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(bəlĭs`tĭks), science of projectiles. Interior ballistics deals with the propulsion and the motion of a projectile within a gun or firing device. Its problems include the ignition and burning of the propellant powder, the pressure produced by the expanding gases, the movement of the projectile through the bore, and the designing of the barrel to resist resulting stresses and strains. Exterior ballistics is concerned with the motion of a projectile while in flight and includes the study not only of the flight path of bullets but also of bombs, rockets, and missiles. All projectiles traveling through the air are affected by wind, air resistance, and the force of gravity. These forces induce a curved path known as a trajectory. The trajectory varies with the weight and shape of the projectile, with its initial velocity, and with the angle at which it is fired. The general shape of a trajectory is that of a parabola. The total distance traveled by a projectile is known as its range. A ballistic missile in the first stage of its flight is powered and guided by rocket engines. After the engines burn out, the warhead travels in a fixed arc as does an artillery shell. In criminology the term ballistics is applied to the identification of the weapon from which a bullet was fired. Microscopic imperfections in a gun barrel make characteristic scratches and grooves on bullets fired through it, but use causes the marks a particular gun makes to change over time.


See E. D. Lowry, Interior Ballistics (1968); R. C. Labile, Ballistic Materials and Penetration Mechanics (1980); A. J. Pejsa, Modern Practical Ballistics (1989); M. Denny, Their Arrows Will Darken the Sun: The Evolution and Science of Ballistics (2011).


That branch of applied physics which deals with the motion of projectiles and the conditions governing that motion. Commonly called the science of shooting, it is, for practical purposes, subdivided into exterior and interior ballistics. Exterior ballistics begins at the instant the projectile leaves the muzzle of the gun barrel; interior ballistics, logically, deals with the events preceding this instant, that is, the events inside the gun barrel.



the science of the movement of artillery shells, bullets, mortar shells, aerial bombs, rocket artillery projectiles and missiles, harpoons, and so on. Ballistics is a technical military science based on a set of physics and mathematics disciplines. Interior ballistics is distinguished from exterior ballistics.

Interior ballistics is concerned with the movement of a projectile (or other body whose mechanical freedom is restricted by certain conditions) in the bore of a gun under the influence of powder gases as well as the rules governing other processes occurring in the bore or in the chamber of a powder rocket during firing. Interior ballistics views the firing as a complex process of rapid transformation of the powder’s chemical energy into heat energy and then into the mechanical work of displacing the projectile, charge, and recoil parts of the gun. In interior ballistics the different periods that are distinguished in the firing are the preliminary period, which is from the start of the powder combustion until the projectile begins to move; the first (primary) period, which is from the start of projectile movement until the end of powder combustion; the second period, which is from the end of powder combustion until the moment that the projectile leaves the bore (the period of adiabatic expansion of the gases); and the period of the aftereffect of the powder gases on the projectile and barrel. The laws governing the processes related to this last period are dealt with in a special division of ballistics, known as intermediate ballistics. The end of the period of aftereffect on the projectile divides the phenomena studied by interior and exterior ballistics.

The main divisions of interior ballistics are “pyrostatics,” “pyrodynamics,” and ballistic gun design. Pyrostatics is the study of the laws of powder combustion and gas formation during the combustion of powder in a constant volume in which the effect of the chemical composition of the powder and its forms and dimensions on the laws of combustion and gas formation is determined. Pyrodynamics is concerned with the study of the processes and phenomena that take place in the bore during firing and the determination of the relationships between the design features of the bore, the conditions of loading, and various physical-chemical and mechanical processes that occur during firing. On the basis of a consideration of these processes and also of the forces operating on the projectile and barrel, a system of equations is established that describes the firing process, including the basic equation of interior ballistics, which relates the magnitude of the burned part of the charge, the pressure of powder gases in the bore, the velocity of the projectile, and the length of the path it has traveled. The solution of this system and the discovery of the relationship between change in the pressure ρ of the powder gases, the velocity v of the projectile, and other parameters on path l of the projectile and the time it has moved along the bore is the first main (direct)

Figure 1. Curves of change in pressure of powder gases (P) and projectile velocity (v) depending on the path of the projectile (l); In is the distance in which the aftereffect of the powder gases on the projectile during the aftereffect period ceases; lg is the length of the projectile’s path to the muzzle face

problem of interior ballistics (see Figure 1). In order to solve this problem the analytic method, numerical integration methods (including those based on computers), and tabular methods are used. In view of the complexity of the firing process and insufficient study of particular factors, certain assumptions are made. The correction formulas of interior ballistics are of great practical significance; they make it possible to determine the change in muzzle velocity of the projectile and maximum pressure in the bore when there are changes made in the loading conditions.

Ballistic gun design is the second main (correlative) problem of interior ballistics. By it are determined the design specifications of the bore and the loading conditions under which a projectile of given caliber and mass will obtain an assigned (muzzle) velocity in flight. The curves of change in the pressure of the gases in the bore and of the velocity of the projectile along the length of the barrel and in time are calculated for the variation of the barrel selected during designing. These curves are the initial data in designing the artillery system as a whole and the ammunition for it. Internal ballistics also includes the study of the firing process in the rifle, in cases when special and combined charges are used, in systems with conical barrels, and in systems in which gases are exhausted during powder combustion (high-low pressure guns and recoilless guns, infantry mortars). Another important division is the interior ballistics of powder rockets, which has developed into a special science. The main divisions of the interior ballistics of powder rockets are pyrostatics of a semiclosed space, which consider the laws of powder combustion at comparatively low and constant pressure; the solution of the basic problem of the interior ballistics of powder rockets, which is to determine (under set loading conditions) the rules of variation in pressure of the powder gases in the chamber with regard to time and to determine the rules of variation in thrust necessary to ensure the required rocket velocity; the ballistic design of powder rockets, which involves determining the energy-producing characteristics of the powder, the weight and form of the charge, and the design parameters of the nozzle which ensure, with an assigned weight of the rocket’s warhead, the necessary thrust force during its operation.

Exterior ballistics is concerned with the study of the movement of unguided projectiles (mortar shells, bullets, and so on) after they leave the bore (or launcher) and the factors that affect this movement. It includes basically the study of all the elements of motion of the projectile and of the forces that act upon it in flight (the force of air resistance, the force of gravity, reactive force, the force arising in the aftereffect period, and so on); the study of the movement of the center of mass of the projectile for the purpose of calculating its trajectory (see Figure 2) when there are set initial and external conditions (the basic problem of exterior ballistics); and the determination of the flight stability and dispersion of projectiles. Two important divisions of exterior ballistics are the theory of corrections, which develops methods of evaluating the influence of the factors that determine the projectile’s flight on the nature of its trajectory, and the technique for drawing up firing tables and of finding the optimal exterior ballistics variation in the designing of artillery systems. The theoretical solution of the problems of projectile movement and of the problems of the theory of corrections amounts to making up equations for the projectile’s movement, simplifying these equations, and seeking methods of solving them. This has been made significantly easier and faster with the appearance of computers. In order to determine the initial conditions—that is, initial velocity and angle of departure, shape and mass of the projectile—which are necessary to obtain a given trajectory, special tables are used in exterior ballistics. The working out of the technique for drawing up a firing table involves determining the optimal combination of theoretical and experimental research that makes it possible to obtain firing tables of the required accuracy with the minimal expenditure of time. The methods of exterior ballistics are also used in the study of the laws of movement of spacecraft (during their movement without the influence of controlling forces and moments). With the appearance of guided missiles, exterior ballistics played a major part in the formation and development of the theory of flight and became a particular instance of this theory.

The appearance of ballistics as a science dates to the 16th century. The first works on ballistics are the books by the Italian N. Tartaglia, A New Science (1537) and Questions

Figure 2. Elements of the trajectory and primary forces acting on the projectile in flight: 0—the point of projectile takeoff; S—peak of the trajectory; C—point of fall; v0—initial velocity of projectile; θ,,-angle of departure; x and y—current horizontal range and flight elevation of projectile; Y-height of trajectory; X-full horizontal range of flight; v c—final velocity of projectile; Ac-angle of fall; R—force of air resistance; q— force of gravity.

and Discoveries Relating to Artillery Fire (1546). In the 17th century the fundamental principles of exterior ballistics were established by Galileo, who developed the parabolic theory of projectile movement, by the Italian E. Torricelli, and by the Frenchman M. Mersenne, who proposed that the science of the movement of projectiles be called ballistics (1644). I. Newton made the first investigations of the movement of a projectile, taking air resistance into consideration (Mathematical Principles of Natural Philosophy,1687). During the 17th and 18th centuries the movement of projectiles was studied by the Dutchman C. Huygens, the Frenchman P. Varignon, the Englishman B. Robins, the Swiss D. Bernoulli, the Russian scientist L. Eiler, and others. The experimental and theoretical foundations of interior ballistics were laid in the 18th century in works of Robins, C. Hutton, Bernoulli, and others. In the 19th century the laws of air resistance were established (the laws of N. V. Maievskii and N. A. Zabudskii, Havre’s law, and A. F. Siacci’s law). At the start of the 20th century an accurate solution of the basic problem of interior ballistics was provided in the works of N. F. Drozdov (1903, 1910); the questions of powder combustion in a constant volume were investigated in the works of I. P. Grave (1904); the questions concerning the pressure of powder gases in the bore were investigated in the works of N. A. Zabudskii (1904, 1914), as well as in the works of the Frenchman P. Charbonnier and the Italian G. Bianchi. In the USSR a major contribution to the further development of ballistics was made during the years 1918–26 by the scientists of the Commission for Special Artillery Experiments. During this period, V. M. Trofimov, A. N. Krylov, D. A. Vent-tsel’, V. V. Mechnikov, G. V. Oppokov, B. N. Okunev, and others carried out a number of projects to improve the methods of calculating the trajectory, to develop the theory of corrections, and to study the rotating motion of a projectile. The investigations of N. E. Zhukovskii and S. A. Cha-plygin on the aerodynamics of artillery shells laid the foundation for the works of E. A. Berkalov and others to improve the shape of shells and increase their flight range. V. S. Pugachev was the first to solve the general problem of the movement of an artillery shell.

An important role in solving the problems of interior ballistics was played by the research of Trofimov, Drozdov, and I. P. Grave who, during the years 1932–38, wrote the most complete course of theoretical interior ballistics. Significant contributions to the development of the methods of evaluation, to the ballistic investigation of artillery systems, and to the solution of specialized problems of interior ballistics were made by M. E. Serebriakov, V. E. Slukhotskii, and B. N. Okunev, as well as by such foreign authors as P. Charbonnier, M. Sugot, and others.

During the Great Patriotic War of 1941–45, theoretical and experimental work was done under the direction of S. A. Khristianovich to increase the accuracy of rockets. This work continued in the postwar period; also investigated were the questions of increasing the initial velocities of projectiles, establishing new laws of air resistance, increasing the accuracy life of the barrel, and perfecting the methods of ballistic designing. There was significant development of projects to investigate the aftereffect period (V. E. Slukhotskii and others), to develop the methods of ballistics to solve specialized problems (smoothbore systems, rocket artillery projectiles, and others) and problems of interior and exterior ballistics relative to rockets, and to further improve methods of ballistic research related to the use of computers.


Grave, I. P. Vnutrenniaia ballistika: pirodinamika, Issues 1–4. Leningrad, 1933–37.
Serebriakov, M. E. Vnutrenniaia ballistika stvol’nykh sistem i porokhovykh raket. Moscow, 1962.(Bibliography.)
Corner, J. Vnutrenniaia ballistika orudii. Moscow, 1953.(Translated from English.)
Shapiro, Ia. M. Vneshniaia ballistika. Moscow, 1946.



Branch of applied mechanics which deals with the motion and behavior characteristics of missiles, that is, projectiles, bombs, rockets, guided missiles, and so forth, and of accompanying phenomena.


The science or art that deals with the motion, behavior, appearance, or modification of missiles or other vehicles acted upon by propellants, wind, gravity, temperature, or any other modifying substance, condition, or force. The art of designing missiles to give them efficient motion and flight behavior within the limitations set up by their purpose.


the study of the flight dynamics of projectiles, either through the interaction of the forces of propulsion, the aerodynamics of the projectile, atmospheric resistance, and gravity (exterior ballistics), or through these forces along with the means of propulsion, and the design of the propelling weapon and projectile (interior ballistics)
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