Measuring Effectiveness of Cartridges: Kinetic Energy

In our last post, we discussed the basics of cartridge effectiveness. In this post, we will discuss one of the methods used to measure cartridge effectiveness, by measuring the kinetic energy of the bullet.

Some of you may recall that in physics class, we were taught that kinetic energy is the energy possessed by a body in motion. Therefore, a bullet in motion has a certain amount of energy in it, given to it by the burning propellant. When the bullet hits a target, it slows down and transfers the kinetic energy onto the target.

The formula for kinetic energy that we learned in physics class is:

where
E_k = Kinetic energy of the bullet
m = mass of bullet
v = velocity of the bullet.

In SI units, if the mass of the bullet is in kilograms and the velocity of the bullet is in meters/sec, then we have the energy of the bullet in joules. Similarly, in imperial units, if we have the mass in pounds (lb. or slugs), and velocity in feet/sec, then we have the kinetic energy in foot-pound force (ft-lbf).

In some American firearms related articles, the kinetic energy is also defined as:
E_k = m * v² / 450240
where
m = weight of bullet in grains
E_k = kinetic energy of the bullet in foot-pounds force

So why is this formula different and where did this 450240 come from. Actually it is simply a reworking of the previous formula.

Recall that 1 grain = 1/7000 pound force (lbf)
Also, acceleration due to gravity is roughly 32.16 feet/sec². Therefore, 1 pound force (lbf) = 1/32.16 pounds mass (lb.)
Therefore, if we measure our weight in grains, we need to convert it into lb. first, which works out to:
Mass in pounds = weight in grains / (7000 * 32.16) = weight in grains / 225120
Now applying this to the formula E_k = 1/2 * m * v², we can write this as:
E_k = 1/2 * weight in grains/225120 * v²

which can be further simplified into:
E_k = weight in grains/450240 * v²

The listing below shows the kinetic energies for some common pistol cartridges in both imperial and SI units.

Average kinetic energies for common cartridges

Cartridge	Kinetic energy
	ft-lbf	joules
.380 ACP	199	270
.38 Special	310	420
9 mm Luger	350	470
.45 ACP	400	540
.40 S&W	425	576
.357 Mag	550	750
10mm Auto	650	880
.44 Mag	1,000	1,400
.50 AE	1,500	2,000

Calculations of the above were taken from wikipedia.

Measuring the kinetic energy of bullets tends to favor bullets of higher velocity and lower mass, because the kinetic energy increases as a factor of the square of the velocity. Measuring the cartridge effectiveness by calculating the kinetic energy does not take into consideration factors such as diameter of the bullet, shape of the bullet, physical characteristics of the bullet (solid vs. hollow point, round nosed vs. flat nosed etc.). Some manufacturers tend to favor this method as it has a basis in science, as well as the fact that it is easy to measure the velocity of the bullet and its mass.