Vibrations of the barrel at the time of the shot. Notes geek
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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.
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:
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.
Blagonravov A.A. Basics of designing automatic weapons
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