Physics Professors...I'm confused about Kinetic Energy Numbers?

To clarify further...in the definition of KE "Foot-Pound" is measured as the Energy required to raise a 1LB weight a vertical distance of 1FT. This makes no mention of Velocity units (only "distance")...yet velocity (including time units) is one of the variables in the KE formula.

(1/2Mass x Velocity^2 = FtLb.)

My "problem" Simply,

1.) if Kinetic Energy of the projectile is measured in FtLb,

and 2.) one of the KE formula's multipliers is "Velocity"...

then 3.) where the heck is the complete Velocity Unit (to include time) in the result?

Why do we throw away the TIME factor of velocity in the KE result? Shouldn't the KE result be in FtLb/second rather than just FtLb? (as a full measure of the "capacity to do work")

If we're going to debate "stopping power" then lets talk about "power" being perhaps more accurate than "energy".
I believe the KE formula itself is flawed in that it drops the unit of TIME from the velocity multiplier.
Please explain this to me.

The problem with this equation for most people is that they don't understand pounds mass (lbm) vs. pounds force (lbf). Remember the force equals mass times acceleration (F=ma).

1 lbf = 1 lbm x g where g is the gravitational constant. Or written another way 1 lbf = 32.2 lbm ft/sec^2

I've gone through the math before and it works out. But right now I'm feeling to lazy to work it all the way through. Maybe someone more ambitious will work it all out for you.

Whoa whoa.. let me stop you right there.

EVERYONE knows that .45 acp has the most stopping power. They load more stopping power powder into the casing and the bullet itself is soooo big you can throw it at someone and it'll stop them.

.45 acp = stopping power




(by the way, this is essentially how some "stopping power" conversation go on other forums)

I'll let someone else explain the math too, since it's only there to confuse people and sell ammo.

MR .44 Spl said:

The problem with this equation for most people is that they don't understand pounds mass (lbm) vs. pounds force (lbf). Remember the force equals mass times acceleration (F=ma).

1 lbf = 1 lbm x g where g is the gravitational constant. Or written another way 1 lbf = 32.2 lbm ft/sec^2

Click to expand...

Still, the TIME factor of the formula is gone in the KE formula result:

1/2M x Velocity^2 = FtLb of energy.

In our KE result,
We don't lose the units of weight (LB)
and we don't lose the units of distance (FT)...
BUT, somehow we just DROP the units of time from the answer?

I'm not asking to explain it with complicated math, as a good physicist should be able to tell me where the units of time went in layman's terms. And yes, I beleive this is the area where the "Ballistic Energy" numbers can be so misleading.

Well, I just cannot help myself on this one so here I go.I cannot help with the math, but will venture that the measure of foot pound's of energy is really meaningless. It is just a tool to measure one particular cartridge's power against another,on paper. However we all know that a bullet with far less ft lb energy can really outperform another that has a lot more ft lb energy in the real world against real target's. A far more relative (to me) measure of a particular cartridge and bullet combo is a measure of mass and momentum. Once again no math to back me up but I do subscribe to the Julian Hatcher train of thought on bullet performance on real live target's. Bullet weight,shape and construction mean far more than just a ft lb comparison. The dwell time, that is the amount of time a bullet is in a target actively doing it's job is also important. This is a personal opinion and not that of anyone else liveing or dead! LOL!

arizonaguide said:

Still, the TIME factor of the formula is gone in the KE formula result:

1/2M x Velocity^2 = FtLb of energy.

In our KE result,
We don't lose the units of weight (LB)
and we don't lose the units of distance (FT)...
BUT, somehow we just DROP the units of time from the answer?

I'm not asking to explain it with complicated math, as a good physicist should be able to tell me where the units of time went in layman's terms. And yes, I beleive this is the area where the "Ballistic Energy" numbers can be so misleading.

Click to expand...

OK try this:
This is simply tracking the units no numbers

energy = 1/2 m v^2 = (lbm) (ft/sec)^2 = (lbm) (ft^2/sec^2) = (lbm ft/ sec^2) ft
Substitute the following into the above
lbf = lbm ft/sec^2
and you get
lbf ft or ft lbf if you prefer

Clear as mud?

MR .44 Spl said:

OK try this:
This is simply tracking the units no numbers

energy = 1/2 m v^2 = (lbm) (ft/sec)^2 = (lbm) (ft^2/sec^2) = (lbm ft/ sec^2) ft
Substitute the following into the above
lbf = lbm ft/sec^2
and you get
lbf ft or ft lbf if you prefer

Clear as mud?

Click to expand...

Almost! I have to let it sink in and bounce around for a bit!

Col. Martin Fackler, when he was in charge of the Wound Ballistics lab at the Letterman Army Institute of Research, felt that Kinetic Energy was mostly BS. What a bullet does when it hits it's target is too complex to simplify to a simple equation. He felt Kinetic Energy was just a sales gimmick perpetrated by the ammunition companies.

Yeah, the whole lb (force) vs. lb (mass) is where the thing falls together -- as MR .44 Spl mentions upthread having the gravitational constant of 32 feet/second squared included in the conversion from lb(f) to lb(m) cancels out the seconds in the final answer. The "seconds squared" are on the denominator of the mass unit and this cancels out the "seconds squared" on the numerator of the "velocity squared" unit.

This is one of the cases where the metric system is a bit easier <ducks > since the mass unit is kilogram and the force unit is the Newton. There is a throrough explanation as it relates to ballistics here.

jag312 said:

Col. Martin Fackler, when he was in charge of the Wound Ballistics lab at the Letterman Army Institute of Research, felt that Kinetic Energy was mostly BS. What a bullet does when it hits it's target is too complex to simplify to a simple equation. He felt Kinetic Energy was just a sales gimmick perpetrated by the ammunition companies.

Click to expand...

No, I do understand this concept about actual performance being different than the energy numbers...that's not where I want to go.

I want to understand the KE formula...and momentum...and power...and work..in PHYSICS terms.
I want to understand what they are, So that I can truely understand WHY they work or don't work as indicators of bullet performance.

I understand that there are infinite variables in REAL life bullet performance.

I just want to understand the PHYSICS of Kinetic Energy fully...because the numbers may be meaningless for bullet choice...but the concept that the bullet's kinetic energy is transfered into the target medium (and does the work of destruction) is still valid...and meaningful. THAT'S what I want to fully understand...even if "momentum" or "power" or "weight" or "mass" or "caliber" or "meplat" or some other actual numbers (or combination thereof) are used for more reliable indication of effectiveness.

Vulcan Bob said:

The dwell time, that is the amount of time a bullet is in a target actively doing it's job is also important. This is a personal opinion and not that of anyone else liveing or dead! LOL!

Click to expand...

Bob, do you remember which research you heard about that concept of "dwell time"? This is another area I want to research more...and I had heard that "dwell time" concept before...and can't remember where.

Dragonfly said:

Yeah, the whole lb (force) vs. lb (mass) is where the thing falls together -- as MR .44 Spl mentions upthread having the gravitational constant of 32 feet/second squared included in the conversion from lb(f) to lb(m) cancels out the seconds in the final answer. The "seconds squared" are on the denominator of the mass unit and this cancels out the "seconds squared" on the numerator of the "velocity squared" unit.

Click to expand...

Dragonfly, thank you for the excellent link!
JBM - Topics - Energy

arizonaguide said:

Bob, do you remember which research you heard about that concept of "dwell time"? This is another area I want to research more...and I had heard that "dwell time" concept before...and can't remember where.

Click to expand...

Arizonaguide, jeez I cannot really remember right now about that one, but I think it was from some military research on terminal ballistic's to obtain the ideal velocity for the 7.62 NATO cartridge and it's effects at different range's. Or maybe it was the 5.56 NATO. Sorry I cannot be more specific, but that was a long time ago!

Well I'm a no-kidding Physic Professor, card carrying, graduate degrees and all that.

You aren't going to like the answer.
A pound is not a unit of mass.

If you use the metric system it is easy.
A kilogram is a unit of mass.
A newton is a uit of force.
All the units work out neatly.

Americans generally won't take the trouble to learn the metric system.
Americans generally don't know the English system.

The fundamental units of mass in the English system is the slug, which you never hear of. Or you can use the poundel, which is the amount of mass to produce a pound of force at standard G (32 feet per second squared). A poundel is 1/32 of a slug. So divide your weight by G (32 feet per sec squared) to get mass in slugs.

The first thing we teach in Physics 101 is the metric system. I start out by proving the students don't know the English system anyway, so they might as well learn the metric.

The British have always had a thing for "dwell time". A couple of years ago I was reading the work of a physicist on terminal ballistics. I understood the basic concept, but the math lost me. IIRC, he was looking at the relationship between velocity loss, bullet expansion, depth of penetration (possibly wound channel volume?) and time. He did manage to explain how different calibers, bullet weights and velocities managed to produce similar terminal effects by producing figures in a similar specific range. But, as noted, I had to take his math on faith.

The exact mechanics of wound ballistics are esoterically interesting but essentially meaningless in the real world. What matters is your skill with the weapon and shot placement.

BTW, momentum is another subject entirely.

OK team, listen to what Professor OKFC05 is telling you. Another earlier poster also has if right. The slug is the unit of mass in the imperial (fps) system. It is the mass that will accelerate at 1 foot per second per second (no, I didn't hiccup) when acted upon by force of one pound-force. A pound-force is one pound acted upon by the standard acceleration due to gravity. All of this plus the poundal are why sane scientists and engineers use the mks system. The arithmetic is easier too. Professor, I'm sure you don't need my validation, I just thought I'd put in my $0.02.

Once upon a crazy time long ago, I would have passed that quiz, I learned FPS jut to be different.

Russ

Isn't mass irrelevant in gravitaional acceleration? In a vacumn a feather, or even a helium balloon falls at exactly the same rate as a bowling ball. This was never adequately explained until Einstein worked out his general relativity.

7tenz said:

Isn't mass irrelevant in gravitaional acceleration? In a vacumn a feather, or even a helium balloon falls at exactly the same rate as a bowling ball. This was never adequately explained until Einstein worked out his general relativity.

Click to expand...

Yes, it is but in the case of kinetic energy calculations, the use of the gravitational constant is to convert lb(mass) into lb(force).

F=ma (virtually everything comes from this in one way or another)

Weight(W) = mass(m) x acceleration(g)

so, rearranging that equation, you get m=W/g

W/g is the term you plug in the KE equation for m...... where W is in pounds. You have to divide grains by 7000 to get pounds.

So the KE equation KE=1/2 m v^2 looks like this when we make all the corrections:

KE = (bullet weight in grains) x (velocity in fps)^2 /(constant)

and the constant is 2 x 7000 x 32.2 = 450,800

Try it, for a 158 gr bullet at 850 fps. First, enter 850, then square it. Then multiply by 158. Then divide by 450800. Out pops 253 ft-lb.

But the OP's question was, what happened to the time factor. Once we corrected the bullet's weight from grains to pounds, we have pounds in the numerator. Velocity squared gives us feet squared in the numerator, and seconds squared in the denominator. The 'g' in the denominator gives us 'feet' in the denominator, and seconds squared in the numerator.

So it looks like this:
(pounds x feet squared x seconds squared)/(feet x seconds squared)

If you remember from many-moons-ago algebra, terms that appear in both the numerator and denominator cancel each other out. Thus, the 'squared' term disappears from the 'feet squared' in the numerator and the 'feet' in the denominator disappears. Then the seconds squared term in the numerator is canceled out by the seconds squared term in the denominator. What are we left with? Only the pounds and feet terms in the numerator or what we also call 'ft-lb', i.e., energy, which in this case is kinetic.

This would have been a whole lot easier both to explain (and understand) with a piece of paper and a pencil. Or a blackboard.

arizonaguide said:

...but the concept that the bullet's kinetic energy is transfered into the target medium (and does the work of destruction) is still valid...and meaningful. THAT'S what I want to fully understand...

Click to expand...

Actually, I think it isn't. It would probably be best to read Fackler or someone else who knows something about wounds, but energy transfer isn't what stops people, or even wounds them. There isn't a lot of energy transfer with a knife, but it can very easily be lethal or immediately incapacitating or both. Repeated punching can involve a lot of energy transfer, but, like with bullets and real estate, location is everything. You can also get significant energy transfer by taking a hot bath, particularly if you are cold to start with.

Gunshot wounds achieve desirable results through very specific mechanisms at very specific locations. If a bullet arrives at an appropriate location and cuts or breaks something important, it will be effective. This is difficult to relate to specific energy levels without knowing more about the shape, frontal area and weight of the bullet. Looking for a prediction of wounding effectiveness based solely on "energy transfer" is a lost cause.