Bullet weight, velocity, and vertical POI

There are three main factors that control POI due to differing loads. I'm going to ignore trajectory because at typical handgun ranges, this is usually not an issue

1. Gun design. Some semi-auto pistols are set up so the slide/barrel move straight backwards while the bullet is in the bore. In guns like that, there won't be much POI change from various loadings because during the time the bullet is in the bore the slide/barrel are pretty much only moving backwards--you get recoil, but the recoil isn't causing significant muzzle rise until the barrel & slide hit the frame and transfer momentum to the frame. In guns where the barrel is fixed to the frame (or some semi-autos with links where the barrel starts tilting almost immediately when the bullet starts moving) then recoil and muzzle rise happen together and you can see significant changes in POI due to different loads.

2. Muzzle momentum. More momentum means more recoil and in revolvers and other guns with the barrels fixed to the frame that means that muzzle rise starts when the bullet starts to move. The more momentum, the more it will rise. Momentum is the product of the velocity of the ejecta (everything that comes out of the muzzle) and the mass of the ejecta. This includes the gases generated by the burning powder, but for the purposes of comparison, you can often get away with just looking at the bullet momentum.

3. Barrel dwell time. In two loads with the same momentum, the one with less barrel dwell time will hit lower on the target.

So let's look at some loadings.

Let's take a 125gr bullet at 1450fps muzzle velocity and compare it to a 158gr bullet at 1147fps muzzle velocity. Both are shot from a 5" barrel gun where the barrel is fixed to the frame.

It turns out that the muzzle momentum is virtually identical for these two loads. So now we just need to see what the barrel dwell time is. We're going to estimate that by taking the average muzzle velocity while the bullet is in the barrel which is just the muzzle velocity divided by two. This estimate should be good enough to give us an idea of what is going on. We take the barrel length (converted to feet) and divide it by the average velocity in the barrel to get the estimated dwell time in seconds. These tend to be very small numbers.

It turns out that the 158gr bullet stays in the bore 26% longer than the 125gr bullet. So with the same amount of recoil (and therefore the same amount of muzzle rise in this gun design) we would expect the 158gr bullet to hit noticeably higher on the target.

What about comparing that 125gr bullet at 1450fps to a 142gr bullet at 1250fps? Again, both will be shot from a 5" barrel gun where the barrel is fixed to the frame.

This one is a little more complicated. The 142gr loading is about 2% lower in muzzle momentum but barrel dwell time is about 16% higher. I would guess that we would see a higher point of impact. Even though the muzzle momentum is a little lower, the bullet's in the barrel significantly longer.

What about a 125gr bullet at 1450fps and a 110gr bullet at 1100fps in our same test gun? Muzzle momentum is about a third lower in the 110gr loading but barrel dwell time is about a third higher. Not easy to tell if there will be a POI difference on this one. This one would give you a good excuse to go to the range and do some testing.

If the barrel is allowed to rise during bullet travel, would this not impart a vertical (generally upwards) velocity vector to the trajectory that would counter the effect of gravity to some extent?

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If the gun is not restrained and the circumstances are such that the muzzle recoils upward, then at the moment that the bullet exits:

1. The muzzle will be pointing upward. This will put the bullet on an upward trajectory even if the bore was level when the gun was fired.

2. The muzzle will be moving upward. This means that the bullet, in addition to being aimed slightly upward will also be "thrown" slightly upward since the bore isn't just pointed upward, it's also moving upward at the moment that the bullet exits.

A fun project would be to measure the position and velocity of the muzzle at the moment of bullet exit on a high-speed video, calculate the effect on the point of impact and then see how close the calculations come to predicting the on-target results.

Then one could break out the two effects and see how much each one contributes.

It can be kind of difficult to wrap one's head around the idea, but the gun definitely moves in recoil before the bullet leaves the bore. If you have a centerfire revolver, you can do a quick experiment with it to prove that this is true.

Get a straight dowel that is as close to bore diameter as you can find and put down the bore. Then place a yardstick across the top of the sights. You will see that the bore is actually aimed DOWN with respect to the line of the sights. In some revolvers, the effect is so pronounced you can see that the bore angles downward with respect to the sights just by looking.

We know that at the point the bullet exits the barrel, the barrel must be aimed slightly upwards with respect to where the bullet is supposed to hit to compensate for gravity.

Some thought will reveal that if the sights are aligned on the intended impact point at the moment of firing and the bore is aimed downward with respect to the desired point of impact at that point, then something has to happen between the time that the gun is fired and the bullet leaves the barrel. What happens is that recoil causes the muzzle to rise between the time that the gun is fired and the bullet leaves the bore.

Do a search for high speed video of pistol bullet leaving the barrel.

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I just gave you an iron-clad way to prove to yourself that the gun MUST move before the bullet leaves the barrel. Here are some more.

Recoil is the result of conservation of momentum. The momentum of the bullet means that the gun is imparted the same momentum as the bullet by the movement of the bullet. If that happens only AFTER the bullet is gone, how is the bullet imparting momentum to the gun when it is no longer in contact with it? Clearly it can not. So then it must happen while the bullet is still in contact with the gun--but if that is true then the gun must begin to move before the bullet loses contact with it.

For every force, there is an equal and opposite force. The gun exerts a force on the bullet that causes it to move. But an equal force is applied to the gun by the bullet that causes the gun to move. That means that the instant the bullet begins to move, the gun must also begin to move.

Finally, if you find high-speed video that is fast enough and filmed close enough to the gun to pick up the movement, it can be seen that the slide starts to move before the bullet is gone. A typical slow-motion video won't show it. The issue is that the gun is much heavier than the bullet and therefore it moves much slower. Physics says that the momentum of the recoiling mass is identical to the momentum of the bullet. If they both weigh the same, then they move at the same speed since momentum is the product of mass and velocity. But if one mass is much lighter than the other, the heavier object must move much slower if momentum is equal. Since the bullet is many times lighter than the recoiling mass, the recoiling mass will move many times slower than the bullet. That means that while the bullet moves a few inches down the barrel, the gun moves maybe a tenth of an inch or less. Hard to see in a typical slow-motion video.

Here's a video filmed at very high-speed and taken very close to the gun so even small movement is visible. At 2:13 in the video there is a closeup of a 1911 muzzle. There are 8 frames showing obvious recoil of the slide before the bullet becomes visible at the muzzle.