Why is Power factor calculated the way it is?

[entropic]

Power (and recoil) seem to be a function of energy rather than momentum. So why isn't the power factor proportional to the square of velocity? If it were, it seems like people would generally use lighter bullets to make the PF.

Dave

[Jim Norman]

Power (and recoil) seem to be a function of energy rather than momentum. So why isn't the power factor proportional to the square of velocity? If it were, it seems like people would generally use lighter bullets to make the PF.

Dave

Dave,

If we were to change the formula and calculate the PF in a different manner. we'd also change the required result to reflect what we already have.

In your example a 180 grain .40 that currently needs to go at 916.6FPS to make major or a 165 PF would still need to do so, but we'd have a result as follows: ((916*916)*180))/1000 for a new PF of 151,261. Which I am sure can be converted to pound-feet or pound inches or some other measurement that is sure to confuse the living daylights out of most people (myself heading that list)

In other words, you might have a more accurate and in some ways more applicable number here, but what we have done works and has works and we'd have to change the entire world to make the change. Not a battle I am up for. Next thing you know, we'd have to do the calculations in Metric to get newtons.

Jim

[ChuckS]

I like it! My 135 gr bullets would only have to go 34.96 FPS to make major!

[entropic]

Yes, of course there would have to be a change to the final power factory requirement if you squared the velocity.

All I'm saying is: Power and recoil seem to be proportional to m*v^2, so the way power factor is calculated places an overemphasis on bullet mass and an underemphasis on bullet velocity.

Do slides operate faster with lighter bullets which creates a reason to go lighter?

[entropic]

I guess the rule as it stands keeps people from having to use a calculator...

Edited October 13, 2009 by entropic

[DarthMuffin]

As I understand it, the reasoning is twofold:

1) In ye olden days of IPSC, chronographs were expensive, few, and far between. To calibrate whether you made major or not, you shot a specific piece of steel and if it swung X inches high you made major. This measures momentum (momentum of the bullet is transferred to the steel), and not energy.

2) Also to do with steel. Momentum is what knocks them down, not energy. A minor load making a specific KE by going very fast with a light bullet might not have the momentum to knock down steel.

Measuring momentum and not Kinetic Energy is why USPSA loads tend towards heavy/slow. You're maximizing the momentum while minimizing the KE (and thus recoil).

[Strick]

I guess the rule as it stands keeps people from having to use a calculator...

Sounds about right.

[SA Friday]

I think the current formula we use is still equatable enough to represent the true recoil of the gun, and yet easier than the standard Ke formula. It's a very good in-between calculation fair to the recoil of the utilized ammo, but easy enough that we don't fry Greg Lent's (Crono-Man) aging brain.

The current formula does favor a heavier bullet when compared to the Ke formula, but this is really what shooters want and what is felt. The felt recoil of the heavier bullets compared to the lighter bullets at faster velocities feels less. The Ke formula would favor lighter bullets at faster velocities contrary to the actual felt recoil impulse.

[entropic]

As I understand it, the reasoning is twofold:

1) In ye olden days of IPSC, chronographs were expensive, few, and far between. To calibrate whether you made major or not, you shot a specific piece of steel and if it swung X inches high you made major. This measures momentum (momentum of the bullet is transferred to the steel), and not energy.

2) Also to do with steel. Momentum is what knocks them down, not energy. A minor load making a specific KE by going very fast with a light bullet might not have the momentum to knock down steel.

Measuring momentum and not Kinetic Energy is why USPSA loads tend towards heavy/slow. You're maximizing the momentum while minimizing the KE (and thus recoil).

This makes perfect sense

[XRe]

Darth's stuff is certainly reasonable/sensible. There's another reason, too, as I understand it. The forefathers of our sport were rather enamored of the .45 ACP cartridge. They set the game up to favor the .45 over anything else (remember, .40 didn't exist then...). Momentum tends to favor a bigger bullet, in this case, so the bigger caliber wins (at least, when the game began). At that point in time, it was held that the .45 was something of a death ray, and it was revered with something approaching religious dogma... (some still do... )

With all the research that's occurred since then, if someone set out to build a "game" with the same intentions, we might see an entirely different target (much smaller high scoring zones), and we'd probably see momentum not be regarded with the same importance it has now (or it would be regarded with some balance against energy, or some other thing like sectional density would come into play along with velocity). Shot placement turns out to be king, assuming a minimum ability to penetrate...

In the end, though, momentum works fine for us - and Darth's right, its a good predictor of how easily the bullet will knock over a big steel target (which is really the place power matters in the match, from a stage setup/operation standpoint).

[Guy Neill]

Going even further back, studies of "stopping power" showed that momentum was more a factor than energy. Since the early days were looked at as training for defensive use of the pistol the momentum factor was considered more important to indicate the power of the cartridge with respect to it's ability to stop an aggressor.

Guy

[Joe4d]

I dont think it had anything to do with favoring the .45ACP, it was a way of scoring the 7+1 1911 45 that the U.S. used against the 13+1 9mm Browning Hipower everyone else used. The system was pretty dang good. If you look at early IPSC championship matches, they seemed to be a toss up between the Browning shooting minor and Colt shooting major. Minor was Milspec ball ammo from a Hipower, Major was GI Ball from a 1911. The weight times velocity simply was a formula to have all the other guns / ammo basically fall in line with those two standards. The formula pretty much went out the window with double stack major pf guns. Basically minor ceased to be competitive.

But if it aint broke dont fix it, weight times mass isnt perfect but close enough and simple enough.

[Patrick Sweeney]

And kinetic energy does not square with reality, at least not before expanding bullets.

If we use Ke, consider the following:

7.63 Tokarev, 86 gr @ 1500 fps, 430 ft-lbs

9mm Parabellum, 115 @ 1150 fps, 338 ft-lbs

45 ACP, 230 @ 825 fps, 348 ft-lbs

All hail the mighty 7.63 Tokarev.

[G-ManBart]

Power (and recoil) seem to be a function of energy rather than momentum. So why isn't the power factor proportional to the square of velocity? If it were, it seems like people would generally use lighter bullets to make the PF.

Dave

I wouldn't go that far. A standard 55gr bullet out of a 22-250 going 3,785fps has a muzzle energy of 1,750ft/lbs. A standard 405gr bullet out of a 45-70 going 1,395fps has a muzzle energy of 1,750ft/lbs. Wanna guess which one is going to have a whole LOT more recoil?

[XRe]

Power (and recoil) seem to be a function of energy rather than momentum. So why isn't the power factor proportional to the square of velocity? If it were, it seems like people would generally use lighter bullets to make the PF.

Dave

I wouldn't go that far. A standard 55gr bullet out of a 22-250 going 3,785fps has a muzzle energy of 1,750ft/lbs. A standard 405gr bullet out of a 45-70 going 1,395fps has a muzzle energy of 1,750ft/lbs. Wanna guess which one is going to have a whole LOT more recoil?

That's because you're talking about conservation of momentum when you get into talking about recoil energy. "Free recoil energy", while an imperfect calculation (and not necessarily a direct correlation to perceived recoil) is the closest calculation we have.... Typical calculation (in a vacuum) would be based on the velocity of the gun at the end of the recoil cycle, if the gun were suspended by strings in a vacuum (ie, it's free to recoil) - and that's derived via. That would be: V = (b*v + c*p) / W - where V is the gun's velocity, b is the bullet weight, v is the bullet's uzzle velocity, c is the charge weight, p is the propellant gas velocity at the muzzle, and W is the weight of the gun. Then use that velocity to calculate the energy of the gun (mass times velocity squared).

The 45-70 bullet described above has over twice as much momentum as the .22-250 bullet - in a rifle of the same weight, the recoil velocity will be over twice as high (charge weight is higher in the .45-70 load, too). That velocity is then squared to come up with recoil energy, which is a lot more than double....

(not arguing, just demonstrating your point, and why bullet energy does not directly determine recoil energy ).

[entropic]

Power (and recoil) seem to be a function of energy rather than momentum. So why isn't the power factor proportional to the square of velocity? If it were, it seems like people would generally use lighter bullets to make the PF.

Dave

I wouldn't go that far. A standard 55gr bullet out of a 22-250 going 3,785fps has a muzzle energy of 1,750ft/lbs. A standard 405gr bullet out of a 45-70 going 1,395fps has a muzzle energy of 1,750ft/lbs. Wanna guess which one is going to have a whole LOT more recoil?

Touche, but momentum isn't proportional to recoil either, or there would be no less recoil with heavier bullets at a lower velocity....and I think most people will agree that in .40S&W for example, there is less recoil with a 220 and 180gr bullet of the same power factor.

[entropic]

However...after thinking about some of the things mentioned, the simple M*V power factor makes a lot more sense now

Thanks guys

Edited October 13, 2009 by entropic

[XRe]

Touche, but momentum isn't proportional to recoil either, or there would be no less recoil with heavier bullets at a lower velocity....and I think most people will agree that in .40S&W for example, there is less recoil with a 220 and 180gr bullet of the same power factor.

You're forgetting about a significant and huge part of the equation. The momentum of the powder charge (the gas is moving at 4000+ fps, depending on who's figures you use). It doesn't sound like a lot, when you're talking about a couple of grains of powder, but one grain of powder adds enough momentum to increase the PF of the whole system by 4 - I think you'd agree that a load at 170 PF is going to feel softer than a load at 174 PF...

[G-ManBart]

Power (and recoil) seem to be a function of energy rather than momentum. So why isn't the power factor proportional to the square of velocity? If it were, it seems like people would generally use lighter bullets to make the PF.

Dave

I wouldn't go that far. A standard 55gr bullet out of a 22-250 going 3,785fps has a muzzle energy of 1,750ft/lbs. A standard 405gr bullet out of a 45-70 going 1,395fps has a muzzle energy of 1,750ft/lbs. Wanna guess which one is going to have a whole LOT more recoil?

That's because you're talking about conservation of momentum when you get into talking about recoil energy. "Free recoil energy", while an imperfect calculation (and not necessarily a direct correlation to perceived recoil) is the closest calculation we have.... Typical calculation (in a vacuum) would be based on the velocity of the gun at the end of the recoil cycle, if the gun were suspended by strings in a vacuum (ie, it's free to recoil) - and that's derived via. That would be: V = (b*v + c*p) / W - where V is the gun's velocity, b is the bullet weight, v is the bullet's uzzle velocity, c is the charge weight, p is the propellant gas velocity at the muzzle, and W is the weight of the gun. Then use that velocity to calculate the energy of the gun (mass times velocity squared).

The 45-70 bullet described above has over twice as much momentum as the .22-250 bullet - in a rifle of the same weight, the recoil velocity will be over twice as high (charge weight is higher in the .45-70 load, too). That velocity is then squared to come up with recoil energy, which is a lot more than double....

(not arguing, just demonstrating your point, and why bullet energy does not directly determine recoil energy ).

Yeah, I was just trying to give the user interface portion that probably nobody would debate...what you feel. You did, however, forget one critical component in the above equations. That would be Vw, or V sub w,....the recoil velocity at which I start to whine

Edited October 14, 2009 by G-ManBart

[XRe]

That would be Vw, or V sub w,....the recoil velocity at which I start to whine

Since that one is added in, though, and not multiplied, we can safely ignore it.... as its always 0...

Actually, I really disagree with the term "free recoil energy" anyway... I mean, recoil costs me at least $1..

[Jim Norman]

anyone want to start back on a mechanical steel calibration device? With aall the math thrown about here someone ought to be able to calculate the required mass (weight for us challenged people) of the hammer and the length of a pendulum that when released and allowed to swing ninety degrees before hitting the exact center of a popper will impart precisely a 120PF blow to said steel face.

We could easily then calibrate all steel for each squad rather than once a day and calibration challenges could take place while the stage was being reset. AND we'd never have a miss or bad hit for a calibration shot again.

I am thinking a ball peen hammer and a delrin bearings axle with a leg to get the proper height. Heck when considering that we only require the calibration hit to be within the circle, one could probably just hold the pivot in your hand (with a properly designed grip), raise the hammer level and let'er fly. Ding, Steel down, or Ding, Steel not down. Very simple. I would calculate a 120-123PF since we allow a shooter to shoot a 125 and compete. And the round will lose some amount of momentum between the barrel and the steel assuming of course that the closest point we can shoot the steel is 21 feet. We should take this drop into account.

Jim

[entropic]

Building a calibration device would be a lot easier to do empirically using a 120PF load and a careful choice of calibrator mass and pendulum length. If someone did a bunch of math to figure it out, it would probably be irrelevant in reality because of all the unknowns (remaining energy of bullet fragments, inelastic collision energy loss between striker and steel, friction, air resistance, movement of pivot point if handheld etc). Just choose the right hammer head...not to light that it bounces off of poppers, and not to heavy that it keeps going in the same direction after the calibrator strikes. The ideal calibrator mass will obviously vary for poppers of different mass/height/moment of inertia, but one that works almost perfectly on larger poppers, should still work on smaller ones, but just result in a popper calibration that takes less than 120PF.

[Bill Nesbitt]

You guys with all your scientific formulas and stuff.

We calculate power factor the way we do because Jeff Cooper told us to do it that way.

[North]

You guys with all your scientific formulas and stuff.

We calculate power factor the way we do because Jeff Cooper told us to do it that way.

Hear, Hear. Now stop all of this heresy.

[Alan Meek]

From the what I was told years ago files from someone that was there with their dad in the early days, Irv Stone.

Power factor was initially divided between the 9mm/38Special and calibers that begin with a 4, (.44special/magnum .45acp)

the 9mm/38Special was minor and the .44/.45s were major.

The gamers at the time were downloading their .45s, and using 7lb springs, to velocities where you could literally watch the slide cycle.

The venerable Jeff Cooper decided that to establish the numbers for power factor, the ammo had to meet the performance (momentum) of Military ball ammo as fired out of a 1911 commander.

That was what I was told, years ago.

Alan