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Study of Mass; Slug Unit, Moment of Inertia, Drag Force, Velocity, Bullet Penetration, Momentum & More

Mass is the amount of material of an object. Pounds are a weight unit, i.e. mass in a gravitational field. Most formulas that are involved in shooting compensate and convert the weight to the mass unit, the slug. The international SI unit is based on the kilogram. It is either milligrams (1/1000th of a gram) or centigrams (1/100th of gram). The kilogram and its derivations are a mass unit and no conversion is necessary.

Mass Moment of Inertia

But the unit of mass is also the unit of inertia. Most think of inertia according to Newton’s first law of motion and inertia in the reference frame of getting something to move. But it also works on something that is already moving. Newton’s first law states that an object either remains at rest or continues to move at a constant velocity unless acted upon by a force.

Drag Force Example

As that bullet plows through the air, it experiences drag. Drag is a force, hence the importance of a higher mass for that projectile to retain more velocity, all factors but perhaps velocity being the same. Heavier bullets in the same cartridge will tend to have lower muzzle velocities. Chamber pressures must be kept with the limits set for that cartridge. It takes more powder to create the pressure to overcome the rest inertia of the bullet. To keep pressures within limits results in the heavier bullet having a drop in muzzle velocities for the cartridge. Take a .30 caliber rifle. The muzzle velocity for a 150-grain bullet from a .308 Winchester is peaks out in most loads between 2700- 2800 feet per second (fps). Whereas a 200-grain will move out at about 2400 fps. In the US we tend to use Imperial units of measure. Powder and bullets are measured in grains (1/7000th of a pound), velocity is in feet per second and range is in yards. The SI units would be grams for bullets and powder measure and the meter for velocity and range. Because a heavier bullet has more mass it can better buck the air on its travels. Given similar profiles in bullet shape, the heavier bullet will usually shoot flatter than a lighter projectile, even if the muzzle velocity for the heavier one is lower than the light one.

Bullet Penetration

Another factor of mass and inertia is that the bullet will penetrate deeper into the target. This is important for the hunter. Momentum (ρ) is the mass(m) times the velocity (v) or ρ = mv. It is the momentum that is the factor that determines penetration, both air and target. As the game weight goes up so does the weight of projectile that is recommended. After all dangerous game cartridges usually couple moderate velocities with big, heavy bullets. After all you don’t want to hunt bear with a .223 Remington. You want the most you can carry if hunting big dangerous critters and, in all cases, you want clean humane kills. What it comes down to, you will want 150 grains for mule deer and 180 – 200 grains for elk in that .30 caliber or a larger caliber.