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Recoil 101 (Page 3) |
Lets put some simple numbers into these equations to illustrate. If we have a rifle that weighs 7 pounds and there are 7000 grains in a pound then the rifle weighs 49,000 grains. For simplicity sake lets say that the rifle is a .308 shooting a 150gr bullet. Rather than get into the exponents and acceleration constants, we'll give the bullet a generic acceleration value of 100 since we're not specifying units of measurement, just figuring relative values. Therefore, if we put this information into the ma[rifle]=ma[bullet] equation from last section we get the following: 49,000(a)=15000 a[rifle]=0.306 or 0.306% of the acceleration of the bullet (0.306/100) It is now obvious how our previous statement about changing the weight/acceleration of the bullet or the weight is going to change the acceleration (recoil) of the gun. But wait, there is more forces involved in recoil than just the bullet acceleration. Although the propellant is burning it is retaining most of its mass, it is only changing from a solid to a gas. There is also a secondary acceleration of the propellant once the bullet leaves the muzzle. Once the bullet is out of the way, the propellant will suddenly accelerate a lot faster forward, creating more recoil force rearward. Since the forward acceleration forces are going to be equal to the rearward acceleration forces, we can reasonably calculate how much these additional factors are going to change the recoil. We will make a very conservative estimation that the propellant is going to make a 25% acceleration rate increase once the bullet leaves the barrel but only for 1/4 of the previous time, therefore we will list that force seperately in the equation to keep things simplified. First we have to account for the forces. ma[rifle]=ma[bullet]+ma[propellant]+.25m(1.25)a[propellant 2nd] We're going to figure on a 150gr bullet again and 50gr of propellant. 49,000a=15,000+5000+1562.5 49,000a=21,562.5 a[rifle]=0.440 or 0.44% of the acceleration of the bullet (0.440/100) In this scenario there is a 43.8% increase in rearward acceleration (recoil) over what would be created by just accelerating the bullet. To learn how a muzzlebrake reduces this recoil, advance to Recoil 102. |