nobody has any sort of agreement on what the wounding profile means for lethality. Big sticking issue is how much effect temporary cavity has on lethality: some people use temp cavity as a direct analogue for lethality, others discount it completely. Wounding science has the unfortunate distinction of having the most difficult time obtaining empirical results.

  • Joel

    “This brings me to a core concept that I don’t think is often explicitly outlined. That is that higher impact energy allows for more work to be done, increasing the wounding potential of a projectile, but it does not ensure more severe wounding.”

    We used to say that energy was the “ability” or “capacity” to do work. Work, in this case, is the breaking of things.

  • Dracon1201

    …And that’s exactly what I was explaining in my original ballistics arguments with you, lol. Our arguments were closer than you thought.

    • I am not sure I remember what the subject of our arguments was, do you have a link?

      • Dracon1201

        I don’t even remember which one it was. Suffice to say, this article proves we found our understanding, no matter how bad I was at stating it.

  • Uniform223

    Because of science!

  • Kivaari

    The budget of a 7.62×39 FMJ v. JSP with all other elements being the same, gives the JSP a bigger budget? Like the 7.62 PS FMJ-BT v. M63/8 flat base, where the flat based bullet tumbles.

    • iksnilol

      Nah… amount of energy = how much wounding it *can* do. FMJ vs JSP if its the same velocity and weight then the budget isn’t really changed, but the wounding is more effective with the JSP (presuming it works) since it uses the energy more efficently (into opening up).

      Is possible I messed up but that’s how I understood it.

      • Kivaari

        All the Newtonian laws and such. I just view the JSP as having a better interest rate.

  • Kasper

    Work is energy. There isn’t a relationship, they are the same. The unit of work in SI is Joule. Initial use was a weight moved by a force, which is also the definitions of Joules.

    The work being done is the displacement and tearing of matter.

  • Roguewriter

    So what about rounds like the Lehigh bullets used in Underwood’s Xtreme Defender ammo?

  • Ugh, Gary Roberts. OK, first of all, he’s probably right. 1,900 ft/s sounds about right for the frag limit for Mk. 318/319, but that’s an educated guess on my part, not because I’ve seen any tests for the round.

    Second, I don’t trust the Dentist as far as I can throw him. If he writes something completely unsourced and with no additional information, I just dismiss it.

    • Gorilla Biscuit

      I just look for good data from credible sources. I’ve never read anything from him that was way off base or flat out wrong. I’m interested in why you don’t trust his information? Maybe I’m not seeing something that I should be.

      • I do not trust his information because I have seen him fabricate “facts” several times in service to an agenda. I am not talking about outrageous statements or things I disagree with, but rather actual statements he made that proved to be false (and which he apparently knew to be false). An example would be that 6.8 SPC rifles could work with 5.56mm magazines when fully loaded, something he admitted later in the thread was incorrect. Another would be his manipulating of Martin Fackler’s wound profiles to try to make points (the profile overlaid on a torso on Page 7 is not M855, it is actually a .30 caliber round that he has photoshopped to have a longer neck). Yet another example would be this paper, where when he wants to bash 5.7×28, he portrays 5.56mm as a reliable killer, but just two sections later he describes it as being a very poor performer when he wants to make 6.8 SPC look good.

        Another questionable incident was when Roberts claimed that the JSWB-IPT report Small Caliber Lethality: 5.56mm Performance in Close Quarter Battle was essentially doctored to remove all evidence that the 6.8mm round was the superior choice. I believe, frankly, that this is horse dung. I actually correspond with Colonel Glenn Dean, who co-authored the report, on a regular basis, and I am very suspicious that Roberts is simply blowing smoke here. I’ll be able to confirm or deny that suspicion soon, too.

        There’s also controversy over some of the initial testing that was done with 6.8 SPC, which Roberts is a huge proponent of. It seems there’s some evidence to suggest that the initial 6.8 rounds tested were in fact Hornady V-Max bullets with removed tips; in other words, they were fully expanding hollow point rounds. Roberts denies that the IWBA ever tested this batch of so-called “OTM”s, but see for yourself:

        http://i459.photobucket.com/albums/qq319/DocGKR/IdenticalKE.jpg

        http://i11.photobucket.com/albums/a185/InfernoMDM/lightfighter/40052-MilitaryAssaultRifleWPcopy.jpg

        Note how the “110gr Hornady OTM” has almost identical performance to the 7.62×39 soft point, and completely different performance than an actual OTMs like Mk. 262.

        So that’s the skinny on my perspective on Gary Roberts. I do not believe Roberts is an evil person, or that he is deliberately telling untruths, but I think he is not cognizant of his own biases, which leads him to deceive (although I do not think he would consider it to be deceiving).

        I think he really does believe the 6.8mm round is the best intermediate caliber, and I disagree with him on that, but that disagreement isn’t why I do not trust his statements when they are unsubstantiated. Now, Roberts has substantiated quite a bit of what he’s said; in fact, I think by and large he is correct when he talks about terminal effectiveness and wound ballistics, especially with regards to handguns. He has, after all, studied much of the relevant literature. However, his biases affect his opinions, so I ignore them if they aren’t substantiated elsewhere.

        • Gorilla Biscuit

          Very good points. I remember a lot of the 6.8 agenda shenanigans from tacticalforums. It’s been so long that it had completely slipped my mind.

          Got any more info on the initial 6.8 testing, w tipless v-maxes and such?
          This is all very interesting to me.