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Experiment: Recoil vs. Muzzle Velocity (ammolytics.com)
134 points by wizdumb on Dec 21, 2018 | hide | past | web | favorite | 61 comments

I wrote a long-form article about an experiment that I conducted this summer to explore the question of whether or not recoil-management techniques have an effect on muzzle velocity. It involved a bit of data science (Python, pandas, plotly), some hardware (arduino, 3d printing), and math (LaTeX). I hope that this content is high quality enough to justify the time you spend reading it, and how much time it took me to create it!

I’d love to hear your feedback and answer any questions!

That's a great article even if the results were a little inconclusive due to unanticipated uncontrolled factors (bullet length). I'm just happy to see someone showing how the worlds of firearms and hobbyist hacking can fit together.

It's unfortunate that everything related to firearms is now viewed as political. There are just so many interesting things unique to thos subject matter that inquisitive and mechanically inclined people, like those on HN, are missing out on.

I think Destin Sandlin, of the youtube channel SmarterEveryDay does a good job of having firearms related physics videos (in addition to other science, physics and space videos) that are non-political.

Thank you for reading it and sharing your thoughts!

I'm just here to learn and share. Hopefully this will help towards breaking down some negative stereotypes about a fun an interesting hobby!

Very interesting article! One comment - when the firing pin is released and moves forward, the gun recoils backwards slightly to conserve momentum.

I suspect what you saw was the sudden release of the couple of pounds of rearward trigger pressure causing the gun to move forward shortly before the pressure buildup and recoil drove it backwards. That would swamp any small recoil associated with the firing pin.

Great feedback! It's definitely true that I need to do some more research on this particular aspect. My trigger is set to 1 pound before it breaks (some folks set theirs to 2 oz!) Pulling it gently, like you're supposed to, shouldnt generate the same acceleration as if you were to "slap" it (which is a bad practice for accuracy and precision).

It may require faster data acquisition, so I hope that folks will contribute to the accelerometer project that I open-sourced to make that possible! https://github.com/ammolytics/experiments/tree/master/recoil...

Thanks again!

I'm not sure if you are correctly interpreting wrycoder's explanation. Or maybe I'm not, but I think his point is not about how fast the trigger is pulled, but about what happens as right after the trigger mechanism releases, independently of proper technique trigger finger technique.

Just before the trigger releases, you are pulling back with 1 lb of force on the trigger, and to maintain aim, are pushing forward with 1 lb of force on the butt (likely with your shoulder). When the trigger releases, suddenly there is no more force being applied by your trigger finger, but the same amount being applied by your shoulder. In response, the gun starts moving forward. It keeps moving until the trigger bottoms out and the force from your finger stops the forward progress, or until the recoil from the acceleration of the bullet begins.

I'm not sure he's right, but I think this is what he's saying, and I think it fits what you measured. I am confused though how the gun can move forward in the "preloaded" case. Isn't the gun already pushed forward as far as it can go against something incompressible? If so, how does it accelerate forward?

The easy way to control for this is to run the same measurements with a spent cartridge chambered.

I enjoyed the article, and you did a great job presenting the data in a clear way. Whats the name for the type of graph that looks like a box and whisker plot inside of a probability distribution?

Thank you! Yes, as merlincorey correctly mentioned, they're called "violin plots".

Are you talking about the Violin plots?

yes, thanks

If the violin plots don't do it for you I recommend Georgia O'Keefe paintings as an alternative.

This is cool. When looking to muzzle velocity, did you measure the diameter / weight / length of the bullets? It seems there could be some interesting effects there.

1. Interference with the rifle barrel 2. Interference with the shell casing (is there a measure of how tight a shell fits the bullet that changes the velocity / is more interference fit good?) 3. do slight variations in diameter or weight matter more?

Great work!

Thank you! As I mentioned in the Next Steps section of the article, measuring the effects of bullet sorting by weight & length is definitely a topic for a future article.

I really enjoyed this. I'm not a shooter, but it's hard not to be excited by the analysis you've done. I learned a ton.

Thank you so much, this really means a lot to me!

Yes. Uncontrolled recoil has effect. It is a physics problem most undergraduates do (throw something heavy on ice, two bodies move in opposite directions, energy spent sliding the thrower is removed from the projectile due to conservation of energy, etc). The question is not whether it does, but to what degree?

It looks like youre measuring muzzle velocity with a device mounted to the barrel. If that's true, i suspect it almost entirely negates the difference you are looking for because the rifle recoiling adds perceived muzzle velocity that the target (and the rest of us) do not experience.

Thanks for the feedback! I've heard this suggestion a few times, and it is an interesting thought. I believe that the calculations I did which show that the bullet has left long before the rifle moves under recoil contradicts this.

That said, I'm more interested in the truth than who is right or wrong. I've open sourced all of my data and want others to try this experiment for themselves and share their results rather than rely on me as a source-of-truth!

Excellent article, I learned a few things.

Thank you for taking the time to read it!

Wow, fascinating article. I'm a little surprised that the bullet has left the barrel before the rifle recoils, but I guess that makes sense with the differences in mass.

It really does mean that my poor accuracy with a large caliber handgun is from flinching. I sort of thought it was from being unable to control the recoil but it sounds like that has no bearing on where the bullet is heading, and so I guess I'm just flinching in anticipation.

Btw, where do you live that you have a 300yd range? I'm jealous. Here near Chicago (well, NW Indiana) I mostly make do with small indoor ranges and a .22 rifle which is typically allowed, but would love to get into shooting larger calibers longer distances.

> It really does mean that my poor accuracy with a large caliber handgun is from flinching.

When I shoot my revolver, I will load empty shells in a couple random spots, spin it, and close it. This immediately exposes any flinching or anticipating I'm doing. I squeeze the trigger, the gun moves slightly downward and no round is fired.

Do that a couple times and you learn to remain neutral pretty quick.

It's not as easy on a magazine-loaded pistol. I imagine you'd need to get some purpose-made dead rounds. And the randomization is harder.

Snap caps make great "dummy" rounds for these drills on semi-automatics.


Randomize by loading a few mags with different patterns of blanks, and then shuffle the mags until you don't know which is which.

Blanks fire/have recoil. Dummy rounds exist that you can manually extract though.

Or have someone load them for you.

Thank you! Funny story: I built the accelerometer with the original intent to see if I could correlate "bad" shots during 600 yard matches to flinching. That's still a work in progress, but because I had it working I was able to use it for this experiment as well!

I live in Oregon and am fortunate enough to be within 40 miles of an amazing club where I can shoot out to 600 yards every week with an awesome group of people! For what it's worth, you can (and should) drive out to Ohio for the National Matches at Camp Perry in the summer. It's on your way to Cedar Point ;)

> "It really does mean that my poor accuracy with a large caliber handgun is from flinching."

It may also be how how you're pulling/squeezing the trigger. That's the problem I have, and consequently I am far more accurate with revolvers when using single action trigger pulls (hammer already cocked back, so the trigger pull is very short and crisp.)

> Wow, fascinating article.

Indeed. Outstanding work :)

> I'm a little surprised that the bullet has left the barrel before the rifle recoils, but I guess that makes sense with the differences in mass.

That puzzles me too. I mean, once the bullet has left the barrel, what force could be accelerating the rifle?

Two possibilities came to mind. One was ongoing gas expansion, but that seems unlikely, because the chamber pressure is small after 2.5 msec.

The other is something mechanical about the rifle. Could the barrel stretch, as the bullet is exiting? And then contract afterward? Or maybe some elasticity in the attachment of the barrel?

Thanks for the question! Keep in mind that a huge explosion (with 40,000 PSI) is happening inside the chamber of the gun. Some of that energy pushes the bullet forward and the rest pushes the gun backward. You're right though, the gases escaping the barrel also contribute to this, similar to a rocket engine!

Based on my understanding of the physics involved, it's entirely possible that the rifle has accelerated to the recoil velocity by the time the bullet leaves the barrel, yet not actually moved measurably yet.

Well, but he says that he's measuring acceleration, not velocity. The bullet's in the barrel for just ~2 msec, and there's appreciable acceleration -- not just movement -- for >50 msec. It's true that his custom accelerometer only records data at ~6 msec intervals, but I don't see how that could smear ~2 msec out to >50 msec. Unless maybe there's some design limitations of the sensors that he used.

The PRB covers the role of propellant gases in recoil, and measures effectiveness of muzzle brakes.[0] He talks about 20%-50% reduction in recoil with muzzle brakes. And that implies that gas expansion from the muzzle accounts for at least 50% of recoil.

Even so, some additional measurements might be useful. It'd be interesting to know, at sub-msec sampling rates, the velocity of gas leaving the muzzle. And if there's still appreciable unexplained recoil: 1) the length of the barrel; 2) the displacement of the barrel from the stock; and 3) the diameter of the barrel, measured at maybe 4-5 points from the chamber to the muzzle.

Because steel is, after all, notoriously elastic. And the barrel may be attached to the stock in a way that smears out recoil. Also, the rifle may have other recoil-management features that reduce recoil, and smear it out. It's bolt-action, so there's no blowback, and I don't see a muzzle brake, but ???

0) http://precisionrifleblog.com/2015/07/01/muzzle-brakes-recoi...

The barrel and the entire gun must stretch and flex while firing. That flex will store some acceleration.

Also consider that multiple bits of the gun are mechanically attached to each other. It looks like the accelerometer is attached to the barrel, whereas the majority of the rearward forces before bullet leaves the barrel is acting on the bolt. Even as a bolt action, there's plently of interesting mechanical interfaces to absorb energy and movement before transferring to the barrel.

Thanks. In the PRB post that I cited, it's noted that recoil force can be "in excess of 1,000 pounds", but that "the recoil event is very short, lasting only about 10 milliseconds". So yes, I suspect that the gun is absorbing most of that elastically, and then relaxing on a longer timescale.

0) http://precisionrifleblog.com/2015/07/01/muzzle-brakes-recoi...

The interesting thing is that powder particles will leave the barrel before the bullet does. My guess is they have enough energy to squirt around the bullet before the rifling can deform it and create a seal.


> I'm a little surprised that the bullet has left the barrel before the rifle recoils

Well not 100%.

That's why it's important to hold a rifle in a position where it will kick back in a straight trajectory.

There’s a 1000 yrd rifle range in Wolcottville, IN (near Elkhart). Young’s Long Shot Range.

In Ann Arbor we have a range outside of town that lets you shoot out to 600 yards.

> Does one directly affect the other?

Thought experiments:

1. Bazooka-like barrel open on both ends with identical bullets shooting out each end. I would say that each bullet got approximately half the energy.

2. Fixed barrel, hard mounted, no recoil movement. Bullet should get about double the energy of (1). If you imagine the expanding gas between the bullets of (1) but then change it to operate in half the volume (split down the middle), the pressure would be double but not quite since combustion rates may differ.

3. Barrel with very long throw, very low spring force. Bullet gets most of energy, peak recoil force is low.

But always true:

  - Newton's third law: For every action, there is an equal and opposite reaction.

  - Conservation of momentum: p = m v
    considering impulses: F t = m = p / v, p = F t / m

Thank you! As I mentioned, I hope to tackle the physics portion of this topic in another article. I had originally included it when drafting, but it got way too long and off-topic.

That said, you're spot on with your equations, though there are a few others I'll cover as well!

Looking forward to the follow up article. I broadly mentioned some of the relevant bits but would be so much better to have it tied to more concrete examples. Like maybe subjective quantification of recoil or various hybrid configurations.

"Regardless, these results strongly suggest that the bullet is long gone before the rifle moves under recoil. How long gone? In my case, the bullet was already 23 ft (7 m) down range. This makes sense because the rifle is nearly 900x heavier than the bullet, so it cannot accelerate as quickly."

I've heard that before, but this is the first time I've seen actual data. Nice work!

Thanks, I'm glad you found it helpful!

Wow, this was a fascinating article and of deep interest to me as both a shooter and a geek. I'm glad to see this type of content on Hacker News.

Thanks! It's my first time sharing on HN and I'm thankful that it has been well-received.

Great article, shared it with some friends who are geeks and shooters.

The presentation of the information was well done, I'd say. It's very nearly a proper paper, if you ask me.

Thanks for sharing!

I especially enjoyed the pictures of the arduino and gear setup.

Thank you for taking the time to read it, and for the positive feedback!

Very cool experiment and excellent writeup!

You can also do some meta-analysis with all of the high speed video on YouTube. Get something like Tracker[0] to watch the barrel displacement while the bullet is travelling down the barrel. This video from SmarterEveryDay [1] provides some good examples.

I've watched tons of these vids and my basic observation is that there is some motion while the bullet is in the barrel, but as soon as it leaves you basically are left with a rocket trying to launch into the shoulder of the shooter. Even at high frame rates there's a perceivable increase in rearward acceleration once the gases start escaping.

Looking forward to future articles! Particularly with the improved accelerometer, it feels like there's a story in the gaps. I'm sure you've got plenty of ideas when you start a blog with that name, but here are a few I've been mulling about while chasing a lawnmower around the yard (some of these may be tired stories for folks into match shooting).

- Benefit of powder sorting for uniform and/or even distribution of grain size/weight (maybe via sieve or some kind of scattering method?)

- Benefit of tip conditioning in terminal ballistics (e.g. precision shaping/polishing)

- Building a press + strain gauge to push bullets through barrel to characterize impact of variations in diameter/length on energy required to make the trip.

Last bit of spam from me. I did take a quick peek at the data. It looks like the area under curve measurement more closely correlates with velocity than peak pressure, but not by much. Not sure what the data column on the left represents in the PTC file.

[0] https://physlets.org/tracker/

[1] https://www.youtube.com/watch?v=7pOXunRYJIw

Is there any plausible physical model in which the difference in velocity of the bullet, on account of the recoil, could be greater than the change in velocity of the barrel over the time that the bullet is traveling in it? With the bullet taking 2ms to leave the barrel, and maximum recoil acceleration of 100 ft/sec/sec, that effect would seem to be at least two orders of magnitude smaller than the 20 ft/sec claimed in the article that prompted this project.

The one extra thing I can think of so far is that the recoil reduces the effective length of the barrel by the distance it has moved by the time the bullet exits the muzzle, but again that seems too small an effect (~0.2 millifeet, four orders of magnitude less than the barrel length?)

There are several physics equations (some I linked to in the article) which discuss this topic. One of the main takeaways I learned from running this experiment and doing some of the math was that my rifle is 900x heavier than the bullet, which is why it is able to accelerate so much faster and leave before the rifle/barrel move at all.

It does bring up a good point though, which I'll cover in the article where I deep-dive into the physics: Knowing the acceleration of the rifle, I should be able to calculate how far it has moved in the same amount of time it took for the bullet to leave.

Thanks for taking the time to read it, and for your feedback!

I agree. Recoil or no recoil, the bullet moves the same in the reference frame of the rifle. Proportionally to the masses ratio, the bullet acceleration is about 500x-1000x the rifle acceleration, thus the speed of rifle reference frame in the recoil case at the moment of the bullet leaving the muzzle would be just about 3-6ft/s - an order of magnitude difference vs. claimed 20ft/s.

Edit: forgot about the powder which as hot gas is subjected to pretty much the same acceleration as the bullet. With the powder being about 2-4x bullet mass it makes the rifle only 150x-300x heavier than the [bullet+powder] and that brings us to the 20-10ft/s of the rifle recoil speed, ie the article claim pretty closely matches the theory.

A good point, but the puzzle is, though, that the author isn't recording those sort of velocities (or, rather, the acceleration that would lead to them) while the round is in the barrel.

Not all the gas reaches the bullet speed. We might guess that it averages half that, but that is assuming, I think, a uniform density and complete gasification of the charge (though with regard to the latter, is there a reason for there being a larger charge than that?)

This argument also suggests that the recoil firing blanks would be a substantial fraction of the recoil with a live round, which is not how I recall it.

A long running argument: does leaving your silencer on cause a repeatable velocity delta?

I suppose I could just break out the screens and find out, but it's nice to argue over beers.

I shoot with it all the time and haven't noticed any variation because of it (though I admit I have not tested this directly). FWIW, I was able to earn my F-Class Mid-Range High Master classification while using it.

I've noticed not only group movement, which I think everyone sees, but group dispersion. I will mark that up to "I don't shoot rifles enough to know how to shoot them" and move on :)

[shameless plug] I hope I can convince you to subscribe for when I tackle this topic in a future article! ;)

Sure thing. Shameless plug: come have fun with us in Idaho? http://boomershoot.org

What kind of pervert mixes imperial and metric units like that. Velocity is expressed in ft/s while peak acceleration is expressed in m\s²...

I believe I provided both imperial and metric units for every equation. Maybe I missed one? I'd be happy to correct it if you can point me to the specific instance!

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