Here's a question I've always wondered about. Lets say you have two bullets of different calibers, one weighs 100 grains and the other 200, and they both have an equal sectional density and BC. If these two bullets are both solids (no deformation or change of shape on impact) and you launch them both at the same velocity, will they both penetrate equally?

Pete

You're dealing with more than just SD and BC.The heavier bullet will also have more momentum and therefore will penetrate more.

But Mete, the smaller caliber bullet will have less resistance.

Looking at tables the closest I can find ,to give an idea with real bullets , is ; .243, 100gr, SD .241 and .338,200gr, SD .250.

In theory...yes, they will... same bullet materials and profile, same medium on impact, etc.

The problem is that it is impossible, for all practical purposes, for this situation to exist. Soooooo, it makes an interesting topic ofr discussion, but that's all.

CDH = 10X



To illustrate the apples and oranges comparison look at this and tell me what you think about it. From the Lyman Black Powder Handbook, I provided SD numbers however, and they are rounded to nearest value. This cuts to the heart of the reason that larger bores carry higher BC values for a given form. Remember while you ponder this, they are round balls, and of the same form.



Round Balls:



.360" Weight 71 grains BC .049 / SD .078



.495" Weight 180 grains BC .070 / SD .105



SD=W/D^2, where W=weight in pounds and D=bullet diameter

Why would this be impossible?

For example:
150 gr. 7mm NBT, SD .266, BC. .493
250 gr. 9.3mm NBT, SD .267, BC .494

So, it these were solids and were shot at the same velocity, they would penetrate equally?

Pete

What CDH said is that in theory, YES, but I add the qualifier that the velocity not be equal, but rather the energy level. If all else is equal, two bullets of different weight at the same velocity carry different energy levels. I think that your question properly phrased, should be, "If all else is equal, will bullets of equal SD penetrate equally regardless of caliber?" Velocity does not penetrate, energy does. In practical application, it is a difficult if not impossible scenario to create. Ergo, it is an academic discussion.



Your selected bullets are near enough identical in numbers for your comparison, but then you say "IF". Well, the internal construction of those two is different in regard the ratio of lead to copper jacket, and IF they were solids the numbers would not match so conveniently. Another fly in the ointment is that those two will not have the same form. Yeah, sure, they kinda sorta look alike but they are not, and that has a fair amount of influence on penetration...for solids.



There is a message in my previous post. Do you get it?

talentrec,

Let's look objectively at your example. First off it is MOMENTUM DENSITY which provides insight into penetration. Sectional Density is much grayer.

Your example problem:

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Why would this be impossible?

For example:
150 gr. 7mm NBT, SD .266, BC. .493
250 gr. 9.3mm NBT, SD .267, BC .494

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A few more assumptions.

1.) Both bullets have the exact same point (penetrator) geometry

2.) Both bullets have the same length to cross sectional area ratio (this speaks to subsonic drag issues with the shank or body of the bullet in the penetrated media).

3.) Both bullets have a velocity of 2500 fps (magnitude is not essentially important but equivalency is)


Working the problem:

7 mm bullet of 150 grain mass and a velocity of 2500 fps has a momentum of 642.857 lbm-in/sec

9.3 mm bullet of 250 grain mass and a velocity of 2500 fps has a momentum of 1071.429 lbm-in/sec

7mm bullet has a cross sectional area of 0.06335 in^2

9.3 mm bullet has a cross sectional area of 0.1052 in^2

The momentum density (momentum / cross sectional area) of the two projectiles @ 2500 fps velocity are:

7mm bullet (150 gr @ 2500 fps) = 10,147.7 lbm/in-sec

9.3mm bullet (250 gr @ 2500 fps) = 10,184.69 lbm/in-sec

Pretty darned close!

Lets consider the deformation question (there is NO SUCH THING AS A NON-DEFORMING BULLET). Deformation is strain (in it's raw form), and we know that unit strain and unit stress are related to each other, for any given material, via Young's Modulus (Modulus of Elasticity). We also know that unit stress can be calculated based upon force and geometry characteristics of the system in question. We know that the force acting on this systems (7mm and 9.3mm) (assuming a consistent applied resistance from the media being penetrated for both bullets/systems) is nothing more than the time rate change of momentum!

If we get REAL simplified here and just call stress Force / cross sectional area, we see that the time rate change of the Momentum Density provides us with the "stress" (simple stress now NOT unit stress) acting upon the system(s). Since the Momentum densities are practically the same for both these bullets, and we are ASSUMING a consistent applied resistance from the penetrated media for each bullet, we can see that the SIMPLE STRESS acting upon both bullets (and conversely acting upon the penetrated media in the form of "shear stress") are EQUAL to one another for each bullet! This means that BOTH bullets SHOULD deform the same, and should penetrate to the same depth.

Now the REAL difference is that the bigger BULLET will MAKE A BIGGER HOLE! (WOW, isn't everybody glad I am around here to tell you that bit of information, ) DUH DUH DUH.

I have validate this out several times in penetration tests. It is true like it or not.

For hunting, I prefer to use the BIGGER bullet, as it makes a BIGGER hole (DUH) and therefore typically kills and/or incapacitates the game FASTER!

We can get AWHOLE lot more technical, but I doubt it would really matter as VERY few would understand the math (probably lost most everyone already).

Hope I answered your question, but in case I lost you, the answer is yes both bullets should penetrate roughly the same. The bigger bullet will however make a bigger hole, which typically is advantageous to rapid animal expiration (furbearers probably would not like the bigger hole though).

ASS_CLOWN

DD-

I think I missed the message...

DD,

Engery doesn't penetrate, MOMENTUM does. Well to be completely honest FORCE penetrates.

Since the time rate change of momentum IS force I say that momentum is a FAR more accurate indicator of penetration than ANYTHING besides FORCE.

ASS_CLOWN

AC, I won't quibble over the term with you, but velocity is only a reference in the time/distance equation. I have yet to kill anything with velocity. I was trying to avoid complexicating the whole friggin' thing. So, yeah, when you take a bullet that has velocity, it would appear that it is imbued with energy in the form of momentum. When all is said and done it's the bullet that carries the message. Or is it AOL?

DigitalDan,

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AC, I won't quibble over the term with you, but velocity is only a reference in the time/distance equation. I have yet to kill anything with velocity.

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I really do not understand your argument with me at all! You said energy penetrates. I assume you are referring to kinetic energy, which by definition is 1/2*mass*energy^2.



So by your very argument, not only does "velocity kill" but it does so to the second power!



Now all that velocity, energy, momentum, crap aside, here is the FACTS JACK, to quote Bill Murray.



Penetration occurs ONLY when the shear stress imparted by the bullet to the target EXCEEDS the SHEAR STRENGTH of the target ! Do you ALL understand that concept? This concept IS FUNDAMENTAL , and the BASIS for ALL penetration.



Shear stress is equal to FORCE / Cross Sectional Area.



Now Force = Mass * Acceleration (also known the world over as Newton's Second Law)



How do we get the "FORCE" (consult Yoda, NO I don't think so). We look at the MOMENTUM. WHY momentum? Because of what MOMENTUM is!



MOMENTUM = mass * velocity



What is the difference between FORCE and MOMENTUM? Acceleration and Velocity!



What is the difference between Acceleration and Velocity?

Acceleration is the time rate change of velocity !



So if we apply a little more of Sir Isaac's (that would be Newton) contributions to the world, namely CALCULUS, we can transform MOMENTUM into FORCE!



Enough physics lessons for the day!



Ain't it amazing what one finds in the bottom of a Cracker Jack box, or was it a Google Search???



DD, this entire post ISN'T aimed at you (just the first part where I am poking fun at you with regard to velocity).



CHD,



You said a MOUTHFUL (or is that a keyboard full) when you said the wound channel would be very different between these two bullets (7mm vs 9.3 mm). It IS THE WOUND CHANNEL which does the KILLING!



ASS_CLOWN

Every once in a while you post something interesting AC. Then ya gotta spoil it by reminding me of my Ex. Google search that when you get a chance ol' sport.

DigitalDan,

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Every once in a while you post something interesting AC. Then ya gotta spoil it by reminding me of my Ex. Google search that when you get a chance ol' sport.

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I hope you found my posts on this thread interesting.

I sincerely hope you don't actually think I "Google Searched" up all that information! I wish it were that simple! If is was in fact as simple as a "Google" search it would have saved untold thousands of dollars on higher education!!

I do apologize if any of my comments toward you were too smart-assed! They were meant in good natured fun (I am refering to the velocity comments).

ASS_CLOWN