More info to muddy the water:
http://www.pinnaclearmor.com/new/ballistic_chart.html
No offense, but I must say that explanation in terms of F=Ma made me chuckle. It was sort of in the right direction, but not exactly good physics.
First off, due to the frictional loss of velocity, the bullet will have less kinetic energy when it arrives at the target than when it left the barrel. KE = (1/2) * m * v ^ 2.
Remember we’re not merely dealing with a force (during the firing of the rifle and the impact of the projectile), but we’re dealing with a force exerted over a distance. That is work. Work is defined as the dot product of the Force vector with the direction vector which can also be written as W = F * d * cos(angle_between_the_vectors). In our case, all of the forces are in the same direction as the movement, so W = F * d.
Now, work is also equivalent to the change in kinetic energy. We will assume that after the bullet impacts the vest, it no longer has any velocity left, and therefore no kinetic energy after impact. That allows us to equate the kinetic energy of the bullet with the work done in stopping the bullet. KE = F * d.
Let’s throw out the small amount of energy lost due to air friction (at close ranges) and say that the KE of the bullet at the muzzle equals the KE of the bullet at the vest.
Because the bullet is at rest before firing, the work done in accelerating the bullet out of the muzzle is equivalent to the KE of the bullet at the muzzle, which is equivalent to the work done by the vest to stop the bullet.
Now, let’s call F1 the force of the gun powder propelling the bullet. Let’s call d1 the distance over which F1 operates, which is the length of the barrel. F2 is the force the vest exerts to stop the bullet and d2 is the distance over which the vest moves while exerting that force.
Using our mathematical reasoning, F1 * d1 = F2 * d2. Now let’s play with some real numbers:
Let the rifle barrel be 21 inches long. Say that the combined movement of the vest deformation and the reward motion of the person being shot is 3 inches by the time the bullet comes to a complete stop.
21 / 3 = 7. Therefore, the force of the vest stopping the bullet is 7 times larger than the force exerted on the shoulder of the shooter.
Also keep in mind that the cross-sectional area of a .30 caliber bullet is Pi*(0.3)^2 = 0.283 square inches. The surface area of butt of the rifle is probably on the order of 10 square inches. This means that there is about 250 times the pressure exerted on the small area of the vest than there is on the shooter’s shoulder. (Pressure is force per unit area.)
Now you can start to see why shooting your M1A doesn’t wound your arm, but the flesh of the target you’re shooting at is damaged severely.
The vest must stop the bullet from entering into the body and must spread out the force of the bullet across as much area as possible. After seeing these numbers, it is entirely believable to me that a good vest could stop a .308..... But it will hurt like hell.
Now let’s look at “knock down”. It’s 3 AM and I don’t feel like getting into momentum, impulse (a force exerted over time), and integral calculus, so I’ll make this simple.
The force exerted on the shooter is spread out over a longer time than the force exerted on the target. So even though the target gets 7 times more force, that force is probably 7 times shorter in duration.
F = M * a. Therefore, a greater force leads to a greater acceleration (i.e. the body of the target is moved by the bullet’s impact). However, the time over which the acceleration operates is very short. How quick does a bullet stop when it hits a brick wall? Therefore, I would expect that a brief but strong force to jar the target’s body. It’s hard to say if this is enough to knock someone over, but I think that the force is so brief that it would be like a jaring sensation. It might have more of a stunning effect on the target. I think that if the target is “knocked” over, it is because of their own reflex reaction, not because they are pushed over from the force of the bullet. Perhaps if the target was in a position to be tipped over easily, it would be “knocked” over.
All of this typing and figuring makes me want to go shooting.... at paper targets or mannequins wearing Level III and IV vests.
good night.... errrr morning.