Muzzle energy is the measured energy in translational kinetic energy (Et) imparted to a projectile or bullet at the muzzle. Muzzle energy is also the same energy as kinetic energy (Ek), recoil energy, down range energy or impact energy. The difference between these five energies is the location of the body in motion: your recoiling firearm rearward, a bullet just exiting the muzzle, a projectile moving down range or impacting a target and kinetic energy being all the above. Muzzle energy is expressed by the Joule (J) or Foot-pound force (ft-lbf).
Calculating Muzzle Energy
Muzzle energy is calculated by using the known velocity and weight of a projectile. Here are the two formulas for a calculation of, or more correctly the measurement of muzzle energy.
In SI (metric) units of measure
Muzzle energy = ½ x bullet mass x bullet velocity 2 / 1000.
- Firearm: Weatherby Mark V chambered in .378 Weatherby Magnum.
- Projectile: monolithic solid type bullet weighing 19.5 grams with a muzzle velocity of 884 meters per second.
- 7619 J = 0.5 x 19.5 x 884 2 / 1000.
In English units of measure
Muzzle energy = bullet mass x bullet velocity 2 / ( 2 x dimensional constant x 7000 ).
- Firearm: Weatherby Mark V chambered in .378 Weatherby Magnum.
- Projectile: monolithic solid type bullet weighing 300 grains with a muzzle velocity of 2900 feet per second.
- 5603 ft-lbf = 300 x 29002 / ( 2 x 32.163 x 7000 ).
The energy of a projectile is a calculation based in the acceleration of gravity here on earth, which is 9.80665 meters per second or 32.1739 feet per second.
Whether you drop 1 ounce lead ball, throw it or shoot it from a gun, if it has the same velocity it will have the same energy. The difference is throwing and shooting are artificial means of accelerating the lead ball where as dropping it is a natural means of accelerating it. Also, not only will the lead ball possess the same energy, but it will possess the same ability to penetration.
The problem with trying to apply energy to penetration and or effectiveness is that energy is a base unit or constant. If using a bullet as an example, it does not matter how big the bullet is (size in caliber as long as it still weighs the same) or how big the target is. The energy at the muzzle, downrange, or at the point of impact will be the same. However, in this case if the bullet is bigger or smaller in caliber then the penetration will be different due to the change in sectional density. Again, the bullet weight remaining the same.
There are four factors in calculating applied energy: projectile energy; projectile construction; projectile sectional density and target construction. Typically the projectile's energy is known due to weight and velocity. However, many times a projectile's construction and projectile's sectional density is not known or well understood. It is rare, other than in military or governmental applications that the target's construction known.
For these reasons (which are infinite) no firearm or ammunition manufacturer will specify a particular bullet or bullet/cartridge combinations ability to work on a particular target. It is then left up to an individual to make their own conclusion on the effectiveness or potential of a bullet/cartridge combination within a specific gun by including all four factors.
The difference between the Joule and Foot-pound force
The Joule is a product of mass and velocity in SI units of measure. The equation; half mass multiplied by the velocity squared may be that of the classic statement for kinetic energy, but it is not the equation used. Kinetic energy is energy of motion and applies to many disciplines within physics and engineering. The Joule as it pertains to projectiles in motion and specifically muzzle energy is translational kinetic energy from Newtonian mechanics.
The translational kinetic energy equation as written in SI is 0.5 x bullet mass x bullet velocity 2 / 1000. The equation contains the four units of measure within it that gives a projectile its measure for the Joule: kilogram; meter; kilogram force and second. When using translational kinetic energy equation as written in SI, there is no need for a dimensional constant (kilogram force); it is assumed to be there. We always assume the kilogram, meter and second are there because we know the bullet weight (grams) and velocity (meter per second). The 1000 that is added into the equation at the denominator is to set the equation equal to kilograms when using grams as the projectile weight.
The Foot-pound force is a quotient of half mass time velocity squared divided by the dimensional constant. The translational kinetic energy equation as written in English is bullet mass x bullet velocity 2 / ( 2 x dimensional constant x 7000 ). The equation also contains the four units of measure within it that gives a projectile its measure for the foot-pound force: pound; foot; pound force, second. Again, we always assume the pound, foot and second are there because we know the bullet weight (grains) and velocity (feet per second). However, we do not assume the dimensional constant. Along with the 7000 that is added into the equation to set the equation equal to pounds when using grain, we also add into denominator the dimensional constant. This dimensional constant (gc) is 32.163. This particular numerical coefficient is based in the local acceleration of gravity rather than the standard acceleration of gravity.
Furthermore there is the number 2 as the first numerical coefficient with in the denominator. This “2” represents the word “half” in the classic kinetic energy statement. In reality the “2” is actually the average velocity of the falling body within the original experiment and equation for kinetic energy (PE = wz); see the above photo. In the SI equation the “2” is represented by its reciprocal within the numerator of that equation as “0.5”.
Also, the numerical coefficient of 32.163 is normally used in the United States as the dimensional constant for all advertised muzzle energies. For this reason, the muzzle energy may differ slightly if converted from published SI units of measure to published English units of measure or vice versa. Remember, SI is equal to 32.1739, based in the standard acceleration of gravity and English as used in the United States is 32.163, based in the local acceleration of gravity.
Another difference in the Joule and Foot-pound force can be seen when observing them by their conversion factors. This will also emphasize that muzzle energy and its associated energies are a product of the gravitational pull of Earth.
The conversion factors that represent the four units of measure within the translation kinetic energy equation are: m = kilogram (kg) and pound (lb); d = meter (m) and foot (f); t = second (s); F = kilogram force (kgf) or Newton (N) and pound force (lbf):
- 1kg = 2.204623lb
- 1m/s = 3.28084ft/s
- 1lbf = 4.448201kgf or N
Then we multiple these three conversion factors together, to yield the standard acceleration of gravity:
- 2.204623 x 3.28084 x 4.448201 = 32.1739
The reason we don't see the dimensional constant of 32.1739 is because it is held within the SI units of measure above the divisor bar in the SI equation. When we change to English units of measure here on Earth were pull the numerical values for SI units of measure below the divisor bar. In doing so, this gives the pound, foot, second and pound force its correct value.
By pulling the dimensional constant below the divisor bar you can also calculate the muzzle energy and recoil energy of your gun on any moon, planet or star within the known universe. This is done by multiplying the dimensional constant by difference in the Earth's gravitational pull and another celestial bodies gravitational pull. Since there is no difference in the Earth's gravitational pull and itself the base value of 32.1739 stays the same.
The Origins of Foot-pound force
Energy is the ability to actively do work on/or between an open or closed system. Within these two systems, energy can be potential, kinetic or translational. Energy is a both a non-conserved quantity (open system) and conserved quantity (closed system).
Kinetic energy is the general statement and Translational kinetic energy is the specific statement. The measurement for translational kinetic energy is called, "Foot-Pound force". Kinetic energy and translational kinetic energy are defined as the energy possessed by an object due to its motion and are mathematically stated as:
Ek = 1/2 mv2
Et = mv2 / 2gc
When restated as the original kinetic energy equation, then factored and reduces this equation will reveal the origins of foot-pound force.
The kinetic energy equation restated:
- Et = wz.
Then w and z are restated:
- Et = mgvt / gc
Then w and z are factored:
- Et = mdFt2dtt / t2mdt2
Now, the fully factored term of wz is reduced by cross cancellation:
- Et =
mdF t2dtt/ t2mdt2
Finally leaving the fully reduce equation to is only two factors:
- Et= dF
- Et = ft x lbf
Therefore, translational kinetic energy and its quotient is Foot-Pound force:
- Et = ft-lbf = Foot-Pound force