firearms foot pounds of energy VS real foot pounds per second

[Valiant Champion]

Maybe you guys who have some knowledge of physics can explain to me why firearm cartridges are measured in "ft lbs of energy" i.e.

mass in grains x velocity x velocity / 450240 = ft lbs in firearms

actual momentum _____mass in lbs ( grains / 7040 grains to one pound) x velocity = ft lbs

The second equation is the one that determines a projectile or objects momentum when it hits and object and transfers its energy over. Say for instance a 12 guage shotgun slug

440 grains / 7040 x 1600 fps = 100 ft lbs of energy / theoretically this should move a frictionless 100 lbs object 1 foot.

In stark contrast the same projectile is rated as having about 2500 ft lbs of energy using firearms terminology ft lbs of energy.

Another example is that a .308 with 150 grain bullet traveling at 2800 fps.

150/ 7040 x 2800 = roughly 59 ft lbs of energy

However in firearms terminology it generates 2600 ft lbs of energy.

More than a 12 guage slug.

Yet we know that a 12 guage slug is far more powerful momentum wise. recoil is nearly twice as hard due to the effects of Newtons law (for every action there is an equal and opposite reaction).

Then we introduce Taylor's KO formula. He was an expert dangerous game hunter and wanted to find a way to calculate just how much stopping power a bullet has.

His calculation

diameter of bullet in inches * (bullet weight in grains / 7040 ) * velocity = KO factor

Taylor obviously thought that bullet momentum in ft. lbs. was a more realistic than the ft lbs used in common firearms terminology.

So you can see why I am somewhat confused as to why the firearms industry and media relies on "muzzle energy" to measure cartridge performance aside from being able to print staggering numbers for the eye candy.

Am I in error to have this opinion?

[Adar]

Maybe you guys who have some knowledge of physics can explain to me why firearm cartridges are measured in "ft lbs of energy" i.e.

mass in grains x velocity x velocity / 450240 = ft lbs in firearms (1)

actual momentum _____mass in lbs ( grains / 7040 grains to one pound) x velocity = ft lbs

Your comparing a mass*velocity*velocity (=energy) with a mass*velocity (=momentum).

I think you've misssed this becuase you put both = ft lbs which is wrong. The energy equation (1) should yeld (lbs*ft^2)/s^2 not ft*lbs. Likewise you final expression of (2) should be (lbs*ft)/s. This show that you in one case have calculated the kinetic energy of the bullet and in the other case the momentum of the slug.

My guess is that the different measurements between slugs and bullets is caused by how they behave when they hit something. A shotgun blast is expected to transfer it's entire momentum to the body it hits (ie all the fragments stop somewhere inside the body). A shotgun fragment also much more quickly looses it's velocity which mean that you might want a measurement less reliant on velocity.

A bullet is however much more likely to go through the body and therefor won't transfer it's entire momentum to it. Neither will it transfer it's entire kinetic energy (quite obvious since it's still moving after leaving the body) but kinetic energy is normally a more commonly used standard of measurement than momentum.

You also have this beautiful concept of tradition. It is normally very difficult to overturn an established measurement. Your for example still using lbs, I'm using the metric system which simplifies [mass in grains] x velocity x velocity / 450240] into [(kg*velocity*velocity)/2]. Likewise, when I'm doing particle physics am I using Joule as my measurement of energy. But in thermodynamics kcal (kilocalories) is used becuase it have always been that way and the whole system is built around this way of measuring (1kcal = 4184 Joules).

Basicly it's easier to teach all newcomers a different way of counting that it is to reform the whole field.

Edit:Taylors KO factor is probably the best measurement of how dangerous a bullet is. The problem is that most people doesn't know what the number represent. Most people probably doesn't really know what 5000 J means for a firearm cartridge, they do however understand that it will hurt more than the 4000 J cartridge.

[Sphere]

This is a big mess, and is quite flawed. Most notably, equating momentum and energy, but also somehow equating pounds-mass and pounds-force which are not the same thing (1 lbf = 32.2 lbm (ft/s)). To make a long story short, here is a list of acceptable units for Energy and Momentum in Imperial Units.


Energy

ft x lbf (the previous poster was mistaken, lbf-ft ~ N-m and is the common unit for Energy)


Momentum

(ft/s) x lbm

(ft/s) x Slug (a slug is the Imperial equivilent of a kilogram, where 1 lbf = 1 slug (ft/s2))

(s) x lbf (Goofy, I know, but I checking my unit conversions twice)


When doing a typical conservation of momentum equation, you can use lbf-(ft/s) because the 32.2 factor will cancel out, but technically that isn't momentum (mass x velocity) it's (force x velocity). Its like doing a conservation of momentum equation in N-(m/s) instead of kg-(m/s) which isn't done, but will yeild the correct answer.


But I think the root of the problem is that energy and momentum are getting equated somehow, when they are two totally different things. Both increase with more mass and higher velocity, but energy increases by; Mass x (Velocity)^2 while momentum increases by; (Mass) x (Velocity). Momentum is useful because it can explain the results of collisions, but energy can be used in many more situations.