Firing range optimization of a 155mm uni-modular charge howitzer by ETC technology

Electrothermal-chemical (ETC) launch technology can accurately control and enhance the ignition and combustion of solid propellants to improve the consistency and accuracy of ballistics. In this paper, a calculation model including the transient burning rate formula and six-degree-of-freedom rigid body trajectory equation is established to simulate both interior and exterior ballistics processes for a 155mm uni-modular charge howitzer. The simulation results show that the muzzle velocities are optimized via the ETC technology. The 155mm uni-modular charge ETC howitzer can effectively obtain the minimum range, increase the range overlap and maximum range, and improve the ballistic stability and consistency.


Introduction
In our previous work [1,2], the application advantages and prospects of electrothermal-chemical (ETC) launch technology in a 155mm uni-modular charge howitzer were discussed from the perspective of the technology development and actual applications, respectively [3][4][5]. Results show that the ETC launch technology can be combined with the uni-modular charge technology to apply in the 155mm uni-modular charge howitzer to advance the ballistic performance.
In this paper, a calculation model including the transient burning rate formula and sixdegree-of-freedom rigid body trajectory equation is established to simulate both interior and exterior ballistics processes for a 155mm uni-modular charge howitzer. The firing range and range overlap are discussed to verify the advantages by ETC technology.

Calculation model
A calculation model including the transient burning rate formula [6] and six-degree-of-freedom rigid body trajectory equation [7] is established to simulate the ballistics processes for a 155mm uni-modular charge howitzer.

interior ballistics model
The propellant combustion process can be described as: where, Z is the relative burned thickness of propellant. χ, χ s , λ, λ s , µ are the shape function of propellant. Z b is the relative burned thickness when the propellant begins to be regressive. r is the propellant burning rate. e 1 is half of the propellant web thickness. The dynamical equations of the projectile in the barrel are shown as: where,v is the velocity of projectile. l is the length of the barrel. S is the sectional area of the barrel. m is the projectile weight. p is the mean pressure in volume behind projectile. ϕ is the coefficient of second work. ρ p is the density of the propellant. ω is the propellant charge weight. α is the gas covolume of the propellant. E p is the plasma energy injected into the chamber. And E p = 0 when in conventional ignition. V = Sl, θ = k − 1, here k is the ratio of specific heat. The propellants have been manufactured and tested in an improved closed bomb vessel into which electrical energy was discharged. The phenomenon of enhanced gas generation rates (EGGR) during the electrical discharge has been reported. Clive R. Woodley added an EGGR coefficient into the Vieilles law to simulate the effect of EGGR [8]. Dr. Yanjie Ni was introduced a transient burning rate formula of propellant including the influence of pressure gradient and an EGGR coefficient by electrical power. And this new formula is employed into our calculation model to instead of the geometric burning law.
The transient burning rate formula [6] is shown as follow: where, u 1 is the burn rate coefficient of the solid propellant. n 1 is the burn rate index. α(t) is the time variable function of pressure and flame structure. P e is the electrical power(MW). β e is the EGGR coefficient(MW −1 ).

exterior ballistics model
A conventional six-degree-of-freedom rigid body trajectory model is introduced to simulate the exterior ballistic performance. To acquire a more precise describe of the motion of a spinning projectile, six degree of freedom flight dynamic equations are used in this paper. The detailed expression are as follows: The The physical meanings of every variable in equation (5)-(14) and other unlisted equations all can be found in reference [7].

Results and discussion
The internal and external ballistic performance of the 155mm uni-modular charge howitzer is analyzed by using the above calculation model. The main conditions for calculation are as follows: • standard meteorological conditions; • caliber 155mm; • barrel length L/52; • chamber volume 23L; • HE projectile 45.5kg.
The uni-modular charge is composed of 37 holes triple-base propellant and 19 holes coated triple-base low temperature sensitivity propellant. The total mass of the uni-modular charge is 3.0kg.
The muzzle velocity classification of large-caliber artillery directly affects the firing command strategy, firing hit rate, ballistic maneuverability, effective firing time and firing feasibility of the artillery. In the design of ballistic trajectory, the firing accuracy of the whole system should be considered.
Firstly, conventional ignition condition is calculated as a criterion for our discussion. The conventional muzzle velocity classification is shown in table 1. It is assumed that the input electric energy in the ETC launch is 400kJ [9]. The average bore pressure and projectile movement curves of each charge are shown in figure 1 and figure 2, respectively.   Muzzle velocity v 0 (m/s) 397 560 690 812 920 1038 The firing ranges and heights of the above two muzzle velocity classification of conventional and ETC launch at different firing angles are calculated, respectively. The specific calculation results are shown in the table 3 and table 4. The maximum range, minimum range and range overlap are calculated according to the above tables. According to the Chinese military standard, the minimum firing angle of the cannon is 20 0 and the maximum firing angle of the howitzer is 70 0 . The external ballistics and the firing table compilation method stipulated that the range overlap R RL of each number of charges should be 4%.
The range overlap is defined as the following equation: The where, X jmax is the maximum range of No.j charge. X imin is the minimum range of No.i charge. Normally, we have j = i − 1 and j from 1 to 5.
Hence, the range parameters are calculated and shown in table 5 and table 6.     It is shown in figure 3 that the No.1 charge situation (red data as shown in table 3) must be abandoned in conventional launch because of the lower bore pressure, which cannot satisfy the