Physics and Firearms


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So you are into reloading and you wonder how well that little package with 77 grains of IMR 4350 powder behind a 300 grain round nose, full metal jacket bullet will do. Well, you can do two things, a little bit of physics calculations, or go out and touch it off, hoping that it doesn’t explode in the barrel! I would choose to do a little physics myself… By using some basic physics equations, you can figure out just about any part of the rifles ballistics data. For instance, if you know a few variables, you can predict range with physics, or if you like you can figure things like drag on the bullet, pressure and expansion values inside the gun, on the bullet and much more, all from physics.

So, lets take a look at both the potential and kinetic energies of the .338 Winchester magnum. I will use a load given by the Winchester Reloading manual, which can be found online at:
http://www.winchester.com/reloader/index.html

This load is a 300 grain bullet, using 59.8 grains of Winchester 760 powder, and this gives a muzzle velocity of 2285 ft/sec.

For potential energy we know that PE=mgh, where PE= Potential Energy, m=mass, g=acceleration due to gravity, and h=height.

So for a 300-grain bullet, the potential energy is calculated by first finding the mass. To do this, take 300grains/7000grains/pound. This gives you a value of .042857lbs. Then we need to convert pounds to slugs (slugs are the units of mass…) .042857lb/32.2ft/s^2=.001331slugs. Now we can calculate the potential energy of our 300-grain bullet. We will assume that h=six feet, since that is roughly the height of the barrel when I shoot from a standing position. So, since PE=mgh, we get PE=(.00133slugs)(32.2ft/sec^2)(6ft)=.256956lbft. The answer is pretty much nothing and so we can pretty much ignore the potential energy of that bullet sitting at six feet in the air, but now lets look at the Kinetic energy of this bullet when shot. Since this bullet will be twisting when it flies, it will have rotational kinetic energy, but I really don’t want to get into those calculations and from what I have read, the amount of energy given by rotation versus that of the charge behind the bullet is really insignificant so I will only calculate the KE as if the bullet is not rotating. The formula is KE=1/2mv^2.

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We know the values for m and the muzzle velocity so all we do is plug in numbers, pretty simple! KE=(1/2)(.00133slugs)(2285ft/sec)^2=3472.11ftlbs! That is a lot of energy for that little chunk of lead! So with just a little bit of physics we have calculated the potential and kinetic energies of a .338 Winchester magnum.

So you have your rifle or pistol at the range and you wonder what type of range you can expect to get. If you know the velocity as the bullet leaves the barrel and the angle at which you fire the gun, you can calculate range. Yes it is that simple! The range equation for projectile motion is R=(Vo^2/g)sin2q,where R=Range, Vo=Initial Velocity, g=Acceleration due to gravity, and q is the angle at which the gun is fired. So for our .338, fired at an angle of 1/2 degree, we would expect a range of: R=((((2285ft/s)^2)/(32.2ft/s^2))*(sin(2(1/2))))=2829.9ft! That is impressive range. Since we know that firing an object at 45 degrees will give you maximum range, we can calculate what our .338 would do. Using the range equation, we get a range of 162,149.85ft or roughly 30 miles! This is of course neglecting things such as drag, but it is still impressive figure.

Using Winbalistics, the trajectory for my .338 Winchester Magnum with a 300-grain bullet, and in ideal conditions (standard temp, pressure, no wind... this of course NEVER occurs when you are out in the woods with the sight on a moose!!!) So as you can see from the data, this rifle is sighted in at 200 yards, and a significant drop occurs at ranges past 250 yards or so. So while the range calculation may give you a big number, this shows that the effective range is much smaller. If you are interested in the Winballistics program, it can be found at http://thor.prohosting.com/~byeater/wbdwnld.htm

For some very excellent ballistics calculations, check out http://www.lascruces.com/~jbm/ballistics/ballistics.html. In here you will find calculations for almost every aspect of small arms ballistics! Even if you don't understand all of what is involved in ballistics, this site lays it out very nicely and tells you exactly what you are calculating, and how. I have to say that I am impressed with the amount of information in their ballistics area. I haven’t yet spent much time on their site, but they have software and many other useful resources too, so for the hand loader out there, I would recommend their site as a starting point for gathering information.



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