Physics and Firearms

This post could be subtitled "Little Guns Suck", because that's the argument I am making. Instead of me saying that outright, I'm going to use some basic math to support 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 everyday things. It allowed people to predict things, which I've always thought was quite handy. 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. So often I find non-shooters want to buy a little gun because they assume little = easy. Often the opposite is true. 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 (F), Mass (M), and Acceleration (A). The equation explains 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 with particular values, but use it to illustrate why light guns recoil more.

For purposes of this discussion I'll choose a value that is close to the most common handgun cartridges. We'll give that a value of 300, which may be a little low or a little high depending on the exact cartridge you shoot. Any cartridge, like 9mm or .38 Special, is going to generate a certain amount of acceleration when fired. That powder charge is going to accelerate a bullet forward out of the barrel and also accelerate the gun back into your hand. 300 meters per second squared is within the ballpark of 9mm, .38 Special and .380, so I'll stick with that nice round number for this exercise.

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 * 300
or
F = 3,000

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, 3,000.

3,000 =( 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

3,000 / (Mass of the gun) = (Acceleration or recoil)

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

3,000 / 2 lbs = 1,500

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

3,000 / 1 lb = 3,000

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. I will state that again, since it's the whole point here:

A gun that weighs half as much will kick twice as much

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 my original point. Little guns kick more. 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 kick. In some cases a lot more felt recoil. 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. If you are a new shooter, it will likely take more practice to shoot well with a small, light gun, than a larger, heavier one. Choose accordingly!

FYI- this is a repost with edits from my old blog.