Warning: Physics Content! Penetration equations anyone?
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Hm, it's not showing up right for me. Darn finicky forum software. Oh, well, extra stuff won't hurt, and I didn't have to change around any of the equations themselves.
Oh, I forgot to say, modeling gelatin as an incompressible soft solid flow is probably fine, as testing done by Fackler has shown that supersonic impact velocities, in excess of 5,000 fps, do not result in anything strange or any sudden differences at all, that aren't accounted for by other things like increased projectile deformation.
Big edit:
I found the journal article copy I cribbed the equations from. Looks like I misremembered, and all the equations were from Peters. So I don't have to worry about your quote, everything should be fine. I mainly wanted to avoid any possible misattribution problems.
I've attached a copy to this post.
Oh, I forgot to say, modeling gelatin as an incompressible soft solid flow is probably fine, as testing done by Fackler has shown that supersonic impact velocities, in excess of 5,000 fps, do not result in anything strange or any sudden differences at all, that aren't accounted for by other things like increased projectile deformation.
Big edit:
I found the journal article copy I cribbed the equations from. Looks like I misremembered, and all the equations were from Peters. So I don't have to worry about your quote, everything should be fine. I mainly wanted to avoid any possible misattribution problems.
I've attached a copy to this post.
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Shear_stress
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Again with the attitude? I don't remember kicking your dog.
Let's see. You start a thread to discuss ballistics penetration formulae and you list one. I, making the mistake that we were somehow discussing the "physics content" promised in the thread title, tell you the formula you provide falls flat on first principles. This touches a nerve with you for some reason:
If this is how you handle constructive criticism I am frankly amazed anyone is willing to help you.
You're so welcome
Good luck!
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OP
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Shearstress: said:
Again with attitude? I don't remember kicking your dog.
Let's see. You start a thread to discuss ballistics penetration formulae and you list one. I, making the mistake that we were somehow discussing the "physics content" promised in the thread title, tell you the formula you provide falls flat on first principles. This touches a nerve with you:
If this is how you handle constructive criticism I am frankly amazed anyone is willing to help you.
You're so welcome
Your persistence would indicate that you are clearly in search of a fight and I have no desire of entertaining your poor behavior. No one is asking for your particpation anymore, in fact, I'd just as soon you took your leave since you have nothing to offer other than contentious, argumentative behavior.
Bye.
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RyanM: said:
Ryan,
Yeah, I remember that paper. Fackler's "High Velocity Impacts @ greater than 1.5 Kps in calibrated gelatin". If I remember correctly, he establishes supersonic velocity in calibrated gelatin @ 4,900 fps. Very good article.
Thanks again for the .pdf. Much good reading, just what I was looking for.
ETA:
Found this on another website ( http://www.stormloader.com/rwc/ballistics.html ) , supposed to be applicable to penetration in human tissue (take that with a grain of salt, I sure did)-
Equation for penetration into human tissue:
P = 46.3R[ln(V ÷ 84)]
r = radius of bullet (centimeters)
ln = natural log
v = velocity of bullet upon impact (meters per second)
Seems to be another "logarithmic approach" to the problem, but I question its validity.
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OP
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Ryan,
I found the definition for "a" on page 307 of the .pdf that you so kindly provided.
It is a scalar correction value, specifically relating to data obtained via "dynamic penetration distance" (see paragraph in the upper right hand portion of page 307) and is not applicable to the "Rupture Modulus" U6 value (U6 = 57 mps +/- 8 mps) attributed to Fackler, et. al. for that value in 10% calibrated ordnance gelatin.
Accordingly, that paragraph (its last sentence actually) assigns the correction value of 1.200 to "a" for the "Type 2" "dynamic penetration measurements" as found on page 306 of the .pdf .
The Rupture Modulus, U6, is simply the first derivative of the impact velocity divided by the projectile diameter. (see pages 304 and 305 of the .pdf)
Therefore, the equation under consideration reduces from this...
Xcm = ln [[Vo/(a x U6²)] + 1] / r
to this...
Xcm = ln [(Vo/U6²) + 1] / r
....where U6 (57mps) + 8 mps = 65 mps and r = .00103 kg/cc.
V is expressed in mps also.
Ryan, I just wanted to thank you very much for all that you've done for me over the brief course of this thread.
Great .pdf!
Thank you so much.
I found the definition for "a" on page 307 of the .pdf that you so kindly provided.
It is a scalar correction value, specifically relating to data obtained via "dynamic penetration distance" (see paragraph in the upper right hand portion of page 307) and is not applicable to the "Rupture Modulus" U6 value (U6 = 57 mps +/- 8 mps) attributed to Fackler, et. al. for that value in 10% calibrated ordnance gelatin.
Accordingly, that paragraph (its last sentence actually) assigns the correction value of 1.200 to "a" for the "Type 2" "dynamic penetration measurements" as found on page 306 of the .pdf .
The Rupture Modulus, U6, is simply the first derivative of the impact velocity divided by the projectile diameter. (see pages 304 and 305 of the .pdf)
Therefore, the equation under consideration reduces from this...
Xcm = ln [[Vo/(a x U6²)] + 1] / r
to this...
Xcm = ln [(Vo/U6²) + 1] / r
....where U6 (57mps) + 8 mps = 65 mps and r = .00103 kg/cc.
V is expressed in mps also.
Ryan, I just wanted to thank you very much for all that you've done for me over the brief course of this thread.
Great .pdf!
Thank you so much.
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MCgunner
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Lots of "mathematics" gets invented to try to prove a point someone has about terminal ballistics, like big, slow is better than small, fast, like the infamous "TKO" factor. Gimme a break. I'm wary of trying to use simple algebraic equations to explain such complicated subjects, bunch a high school amateur mathematicians trying to sound smart. Reminds me of some second rate engineers I've worked with, "if you can't dazzle 'em with brilliance, baffle 'em with BS". Such a subject involves fluid dynamics and the fluid changes as a bullet passes through it, maybe encountering solids in the process (bones). I think it's better just to gather data from testing rather than build some computer model.
I'm wary of trying to use simple algebraic equations to explain such complicated subjects, bunch a high school amateur mathematicians trying to sound smart. Reminds me of some second rate engineers I've worked with, "if you can't dazzle 'em with brilliance, baffle 'em with BS". Such a subject involves fluid dynamics and the fluid changes as a bullet passes through it, maybe encountering solids in the process (bones). I think it's better just to gather data from testing rather than build some computer model.
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MC,
Yep, I agree. Not looking for dimensionless yields.
At this point, it appears that this is gonna enter the realm of Calculus and Fluid Dynamics and I am cool with that.
RyanM's .pdf was a good step in that direction, but it would seem that MacPherson's work is going to be "more in line" with what I am ultimately seeking. (there appear to be some promising integral equations that address this phenomena)
Thanks.
Yep, I agree.
Not looking for dimensionless yields.At this point, it appears that this is gonna enter the realm of Calculus and Fluid Dynamics and I am cool with that.
RyanM's .pdf was a good step in that direction, but it would seem that MacPherson's work is going to be "more in line" with what I am ultimately seeking. (there appear to be some promising integral equations that address this phenomena)
Thanks.
It's not always the case that a simple algebraic model is poor (though it obviously is in this case). Plenty of things follow simple linear models.
Also, empirical testing is not always good. I've seen plenty of really crappy testing where the parameters were quite blatantly controlled so that the "researcher" could arrive at a predetermined outcome which matched his own pet theory.
For example, there's this one guy who tried to determine if an English longbow would be capable of penetrating chainmail at long range. So he used some kind of complete BS math to "prove" that a 70 pound longbow at point blank range would hit just as hard as a 110 pound longbow at 250 yards range, then proceeded to shoot the crap out of chainmail with said 70 pound longbow at point blank. What do you want to bet that guy also thinks that a constitutional monarchy is the best system of government ever?
Another fun one, there's a yearly race between human marathon runners, and guys on horses, allegedly to see if a human really can go a very long distance faster than a horse. Except the distance is very carefully controlled to be shorter than the distance at which humans would consistently win. And on the year that a human won anyway, they retroactively changed the rules in order to steal that victory away from him. What do you want to bet that the organizers of that race... uh... fill in the blank yourself.
MCgunner
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Well, the more the variables, the less likely your model is going to be linear. And as some scientists often say about computer models, especially now when "experts" are trying to prove the merits of man made global warming, you can make a model prove your point fairly easily.
It is JMHO, but I don't think terminal ballistics is so simple as to be properly modeled with simple linear equations. Even exterior ballistics involves the movement of bullets through a fairly constant medium (air) has to be modeled using some pretty wild differential equations. I've done that math before, from algebraic formulas derived from said differential equations which I wrote a BASIC program to handle so I didn't overload my feeble mind doing hand calculations. This was back when all I had was a Tandy Color III. Remember those? Terminal ballistics are more complicated even if you're using a consistent medium for your model. And, even once you get it down for jello, how does that relate to actual flesh? We use jello as a standard, of course. Knock yourself out on modeling it, but I'll just do the shooting or read about it like I've always done. I see merit to the rifleman in exterior ballistics models. I don't see much merit in modeling penetration potential of a slug, especially if it's not an expanding slug, since I don't carry ball. If it's just for an educational exercise, well, I understand the desire for more understanding, just that it's rather impractical.
I guess if you work for a bullet maker, there's merit to such models, but I'm not a ballistics engineer. I do good to balance my check book.
It is JMHO, but I don't think terminal ballistics is so simple as to be properly modeled with simple linear equations. Even exterior ballistics involves the movement of bullets through a fairly constant medium (air) has to be modeled using some pretty wild differential equations. I've done that math before, from algebraic formulas derived from said differential equations which I wrote a BASIC program to handle so I didn't overload my feeble mind doing hand calculations. This was back when all I had was a Tandy Color III. Remember those?
Terminal ballistics are more complicated even if you're using a consistent medium for your model. And, even once you get it down for jello, how does that relate to actual flesh? We use jello as a standard, of course. Knock yourself out on modeling it, but I'll just do the shooting or read about it like I've always done. I see merit to the rifleman in exterior ballistics models. I don't see much merit in modeling penetration potential of a slug, especially if it's not an expanding slug, since I don't carry ball. If it's just for an educational exercise, well, I understand the desire for more understanding, just that it's rather impractical. I guess if you work for a bullet maker, there's merit to such models, but I'm not a ballistics engineer. I do good to balance my check book.
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And with exterior ballistics, the projecctile isn't continuously changing shape. Even with ballistics tables, shooters have to adjust for other factors like wind, rotation of the bullet, air density (altitude), etc.
You may be able to come up with an emperically derrived formula to predict how a particular weight of a particular caliber of a particular bullet will penetrate at different velocities, but with Excel, you could just plot your data and ask Excel to puke out an equation to fit to it, and you could use that to interpolate (not extrapolate). If you wanted to be fancy, you might take one caliber and do different weights at different velocities with the same bullet type, then you would have a surface plot. That's 2 variables, and I'd stop there.
You may be able to come up with an emperically derrived formula to predict how a particular weight of a particular caliber of a particular bullet will penetrate at different velocities, but with Excel, you could just plot your data and ask Excel to puke out an equation to fit to it, and you could use that to interpolate (not extrapolate). If you wanted to be fancy, you might take one caliber and do different weights at different velocities with the same bullet type, then you would have a surface plot. That's 2 variables, and I'd stop there.
Nicodemus38
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a few points that need to be focused on, that havent completely been touched upon. im not a scientist but..
1. variable density of the target media has massive effect upon the bullets penetration. its easy to penetrate jello or water with a bullet, but if you have a bucket of tennis balls filled with water to shoot at, you get very different results.
2. bullet profile. nice pointy spitzer is going to penetrate farther and easier then a full wadcutter at the same velocity.
3. the formulas above all assume the bullet changes diameter instantly upon impact ie pre impact with target the bullet is nominal .357 and upon impact its automatically assumed to be at maximum expansion, typically .61 with the old federal nyclad.
nothing calculates the penetration of the bullet as it mushrooms out. although that may not have the big impact i think it does. most likely linnear reduction.
4. tumbling is not considered or adjusted for. although tumbling cannot be predicted very easily, it does have effect. for example a half inch long bullet with a diameter of .357 penetrates better when the .357 cross section is the frontal plane. put the .5 inch x .357 rectangular section as the frontal plane of penetration, you loose energy and penetrating power fast.
calculate the energy and penetration lost by the actual tumbling of the bullet upon itself, the effect increases.
5. nothing factors in an exploding bullet. example the cast lead hollow point for 30-30 that is gaurunteed to explode in impact, and shed everything around teh cavity to let the miniscule base section blow through the animal.
that really reduces bullet mass, velocity, and penetration.
on the other hand, most calculations would say 38 special is poor at penetrating, yet hard cast slugs have been known to penetrate through blackbear at shortrange.
1. variable density of the target media has massive effect upon the bullets penetration. its easy to penetrate jello or water with a bullet, but if you have a bucket of tennis balls filled with water to shoot at, you get very different results.
2. bullet profile. nice pointy spitzer is going to penetrate farther and easier then a full wadcutter at the same velocity.
3. the formulas above all assume the bullet changes diameter instantly upon impact ie pre impact with target the bullet is nominal .357 and upon impact its automatically assumed to be at maximum expansion, typically .61 with the old federal nyclad.
nothing calculates the penetration of the bullet as it mushrooms out. although that may not have the big impact i think it does. most likely linnear reduction.
4. tumbling is not considered or adjusted for. although tumbling cannot be predicted very easily, it does have effect. for example a half inch long bullet with a diameter of .357 penetrates better when the .357 cross section is the frontal plane. put the .5 inch x .357 rectangular section as the frontal plane of penetration, you loose energy and penetrating power fast.
calculate the energy and penetration lost by the actual tumbling of the bullet upon itself, the effect increases.
5. nothing factors in an exploding bullet. example the cast lead hollow point for 30-30 that is gaurunteed to explode in impact, and shed everything around teh cavity to let the miniscule base section blow through the animal.
that really reduces bullet mass, velocity, and penetration.
on the other hand, most calculations would say 38 special is poor at penetrating, yet hard cast slugs have been known to penetrate through blackbear at shortrange.
45crittergitter
Member
Still haven't seen any derivation of the "equations" or "formulas" tossed about. Maybe we should just all "provide" our own formulas to make each of us happy.
The API formula ( SD*Ke/S ) is a good all around formula.
For game penetration, I find this formula, relatively near from the facts :
3*square root of ( W/7000/(C*(0,5+C))*V )
W = Weight ( grains )
C = Calibre ( inch )
V = Velocity ( ft/s )
It is just a empiric formula, not a scientific one. It don't care about bullet design, which of course change a lot of thing. It is good for comparison beetween classic round nose and SWC.
Some results :
9mm ( 115gr*1200ft/s ) : 24
45ACP ( 230gr*850ft/s ) : 24
44mag ( 240gr*1400ft/s ) : 33
458winchester ( 500gr*2050ft/s ) : 55
600NE ( 900gr*1950ft/s ) : 56
50BMG ( 650gr*3000ft/s ) : 70
For game penetration, I find this formula, relatively near from the facts :
3*square root of ( W/7000/(C*(0,5+C))*V )
W = Weight ( grains )
C = Calibre ( inch )
V = Velocity ( ft/s )
It is just a empiric formula, not a scientific one. It don't care about bullet design, which of course change a lot of thing. It is good for comparison beetween classic round nose and SWC.
Some results :
9mm ( 115gr*1200ft/s ) : 24
45ACP ( 230gr*850ft/s ) : 24
44mag ( 240gr*1400ft/s ) : 33
458winchester ( 500gr*2050ft/s ) : 55
600NE ( 900gr*1950ft/s ) : 56
50BMG ( 650gr*3000ft/s ) : 70
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