Caliber, velocity, energy, relating to damage Theory

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If one wants a large cavity, use a .357...if one wants a really large crush cavity, use a lever action 30 caliber rifle...a tried and true combination. :)
 
As most of us know. The energy of a bullet in flight is an equation of velocity and mass.
The more energy the bullet has, the harder it is to stop and in theory will do more damage to its intended target.

Thus a 230 grain bullet traveling slower then a 115 grain bullet can have more energy and thus in theory create more damage.

However, I ask, wouldn’t the cross section diameter otherwise known as caliber of the bullet also have an impact on damage on a target.

Example being two 185 grain bullets traveling at the same speed, with one bullet being 9mm and the other being 45 caliber. Wouldn’t the 45 caliber do more damage due to its cross sectional diameter being larger? Yes the 45 caliber bullet would be shorter and the 9mm longer, but the 45 caliber should produce a larger hole? Correct? (Yes, 185 grain 9mm bullets are rare, to non-existent, but this is just an example for discussion on damage theory)

Thus the reason we have hollow points and other various types of bullets that use expansion techniques to increase their cross sectional diameter either in flight, or upon impact with the target.

Thus if we were to invent/discover a damage equation, it would have to include not just the bullets weight and speed, but it’s cross sectional diameter? Correct?

Does a damage equation even exist?

Example again which would cause more damage, (assume FMJ-RN) a 9mm bullet with energy of 300 foot/lbs or a 45 caliber bullet with 250 foot/lbs? Yes the 9mm has more energy, but it’s also a physically smaller bullet then a 45 caliber bullet. How many foot/lb difference of energy would be needed to make the smaller 9mm create more damage? (Yes, I realize the energy example may not be realistic energy amounts for said caliber but this is just an example for purposes of discussion)

IMHO Damage to the intended target is an important consideration when choosing caliber and ammunition be it for hunting, or even self defense against animals, or humans, and the location we are wanting to use our firearm and ammunition. Ie, in many instances, we want to reduce any potential for collateral damage.ba

The other question I ask to everyone, is how important is your consideration of damage to your target do you consider when choosing a caliber and ammunition for said caliber?

The first mistake in your reasoning is you are asking a board full of strangers... 99%+ of whom have never killed anybody, have never shot anybody, have never been shot or have ever seen a human gunshot wound... but are somehow expected to have some magical ballistics expertise. (I include myself in that 99%+). Amongst my fellow 99%'ers bullet lethality seems to have more to do with religion than science. Personally, I subscribe to the bigger the diameter the better camp... but there are so many variables I don't believe it is possible to pick one bullet that is going to be the best in every possible situation.

With the long history of 9mm in Europe and the long history of .38 diameter projectiles in the US I would bet this diameter bullet is responsible for more human deaths than all other handgun calibers put together.

Carry what you are comfortable with and quite worrying about what the next guy thinks is the ultimate self defense round.
 
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The first mistake in your reasoning is you are asking a board full of strangers... 99%+ of whom have never killed anybody, have never shot anybody, have never been shot or have ever seen a human gunshot wound... but are somehow expected to have some magical ballistics expertise. (I include myself in that 99%+). Amongst my fellow 99%'ers bullet lethality seems to have more to do with religion than science. Personally, I subscribe to the bigger the diameter the better camp... but there are so many variables I don't believe it is possible to pick one bullet that is going to be the best in every possible situation.

With the long history of 9mm in Europe and the long history of .38 diameter projectiles in the US I would bet this diameter bullet is responsible for more human deaths than all other handgun calibers put together.

Carry what you are comfortable with and quite worrying about what the next guy thinks is the ultimate self defense round.

Google
Dr. Martin Fackler
Dr. Gary Roberts
Dr. Sydney Vail

Read their work.

I'll start you out with an article from Dr. Vail

https://thesurvivalsummit.com/2016/01/23/2016-1-23-9mm-or-40-caliber-your-answer-here/
 
The US Army went back to 45 caliber over 38 caliber in the early 1900s versus the Moros. Why? The 45 caliber would put them down there.

http://fmapulse.com/fma-corner/fma-corner-juramentados-and-development-colt-45-caliber-model-1911/

Bullet shape does effect damage. A wadcutter or flat point bullet hole punches (like a literal hole punch for putting holes in paper) flesh. A round nose bullet crushes flesh and slides it out of the way, thus a smaller hole. A hollowpoint penetrates and is supposed to expand, but acts as fmj if it doesn't.

Higher velocity effects damage, to a certain extent, at some point losing effectiveness when the velocity exceeds bullet construction. If the bullet stays together and is shaped correctly (flat point) it can put a larger wound track than it's initial diameter, and penetrate through the flesh and bone. There used to be an article with the data in it, from the cast performance website, but I cannot find it.
 
The question was about "damage", not lethality.

Lethal is defined by "what or where" a bullet hits; a fragmenting, yawing or any bullet does a lot of damage even when it isn't lethal. Judging by the NRA's Armed Citizen column, when a criminal gets shot; they go to the hospital for treatment; if they are killed they go to the coroner's office.




 
The more energy the bullet has, the harder it is to stop and in theory will do more damage to its intended target.

Flawed premise. A sintered (frangible) bullet going very fast will still be easy to stop, it will travel very little after hitting almost any target. You are correct about it doing damage to biological targets, damage is less reliable with other targets. Same goes for varmint bullets.
Bullet construction, both concerning design and material, is definitely a factor.
 
Yes, and so is its ability to effect a rapid physical stop.

When facing a serious threat to their life; most will shoot without considering if the shot will be lethal, a rapid physical stop or a flesh wound. They won't consider the "reactionary gap", the Tueller Drill or anything else except stopping the threat.
 
If we are constrained to damage, and not lethality, then kinetic energy is king. Damage to material is the result of work, work takes energy and the ONLY energy a bullet has when it arrives at the target is kinetic energy (assuming no energetic payload). That energy may or may not do what you want the way you want it but that is the only energy source you have to effect the target.
 
When facing a serious threat to their life; most will shoot without considering if the shot will be lethal, a rapid physical stop or a flesh wound. They won't consider the "reactionary gap", the Tueller Drill or anything else except stopping the threat.
Yep!

Damage to material is the result of work,
Yes indeed!

... work takes energy...
Work is energy.
 
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If we are constrained to damage, and not lethality, then kinetic energy is king. Damage to material is the result of work, work takes energy and the ONLY energy a bullet has when it arrives at the target is kinetic energy (assuming no energetic payload). That energy may or may not do what you want the way you want it but that is the only energy source you have to effect the target.

Why is "energy" king when discussing fluid dynamics with service calibers? There are those who are a lot smarter than me who argue that momentum/penetration is primary... :)
 
The more energy the bullet has, the harder it is to stop and in theory will do more damage to its intended target.

As Entropy said, that is a flawed premise, so all the discussion that follows is irrelevant. Momentum is the measure of how hard something is to stop.
 
"Caliber, velocity, energy, relating to damage Theory"

If we are getting stinky about terms in physics let us not forget that velocity is a vector quanity, which possesses both magnitude AND direction.

The appropriate term in this case would be "speed", a scaler quantity.
 
Why is "energy" king when discussing fluid dynamics with service calibers?
We are not discussing fluid dynamics.

There are those who are a lot smarter than me who argue that momentum/penetration is primary...
Iy was a forgone conclusion that someone would bring up the subject of momentum here.

Yes, penetration is primary. But penetration of material that has compressive strength, shear strength, and tensile strength involves causing damage to that material, As mcb posted," ... kinetic energy is king. Damage to material is the result of work, work takes energy.... ".

That is absolutely correct, and it is incontrovertible.

As Entropy said, that is a flawed premise, so all the discussion that follows is irrelevant.
Nope, not at all.

Momentum is the measure of how hard something is to stop.
More accurately, momentum is the measure of how the velocities (speeds and direction) of objects change when they collide.

We see that phenomenon when we shoot at steel plates that are free to rotate around a hinge, and when we shoot at bowling balls that are free to roll. The combined moment um of the ricocheting bullet and the plate, and the combined momentum of the ricocheting bullet and the ball, are the same as the momentum of the bullet before it hit the target. Again, that involves both speed and direction.

Of course, momentum is not the measure of how to stop a charging human or animal attacker. That physical stop requires damaging tissue. There is no where near enough momentum (which is measured in newton-seconds) in a bullet to stop a large moving mass, or to significantly change its velocity in any other way.

I hope this helps.
 
Duncan MacPherson argued that kinetic energy per se is not the thing. Even kinetic energy transfer or deposit does not necessarily result in wounding. MacPherson described thresholds of velocity for cavitation to occur in different tissues and how a portion of the projectile's kinetic energy is used to create the crush path, and another portion is used to create cavitation in a radial path around the projectile's path (the temporary cavity). The velocity at which this cavitation occurs can depend on the type of tissue, and in some tissues, an insignificant amount of cavitation (temporary cavity) will occur. Additionally, different types of tissue have different levels of elasticity where they can be stretched, pushed, or disrupted without a serious wounding effect. So a larger temporary cavity may have less effect in the gut than it would through the liver. But going back to just the idea of kinetic energy, we can see that birdshot will hardly produce any temporary cavity -- practically all its kinetic energy is devoted to the immediate crush path of the shot. Whereas a non-fragmenting round from .22-250 will open up a large temporary cavity with about 90% of it's kinetic energy going into blowing out that cavity.

"The common assumption that the volume of the temporary cavity volume is proportional to the bullet kinetic energy is reasonably good for rifle bullets, but not for
other common small arms projectiles. " Wound Ballistics Review, 1999, Volume 4, Issue 2

Neither the birdshot nor rifle wound may be very serious if the penetration is insufficiently deep to reach vital organs or structures, or if the tissue can withstand the stretching or disruption without damage. Either way, kinetic energy is a poor measure of wounding, but kinetic energy is nevertheless vital to having the potential to wound. If there is not sufficient kinetic energy in bullet velocity to cause cavitation in the surrounding tissue, and great enough that it stretches the tissue to the point of tearing, the wound will be limited to crush path.

Crush path is reliable. It's made shotguns work for centuries. It made the .45-70 work. There is some consensus that it's all that makes handgun bullets work, though I have my doubts about that. For sure, effective wounding is most reliable when the crush path is deep enough to reach vitals.

Momentum is important to penetration, but it cannot be considered independently of the drag of a projectile in tissue. An "expanded" or deformed 230 gr. .45 ACP bullet has a lot of momentum, but it also has a lot of drag. A really sleek SMK bullet from a rifle can have a lot of momentum too, and it may just pencil right through a lot of targets without deforming or tumbling until it's penetrated more than 40 or 50 cm, and that may be well past the target. I suppose what matters is the momentum as well as the sectional density of the projectile as it's passing through, which may be different than when it's loaded if it opens, deforms, or tumbles during its course of penetration.
 
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McPherson argued that kinetic energy per se is not the thing.
kinetic energy , which is equal to work is "the thing" in penetration via tissue destruction.

Energy that does not tear, crush, or cut tissue does not permanently wound.

As you say, some energy is consumed in creating temporary wound channels--in a way that is rather analogous compressing a spring, where kinetic energy is converted to potential energy.

Also, some of the energy goes into making the bullet expand.

Penetration involves mass and velocity, and it is also a function of sectional density, the ogive, and the design and characteristics of the point and the expanding jacket.

Penetrating tissue by damaging it is a function of energy, as mcb explained, but as you correctly point out, not all of the energy of a projectile goes into damaging tissue.

Now, how about momentum? Well, when the bullet encounters material that is free to move without constraint, such a blood corpuscles, fluid molecules, etc., the law of conservation of momentum comes into play.

The human body is structured in ways so complex that it would be impracticable to try to correlate penetration concisely with either kinetic energy or momentum. Nor is it necessary to do so.
 
<minor rant>

I am going to step back and somewhat retract my, "kinetic energy is king" comment. I am an engineer by profession and kinetic energy is a quantity I have been using since high school physics. I like kinetic energy, it's what does the work in a collision and it gives you a nice idea or cap on how much work/damage is possible, but that really gives you very little information on what that work/damage will look like and if it's useful work. It also means a lot more to me than just that one simple number since I understand implicitly at this point where it came from and the other stuff that number drags along in the background, but ultimately you can't simplify terminal ballistics to just kinetic energy or just momentum.

Energy and momentum are inseparable quantities. P = mv and KE = 1/2 mv^2. So if a bullet has a particular mass (m) and velocity (v) then there is nothing you can do to effect that bullets momentum (P) without effecting its kinetic energy (KE) and vise-versa. When you really get into the dynamics of high velocity collisions (ie graduate level college course type work) you solve these problem using every bit of information you can, the projectile's mass, velocity, shape, & material properties; the target's shape and material properties, impact geometries and deformations in all their glorious vector quantities, etc. There is no simple answer that only uses energy or only use momentum as you might see in a high school level physics course. They have made a bunch of simplifying assumptions to teach basics principals. These first year physics problems are a very poor reflection of most real world collision especial such complex realities as bullet target interactions.



This dynamic finite element model of a jacketed AP round hitting an aluminum plate and has alot more inputs than just momentum or just energy. Look at all that geometry and how it deforms both elastically and plastically. Imagine if the bullet had the same mass and velocity (same energy and momentum) but the core was soft lead instead of the hard tungsten modeled, the outcome would have been very different. And this model is relatively simple given it involves only simple solids (no strain rate dependencies) with elastics and plastic deformations. Now if we make the target a biological target with non-Newtonian fluids, gases and vaporized liquids, and strain rate dependent solids and the math starts to get hard. We do terminal ballistics a disservice by trying to simplify it to just one number. We all do it, myself included, but we need to stop IMHO. It just ain't that simple.

</minor rant>
 
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There is no simple answer that only uses energy or only use momentum as you might see in a high school level physics course.
Correct. They are both pieces of the puzzle, but getting the whole puzzle figured out takes more than just two small pieces.
We do terminal ballistics a disservice by trying to simplify it to just one number.
Well said.
 
It was the .38 Long Colt, a blackpowder round--considerably less powerful than the .38Spl
 
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