Thursday, December 29, 2011

Physics and Firearms

This post should be subtitled "why little guns suck", because that's basically the theme.  Only instead of me saying it, I'm going to use math to "prove" that point.  I know somewhere my high school math teacher is saying "See!  You will use math in the real world!".  I hope I've made his day if nothing else.

As a student you may or may not have loved physics.  Personally I loved it.  It used math to explain why things happened the way they did.  It allowed people to predict things, which I've always thought was super cool.  So I'll be sharing my love of applied math with you in an article about why maybe that cute little lightweight handgun may not be the best choice for a starting shooter.  We have to start with an equation, but it's super basic.

F = M * A

Hey, that's pretty easy right?  We only care about three things here.  Force, Mass, and Acceleration.  So, what the equation states is that Force (in this case the force you feel in your hand called recoil) is equal to Mass times Acceleration.  We don't even have to work out the equation, but use it to illustrate why light guns recoil more.

For purposes of this discussion I'll pick a mythical cartridge that offers an acceleration.  We'll give that a value of 100.  A cartridge, like say 9mm or .38 special, is going to generate a certain amount of acceleration when fired.  That powder charge is going to propel or accelerate a bullet forward out of the barrel and also accelerate the gun back into your hand.  Rather than break out actual values like 322 meters per second squared, we'll just call it 100.  So whatever cartridge we are going to shoot in these guns generates an acceleration of 100.

The primary purpose of that acceleration is to move the bullet.  An average handgun bullets weighs around 10 grams (10 grams equals 160 grains or so).  So if we plug that in as the Mass value, we end up with:

F = 10 * 100
F = 1,000

Well great, we know the force on the bullet.  That's not the answer we wanted.  To get that, we have to work that same equation again.  Newton's third law states "Every action has an equal and opposite reaction".  OK, we can work with that.  The Force that pushes the bullet forward is going to also push that same Force back into your hand.  To figure out how much that gun is pushing on your hand, we just need to do that equation again from the perspective of the gun, not the bullet.  We know the force this time, 1,000. 

1,000 =( Mass of the gun) * (Acceleration or recoil)

We'll need to divide both sides by the Mass value to get the Acceleration alone on one side

1,000 / (Mass of the gun) = (Acceleration or recoil)

If a gun weighs two pounds, like, say a Sig P226, we'd end up with:

1,000 / 2 lbs = 500

If a gun shoots that same cartridge but only weighs one pound, like a Ruger LC-9, we get:

1,000 / 1 lb = 1,000

The specific numbers don't matter here, obviously I calculated the bullet's weight in grams and the gun's weight in pounds.  I could convert pounds to grams for the gun weight but then my equations aren't pretty any more.  The point I'm making is the gun that weighs half as much is going to recoil (or kick) twice as much.  That's a big deal.

This is compounded by the fact that lots of guns that weigh less are smaller as well.  If a gun has a grip that's 1 inch wide by 4 inches it's going to spread it's recoil out on that whole area, so 4 square inches.  If the gun has a grip that is 3/4" wide by 3" tall it's going to spread out it's recoil to a smaller area, in this example 2.25 square inches.  So not only does the smaller gun recoil more, that recoil is focused at a smaller area making it feel like it's kicking more.  The larger gun spreads out the recoil over your whole hand, the smaller gun focuses it on certain spots.

Take the same analogy and apply it to a rifle.  If you have a pistol that weighs a pound that fires 9mm and compare that to a rifle that shoots 9mm that weighs 5 lbs you can imagine it will be more pleasant to shoot the rifle.  

Now that you've suffered through this explanation, I can make the original point.  Little guns kick more.  So if you are browsing the gun counter at your local shop thinking "This gun is nice and little and easy to hold.", keep in mind that lighter and smaller means more ouch.  In some cases a lot more ouch.  Little guns can be pretty unpleasant to shoot, but they are handy to carry around.  Each person has to find a compromise they are comfortable with.  But if it's a gun you plan on shooting a lot you will appreciate some extra weight and/or size.

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