Method of Conversion for the Ballistic Coefficient of Bullets
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METHOD OF CONVERSION FOR THE BALLISTIC COEFFICIENT OF BULLETS I. B. Chepkov,a A. V. Hurnovych,a,1 S. V. Lapyts’kyi,a
UDC 669.539.43
B. O. Oliiarnyk,b V. H. Trofymenko,a and O. A. Maistrenkoa A method is examined that permits the ballistic coefficient (BC) of a bullet to be converted based on universal expressions: in the Ciacci law and the air drag law of 1943, i.e., within the framework of laws that extend to the territories of the former USSR countries; to the standards G7 and G1, i.e., within the framework of standards that are the most-used worldwide; in the air drag law of 1943 and to the standard G7, i.e., bringing a BC value to the form that is used on the territories of the former USSR countries (including Ukraine) or to the most-used form worldwide (including NATO member-countries). The relation is formulated on the basis of the central design of an experiment that describes the range of values for an examined process. The above approach enables BC to be brought to an easy-to-use form on the basis of its known value in any law (or to a standard) for analysis of exterior-ballistic characteristics or computations of a bullet velocity at an arbitrary range during field tests of armored targets without bulky equipment for bullet velocity measurements. An examined process is reliably described with the approved mathematical model of bullet motion in air, as the solid body motion, based on the system of four differential equations of the first order. The adequacy of empiric expressions is verified by estimating the standard deviation of values gained with the mathematical model of bullet motion and polynomial as well as by their comparison with the accuracy of determining the ballistic coefficient (no more than 10 -3 for the G7 and G1 standards and no more than 10 -2 for the Ciacci and 1943 laws). Keywords: ballistic coefficient, quadratic polynomial (quadric), system of differential equations of the first order. Introduction. The ballistic coefficient is the exterior-ballistic characteristic of a bullet, which permits of trajectory computations and its velocity assessment at different flight ranges, and, correspondingly, evaluation of the target hit efficiency. The majority of bullet manufacturers specifies the ballistic coefficients of their bullets to the standard G7 (air drag law for the flight of a long boat tail tangent ogive bullet) and to the standard G1 (Krupp air drag law for the bullet flight) [1]. The above standards for bullet specifying are used in the countries of Europe and USA (including NATO member-countries). At the same time, BC computations in the Ciacci law and air drag law of 1943 are common in Ukraine (as in the time of the USSR) [2, 3]. Therefore, the problem arises that is associated with the necessity of BC converting from the available form to the form wherein it can be used for bullet flight trajectory computations with the existing model. Statement of the Problem and Its Solution. The bullet BC value is not a constant. It is dependent on the bullet velocity; therefore, the BC conv
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