Tecnologia/Technology THEORETICAL AND EXPERIMENTAL STUDY OF THE INTERIOR BALLISTICS OF A RIFLE 7.62 P. O. Cronemberger, ABSTRACT E. P. Lima Júnior, This study aims to examine theoretically and experimentally the interior J. A. M. Gois, ballistics of a rifle 7.62. Three theoretical methods are employed: the Vallier-Heydenreich, which is based on empirical data tables; the lumped and A. B. Caldeira parameters that is represented by a differential-algebraic system of equations, describing the propellant combustion, the thermodynamics of the gas inside the gun and the projectile dynamics; and the commercial software Instituto Militar de Engenharia PRODAS. The theoretical solutions furnish the pressure, the projectile velocity and the projectile position inside the gun, the maximum pressure, Seção de Engenharia Mecânica e de Materiais the muzzle velocity and the total time of the interior ballistics. The CEP 22290-270, Rio de Janeiro, RJ, Brasil experiments measure the pressure along of the time and the projectile [email protected] velocity at seven meters ahead of the barrel. The proposed lumped parameter model indicates alternatives to model the energy lost and the resistance pressure functions. The theoretical solutions are compared with experiments. A thermodynamics analysis of the energy conversion in the Received: October 29, 2014 gun is provided. The results are analyzed and the relevance of each method is highlighted. Revised: November 30, 2014 Accepted: December 30, 2014 Keywords: interior ballistics, rifle, Vallier-Heydenreich, lumped parameter NOMENCLATURE Subscripts a pressure index of the propellant atm atmospheric B burning rate constant of the propellant avg average c co-volume cc combustion chamber D projectile diameter g gas E energy i igniter f web fraction lost lost F impetus of the propellant m projectile at maximum pressure k form function coefficient p propellant m mass r resistance M mass of the projectile 0 muzzle P gas pressure Q heat INTRODUCTION R constant of the gas V velocity of the projectile “A conventional gun is essentially a heat engine Vol volume in which the propellant contained or injected in the S projectile position gun chamber is ignited and combusted, transferring L barrel length its chemical energy into kinetic energy of the t time projectile” (Maag and Klingenberg, 1996). The T gas temperature interior ballistics is the science devoted to study the z form function of the propellant processes inside this heat engine. Then, “interior U internal energy of the gas ballistics deals with the interaction of the gun, W kinetic energy of the projectile projectile and propelling charge before emergence of Web web thickness the projectile from the muzzle of the gun” (Carlucci et al., 2008). Greek symbols Interior ballistics is not restricted to the gun propulsion. It is also applied to others propellant ratio of specific heats of the gas combustion systems such as: rockets, airbags, gas dimensionless shot travel generators, closed vessels and primers (Corner, 1950, density of the propellant Lipanov, 2000, Oliveira et al., 2005, Rodrigues et al., thermal efficiency 2006, Eisenreich et al., 2007, Seo et al., 2011). , ,, , , , , , Vallier-Heydenreich The mathematical models of the interior functions ballistics are very important, since experiments are difficulty and expensive. The total elapsed time of the interior ballistics of a gun is the order of 20 Engenharia Térmica (Thermal Engineering), Vol. 13 • No. 2 • December 2014 • p. 20-27 Tecnologia/Technology Cronemberger, et al. Theoretical and Experimental … milliseconds. Furthermore, the pressure and the ballistics of a rifle 7.62 M964. This software has a temperature inside the barrel can exceed, library of typical weapons, ammunitions, propellants respectively, 400 MPa and 3000 K. and primers. The ammunition 762 80M, the Large Interior ballistics experiments should not be Rifle Primer 762 and the rifle M14 762 are chosen intrusive and they are generally conducted by using from this library to simulate the interior ballistics. test barrels. These experiments can measure the Furthermore, Tab. 1 shows the complementary input muzzle velocity, the maximum pressure and some of data used in the PRODAS simulation: the barrel them the pressure evolution inside the barrel. Two length, L, the volume of the combustion chamber, types of pressure meters are usually employed: the Volcc, the maximum pressure, Pm, which is the piezoelectric and the crusher (Vincent, 1987). The maximum gas pressure inside the gun, and the piezoelectric measures the pressure along of the time projectile velocity at the muzzle of the gun that is and the crusher only measures the maximum usually named muzzle velocity, V0. pressure. The muzzle velocity can be measured by The PRODAS simulation is first conducted by optical devices: high speed camera or light screens. using the Empirical module. Then, these results are Nevertheless, indirect measurements could be done introduced in the Baer-Frankle module, which solves by inverse problems techniques (Lipanov, 2000, the interior ballistics by using a modified Baer and Oliveira et al., 2005, Rodrigues et al., 2006, Arkhipov Frankle (1962) model, which is a lumped parameters et al., 2010, 2010b). Such techniques frequently need model. a mathematical model of the direct problem that should be evaluated many times (Colaço et al., 2006). Table 1. PRODAS input data. Then, to reduce the computational cost of the inverse PARAMETER VALUE problem solution, simple mathematical models of the Barrel length (Se) 533 mm direct problem should be used. Volume of the combustion chamber 3209 mm3 Moreover, for engineering purposes, simple (Volcc) mathematical models, mainly the lumped parameters Maximum pressure (Pm) 320.34 MPa ones, are still in use and they are relevant tools to Muzzle velocity (V0) 840 m/s design: propellants, ammunitions and guns (Li and Zhang, 2011, 2012, Cheng and Zhang, 2012). These The simulation describes the thermodynamic models are employed in optimization problems to state of the gas inside the gun and the projectile compute the pressure, the projectile velocity and dynamics, the rotational and translational movements projectile position inside the gun. Consequently, of the projectile, as well as the resistant pressure, despite the evolution of the interior ballistics models which is linked to the friction force and the forces of that take in account multiphase flows and turbulence the rifled bore on the projectile. in multidimensional domains (Krier and PRODAS considers that the rifled bore imparts Summerfield, 1979, Jaramaz et al., 2011), simple spin to the projectile. The breech pressure and the mathematical models that retain the main features of pressure, acting in the base of the projectile, are the interior ballistics phenomena are still in scene. computed. So, the PRODAS simulation shows a The present work is devoted to the interior pressure gradient inside the barrel computed by ballistics of a rifle 7.62 by using theoretical methods empirical functions. and experimental measurements. Three theoretical approaches are employed: the Vallier-Heydenreich Vallier-Heydenreich method method, the lumped parameters method and the commercial software PRODAS. The theoretical The Vallier-Heydenreich method is based on simulations furnish the pressure, the projectile empirical data tables (Oerlinkon-Buhrle AG, 1981). velocity and the projectile position inside the barrel; These data are functions of the pressure ratio, , or of the maximum pressure; the muzzle velocity and the the dimensionless shot travel parameter, . total time of the interior ballistics. The experiments measure the pressure, during the interior ballistics, Pavg and the projectile velocity at seven meters ahead of (1) the barrel. The theoretical solutions are compared Pm with experiments. The results are analyzed and the relevance of each method is highlighted. The pressure ratio is defined by Eq.(1), where Pavg is the average pressure inside the gun during the interior THEORY ballistics. PRODAS simulation S L (2) m 2 L In the present work, the commercial software tm (3) PRODAS (Projectile Rocket Ordnance Design and V0 Analysis System) is used to predict the interior Vm V0 (4) Engenharia Térmica (Thermal Engineering), Vol. 13 • No. 2 • December 2014 • p. 20-27 21 Tecnologia/Technology Cronemberger, et al. Theoretical and Experimental … The empirical data tables of the functions (), Equation (11) reveals that the work done by the () and () are employed to determine, at the gas on the projectile is equal to the kinetic energy of moment of the maximum pressure: the projectile the projectile plus an approximation of the kinetic position, Sm, Eq.(2); the time, tm, Eq.(3); and the energy of the gas in the Vallier-Heydenreich method, velocity, Vm, Eq.(4). considering that all of the propellant is burned. Thus, Eq.(1) to (10) can be used to compute the 2 L main variables of the interior ballistics: P, V, S and t. t (5) 0 V The Vallier-Heydenreich method is a useful tool 0 to determine, quickly and approximately, the interior P0 Pavg (6) ballistics of a gun, complementing experimental data. Then, if the maximum pressure and the muzzle velocity are measured, the interior ballistics can be The total time of the interior ballistics, t0, and described by the Vallier-Heydenreich method. The muzzle pressure, P0, when the projectile exits the barrel, are also determined by the empirical data other hand, the initial moments of the interior tables of the functions () and (), applying ballistics cannot be evaluated by this method, because Eq.(5) and (6). the minor available is equal to 0.25. Consequently, information about the igniter (or primer) is not S required. (7) Sm Lumped parameters method After determined the projectile position at the The Lumped parameters method (Farrar and moment of the maximum pressure, the dimensionless Leeming, 1983) is based on the projectile dynamics shot travel parameter, , defined in Eq.(7), can be and on the thermodynamics of the gas provided by computed. In this equation S is the projectile position the propellant burning. The propellant burning inside the barrel.