Power Formula: the 9mm smokes the 45ACP!!!

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New_comer

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Hi, everyone! :D

I'd like to share with you a simple formula I worked out from the basic relationships between distance, time and mass. I want to determine which of the two calibers really does have the greater ooomph! as far as impact dynamics is concerned :confused: :rolleyes: . Here goes:

Velocity (V)=distance/time (s)/(t)
Acceleration(a)= change in Velocity/time elapsed (Vf-Vi)/(t)
Energy(E)= 1/2 * mass(m)* Velocity sqrd (V^2)
Power (P) = Energy spent/time elapsed (E)/(t)
Gravity constant (g) = 32 ft/sec^2
1 Horsepower = 550 ft-lb/sec

From these relationships, it is possible to develop this statement:

Power(P)= mV^3/(4s)

Simplifying the equation, so that we could immediately substitute terms that we regularly use - like grains, fps and inches of penetration - I came out with this rough result (drum roll please):

Power (P) = [(w*V^3)/(41*s)] * 10^-6 horsepower

where:
w = weight of slug in grains
V = Velocity of slug before impact and with NO exit wound (if so, this baby will become more complicated, and I don't want to have a headache)
s = inches of penetration

Let's try it:

For a 115gr 1200fps 9mm JHP slug penetrating a modest 12", the target is subjected to an average energy release equivalent to (gasp!) 404 hp! :eek: :eek:

With a 230 gr 850 fps 45ACP also penetrating 12", energy is dumped at only 287 hp. Now, that's no paltry amount by any means. I wouldn't want to get trampled on by 287 horses ;) , but by 404 horses? Even for a split of a split-second, man, whatever's in the way of that "fast and light" slug, it's gonna be pulp!

Like lightning in a brass bottle... I wonder how a 10mm or 357SIG would do...

I am not trying to start yet another caliber war, I've had enough of that already. But as far as I am concerned, data speaks louder than perception - everytime.

Your thoughts?
 
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BobR

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So, what does a 85gr projectile at 1450fps do?
I am just to lazy, and tired to use your formula.

bob
 
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C.R.Sam

New member
Which is roughly equal to the force applied to the hand of the shooter.

Deceleration rate is not constant.

Sam
 
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Marmy7451

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muzzle energy

velocity in fps, bullet wt in grsins:

M.E.= bullet wt *velocity*velocity/454400

answer is in ft. lbs.
 
N

New_comer

New member
Ooops! My bad...

It should have read "energy release rate" so as to indicate power, not energy. Thanks, Lord Grey! :D

BobR,

Assuming the same 12" penetration, the equation will yield 526 horsepower. Hey, not bad! :D What ammo is that? RBCD? Magsafe?

Snowdog,

I haven't yet toyed with the relationship between projectile impact power and muzzle energy. But I promise you, one of these days, I may come out with something. Although it is already apparent in this here exercise, that the bullet stats i've considered do have the same muzzle energies. Hmmm...

Anyway, allow me to reformat the formula once more, but this time we'll focus on the "relationships" rather than the result...

where: K=numerical constant

P=K*w*V^3 ÷ s

From this statement, we can obtain the following deductions:

1. Power is proportional to mass - It only goes to show that the heavier slug is more powerful than a light one, when penetration and speed are equal. Therefore, a subsonic 147 gr 9mm slug could never be as powerful as a full size 45ACP. It just ain't possible. Unless, of course, both have yet to be fired :D , therefore power is "0". :D :D

2. Power varies inversely as the depth of penetration - the shallower the wound, the more "spectacular" (if I may use the word) the result. This is the essence of the exotic bullets. They do not penetrate as deep as the standard JHP's, but the "blast" effect is so pronounced that impacted flesh has nowhere to go but outwards, like a crater formed by a meteorite. There is a threshold that must be surpassed before a slug could induce such flesh devastation, similar to a meteor impact, but the principle is there... and the third and most important component of the equation has a lot to do with this.

3. Power varies proportionally to the cube of the velocity - this is where the "fast and light" principle really gains solid ground. Instead of simply slithering through or pushing the flesh aside, the slug overwhelms the static inertia of the flesh along its path, and would result to a more successful "crushing" of tissue. Much like jerking out a tablecloth cleanly off with the plates still arranged on top of it. Or a baseball punching a clean hole through a glass window. And we all know that "crushing" would promote faster bleeding, as more capilliaries / veins would be damaged by the "fast" projectile.

Regardless of my own opinions on the matter of bullet selection, what does this exercise tell me?

I've proven that the 9mm JHP definitely has merits that cannot be ignored, and anyone using a good 9mm, or any other "puny" caliber should not feel "underpowered". In fact, when placed properly, the 9mm JHP has the potential to inflict greater damage than the bigger calibers (i like this trait most of all) :D . I know very little about actual street shootings involving the different calibers, but i know the better 9mm's are way up there in the list.

It's almost 3 in the morning now. I'm getting dizzzzzzzzz... Huh?

Oh! <YAWN> Goodbye for now... ;)
 
F

FLM

New member
Here's a short form for figuring Muzzle energy for lazy people like me.

185 gr at 1140 MV

114x114= 12996 divided by 4504=2.89x185=534

Not quite as exact as the full formula, but close enough.
 
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rkc

New member
All these formulas fly in the face of experience and history.


I have a better idea. I am replacing Paintball with Dukeyball.
Will really teach people to take cover.
 
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Ceol Mhor

New member
Hold on a sec, New_comer...

You said that "Power (P) = Energy spent/time elapsed (E)/(t)". That's not quite right, because power = work / time, not E/time. As a result, your final number is in units of m^3/sec^3, which have no particular significance in physics. What you have is simply an arbitrary way to compare bullet proerties that puts a heavy emphasis on velocity. You don't end up with horsepower.

Here's what power actually is:

Power = Work / Time
Work = Force exerted * Distance moved (which would be depth of penetration, I believe. )
Force exerted = mass (of the bullet) * acceleration
Acceleration = Velocity / time
Velocity = Distance moved (depth of penetration again) / time

What you end up with is

Power = (Bullet Mass * Bullet velocity * Penetration depth) / (Time for the bullet to come to a halt after entering the body) ^ 3
The units for that are (using metric units for everything) are Joules/second, or Watts, which are the correct unit of power. However, it's a pain to find the time component of the calculation (although you should be able to find it, give penetration depth and initial velocity), which makes calculating bullet power cumbersome.
 
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rkc

New member
Just the same, the ability of some of my friends on this channel with mathematics is amazing and enjoyable.



The .45 has twice the frontal area of the 9mm
I am trying to work up a pet formual to make the .45 appear better but I have gotten a headache.

I am sure it is coming.
 
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Hoss Cartwright

New member
The amount of power that a handgun round produces is really rather miniscule.

POWER (in horsepower) = (WEIGHT (in grains))x(VELOCITY(in fps))/3,850,000(approx)


It takes a fairly powerful person to generate 1 hp. If a handgun came even close to developing that much power, there is no way that a person could control it.
 
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gorlitsa

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This is exactly why the physicss dept here needs to offer PHYS 279: Practical Balistics. Lots of guns and balistic gelatin. :D
 
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Dave T

New member
OK, you win. The 9mm is the King! It is vastly superior to the 45 ACP. How could I have ever been so stupid to have not seen this. And how on earth could all those thousands of other people who trust their lives to the 45 ACP have been so stupid. And to think it took a genious like you to explain it all to us. I am so embarassed.

Now. Since I'm getting old and set in my ways, not to mention I have tens of thousands of rounds of 45 ACP brass, bullets, LP primers, and a couple thousand rounds of loaded practice 45 ACP ammunition, and a Star progressive reloader set up for 45 ACP, and then we have a number (quite a number to be honest) of pistols in that chambering - so given all that:

IS IT OK WITH YOU IF I DON'T BUY A SILLY MILLIMETER?
 
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