November 26, 2018
By Brad Miller PhD
The amount of recoil we feel is determined by bullet velocity, bullet weight, and gun weight. Faster velocity means more recoil. Heavy bullets produce more recoil than light bullets when traveling at the same speed. Lightweight guns kick harder than heavy guns with the same ammo. No surprises here. There is one more thing we have to take into account that you might not have thought about: the gunpowder.
Gunpowder contributes to recoil force, and it’s not just that more gunpowder pushes the bullet faster and the bullet’s additional speed creates more recoil. No, the gunpowder’s weight contributes to the recoil force.
Here’s what this means. The mathematical formula that calculates recoil force requires four values: the bullet’s speed, the bullet’s weight, the gun’s weight, and the gunpowder’s weight. Why the gunpowder weight? Because the gunpowder comes out of the barrel, too. Well, more specifically, it’s the gas produced by the burning gunpowder.
The gas is considered part of the ejecta—that is, what exits the barrel along with the bullet. This arises because of the principle of conservation of mass, which means the weight of everything coming out of the barrel must be included in the calculation. This means the 230 grains of bullet weight plus the 6 grains of powder that propels it, for a total of 236 grains, every time you squeeze the trigger on your .45 ACP pistol.
The gas exits the barrel at very high speed. In fact, it travels faster than the bullet. Once the bullet exits, it’s like uncorking a bottle of champagne; the gas pressure in the barrel is very high and blasts out at terrific speed. For this reason, the gunpowder has a greater contribution to recoil than would the same weight simply added to the bullet. For example, 10 grains of powder produces more recoil force than 10 grains of bullet. That’s because the gas exits faster than the bullet.
How much more force does the gas have than the bullet? That’s a good question. There is some disagreement about what value should be applied to the speed of the escaping gas. Some folks use 4,000 fps for small arms, 2,000 fps for blackpowder, and 4,700 fps for cannons. Another approach is to use the propellant’s speed as some proportion of the bullet’s speed. That value is generally considered to be between 1 and 2. The SAAMI recommendations are 1.25 for long-barreled shotguns, 1.5 for handguns and average-length shotguns, and 1.75 for high-power rifles. To give an example, if you use the 1.5 proportional speed, and the bullet exits at 1,000 fps, then the gas would exit at 1,500 fps (1,000 times 1.5).
Let’s go back to the .45 ACP example. You have a 230-grain bullet and 6 grains of powder. If we use the 1.5 value for the gunpowder, its new weight value is now 9 grains. Let’s do the math. First, let’s start without including the gunpowder weight. A 230-grain bullet exiting at 850 fps in a 2.5-pound gun produces 4.85 ft-lbs of recoil. Now let’s add the gunpowder, but in this case, let’s only give it a weight factor of 1.0. That is, 1 grain of powder is like 1 grain of lead. Now it produces 5.11 ft-lbs of recoil, the same as a 236-grain bullet without adding in the powder weight. If we now give the powder its 1.5 weight factor, it produces 5.24 ft-lbs of recoil, the same as a 239-grain bullet without adding in the powder weight. See how that works?
One might think that gunpowder doesn’t add that much to recoil, and in this example, it doesn’t. In the case of a 230-grain bullet at 850 fps with 6 grains of powder, the powder accounts for 7.4 percent of the recoil force. That’s not a lot. But the powder weight varies depending on which gunpowder you use. If you use a different gunpowder that pushes the same 230-grain bullet to the same 850 fps, recoil force can go up or down depending on how much powder is required.
The fifth edition of the Sierra loading manual lists 23 powders for 230-grain bullets in the .45 ACP. The powder that requires the least weight to push a 230-grain bullet to 850 fps is Bullseye with 4.9 grains. With this load, the powder accounts for 6.0 percent of the recoil. The powder that requires the most weight is Accurate No. 7 at 10.3 grains. Using this powder, the recoil goes up, and the powder now accounts for 12.1 percent of the recoil.
The .45 ACP doesn’t use much powder, but other handgun cartridges do. Full-house .357 Magnum loads can use up to 20 grains of powder, the .44 Magnum up to 30 grains of powder, and the .500 S&W up to 50 grains of powder.
How much the large powder weights contribute to recoil depends somewhat on the bullet weight and velocity, and it isn’t always simply that larger calibers, which require more powder, will result in attributing a greater percentage of the recoil to the powder. For example, in handgun cartridges, the .327 Federal Magnum might use a powder that contributes to 29.5 percent of the recoil force, where the .44 Magnum’s powder might contribute only to 22.1 percent of its recoil force.
Let’s take a look at a rifle caliber, where you have a case that holds a lot of powder with a relatively light bullet. With the .223 Remington, a load for a 55-grain bullet at 3,000 fps might require 25 grains of powder. If we multiply the powder weight with the recommended 1.75 powder factor for rifles, that 25 grains of powder is now equivalent to 43.75 grains of bullet weight. Adding that to the bullet weight, we get 98.75 grains of mass exiting the barrel. The math tells us that the powder accounts for 68.9 percent of the total recoil force. The powder contributes more to the recoil force than the bullet!
There are some interesting surprises in the rifle calibers. The .17 Remington’s gunpowder contributes to a whopping 89.8 percent of its recoil force. I didn’t expect that. Compare that to the .375 H&H Magnum, a large case that holds lots of powder, where the powder contributes to 51.9 percent of the recoil force. The contrast seems odd, but it tells us a lot about what’s involved in determining recoil force. Bullet weight and speed are big players, but so is the gunpowder.
The accompanying chart show loads for several handgun and rifle calibers to demonstrate how much of the recoil force is solely the effect of the powder’s weight. There are simply too many different powders and bullet weights used in a given caliber to say that gunpowder always contributes “X” percent to a caliber’s recoil force. The powder, bullet weight, and velocity in the chart represent only one combination for that caliber. It doesn’t represent the full range of recoil that can be attributed to the different powders and bullet weights that caliber might employ. But they demonstrate that powder can have a large effect on the recoil that we deal with in our hand or shoulder.
If you want to study this topic closer, grab a loading manual and do the math. I recommend the recoil calculator at kwk.us/recoil.html.
The next time you’re at the range and getting ready to squeeze the trigger, think of how much gunpowder is in your ammo. Then imagine how much more pleasant some guns would be to shoot if we could Harry Potter the bullets down the barrel instead of using gunpowder. Until that day comes, hang on tight!