Junbo Xiao, Hongqiang Li, Zhenqiang Liao, Ming Qiu and Jie Song

(School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China)

Abstract: To deal with the problem that the initial velocity of the bullet is difficult to increase, the research on the super-high initial velocity propulsion in the barrel weapon with an adaptive pressure-maintaining chamber are conducted. Considering the law of gun-powder burning and the flow characteristics of gun-powder gas in multi-chamber, the scheme of super-high initial velocity propulsion with an adaptive pressure-maintaining chamber is designed, the ballistic model of the barrel weapon with super-high velocity bullet propulsion is established. The research results show that the technical scheme can greatly increase the initial velocity of the bullet with the peak pressure keeping nearly the same as the tradition barrel weapon. The research results can provide a theoretical foundation to significantly increase the initial velocity in barrel weapons using solid propellants, and have an important reference value to comprehensively increase the power of the barrel weapons.

Key words: inner trajectory; adaptive pressure-maintaining chamber; super-high initial velocity propulsion; barrel weapon

Increasing the initial velocity of a bullet is an effective way to improve its penetration ability and range. The traditional way to increase the initial velocity is to increase the charge. But increasing the charge can result in excessive pressure which can cause the pre-mature explosion, fuse failure or the muzzle explosion. In order to assure the integrity of weapon barrel under high pressure, the size and quantity can be increased but this is not very good for the flexibility of the weapon. Furthermore, because of the high pressure, the recoil force will be increased and it will be more difficult for the weapon to be mounted on a plane, tank or naval ship. The resistance of the shell of the bullet will also be increased under high pressure which deteriorates the safety of the weapon when it is shooting. So, how to increase the initial velocity without increasing the pressure is a very important problem for the further development of traditional weapons.

There are a lot of studies on this problem at home and abroad. Although big breakthroughs have been made in electro-thermal chemical emission[1], system integration, electromagnetic compatibility, weaponry structure and continuous ammunition technology, these are not ready for use. Though light gas guns[2]can give the bullet an initial velocity of over 4 000 m/s through expansion of low molecule at high temperatures[3], it is still in an experimental phase. Even though in electromagnetic rail guns, the initial velocity can be increased significantly, there are a lot of problems, for example, the rail is too long, superconducting magnet needs low temperature and the barrel of the gun will get very hot because of the heavy current. Therefore this kind of technique cannot be applied on the traditional weapons (especially on small and medium caliber automatic cannons which require high flexibility). Also, changing the mode of powder ignition[4]or the method of burning the powder[5-6]cannot increase the initial velocity significantly.

So, a new way should be developed when the initial velocity is increased but the pressure is not increased while the strength of barrel flexibility can be assured. The shape of the traditional internal trajectory pressure curve is: the pressure in the barrel of the weapon increases very rapidly with time, but after the pressure peaks, it decreases very rapidly. This kind of pressure curve shape means the integration area of the curve is small, so the pressure cannot create huge momentum for the bullets and the initial velocity is not very high. So the ideal curve is: the pressure increases significantly with time and when it reaches a peak, the pressure is kept stable basically through some way. Then the integration area can be increased and the initial velocity can be increased. In order to realize this goal, the structure of the barrel of the weapon should be changed and the new structure should be more complex, able to keep the pressure stable when the pressure reaches peak. This paper provides a way to increase the initial velocity significantly without increasing the pressure or changing the shooting method.

1 Physical Model

The principle of super-high initial velocity propulsion with an adaptive pressure-maintaining chamber is listed as follows. As shown in Fig.1, a new pressure maintaining chamber is designed with a preset pressure, which can be get by blank ammunition or by other ways.There is an expanded chamber on the right side of the piston which will be affected by the pressure gas created by the gunpowder. Once the bullet is shot and passed the gas port, the high pressure gas transfers into the expanded chamber. When the pressure is higher than the preset pressure, the piston will be pushed to the left and the volume of expanded chamber will increase, so part of the high pressure gas energy will be stored in the expanded chamber. As the bullet moves, the pressure in the barrel decreases. Once the pressure in the barrel is lower than the pressure in the expanded chamber, the high pressure gas stored in the expanded chamber will move into the barrel to become the momentum of the bullet.

1-Barrel; 2-Pressure maintaining chamber; 3-Piston; 4-Expanded chamber; 5-Gas port; 6-BulletFig.1 Structural diagram

2 Mathematical Model

In this paper, some assumptions have been made: the powder burns instantly and the surface of the powder burns simultaneously; the process of bullet gradually squeezing into the rifling is disregarded;the powder burning obeys the geometric burning rule, the pressure and the powder left over after shooting obey the Lagrange hypothesis that the gas mixture is even; frictional resistance when the gas moves along the wall of the barrel after shooting is not considered; the pressure and gas velocity are uniform throughout the barrel.

According to the assumption of the powder burning geometric rule, the shape equation for the powder before and after explosion is

(1)

The equation for the speed of powder burning is

(2)

Consider the loss of the powder energy when the bullet moves, the equation for the internal trajectory is

(3)

(4)

In Eqs.(1)-(4), the relevant parameters are shown in Ref. [7].

Because the bullet moves so fast, the air is condensed and a shock wave is produced. Actually, the shock wave becomes resistance for the bullet and cannot be neglected. Assume that the velocity of the bullet isv, the velocity of shock wave isD, the state of the gas isρ1,p1,u1=0 before shock wave, the state of the gas isρ2,p2,u2=vafter shock wave, as shown in Fig.2.

Fig.2 Shock wave before the bullet

Based on the conservation of mass, momentum and energy, the ratio of pressure after and before the shock wave is

(5)

wherec1is the speed of sound before a shock wave,kis the Adiabatic coefficient of the gas. Consider the resistance for the fast-moving bullet, the moving equation for bullet is

(6)

When bullet moves and past the gas port in the barrel, the high pressure gas moves into the expanded chamber. When the pressure in the expanded chamber is higher than the preset pressure in the barrel, the piston will be pushed moving and the space of the expanded chamber will be increased. When the pressure in the barrel is lower than the pressure in the expanded chamber, the high pressure gas will move into the barrel from the expanded chamber. Based on the theory of gas dynamics, when the ratio between the pressure in the barrel and the pressure in expanded chamber is bigger than the critical pressure ratio, the gas moves at sonic speed, otherwise it moves at a subsonic speed. The mass flow rate equation for the gas flow between the barrel and the expanded chamber is

(7)

(8)

Based on the conservation of energy, the quantity and energy of the pressure gas which flows into the expanded chamber equals the quantity and energy of gas increase in the expanded chamber[8], that is

(9)

(10)

(11)

(12)

(13)

The piston leakage is not considered and the equation of the change of the pressure in the expanded chamber is shown as

(14)

The equations for the gas parameters in the expanded chamber and the movement of the piston are

(15)

whereμbis the gas flow coefficient in the expanded chamber;Sbis the area of the gas port;Pq,ρqare the pressure and density in the expanded chamber;P,ρare the pressure and density in the barrel;γis the adiabatic coefficient of powder gas;ξis the critical pressure ratio;Vq,Vq0,Fq,Fq0are the current volume, initial volume, dissipation area, initial dissipation area, respectively;Sh，xh，vh,mh,dhare the piston area, distance, velocity, quantity, and diameter, respectively.Pfis the preset pressure.

Eq.(3) is derivative to timet, and then substituted into Eq.(6), solving with Eq.(2), considering the change of gas energy flow between the pressure-maintaining chamber and the expanded chamber, the gas pressure in the expanded chamber changes over time as follows

(16)

3 Model Design and Analysis

According to Eq.(16), when the expanded chamber is added, the speed of powder burning and the speed of the bullet and gas flow from the gas port are the main factors for the change of pressure in the barrel. So, the powder of burning in the internal trajectory is divided into several different stages.

The first stage is the early stage. The powder is burning at a constant rate and the bullet is not moving. The gas port is not open and the pressure in the barrel is only related to the speed of burning powder.The pressure is increasing because of the burning powder.

The second stage is from the moving of bullet to the end of the powder burning. During the stage, the gas port is just open and the speed of the bullet is not very fast. With the burning of the powder, the pressure in barrel is increasing. When the gas pressure in the barrel is higher than the gas pressure in the expanded chamber, the high pressure gas in the barrel moves into the expanded chamber to decrease the pressure in the barrel. Once the gas pressure in the barrel is lower than the gas pressure in the expanded chamber, the high pressure gas in the expanded chamber will move into the barrel to increase the pressure in the barrel. Then the speed of the bullet and the volume behind the bullet increases, the increase of the created pressure from the burning powder is slower than the decrease of the pressure from the expansion of space behind the bullet, then the pressure in barrel decreases.

The third stage is from the time when the powder is finished burning to the time when the bullet exits the muzzle. The expanded chamber cannot release too much the high pressure gas for the barrel, so the pressure in the barrel continues to decrease and the bullet gets its initial velocity at the muzzle.

According to the analysis, in order to get the super-high initial velocity, a reasonable structure should be designed based on the second stage. The design of the gas port and piston as well as chambers are very important. The suitable position and the size of the gas port and the piston can assure the high pressure gas in the barrel moves into the expanded chamber in time.

Based on Eq.(6), the speed of the bullet is related with its cross-sectional area, the mass of the bullet, the quantity of powder and the integration area of the pressure. Therefore, it is relatively easier to get the high initial velocity for the light bullets. This paper is based on a 45 mm caliber weapon with an initial velocity of 2 000 m/s and a peak pressure of 400 MPa.

The values of the relevant interior ballistic parameters are shown in Tab.1.

Tab.1 Table of interior ballistic parameters

According to the calculation data above and solving the equations of interior ballistic equations numerically, the variation curve of parameters can be obtained during the interior ballistic period, such as the gas pressurePin the barrel, the gas pressure in the expanded chamberPq, the speed of the bulletv, the movement of the pistonLhand so on.

Based on the results of the calculations, when the pressure in the expanded chamber reaches the preset pressure, the piston moves at 0.6 ms and maintain the peak pressure, which is reached at the time of 1.37 ms (Fig.3). When the piston moves in reverse, at the time of 1.55 ms, the pressure in the expanded chamber reaches the second peak. When the bullet is moving in the barrel and the piston is moving in reverse, the pressure in the expanded chamber is always higher than the pressure in the barrel which can slow down the rate of speed of pressure decrease in the barrel and increase the integration area of the curve. Then the initial velocity can be increased, as shown in Fig.4.

Fig.3 Curves of P-t and Pq-t

Fig.4 Curve of V-t

Fig.5 Curve of Lh-t

When the piston moves back to the original position, it will pull back again because of its inertia. Then the gas in the barrel will move into the expanded chamber. So the time for the piston moving back to the position should be close to the time when the bullet leaves the muzzle (Fig.5). Fig.6 shows the pressure curve without the pressure-maintaining chamber and expanded chamber, the peak pressure reaches 556 MPa, which may endanger the weapon, because the weapons may not be able to withstand such a high gas pressure of gunpowder. But if the pressure-maintaining chamber and expanded chamber is adopted, the peak pressure is only 395 MPa and the initial velocity is 2 019 m/s.

Fig.6 P-t curve of ordinary inner trajectory

4 Conclusions

The analysis results show that, by adopting the structure of the pressure remaining chamber and expanded chamber, a super-high initial velocity of the bullet above 2 000 m/s can be realized under the premise that the gas pressure in barrel is no more than 400 MPa.The new technical scheme can greatly increase the initial velocity of the bullet. In addition, the maximum peak pressure is much lower than that of conventional gun barrel weapons.

Therefore, it is a new theoretical feasible way of bullet propulsion with super-high initial velocity. And it can provide a theoretical foundation for the solid propellant barrel weapon to greatly increase the initial velocity of bullet.