
Experiment: Recoil vs. Muzzle Velocity - wizdumb
https://blog.ammolytics.com/2018-12-12/experiment-recoil-vs-muzzle-velocity.html
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wizdumb
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!

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cc439
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.

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rhinoceraptor
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.

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losvedir
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.

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mirimir
> 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?

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ufmace
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.

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mirimir
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...](http://precisionrifleblog.com/2015/07/01/muzzle-brakes-recoil-
primer-test-equipment-rifles/)

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karmakaze
> 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

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wizdumb
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!

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karmakaze
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.

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mcguire
" _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!

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wizdumb
Thanks, I'm glad you found it helpful!

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tristor
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.

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

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merlincorey
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.

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

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jcims
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/](https://physlets.org/tracker/)

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

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mannykannot
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?)

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trhway
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.

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mannykannot
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.

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jcims
Extreme counterexample, Barrett M82

[https://www.youtube.com/watch?v=AhXaER53CHQ&feature=youtu.be...](https://www.youtube.com/watch?v=AhXaER53CHQ&feature=youtu.be&t=400)

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RyJones
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.

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wizdumb
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.

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RyJones
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 :)

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

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RyJones
Sure thing. Shameless plug: come have fun with us in Idaho?
[http://boomershoot.org](http://boomershoot.org)

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brohee
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...

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wizdumb
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!

