Vibrations of the barrel at the time of the shot. Notes geek

34


"Without the occurrence of vibrations, the exit to the astral projection becomes more complicated."
Wisdom indian yoga




What determines the accuracy - one of the main characteristics weapons? Obviously, on the quality of the barrel and cartridge. We’ll postpone the cartridge, but consider the physics of the process.

Take a metal rod or a tube of elastic metal and firmly fix it in a massive base. So we get the model of the device under study. Now, if you hit the rod, it does not matter in which place and in which direction either to pull or squeeze it, or, finally, inserting a cartridge into the tube, to make a shot, we will see that the rod (trunk) has come into a damped oscillatory motion. These vibrations are decomposed into the simplest, and each type of such simplest vibrations of the barrel will affect accuracy (accuracy) of firing in its own way.

Vibrations of the barrel at the time of the shot. Notes geek


Let's start with the oscillations of the first order or the fundamental tone. As can be seen (Fig. 1), such oscillations have only one node at the point of attachment, the largest amplitude, the longest decay time, and the longest time of oscillation of one period. This time is 0,017-0,033 seconds. The passage time of a bullet through the bore is 0,001-0,002 seconds. That is much less than the cycle of one oscillation, and therefore this type of oscillation does not have a significant effect on the accuracy of a single shot. But with automatic shooting can get an interesting picture. Suppose the rate of fire 1200 vyst / min, i.e. one cycle time - 0,05 seconds With a period of oscillations of the first order 0,025 sec, we have a multiple frequency ratio. And this is an indispensable condition for resonance with all the ensuing consequences - the weapon begins to shake with such force that it can fall apart.

We turn to the oscillations of the second order (Fig. 2). But I suggest that the humanities first conduct an experiment in order to eliminate the shortcomings of education in the field of physics. You need to take a little boy (you can have a girl), put him on a swing and swing him. Before you is a pendulum. Stand on the side of the swing and try to hit the boy with a ball. After a series of attempts, you will come to the conclusion that it is best to hit when the target is in the first phase of the oscillation — the maximum deviation from the equilibrium point. At this point, the target has zero speed.

Let's look at the scheme of the second order. The second vibration node is approximately at a distance 0,22 from the end of the barrel. This point is a law of nature; it is impossible to create such oscillations for a cantilever beam so that the second node falls at the free end. It is where it is and does not depend on the length of the trunk.

The oscillation amplitude of the second-order scheme is lower, but the oscillation time is already comparable to the bullet passage time through the barrel channel - 0,0025-0,005 seconds. So for single shooting it is already of interest. To make it clear what we are talking about, let us imagine a trunk with a length of 1 meter. The bullet passes the entire barrel in 0,001 seconds. If the period of oscillation 0,004 seconds, then by the time of the bullet, the barrel will reach maximum bending in the first phase. The question to the humanities is at what point (in what phase) is it best to fly the bullet out of the barrel to ensure consistency of results? Remember the swing. At the zero point, the velocity vector of the trunk deflection is maximum. It is harder for the bullet to get to this point on the trunk cut, it also has its own error in speed. That is, the best moment of a bullet departure will be when the barrel is at the highest point of the first phase of deflection - as in the figure. Then minor deviations in the speed of the bullet will be compensated by a longer time the barrel is in its most stable phase.

A graphic representation of this phenomenon is clearly seen in the diagram (Fig. 4-5). Here - Δt is the error in time with which the bullet crosses the muzzle of the barrel. In fig. 4 is ideal when the average bullet departure time coincides with the zero phase of the barrel oscillation. (Mathematicians! I know that the velocity distribution is non-linear.) The shaded area is the trajectory spread angle.



In Fig. 5, the barrel length and velocity error remain the same. But the bending phase of the trunk is shifted so that the average time of departure coincides with the maximum deflection of the trunk. No comments?

Well, is it worth it? How serious can deviations be caused by second order oscillations? Serious and very much so. According to the Soviet professor Dmitry Alexandrovich Venttsel, in one of the experiments, the following results were obtained: the radius of the median deviation increased by 40% when the barrel length was changed only by 100 mm. For comparison - high-quality processing of the trunk can improve accuracy with only 20%!

Now let's look at the oscillation frequency formula:

where:
k - coefficient for oscillations of the second order - 4,7;
L is the length of the trunk;
E is the modulus of elasticity;
I is the moment of inertia of the section;
m is the mass of the trunk.

... and proceed to the analysis and conclusions.

The obvious conclusion from the 4-5 figures is the speed error of the bullet. It depends on the quality of the powder and its weight and density in the cartridge. If this error will be at least a quarter of the cycle time, then everything else you can give up. Fortunately, science and industry have achieved very great stability in this matter. And for the most sophisticated (in benchrest, for example) there are all the conditions for self-assembly of ammunition to fit the bullet departure phase exactly to the length of the barrel.

So, we have a cartridge with the lowest possible velocity spread. The barrel length was calculated based on its maximum mass. There is a question of stability. We look at the formula. What variables affect the change in frequency? Barrel length, modulus and mass. During firing, the barrel heats up. Can the heat change the length of the barrel, so that it affects the accuracy. Yes and no. Yes, since this figure is within hundredths of a percent for the temperature 200 C. No, since the change in the modulus of steel for the same temperature is approximately 8-9%, for 600С - almost twice. That is many times higher! The barrel becomes softer, the bending phase of the barrel moves forward by the time the bullet is taken out, accuracy decreases. Well, what would a thoughtful analyst say? He will say that it is impossible to get maximum accuracy in cold and hot mode on one trunk length! Weapons may have a better rate with either a cold or a hot barrel. Accordingly, it turns out two classes of weapons. One is for ambush actions, when the target must be struck from the first - “cold” shot, because the accuracy of the second will be worse due to the inevitable warming up of the barrel. In such a weapon there is no urgent need for automation. And the second class - automatic rifles, the length of the barrel which is fitted under the hot barrel. In this case, the possible miss due to the low accuracy of the cold shot can be compensated for by a quick, subsequent, hotter and more accurate shot.

The physics of this process was well known to EF Dragunov when he designed his rifle. I propose to read the story of his son Alexei. But first, some people have to break their brains. As is known, two samples of Konstantinov and Dragunov approached the final of the competition for the sniper rifle. The designers were friends and helped each other in everything. So, the Konstantinov rifle was “tuned” to the cold mode, the Dragunov rifle to the “hot” one. Trying to improve the indicator of accuracy of the rival's “rival”, Dragunov fired his rifle with long pauses.



Let's look at the formula again. As you can see, the frequency depends on the mass of the trunk. The mass of the barrel is a constant. But hard contact with the forearm forms an unpredictable positive feedback on the trunk. The system - the trunk-fore-arm (support) will have another moment of inertia (a set of masses relative to the attachment point), and therefore this too can cause a phase shift. That is why athletes use soft footing. The same feature is connected with the application of the principle of “hung trunk”, when the gun shank does not have a hard touch with the barrel and is rigidly attached to it (the weapon) only in the receiver area, and the second end either does not touch the barrel or touches it through a spring-loaded articulation (SVD ).

Final thought. The fact that, with a single barrel length, it is impossible to get the same accuracy at different temperatures, it gives an excellent reason to brainstorm. It is necessary only to change its length and (or) mass when the temperature of the barrel changes. Without changing neither the length nor the mass of the trunk. From the point of view of humanities, this is a paradox. From a technical point of view, the ideal task. With the solution of such problems is connected the whole life of the designer. Sherlock rest.

References:
Blagonravov A.A. Basics of designing automatic weapons
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34 comments
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  1. +2
    February 28 2013
    Thanks for the article, informative.
  2. +2
    February 28 2013
    The frame from "Video on the topic" served as the basis for creating a memorial plaque on the house where the designer lived.
  3. Fox
    +1
    February 28 2013
    tin ... the brain almost sprained ... but interesting and informative. it turns out that it is impossible to create an "absolute" small arms. but ours will do it. I'm sure.
    1. Gladiatir-zlo
      0
      March 19 2013
      Oh Fox, hi, so I'm not alone in my ignorance about internal ballistics, although I really liked the article. It’s interesting, but can I now conduct a conversation with the techies on equal terms about the trunks?
  4. +2
    February 28 2013
    I learned with interest about the "spring-loaded gas outlet" in the SVD, it will be necessary to take a closer look at the drawings.
    I’m thinking - and if, within the limits of the serial SVD, make a version with a heavier barrel and a switchable gas engine - how much will this improve accuracy ??
    1. 0
      March 1 2013
      Quote: Mikhado
      and switchable gas engine


      And what's the point? The highlight of SVD is in automation. For single shooting there are boltoviks.
  5. +1
    February 28 2013
    The absolute is impossible, but it is very necessary to take into account all of the above. The conclusion suggests itself - the design of a sniper rifle is based on the "cold" weapon, and a machine gun, for example, AK, from the hot version. And the task at the end of the article is generally super)))
  6. +3
    February 28 2013
    wink There is no spring-loaded gas outlet. There is a "spring-loaded" joint at the front of the forearm. If you can call it that. The front ring, which connects the two halves of the forend, moves freely along the barrel. The piston is in the gas chamber, also separate from the pusher. So the barrel has only one "hard" point of contact with the weapon in the area of ​​the box. At the moment the bullet passes through the bore, the gas engine does not affect the accuracy in any way. But for the next shot, I think the idea of ​​turning off the gas. engine takes place. (At least in order not to look for a cartridge case after the shot wink ) But this is a separate topic for discussion.

    From the point of view of improving accuracy, I can say one thing - there is no limit to perfection. In the case of SVD, as you know, the accuracy was deliberately impaired due to the need for the possibility of using various ammunition. It is sufficient to return the pitch of the rifling to its original state and we will already get the result (but not for all cartridges) and without any increase in mass.

    Suppose we have a weapon with an optimal barrel length. And they decided, by increasing the mass, to increase the rigidity of the barrel. Then, to maintain the phase, we will be forced to slightly decrease the length (reduce the mass wink ) See how interesting.

    PS Apply for the invention "Gas engine shutdown ..." I think it will pass.
    1. +1
      February 28 2013
      In my opinion, the simplest (and cheapest) "switch" of a gas engine is best installed in the branch pipe connecting the barrel and the gas chamber, like a samovar faucet. I turned the switch box along the barrel by 90 degrees - the branch pipe is closed, the gas engine is turned off, and ALL the energy of the gunpowder is used to eject the bullet. Turned the switch box back to 90 degrees - the branch pipe is open and the automation works. Make the flag small, not protruding beyond the dimensions of the weapon. In a similar way, it is possible to make Kalash for special forces (especially for optics). soldier
  7. +1
    February 28 2013
    Student memories flooded))) I don't know what the level of universities is now. After "perestroika", many sensible teachers left my faculty abroad, even Kazakhs ((. Although I still hold the opinion that the Soviet school was better than the Western one.
  8. +2
    February 28 2013
    To the author of the article


    Colleague, is there an error in your formula? With transverse vibrations of the rod, the shear modulus, and not the modulus of longitudinal elasticity, is responsible for the frequency. I remember this in my work on measuring the speed of sound in metals and alloys to calculate the elastic modulus. Moreover, the frequency of transverse vibrations is approximately four times less than longitudinal. I note that this is true for an unfastened rod, freely lying on two supports in the nodes.
    1. +5
      February 28 2013
      The formula is taken from the original source and simplified to disgrace. And it is designed only for understanding the essence of the process by humanities. So do not blame me. But for the ratio of the frequencies of longitudinal vibrations to transverse, many thanks! I thought about it myself. In general, if you poke me with your nose where there are ready-made tables of the relations of frequencies and amplitudes, I will be grateful.
      1. 0
        February 28 2013
        Thank. I’ll look now.
  9. 0
    February 28 2013
    Hello. Question
    In one of the articles it was said about cartridges without the release of steam gases
    from the liner, piston method. It turns out that the heating of the barrel will occur mainly with the friction of the bullet along the channel in the grooves, which means that such a cartridge requires a new weapon with a "cold" barrel. And at the expense of what is the recharge if there is no gas outlet.
    Sorry, maybe the wrong question was asked.
    1. 0
      February 28 2013
      Stechkin has an OTs-38 revolver under such cartridges. A curious instance. Google it.
  10. ramsi
    0
    February 28 2013
    as far as I can imagine, the maximum bend of the trunk should be in the middle of the barrel, and the maximum diameter of the incorrect circle described by it should be at the end. I can’t even imagine that in addition to the bipod at the end of the trunk, in the framework of such a wretched system, you can do
  11. +2
    February 28 2013
    This is a very low-power cartridge for pistols. Such accuracy is not needed there. And automation works due to the recoil of the free shutter.

    As long as the bullet moves in the barrel, it is all one object. But then a bullet flies out of the barrel with an energy of 200 J. All that is left, according to the laws of physics, flies in the other direction. If you don't hold the pistol, the bolt will fly away with the pistol. And the way you hold the pistol, only the bolt flies off. The difference is that in a conventional cartridge, the gas presses all the time while the bullet is moving. And in "gasless" only at the initial moment before the cutoff of gases in the sleeve.
  12. +1
    February 28 2013
    Wow, a thousand advantages. smile
    1. +1
      February 28 2013
      Cyril, so where do you live? Now in the south, then in the west!
      1. +1
        March 3 2013
        Abandoned to the enemy for the implementation of reconnaissance and sabotage activities soldier But seriously, I’m lucky with the Internet provider, I’m setting an IP flag, and this shows that I’m in Turkey, then in the EU, while I myself am sitting on the pope in Belarus and am not even going anywhere smile
  13. 0
    February 28 2013
    Wow! Thank you for the article! I’ve thought about something like this for a long time, but I didn’t have enough brains to formulate and mathematically state (for myself). And the explanation in the last paragraph also came to the place: I was always convinced that the posted trunk was needed exclusively to fend off the thermal effect, and I did not even think about dynamic vibrations.
  14. +2
    February 28 2013
    I give two half pages from the "Quick Reference Book on Physics" by H. Ebert.
    Gos. Publisher of physics and mathematics literature. Moscow 1963

    Quote: bunta
    ratio of longitudinal to transverse frequencies


    The reference is old but reliable enough in speed

    Quote: bunta
    ratio of longitudinal to transverse frequencies


    The reference is old but reliable enough in speed
    1. 0
      February 28 2013
      If useful, I will be glad.
      1. 0
        February 28 2013
        This is from Blagonravov.
      2. +1
        February 28 2013
        That's better
    2. +1
      February 28 2013
      Thank. And as they say, from our table, to your table:


      here it does not allow two pictures to be downloaded in one comment. Well, in short, this is the first page, and above the second.
      1. 0
        February 28 2013
        Big grand merci! By the way, I still have a textbook on the compromising materials S. Timoshenko. And he designed the bridge, it seems, in San Francisco.
  15. +1
    February 28 2013
    Very well! It remains to design an absolutely rigid barrel - and the whole business. Or, more paradoxically, make it soft enough to remove any resonance at all. That is, a thick plastic casing and inside a thin-walled, solid barrel. The outer part will have to damp all vibrations that occur inside. Roughly speaking, a plasticine doused pipe.
    And this can only be achieved by appropriate heat treatment.
    1. Passing
      0
      February 28 2013
      I agree, a hard barrel seems a much simpler task than puzzling over the optimization of vibrations and so on. The task is purely technological, such as: barrel - longitudinal stiffeners - external pipe, all this is welded / welded / glued in contact points.
      Or another option - a composite barrel, such as metal oxide fibers (for example) in a metal matrix. We get very high stiffness in combination with the highest temperature stability. True, there are no such technologies yet, only laboratory images, but the technology is useful, it can be very useful, so it will inevitably be developed.
  16. 0
    February 28 2013
    Quote: akm8226
    make it soft enough to remove any resonance at all.

    The idea is not at all paradoxical. For this purpose, steels with high damping can be used, in which the oscillations decay very quickly. However, their value will exceed reasonable limits.
    1. 0
      February 28 2013
      But electronics can not solve this problem? Experience, in principle, is. For the same MLRS packages, where there is also a huge vibration problem.
  17. +1
    February 28 2013
    Quote: crambol
    However, their value will exceed reasonable limits.


    No more expensive than a sniper.
  18. ramsi
    0
    March 1 2013
    Passing,
    I agree, a hard barrel seems a much simpler task than puzzling over the optimization of vibrations and so on. The task is purely technological, such as: barrel - longitudinal stiffeners - external pipe, all this is welded / welded / glued in contact points.
    Now, if you strain the metal: twist the barrel in the direction of the rifling, like a torsion bar, and fix it in the casing at three or four points ... Well. Of course, bipod. Although all this, probably already done
    1. Passing
      +1
      March 1 2013
      Quote: ramsi
      and fasten in the casing at three or four points

      IMHO "fastening" should be continuous along the length of the barrel. If there are 3-4 points of contact, then we will get an unpredictable bending pattern - the inner barrel will be heated more than the casing, respectively, the barrel will lengthen more than the casing during firing, i.e. Compression stresses will appear in the barrel (the connection between the casing and the barrel must be rigid), and since we have 3-4 attachment points, the barrel will "bend" between these attachment points in an arbitrary direction when fired. Instead of a straight barrel, we get a "snake" which changes its bend with each shot.
      However, this is my purely intuitive vision, I did not believe it by calculation, perhaps this bend will be meager and insignificant for accurate shooting.
      1. ramsi
        0
        March 1 2013
        Passing,
        the "anchoring" must be continuous along the length of the barrel. If there are 3-4 points of contact, then we get an unpredictable bending pattern - the inner barrel will be heated more than the casing, respectively, the barrel will lengthen more than the casing during firing, i.e. Compression stresses will appear in the barrel (the connection between the casing and the barrel must be rigid), and since we have 3-4 attachment points, the barrel will "bend" between these attachment points in an arbitrary direction when fired. Instead of a straight barrel, we get a "snake" which changes its bend with each shot.

        my logic was this: since the maximum bend in the middle, then we reinforce there; although with a cold twist, the middle should already be strengthened. Here the problem is more likely - as if during heating all this shit together with the casing did not turn back
        1. 0
          April 11 2013
          I don’t know about the spin, but the outer casing is used FR-f1, for example nobody seems to complain, and you won’t be able to regulate the vibrations, for example, barrel weights? Well, I’m not an engineer as I think. And from practice, a bolt rifle when installing a TG (weight 350g) on ​​average gives accuracy 5mm less than with a DTK (with a 15mm TG with a 20mm DTK per 100m). The trunk is posted.
  19. schta
    0
    March 1 2013
    Somewhere in the wilds of the Internet, I saw a slow-motion shooting of SVTeshki shooting, in which the barrel oscillations were visually very clearly visible
  20. +1
    March 3 2013
    I just found out that Lee-Enfield No.4 Mk also had a hung trunk.
  21. vseprosto
    0
    March 17 2013
    Make pinching at the end of the barrel, and at the beginning of the articulated-movable support.))))
  22. 0
    March 5 2016
    Rigid jamming is shown only in the upper figure, in the middle and lower free hinge. The pattern of vibrations, respectively, should be different.
    Where does the drawing come from?

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